Cornell University Library HB 881.W5 Vital statistics; an in«''0'''"=''°" 'S,,*,!^,? 3 1924 013 756 527 New York State College of Agriculture At Cornell University Ithaca, N. Y. Library LfBRARY JUL S3 OEPT. OF jVe^W-. 6GON. Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924013756527 WORKS OF GEORGE CHANDLER WHIPPLE PUBLISHED BY JOHN WILEY & SONS, INC. The Microscopy of Drinking Water. Third Edition, Rewritten and Enlarged. With a Chapter on the Use of the Microscope, by John W. M. Bunker, Ph.D. xxi + 409 pages. 6 by 9. 74 figures, 6 full-^>age plates in the text, and 19 plates of organisms in colors. Cloth, $4.00 net. Vital Statistics. idi + 517 pages. 4i by 7. 63 figures. Flexible "Fab- rikoid " binding, J4.00 net. By henry BALDWIN WARD AND GEORGE CHANDLER WHIPPLE AND ASSOCIATES Fresh-Water Biology. ix + 1111 pages. 6 by 9. 1547 figures. Cloth, $6.00 net. " VITAL STATISTICS AN INTRODUCTION TO THE SCIENCE OF DEMOGRAPHY BY GEORGE CHANDLER WHIPPLE Professor of Sanitary Engineering in Harvard University Member of the Public Health Council, Massachusetts State Department of Health FIRST EDITION NEW YORK JOHN WILEY, & SONS, Ino. London: CHAPMAN & HALL, Limitbd 1919 Copyright, 1919, BT GEORGE CHANDLER WHIPPLE @ / 3 ^^(f Stanbope ipress F. H.GILSON COMPANY BOSTON, U.S.A. DEDICATED TO THE STUDENTS OF VITAL STATISTICS IN THE SCHOOL OF PUBLIC HEALTH OF HARVABD UNIVERSITY AND THE MASSACHUSETTS INSTITUTE OP TECHNOLOGY PREFACE This book is written for students who are preparing them- selves to be pubUc health officials and for public health officials who are willing to be students. It makes no claim to be an exhaustive treatise or a compendium of facts; it is merely a guide to the study of vital statistics, an introduction to the great world-wide science of demogra- phy — a science yet in the magmatic stage, not yet crystal- hzed. The Great War is bound to develop this science, because hereafter all the nations of the earth must know each other better, and this knowledge, in order to be usable, must be condensed into statistical forms. Specifically the book tells what statistics are and what they are not; it shows how to express vital facts by figures, how to tabulate them and how to display them by diagrams; it shows how to compute birth-rates and death-rates and how to analyze a death-rate; it shows how to adjust and standardize death-rates and how to make life tables; it em- phasizes the need of using vital statistics with truth, with imagination and with power. For the convenience of school instruction, exercises and questions to incite further study are given in each chapter. Many subjects worthy of special study, however, are not even mentioned, loose ends have been left in every chapter, illustrations have been chosen as they came conveniently to hand, and the general arrangement has been informal as to its subject matter. The object in all this tas been to stimulate the reader to critically analyze all vital statistics as they ap- pear before him from day to day. Although the illustrations have been gathered in a haphazard way, an attempt has been made to set forth the elementary principles of the statistical method in a simple and orderly fashion. V VI PREFACE The author wishes to confess that he is not an authority on vital statistics, much less an authority on demography; he is merely a student of the science. He has taken the student's privilege of quoting freely from many writers to whom he wishes to render acknowledgments and thanks. In particular he desires to express his obligations and personal regards to Dr. William H. Davis, Chief Statistician for Vital Statistics, United States Bureau of the Census, who has read the entire proof of this book and given the benefit of his careful criticism. Just a personal word to the health officers of America. A new day is dawning for you. The care of the public health is becoming a distinct profession. The medical pro- fession alone is not. able to cope with it. The young men and women who are to be the executive health officers in the next generation are recognizing the need of special training, based on the principles of preventive medicine, hygiene and sanitation. Schools of public health are coming into exist- ence and receiving warm-hearted support. The health ad- ministration of the future will be in the hands of full-time officials, who are adequately paid and protected in their tenure of office, but who in return for these advantages must be adequately trained for their work. The. ability to use vital statistics in public health work is an important part of this training. Many of you have been in office for a long time, you have forgotten most of your arithmetic — not to mention algebra. You can see the new era coming and you dread the new' methods founded on accurate statistical studies of accident, disease and death. There is no need of this fear. You can use statistics as well as any one, but you must study. This book has been prepared with your difficulties in mind. GEORGE CHANDLER WHIPPLE Cambridge, Mass. January, 1919. Paqb CONTENTS CHAPTER I DEMOGRAPHY Principal divisions of demography — Demography both old and new — History of statistics — Celebrated demographers — Sec- tion of Vital Statistics — The statistical method — Need of the statistical method — Why statistics are thought to be dry — Can you prove anything by statistics? — National bookkeeping — Sta- tistics necessary for health officer — National Vital statistics — Statistical induction — Choice of statistical data 1 CHAPTER II STATISTICAL ARITHMETIC Statistical processes — Collection of data — Statistical units — Errors of collection — Tally sheets — • Tabulation — Inexact numbers — Precision and accuracy — Combinations of inexact numbers — Ratios — Rates — Misuse of rates — Index — Com- putation of rates — Logarithms — The slide-rule — Classification and generaUzation — Classes, groups, series and arrays — Gen- eralizations of classes and groups — The array and its analysis — ' Groups — Group designations — Percentage grouping — Cumu- lative grouping — Averages — The moving average — Mechanical devices 17 CHAPTER III STATISTICAL GRAPHICS Use of graphic methods — Types of diagrams — Thie appeal to the eye — Graphical deceptions — Essential features of a diagram — One-scale diagrams — Diagrams with rectangular coordinates — Use of the horizontal scale — Plotting figures by groups — viii CONTENTS Pa.qe Plotting irregular groups — Summation diagrams — Choice of scales — Diagrams with polar coordinates — Double coordinate paper — Ratio cross-section paper — Logarithmic cross-section paper — Ruled paper — Mechanics of diagram making — Letter- ing — Wall charts — Use of color in diagrams — ■ Component part diagrams — • Statistical maps — Blue prints and other prints — Reproduction of diagrams : — Equation of curves 58 CHAPTER IV ENUMERATION AND REGISTRATION United States census — The census date — Civil divisions — Enumeration schedule of 1910 — Rowley's rules for enumeration — Credibihty of census returns — State censuses — Registration and notification — Registration of births — Advantages of birth registration — Evidences of incomplete registration — Enforce- ment of registration law — Registration of deaths — Uses of death registration — Marriage registration — Morbidity regis- tration — Notifiable diseases — Incompleteness of morbidity statistics — Morbidity from non-reportable diseases — Reporting venereal diseases — Sickness surveys — Other methods of securing data — United States registration area for deaths — United States registration area for births — Need of national statistics 100 CHAPTER V POPULATION Estimation of population — Arithmetical increase — Adjust- ment of population to mid-year — Geometrical increase — For- mula for geometrical increase — ■ Rate of increase — Decreasing rate of growth — Difference between estimate and fact. Revised estimates — Estimation of population from accessions and losses — Estimation of future population — Immigration — Graphi- cal method of estimating population — Accuracy of state cen- suses — Urban and rural population — Density of population — Population of -United States cities — Metropolitan districts — Classification of population — Color, race, nativity, parentage — Sex distribution — • Dwellings and families — Age distribution — Census meaning of age — ■ Errors in ages of children — Errors CONTENTS IX Page due to use of round numbers — Other sources of error — Ag6- groups — Persons of unknown age — Redistribution of population — Redistribution for non-censal years — Prpgi-essive character of age distribution — Types of age distribution — Standards of age distribution — Age distribution of people of United States 129 CHAPTER VI GENERAL DEATH-RATES, BIRTH-RATES, MARRUGE-RATES Gross, or general, death-rates — Precision of death-rates — Corrected death-rates — Revised death-rates — Variations in death-rates in places of different size — Errors in published death-rates — Rates for short periods — Birth-rates — Relation between birth-rates and death-rates — Fecundity — Marriage- rates — Divorce-rates — Natural rate of increase — Comparison of general rates — Marriage-rates, birth-rates and death-rates in Sweden — Downward trend in birth-rates and death-rates — Variations due to population estimates — Birth-rates and death- rates in Massachusetts — Monthly death-rates in Massachu- setts — Marriage-rates in Massachusetts — -^Divorce-rates '. in Massachusetts — Limited use of gross death-rates — • The ideal death-rate 186 CHAPTER VII SPECIFIC DEATH-RATES Restriction of death-rates — Ages of Man — The vision of Mirza — Computation of specific death-rates — Specific death- rates by ages and sex — Specific death-rates as affected by mari- tal condition — Specific death-rates and nationaUty — Influence of age composition of population on death-rate — Influence of racial composition on death-rates — Chronological changes in specific death-rates — Fallacy of concealed classification — Use of specific death-rates — Death-rates adjusted to a standard popu- lation — Examples of adjusted death-rates — ^Adjustment of racial differences — Death-rates for particular diseases — Special deatb-vates 220 CONTENTS CHAPTER VIII CAUSES OF DEATH Page Nosography — Nosology — Purpose of Nosology — History of nosography — International list [of causes of death — Classifi- cation of diseases in 1850 — Present-day classification — Unde- sirable terms — Synonyms of tjrphoid fever — Joint causes of death — Classification of occupations — Nosology not an exact science 254 CHAPTER IX ANALYSIS OF DEATH-RATES Reasons for analyzing death-rates — Two methods of analysis — Useful sub-divisions — Analysis of the death-rate of a state — Comparison of death-rates of two cities — Rates not the only methods of comparison 299 CHAPTER X STATISTICS OF PARTICULAR DISEASES Mortality rate — Proportionate mortality — Morbidity-rate — Fatality — Inaccuracies of morbidity and fataUty-rates — Causes of death in Massachusetts — Study of tuberculosis by age and sex in Cambridge, Mass. — Seasonal distribution of deaths from J^uberculosis — Chronological study of tuberculosis — Tuber- culosis and occupation — Tuberculosis and racial composition of population — Diphtheria in Cambridge, Mass. — Age sus- ceptibility to diphtheria — FataUty of diphtheria — Chrono- logical study of diphtheria — Urban and rural distribution of diphtheria — Statistical study of typhoid fever — Age distribu- tion of typhoid fever — Seasonal distribution of typhoid fever — Chronological reduction in tjfphoid fever — Statistics of cancer — Further studies of particular diseases 308 CONTENTS XI CHAPTER XI STUDIES OF DEATHS BY AGE PERIODS Page Infant mortality — Some definitions — Pre-natal deaths — Infant mortality and specific death-rates of infants — First- year death-rate — Methods of stating infant mortality — Chron- ological reduction in infant mortality — • Reasons for the de- creasing infant mortality — Infant mortality in different places — Deaths of infants at different ages — Specific death-rates of infants at different [ages — Expectation of life at different ages — ■ Infant mortaUty by age periods — ■ Causes of infant deaths — The Johnstown studies — Other studies of the Childrens' Bureau — Infant mortality problems — Maternal mortality — Childhood mortaUty — Diseases of early childhood — Proportionate mortal- ities during school age — Proportionate mortalities at higher ages — Median age of persons living — Average age at death 339 CHAPTER XII PROBABILITY Natural frequency — Coin tossing — Chance — Binomial the- orem — Chance and natural phenomena — Frequency curves, including skew cm-ves — Frequency curves shown by summation diagrams — Deviation from the mean — Standard deviation — Coefficient of variation — Computation of coefficient from grouped data — Probable error — Doubtful observations — The proba- bility scale — Probability cross-section paper — Another use of probability — The frequency curve as a conception 376 CHAPTER XIII , CORRELATION Correlation — Causal relations — Correlation and causality — Laws of causation — Methods of correlation — Galton's coefficient of correlation — Example of low correlation — Correlation'shown graphically — Correlation table — Use of mathematical formulse — Secondary correlation — The lag — Coefficient of correlation and the lag — Other secondary correlations — The epidemiologist's use of correlation 402 XU CONTENTS CHAPTER XIV LIFE TABLES Page Life tables — Probability of living a year — Mortality tables — Most probable lifetime — " Vie probable" — Expectation of life — Comparison of the three methods — Life tables based on living populations — Mathematical formulae — Early history of life tables — Recent life tables — United States Life Tables: 1910 — A few comparisons 422 CHAPTER XV A COMMENCEMENT CHAPTER The day after commencement — MiUtary statistics — Army diseases — Eiiect of the war on demography — ■ Hospital statis- tics — Statistics of industrial disease — List of occupations — Economic conditions and health — Accidents — Age distribution of poliomyelitis — Averages and median age of persons living — Average age at death — The Mills-Reincke phenomenon — The sanitary index — Publication of reports 436 APPENDIX I REFERENCES General text-books — Periodicals — Reports — Demography — Arithmetic — Graphics — Census — Population — Death-rates — ProbabiUty — Correlation — Life tables 459 APPENDIX II The Model State Law for Mobbidity Reports 465 APPENDIX III The Model State Law for the Registration op Births and Deaths 472 APPENDIX IV Tabus of Logarithms of Numbers 491 VITAL STATISTICS CHAPTER I DEMOGRAPHY Broadly speaking demography is the statistical study of human life. It deals primarily with such vital facts as birth, physical growth, marriage, sickness and death and incidentally with poUtical, social, educational, reUgious, sanitary, hygienic and medical matters. In a somewhat narrower sense demography is used as a synonym for vital statistics. The word "demography" is derived from the Greek words demos, people, and grapho, to write. It is in com- mon use in Europe, but is not as well known or its meaning as well understood in America. High authority for its use is found in the name of that most important triennial gathering of physicians and sanitarians, the International Congress of Hygiene and Demography. ' Demography cannot be called a science in the sense that it is a classified body of knowledge from which laws have been developed and established. But all sciences in their evolution go through a descriptive stage in which data are collected and hypotheses tested. So regarded demog- raphy may be called a science, — the science of human generation, growth, decay and death as studied by statis- tical methods. 2 DEMOGRAPHY The principal divisions of demography. — Demography may be said to include the following major subjects: 1. Genealogy, which considers individual ancestries and personal records. 2. Human eugenics, which considers heredity from a scientific standpoint, and is to a large extent the appHcation of the statistical method to genealogy. 3. The census, that is, the collection of social, pohtical, rehgious and educational facts concerning popula- tion, usually by the method of governmental enum- eration. 4. Registration of vital facts, such as those concerning birth, marriage, divorce, sickness and death, usu- ally under governmental direction and by the use of individual records. 5. Vital statistics, which is the application of the statis- tical method to the study of these vital facts. 6. Biometrics, which includes anthropometric studies of human growth, stature, strength, etc. 7. Pathometrics, that is, statistical pathology, which in- cludes detailed studies of diseases and their rela- tions to the human body. These facts are obtained largely in hospitals, by health department labora- tories and by life insurance companies. Demography both old and new. — The word "demog- raphy " has come into use during the last generation, and has not even now taken its proper place in the Ust of recog- nized sciences; but the gathering together of facts relating to human life and the expression of these facts numerically has been practiced from time immemorial. Some parts of demography are older than others. Gene- alogy is very old. "Adam lived an hundred and thirty years, and begat a son in his own likeness, after his image; and called his name Seth: And Seth lived an hundred and HISTORY OF STATISTICS 3 five years and begat Enos: And Enos lived ninety years and begat Cainau; And Cainau lived seventy years and begat Mahalaleel:" And so it goes on. Hundreds of years before Christ enumerations of the people were made for purposes of taxation and for other reasons, as one may read in the histories- of Egypt, Persia, Judaea, Greece, Rome or China. Many fragmentary data relating to births, deaths and marriages were recorded in the old church registers of England. Capt. John Graunt compiled the vital statis- tics for the city of London in 1662, which attracted much . attention at the time. In referring to the Great Plague in London in 1666 Pepys tells about the pubhshed " bills," that is, the list of the dead, and gives their statistics. But the appUcation of statistics and the scientific method to genealogy is relatively modern and so are the develop- ments of biometry and pathometry. Sir Francis Galton and Professor Karl Pearson, of England, have been leaders in this and may almost be said to have founded a new school of statisticians. Demography, therefore, is both an old and a new science. History of statistics. — The word "statistics " is nearly two centuries old^ being first used by Gottfried Achenwall, who Uved in Jena, 1719-1772. Before that we learn of the political arithmeticians in France and Italy and of Aristotle who used statistics in describing and comparing different states. The systematic publication of the details of official statistics owes its origin to Anton Biischvig, 1724-1793, who published a voluminous work on historiography and founded a magazine in which statistics for various countries were brought together and compared. Crome in 1785 published important Tabellen-Statistik which contained various data in regard to population in Germany. 4 DEMOGRAPHY Many well-known scientists undertook statistical in- vestigations. Edmund Halley, 1656-1742, the astronomer who discovered the comet which bears his name, compiled in 1693 a series of mortality tables and calculated the ex- pectation of life at each age and thus laid the foundation for scientific life insurance. In 1713 Bernouilli, noted for his hydraulic studies, demonstrated a theory of proba- biUties which a century later, 1813, was perfected by Laplace in his masterly treatise "Theorie analytique des probabilites." John Graunt, already mentioned, laid the foundations for vital statistics when in 1662 he wrote his remarkable "Natural and Political Observations upon the Bills of MortaUty." In 1741 Joh. Peter Stissmilch (1707-1767) published an important work on vital statistics from which he attempted to draw some far-reaching moral deductions. He tried to demonstrate statistically the doctrine of the "Natural Order." From the equaUty of the sexes at marriage (at birth his ratio is 21 sons to 20 daughters) he derives the command of monogamy. From a comparison of urban and rural death-rates (in cities one death to 25 to 32 per- sons, and in the country, one to every 40 to 45 persons) he censures the unnaturalness, immorality, and luxury of city life, "proving statistically" that these bring down the wrath of God. With the accumulation of statistical data various di- vergencies began to appear. The poUtical economists, headed by Adam Smith ("Wealth of Nations," 1776) and followed by Malthus (1804) and others, separated them- selves from the realm of general statistics. Ritter (1779- 1859) led the study of geography apart. At the end of the 18th century the life insurance companies also drew away from the considerations of general populations, and, THE WORLD'S GREAT DEMOGRAPHERS 5 by reason of the accumulation of their own data relating to deaths, began to depend upon thein alone. This split- ting up of the general science of statistics and the multi- plication of the practical apphcations of statistics led to an increasing laxity in method, a condition which we have hardly yet outgrown. Quetelet, 1796-1874, aroused much enthusiasm over statistics as "the queen of all the sciences." His work on probabihty was justly famous and was an inspiration to Florence Nightingale. Since his time, however, this branch of the subject has been more commonly considered as a part of pure mathematics and is treated in books on "Least Squares," the law of error, and precision of meas- urements. Finally, we come to the brilUant works of Galton, Karl Pearson and others, already mentioned. The history of statistics is a fascinating one, as it flits around from country to country, now flourishing in Italy, then in France, England, Denmark, Germany, England again. The United States has had many able statisticians but few statistical mathematicians worthy to be compared to Laplace, Qu6telet or Karl Pearson. The world's great demographers. — Some of the great- est scientists of the world have been enthusiastic statisti- cians. In some cases their greatness has been due to their statistical skill. Even at the present time it is safe to say that the most successful health officers are good statisti- cians, although it does not follow that all good statisticians are successful health officers. The following is a short Ust of men, not now living, who have made important contributions to the study of statis- tics, — especially vital statistics. The student will find it interesting to add to this fist. 6 DEMOGRAPHY Capt. John Graunt (1620-1674), of England. Melchiorre Gioja (1767-1829), of Italy. Sir Francis Galton (1822-1911), of England. William Farr (1807-1883), of England. Louis A. Bertillon (1821-1883), of France. Alphonse Bertillon (1853-1914), of France. Edwin Chadwick (1800-1890), of England. Florence Nightingale (1820-1910), of England. Edward Jarvis (1803-1884), of Boston, Mass. Lemuel Shattuck (1793-1859), of Boston. Samuel Warren Abbott (1827-1894), of Boston. Carroll D. Wright (1840-1909), of Massachusetts. Section of Vital Statistics. — The American PubKc Health Association has always manifested a keen interest in vital statistics. Some of the reports of its committees have had a far-reaching effect. In 1907 a Section of Vital Statistics was organized in this association, and since that date the journal of the association, now known as the American Jour- nal of Public Health, has contained many important articles on the subject. Membership in this section is open to regis- tration officials, statisticians, epidemiologists, sanitarians and other members of the American PubUc Health Associar tion who are interested in vital statistics. The "Statistical Method." — Statistics are facts ex- pressed by figures. Strictly speaking a birth reported and recorded officially is not a statistic, but a vital fact; yet inasmuch as reported and recorded births are commonly counted and the results expressed numerically it is appro- priate to regard such a birth record as a statistical unit or item, that is, as a statistic. It is not customary, how- ever, to use the word in the singular number. By expressing facts by figures it is possible to arrange them in various ways for study and comparison, as, for example, in tables and graphs; to classify them; to make generalizations; to use them in logical processes and thus WHY WE NEED TO USE THE STATISTICAL METHOD 7 to draw inferences and conclusions based on the facts. The various mathematical processes used for this purpose are collectively known as the statistical method. Some of these processes are quite elaborate and involve complicated mathematical methods and conceptions, such as the laws of variation, dispersion, correlation and prob- abiUty. For many years there has been a discussion as to whether "statistics" should be regarded as a distinct science, ranking with physics, chemistry and biology or merely as a method. Westergaard expresses the truest conception when he says that "it is an auxiliary science in many branches of human thought." "There are some statisticians who are statisticians and there are some stat- isticians who are mathematicians." There are theories of statistics which comprise a very considerable part of mathematics. Volumes have been written on the Calcu- lus of Probabilities, on Least Squares, on Variation. On the other hand, many of the statistical processes are ex- tremely simple and do not get beyond the bounds of ordinary arithmetic. The simple processes have a wide general use; the more elaborate processes have their place but are not commonly appUcable or necessary. Why we need to use the statistical method. — People who do not like mathematics often say "Oh! Pshaw! Why do we have to study statistics ? Of what good are they? " The answer is that in a big world we have to deal with many facts and the statistical method enables us to abbreviate facts, to concentrate them so that we can inore readily study and compare them and find out what they mean. If you want to live in a little world and deal with only a few facts then you do not need statistics. The head of a small factory may remember the wages of each one of his employees. Tom gets ten dollars a week, Fred gets twelve, Sam and Bill each get fifteen and Henry 8 DEMOGRAPHY gets sixteen dollars. But the head of a large factory where there are a hundred hands cannot carry all these facts in mind. The bookkeeper of course has a record of them, very necessary for pay-day. The head of the fac- tory may know, however, that ten of the employees get sixteen dollars a week, fifteen get twelve dollars and sev- enty-five get ten dollars. The factory superintendent needs these statistics. He Uves in a large world. The village gossip knows the dates of all the births, marriages and deaths in town since January first, but she Uves irf a little world. To_compare these facts with similar facts for the next town and the one next to that requires that the facts be expressed in figures. Statistics enable one to enlarge his horizon. Why are statistics thought to be "dry"? — Statistics have the popular reputation of being dry, uninteresting, or, as Shakespeare would say, — "flat, stale and unprofit- able." This is very natural, for all figures look aUke. If we are considering one hundred and thirty-seven tons of coal we use the figures 137 and if we are talking about the same number of American Beauty roses we also use the figures 137. If we think only of the figures we see no difference between these statistics. It does not take much imagination to visuaUze 137 roses^ their beauty and their odor; it takes more, perhaps, to visualize 137 tons of coal. And if 37 of the roses are said to be yellow, 60 white and 40 red, we can visualize the whole mass even if we know that they are mixed. The reason why statis- tics are "dry" is because people do not try to visuaUze them. If you don't try to visuaUze the statistics the figures are commonplace and of course uninteresting, while if you do try the mental effort is tiring. Moreover, there is a real difficulty and that is our inability to visualize very large figures. I may be able to visualize a hundred CAN ONE PROVE ANYTHING BY STATISTICS 9 dollars, but I confess not to be able to visualize a million dollars, even though I know that it is one thousand times as much as one thousand dollars. Also visualization is lost, or at any rate confused, when we begin to perform mathematical operations with our statistics. The way to prevent statistics from being "dry" is to keep in mind that statistics are not merely figures, but are figures which stand for facts. Is it true that " you can prove anything by statistics " ? — We often hear it said "Oh! you can prove anything by statistics." Is this true ? Suppose we substitute the mean- ing of statistics and say "you can prove anything by facts if expressed in figures." Obviously this is, not so. Facts are facts whether expressed in figures or not. If the conclusions are wrong the trouble lies not in the sta- tistics but in the way they are used. The drawing of con- clusions is the function of logic, a process of reasoning, and fallacious reasoning should ndt be charged against,, statistics. And yet there is something which underlies the popular statement. When figures are used to express, facts, and when the logical processes are applied to figures, divorced in the mind from the facts for which they stand, it is easy for fallacies to creep in without being recognized; it is easy to compare things which ought not to be compared, to generalize from inadequate data, and to commit all sorts of illogical errors. Thus the unscrupulous may fool the unwary, and the innocent may fool themselves. Hence to use statistics properly one must be able not only to visualize the facts but to think logically. Students who would be statisticians should therefore study formal logic. Some of the common fallacies in the use of statistics will be considered on later pages. Honesty and conservatism are essential qualities for the makers and users of statistics. 10 DEMOGRAPHY There are numerous works on logic. One of the best is "The Principles of Science," by W. Stanley Jevons. It treats not only of logic but of the scientific method in general. The national value of " Vital Bookkeeping." — It is of the greatest importance to a nation that accurate records be kept of its vital capital, of its gains by birth and immi- gration and of its losses by death and emigration, for a nation's true wealth lies not in its lands and waters, not in its forests and mines, not in its flocks and herds^ not in its dollars, but in its healthy and happy men, women and children. A well man is worth more to a nation than a sick man; a man in the prime of life is of more immediate worth than an old man or a child, a married man is poten- tially a greater asset than a single man. Hence, in a na- tion's vital bookkeeping the number of people, their age and sex and conjugal condition, their parentage, their health, the rate of births and deaths, are matters of great moment. Their environment is also important; their con- centration in cities and villages and congested areas, their mode of housing, .their occupation, their state of intelli- gence, their economic condition, their knowledge of sani- tation, all contribute to the sum total of their usefulness to themselves and to society. Vital bookkeeping is carried on much as ordinary book- keeping; there are daily entries of accessions and losses as they occur, corresponding to receipts and payments; there are weekly statements, monthly statements and annual statements; and at longer intervals there is a taking account of stock, that is, a census. One important differ- ence, however, should be noted. Accounts are accurate rec'ords of transactions and if properly kept an exact bal- ance will be obtained Vital statistics are not always accurate, the individual data are incomplete and subject STATISTICS NECESSARY FOR HEALTH OFFICER 11 to error; the results, therefore, lack the precision of mone- tary accounts. It is necessary to keep this fact constantly in mind when interpreting the results of statistical studies. An understanding of the principles of the arithmetic of inexact numbers and of the theory of probability is essen- tial. Vital statistics are useful for many purposes. To the historian they show the nation's growth and mark the flood and ebb of physical Ufe; to the economist they in- dicate the number and distribution of the producers and consumers of wealth; to the sanitarian they measure the people's health and reflect the hygienic conditions of the environment; to the sociologist they show many things relating to human beings in their relations one with another. Vital statistics necessary for health officer. — Vital sta- tistics are not to be collected and used as mere records of past events : an even more important use is that of prophe- sying the future. An engineer in planning a water supply to last for a generation estimates the future population by the previous rate of growth; so also in laying out a system of streets and sewers and transportation service. The whole idea of city planning is fundamentally based on the use of the vital statistics of what has been as a means of estimating what is to be. The health officer of a city or he whose duty it is to col- lect and record the vital statistics should study them as soon as received and not wait until some convenient day when other work is slack and then merely tabulate and make averages for formal reports and permanent records. Vital statistics, especially those of morbidity, should be studied in the making, and just as the meteorologist reads his instruments daily in order to forecast the weather and give warnings of the coming hurricane, so the efficient health officer will daily study the reports of new cases of 12 DEMOGRAPHY disease in order that he may be forewarned of an impend- ing epidemic and take measures to check its ravages. No Ughtihouse keeper on a rocky coast is charged with greater responsibility than he who is set to watch the signs of coming pestilence from the conning tower of the health department. Making another comparison, we may say that the health service should be organized for rapid work Uke a fire department, with its rapid facility for learning that a fire exists and its ever ready apparatus for extinguishing the blaze. If the fire alarm is not rung, the blaze will spread, and if cases of disease are not reported the epidemic will likewise spread. The duty of reporting cases of infectious disease rests upon the practicing physi- cians, and thereby hangs a sad and discouraging tale. National vital statistics. — It has now become well rec- ognized that the maintenance of accurate records of vital statistics is a proper governmental function, and no nation, state or city can be considered as having a complete gov- ernmentg.1 equipment which does not provide for the proper collection and permanent record of such statistics. But, as will be seen, even our longest governmental rec- ords are relatively short, and for that reason w-e should be careful in drawing general conclusions from them. Sweden. — Of modern nations Sweden has a just claim to the longest unbroken series of vital statistics. In 1741 registration of births, marriages and deaths was begun in all parishes and since 1749 a census has been taken each . year. The principal data for this long period (1750-1900), were given in a most valuable paper by Sundbarg at the International Congress of Hygiene and Demography in Berlin in 1907. France. — In 1790 Lavoisier (1743-1794), after the French Revolution, collected extensive data relating to the population of that country, the amount of land under NATIONAL VITAL STATISTICS 13 cultivation, etc., but the first actual enumeration of the inhabitants of Paris was not made until 1817. England. — In England the old parish records date back at least to 1538, when Henry VIII ordered all parsons, vicars and curates to keep true and exact records of all weddings, christenings and burials. It was not until 1801 that a national census was taken, and it was not until 1851 that a complete census was made. United States of America. — America is far behind other civilized countries in its records of vital statistics. There is no national registration system, no complete national record of births and deaths. This results from our dis- tributive form of government, the control of such matters being a state or municipal function, not a federal one. The records vary greatly in different parts of the country. Some of the older states like Massachusetts and New Jersey possess fairly accurate records that extend back for several decades, but in some of the western and southern states the records are either absent or so incomplete as to be worthless. . At the time of the last census, in 1910, the registration area where the death records were considered accurate enough to warrant their being pubUshed included only 58 per cent of the total population of the country. This condition of affairs may be charitably regarded as a youthful sin of omission, but if it is much longer contin- ued it will be nothing less than a national disgrace. The health statistics of our best administered cities are much inferior to the published vital statistics of European cities, as, for example, those of Hamburg^ Germany. The United States Census Bureau, now permanent, has become in- creasingly efficient in recent years, and its reports are of much value, but not until a centralized public health serv- ice has been secured will the nation's vital statistics be put upon a high plane of comprehensiveness and accuracy. 14 DEMOGRAPHY The importance of statistical induction. — In using sta- tistics we necessarily employ the methods of logical think- ing comprised in what is termed "induction," methods by which general tendencies and laws are drawn out of accu- mulations of facts. Statistical induction may be said to be one of the most potent weapons of modern science. Referring to it Royce says that the technique of statistical induction consists wholly in learning how to take fair samples of the facts in question, and how to observe these facts accurately and adequately. Statistics are being constantly invoked for testing hy- potheses in all branches of science. This involves four distinct processes, — , first, the choice of a good hypothesis; second, the computation of certain consequences, all of which must be true if the hypothesis is true; third, the choice of a fair sample of these consequences for a test; fourth, the actual test of each of these chosen hy- potheses. Deductive reasoning as well as inductive reasoning is involved in the use of vital statistics. It is perhaps the natural order of mental processes for the mind -pursuing an inductive study- to leap ahead to some conclusion and then fill in the intervening steps by working backward by deduction. It is by the application of the principles of logic that the statistician is able to keep his conclusion within rea- sonable bounds. Choice of statistical data. — First, there is the complete statistical study which includes a full count of all the units within the desired area or within the specified time. This method, of course, brings the surest results, but it is often impossible. Second, is the monographic method, a pro- cedure in which a detailed and exact study is made of a EXERCISES AND QUESTIONS 15 particular group. Where the group selected for study is a well-chosen type the application of this method yields valuable results but there is danger in generalizing from monographic researches. The third method is the repre- sentative method, a study of certain selected parts repre- sentative of the whole. This is analogous to the method of the analytical chemist where chosen samples are. analyzed and the results applied to the whole. The value of this method depends upon the accuracy of the sampling process quite as much as upon the enumeration of the facts em- braced by the sample. The representative method is widely used. There are two general methods of sampling. One is that of random selection, the other is that of mix- ture and subdivision. The object in both cases is the same, — to secure a sample truly representative of the whole. The tendency to take samples of the obvious and the accessible is one that must be constantly struggled against. EXERCISES AND QUESTIONS 1. How can vital statistics be used to determine relative values in public health activities? [See Am. J. P. H., Sept., 1916, p. 916.] 2. Describe the common method used in compiling genealogies. [Consult some systematic genealogy, — say ihat of your own family.] 3. Prepare a diagram of your own ancestry, giving the names of your father and mother, the dates of their birth (and death) and their birthplaces; also the same information as to your two grandfathers and your two grandmothers; your four great-grandfathers, etc., as far as the information can be readily obtained. 4. Who was Mendel and what is the Mendelian law? [See Rose- nau's Preventive Medicine and Hygiene, Chapter on Heredity and Eugenics.] 5. What are the primary laws of heredity and eugenics? 6. What information can you give as to the heights of your father and mother, your grandfathers and grandmothers? Can you illustrate any 16 DEMOGRAPHY of the laws of heredity, as to height, color of hair or any other char- acteristics, from your own family records? 7. Can you suggest a schedule of anthropometric data to be kept for each person as a matter of family record? 8. Write a short biographical sketch of some person famous for work in statistics, demography or vital statistics. (Name to be assigned by the instructor.) CHAPTER II STATISTICAL ARITHMETIC Statistical processes. — The principal processes used in the study of vital statistics are these : Collection of the facts. Classification of the facts. Generalization from the facts. Comparison of the facts. Drawing conclusions from the study of the facts. Display of the facts. Collection of data. — There are two primary methods of obtaining the data needed in demography — enumeration and registration. In the first case the statistician goes or sends to get the facts. The persons employed are enumer- ators or inspectors. This is the method of census taking and is described in another chapter. In the second case the facts are reported to the statistician in accordance with established rules and regulations. For example, physicians and undertakers are required to send notices of deaths and burials to the proper authorities. Some of the methods in common use and the laws which govern the reporting of vital facts are described later on. It is of vital importance to make sure that the data collected are sufficient in kind and number for the purpose for which the statistics are intended. It saves time and labor in the end to consider carefully at the outset just what data are needed. Where, -as is often the case, the statis- tician has no control over the collection of the data, he 17 18 STATISTICAL ARITHMETIC should make every possible attempt to ascertain the reliabil- ity of the sources of information and not attempt to draw conclusions not warranted by the conditions under which the figures were collected. Statistical units. — The basic statistical process is count- ing. An easy process, — one says; and so it is if we know what to count, and if we know what to include and what to leave out. Here at the very outset we meet our first diffi- culty. Before going on stop and define a " dwelling-house." Is a church a dwelling-house if the sexton lives .in it? Is a garage a dwelling-house if the chauffeur lives in the sec- ond story? Is a building with two front doors one dwell- ing-house or two? Is a " three-decker " one dwelHng-house or three? Or try to define an infant, a birth, a cotton-mill operative or any other unit used in demography. Statistical units are the things counted and represented by numbers. Obviously every fact, every item, counted must be included within the definition of the unit. No part of a statistical study demands more careful study than the definition of the statistical units to be employed. Each unit should not only be rigidly, accurately and in- telligibly defined, it should be steadily adhered to during the investigation. This is by no means easy. In counting the number of deaths in a city should non- residents be included? Should still-births be included in "births"? Has practice in this matter been constant during the last fifty years? Has pneumonia always meant what it means to-day? And what has become of the causes of death which no longer appear on our lists? It is cer- tainly obvious that all statistics relating to the causes of death must be used with the utmost caution, and this is especially the case if the statistics cover a considerable period of time. ERRORS OF COLLECTION 19 Or, let us take, the simple matter of age. What is a seven-year old child? Shall we take the nearest birthday, or the last birthday? Or shall we do as is done in some foreign countries and take the next birthday? In the latter case a child at birth is regarded as of age one. Even the United States census has not always followed the same method of ascertaining age. Errors of collection. — • One of the errors of enumeration is failure to find the units to be counted. In taking a census some persons are never found by the enumerators. They may be accidentally missed, or they may be traveling, away from home or hiding. At the last census in England, where the data are collected on a single day, it is said that some of the suffragettes walked the streets for the entire period, so as not to be at home when the enumerators called, arguing that if they could not vote they ought not to be counted. Failure to obtain complete records is still greater when the data are obtained by registration. The opposite error sometimes occurs, namely over-regis- tration. This is usually due to carelessness, but padded census records have been known to occur. There are two kinds of errors which need to be distin- guished — balanced errors and unbalanced errors. For ex- ample, if a thermometer is correct it may be assumed that a good observer will be as likely to read too high as too low and that in a long series of readings the errors will balance each other. But if the thermometer is at fault all of the readings will be too low or too high, that is, the errors will be unbalanced. Causes of unbalanced errors must be re- moved if possible or, if not removed, the results must be corrected for them. In recording such quantities as the height and weight of persons the errors may be regarded as balanced, but physi- cians in reporting diseases may by their practice of diagnosis 20 STATISTICAL ARITHMETIC introduce unbalanced errors. Again, the aggregation of the records of various physicians may cause these errors to become more or less balanced. Finally we have the effect of the personal equation of the collector. His mind may have certain grooves through which errors creep into his work. If reading a scale he may have a natural tendency to over-estimate the space between divisions, — if counting units he may have a natural tend- ency to skip some. What is more serious, he may possess the unpardonable statistical sin of carelessness, or worst of all, he may be dishonest. Ignorance and failure to under- stand the definition of the units that are to be enumerated are also fruitful sources of error.- Tally sheets. — When many items are to be counted, and especially when there are different units which must be kept apart it is convenient to use some form of tally sheet. Each item is first indicated by a line or a dot and these are afterwards counted. There are two common methods — the cross-five method and the cross-ten method. In the former every fifth item is indicated by a line which crosses four, making a group of five. In the latter nine items are indicated by dots, the tenth by a cross over the dots. Other devices will doubtless suggest themselves to the reader. (Fig- D- Tabulation. — For purposes of study and display the collected data are commonly arranged in tabular form, that is in columns and lines. The preparation of tables is an important part of statistical work and cannot be done too well. The object of a table is to bring statistics to- gether for comparison, to condense information. Essential qualities of good tabular work are clearness, compactness and neatness. Tables are expensive to print, hence the most should be made of each one. The following sugges- tions, if followed, should yield good results : TABULATION 21 1. Each table should have a title which tells clearly what the table contains. Preferably the title should be short, but clearness is the main thing. It is excellent train- ing in the use of words to produce an artistic title. THE CROSS FIVE METHOD Disease Number Measles lU^ U^ UH // 17 Scarlet-fever .IW /// 8 Whooping-cough IM lU^ IW //// - ZO THE CROSS TEN-METHOD Disease Jan. Feb. Mar. Apr. May June Etc. Meoslee ■J '% ■9:: •f 'i^- 7 Scarlet-fevfT ■^ ■/ a- -■9\ % Whooplng-oongh ^■ ^ ^ I' * •>■ % ;:: ^. ^ ■.:: 2 / f- v^ 1 / ? ^ « ( > Fig. 1.— Tally Sheefe. 2. Each column should have a clear and appropriate heading. As the space for the- heading is often small ab- breviations may be used, provided they are well understood or well explained in the accompanying text. 3. If the heading is complex, that is, if certain parts of the heading cover more than one column, care should be taken to have this clearly indicated by proper rulings. 22 STATISTICAL ARITHMETIC Printers call this " boxing." If there are few columns and if the headings are simple, the rulings are unnecessary. 4. If the different columns of a table are likely to be re- ferred to in the text it is convenient to have each column given a serial number from left to right, placed in paren- thesis, just below the heading. 5. Long unbroken columns of figures are confusing to the eye; especially if the figures of different columns are to be compared on a given line. This trouble can be obviated by leaving horizontal spaces between every few lines or by the use of horizontal rulings. Sometimes, for purposes of reference, each line is given a serial number from top to bottom. 6. The columns of a table should not be widely separ- ated even if there are only a few columns and the page is large. Compactness is a virtue. Much paper is wasted in annual reports by badly arranged tables. On the other hand the type used in tabular work should not be too small. 7. If the figures tabulated have more than three signifi- cant figures it is a good plan to separate them into groups of three. Thus, we should not write 6457102, but 6 457 102. Tables 1 and 2 are given as examples of tabulation and boxing. From this point on students should criticize the tables in this book (a few of which have been intentionally made iroperfect), and they should use great care in the prep- aration of every table involved in the " Exercises and Ques- tions." TABULATION 23 TABLE 1 CAMBRIDGE, MASS. Estimates of Population Census. (2) Estimate based on . U.S. census. (3) Estimate based on U. S. and state census. (4) Estimate based on local data. (5) Estimate used by- local board of health. (6) Estimate used in this report. (7) 24 STATISTICAL ARITHMETIC TABLE 2 CAMBRIDGE, MASS.: BIRTH-RATES Year. Population estimate. Number of Births. Birth-rate. Total. Resident. Gross. Kesident. As stated by, etc. (1) (2) (3) (4) (5) (6) (7) Inexact numbers. — In vital statistics we are usually compelled to deal with data ' which are not strictly accurate. The figures used to express the results, therefore, should be prepared with this fact in mind. Unnecessary figures should be omitted and only those digits should be included which are supported by the data. Two guiding principles should be followed in making numerical statements of data; — first, to have the figures of the compilation depend upon and indicate the accuracy of the observations; and, second, to carry the final numerical result no further than practical use demands. Let us take as an illustration the result of the U. S. Census of 1910, according to which the population of the 1 Do not misuse this word. It is a plural word. The singular num- ber is "datum," but this is seldom used. Do not say, "The data is . . . ," but "The data ari-. . . ." INEXACT NUMBERS 25 country is stated as 91,972,266. Obviously this figure cannot be strictly true. Let us suppose the possible error to be as much as 200,000. We might write the result " 92 million"; but this would be needlessly crude, though accu- rate enough for some purposes. We might say that the population was between 91.8 and 92.2 million, or we might write 92,000,000 ± 0.2 per cent. The U. S. Census Bureau publishes the figures as collected, leaving it for him who uses the figures to abbreviate them into round numbers according to the use which is to be. made of them. Experience has shown that very few measurements or observations of anything are accurate to five significant figures, many not to three, and some are doubtful in the second figure. In tabulating the results of original data it is best to give* the figures as obtained. But in discussing the results it is better to use round numbers, the number of significant figures depending on the accuracy of the data and the needs of the problem at hand. In presenting figures orally to an audience it is especially important to use round numbers. Nothing is more dead- ening than for a speaker to tire the ear with the reiteration of meaningless digits. Example. — Let us suppose that the number of bacteria on a plate can be counted within five per cent, plus or minus, and that three different tests gave the following numbers: — 2790, 4220 and 3470 per c.c. the average being 3493. Five per cent* of this figure is 175; — hence the true result might conceivably lie between 3318 and 3668. Obviously it would be sufficiently accurate and for many reasons better to state the result as 3500 per c.c. Recognizing these unavoidable errors in our present methods the Committee on Standard Methods of Water Analysis of the American 26 STATISTICAL ARITHMETIC Public Health Association has suggested that statements of analysis should be limited in significant figures as follows: Unfortunately the nile has not been lived up to. TABLE 3 RULE FOR STATING THE RESULTS OF BACTERIAL COUNTS IN WATER ANALYSIS Numbers of bacteria found. Records to be made. 1 to 50 As found 51 to 100 To the nearest 5 101 to 250 ' " " 10 251 to 500 ' ■' " 25 501 to 1,000 ' " " 50 1,001 to 10,000 ' " " 100 10,001 to 50,000 ' " " 500 50,001 to 100,000 ' " " 1,000 100,001 to 500,000 ' " " 10,000 500,001 to 1,000,000 ' " " 50,000 1,000,001 to 10,000,000 ' " " 100,000 Perhaps, sometime, O; «-l N n Tti lO to t" CO o> o: tH o: iH M CO ^ lO to t- 00 OS O: iH « CO ni lO to t- 00 at o: «H N CO tH la to t- CO a> o: iH M CO Til lO to t- CO e> O: iH •o oi tM N eo ■* •a eo t- 00 o> 3 0| iH o to t- CO OS o: iH (M CO ^ lO to t- CO 03 iw a 15 :M fl 11 o: iH N eo I* lO to t- 00 OS 0| tH N CO ■* IS to t- CO OS O; iH C4 CO ■* lO eo t- CO OS s s Oi iH « eo ■<* lO to t» 00 OS 3 = 3 O: iH « CO ■>* lO to t- CO OS X O: th eq eo ■* lO to c- 00 OS d "i ih ^ !a 5 3 % s & d S 5 D V3 " k uoTjBdnooo o: iH N eo ■* lO eo t- CO OS oi tH « CO 111 lO CO t- CO OS u P^ X o; th ea CO Ti< lO to t- CO OS § g i^ 1 S 5 > S £ s •DOO Im g ^ a 9 9 O :Q ^ CO g s ■ CO CD 1 o o: ^ fl X3S is t» P«A oi iH « "CO •* lO to t- 00 OS SDuapisaa 0| iH eQ n Date of Birth or 1 a O; iH « O; rH « CO eo ■* lO to t- CO OS O i 1 ^S 1 1 i 1 i-i it 1 1 o: th m 1-1 : 1-1, iH s 3 U3 iH to iH t- iH CO 1-1 OS 1-1 \ o: iH « CO •>» lO to t- 00 OS \^ S^ o ; 1-1 N eo ■* lO to t- 00 OS \. .S2 g o: iH eq CO tH lO to t- 00 OS ^v o; iH N eo •* lO to C- 00 OS ^ ,^rt ■" O • iH 56 STATISTICAL ARITHMETIC EXERCISES AND QUESTIONS 1. Define the following statistical units as used by the U. S. Bureau of the Census. o. A family. i- A rural commumty. 6. A birth. k. The population of a pli c. A death. I. Communicable disease. d. An infant. m. Suicide. e. A dweUing house. n. Age. f. A colored person. 0. A citizen. g- A farmer. P- An industrial accident. h. A cotton-miU operative. a- A sleeping room. i. An urban community. 2. Criticize the tables in the annual reports of any health depart- ment (as assigned by the instructor), as to title, form, boxing, abbrevia- tions, etc. 3. Discuss the tables in the reports of the U. S. Bureau of the Census. Should they be taken as models? 4. Is it good form to use the following abbreviations? a. "No. of Days," for Number of Days. 6. " Pop." for population. c. " Av. " for average. d. " Ty. rate" for death-rate from typhoid fever. e. "T. B. rate" for death-fate from tuberculosis. What other ill-advised abbreviations have you observed? 6. In one ward of a city 517 births were reported, it being estimated, on the basis of past experience, that this figure was within 8 per cent of the true number; in a second ward the report was 730 births, with an estimated error of 20 per cent; in a third the corresponding figures were 910 and 25 per cent; in a fourth, 604 and 18 per cent; what was the probable number of births in the city? And what was the probable percentage error of the total number of reported births? 6. If the death-rate in a certain city was 20 per thousand in 1910, if it decreased 10 per cent the next year, increased 10 per cent the year after, decreased 20 per cent the next year, increased 20 per cent the next year, what was the death-rate in 1914? EXERCISES AND QUESTIONS 57 7. Multiply the following i^umbers by the arithmetic process, by the use of logarithms and by the use of the slide rule. Note the relative accuracies of the result. o. 17 X 215. /. 54,672 X 93,721. 5. 95 X 847. g. 4.7 X 1573. c. 2161 X 1050. h. 0.231 X 1.29. d. 9230 X 40;373. i. 0.507 X 0.062. e. 10,072X736. j. 432.1X13.41. 8. Similarly perform the following divisions: o. 342 -f- 17. /. 20,073 -=- 98. 6. 9467 -^ 872. g. 763.05 -;- 40.39. c. 473,561 -7- 2395. h. 8999 -r- 1101. d. 100,262 ^ 730. i. 30,500 -=- 10.07. e. 0.517 ■^ 2.43. j. 0.03 -^ 76^ 9. Given the following items: Find the mean, the median, the mode, the upper quartUe. a. 6, 7, 6, 2, 8, 4, 9, 6, 7, 2, 1, 2, 1, 9, 8, 7, 3, 6, 6. b. 71, 3, 2, 0, 0, 1, 9, 5, 6, 3, 0, 2, 7, 7, 0, 4, 0, 2, 8. c. 2, 12, 2, 14, 3, 13, 9, 16, 1, 0, 40, 90, 3, 22, 7, 15. 10. Arrange each of the sets of figures in the last question in groups as follows and find the average of each set from these groups. (1) (2) (3) (4) (5) Group limits (inclusive) 0-4 5-9 10-14 15-19 20 and above Nimiber of items in group .... 11. Find the arithmetic and geometric means of: a. 71 and 19. 6. 421 and 7. c. 21, 7 and 11. CHAPTER III STATISTICAL GRAPHICS Use of graphic methods. — Statistics are numerical ex- pressions of facts. When the facts are few in number it is not necessary to use figures to represent them, but as the number of facts becomes larger a point is reached where memory of individual facts must be supplemented by generalizing them, by letting a number stand for a class or a group of facts. In the same way when the numerical processes become complicated, when the figures become unwieldy or attain magnitudes beyond the ordinary range of familiarity, it is useful to resort to another process and represent the figures graphically. And even when the facts are few and simple their representation by diagram is often a distinct aid to the mind in grasping their meaning and fixing them in the memory. There are two distinct uses of graphic methods arid it is important to keep these in mind in preparing diagrams. The first use is for study. The relations between different groups, classes and series of facts can often be understood better from diagrams than from tables of figures. By the use of cross-section paper it is possible to interpolate values between plotted points, to generalize the facts of a series in which the data are more or less irregular, to extend plotted curves ahead of the data, thus enabling statistics to be used as a. basis of prediction, to compare different curves and thus establish correlations. Properly used graphic methods will greatly assist the statistician in understanding his data. 58 TYPES OF DIAGRAMS 59 It is a great mistake, however, to think that all statistics should be reduced to diagrammatic form, and it must be remembered that not one person in ten is able to read a complicated diagram understandingly. Some regard dia- grams as puzzles to be worked out. To such persons dia- grams are of little or no practical value. The other use of graphic methods is for displaying the facts in such a way that they wUl attract attention, that the general results, regardless of details, will fix themselves in the memory. This use of graphic methods has greatly increased in recent years. We see diagrams of all kinds on bill-boards, in advertisements, in pubhc health reports, in popular and scientific articles, even in moving pictirres. The growing importance of the whole subject is shown by the recent publication of a notable book by W. C. Brinton"^ on Graphic Methods for Presenting Facts, which contains several hundred different kinds of graphic repre- sentations — a most useful book for statisticians to study. Thus, on the one hand, we have the diagram forming a part of mathematics, and, on the other hand, we find it merging into the cartoon; hence we may lay down the general principle that graphic methods of depicting statis- tics must be selected according to the use to which they are to be put. Types of diagrams. — The word diagram may be used in a generic sense to include all of the various kinds of mathe- matical graphs, plots, charts, maps and pictorial illus- trations used by statisticians for the display or comparison of numerical data. These may be roughly classified as follows : 1. One-scale diagrams, in 'which different items are compared with each other on the basis of a single magnitude scale. 1 See list of references in Appendix. 60 STATISTICAL GRAPHICS 2. Two-scale diagrams, commonly known as graphs, in which two magnitudes are involved. One of these is commonly represented by a horizontal scale and one by a vertical scale. These graphs take many forms. 3. Three-scale diagrams. It is difficult to- represent three dimensions on a flat sheet of paper, but it is sometimes done by the so-called isometric method. 4. Component -part diagrams, in which a single quantity is shown in sub-division. 5. Pictorial diagrams, or pictograms, a special form of the one-scale diagram used for display. 6. Statistical maps, or cartograms, a special form of the two-scale diagram, in which one scale is area ar- ranged geographically, while the other consists of differently colored or shaded areas. There are also many miscellaneous types of diagrams with specially devised irregular scales, logarithmic scales, probability scales, etc., and with one scale superposed on another. These are for study and not for display. The appeal to the eye. — Diagrams are intended as an appeal to the eye, and advantage is taken of the abiUty of the eye to observe quickly and with fair accuracy: (a) Distances, as, for example, the relative heights of different points above a base line or the relative distances of points from some other point or from some axis. (6) Areas, as shown by comparison of similar figures, that is by circles, squares, rectangles or even irregular figures. (c) Volumes, as shown by comparison of similar cubes, cyUnders, spheres and irregular figures. (d) Ratios, such as the relative lengths of parallel lines, areas or volumes similar in general shape. GRAPHICAL DECEPTIONS 61 (e) Slopes, or the relative inclinations of different lines from a base line. (/) Angles, as shown by the sub-division of the 360 de- grees about a point. (g) Shades and colors, as shown by areas on pietograms and maps. Graphical deceptions. — In preparing diagrams it is well to bear in mind that the eye may be deceived. There may be graphical fallacies as well as statistical fallacies. Some of these may be illustrated by well-known optical illusions. In Fig. 9 the line A appears to be longer than B. In reality they have the same length. The shaded area D ap- pears to be taller than C. In reality they have the same height. Astigmatism is also the cause of optical illusions. Those whose business it is to prepare diagrams for display should study these optical conditions. But there are other and more important ways in which diagrams may deceive. In pietograms we sometimes see two objects of different size — say two men, one large and one small, illustrating the relative numbers of persons who have died from two diseases. If the relative numbers are as 2 is to 1, the figures would naturally be drawn with the heights in that ratio. But to the eye the larger man would appear to be more than twice the size of the smaller one, because the eye would here judge not the height alone, but the whole aiea of the figure This very common fallacy in which one dimension is used* for plotting, with no reference to the other dimensions which automatically changes, may be illustrated by the two circles E and F. The diameter of F is only twice that of E, but the circle F seems to be much more than twice as large as E. This fallacy may be called that of plotting by hne and seeing by area. Similarly when a polar diagram is made to illustrate 62 STATISTICAL GRAPHICS the seasonal distribution of some disease, the number of cases per 1000 persons being indicated by the distance of each plotted point from the center, an incorrect idea is obtained. In Fig. 21 the death-rate for April and May Fig. 9. — Optical Illusions. was in reahty only three times that for August and Sep- tember, but from the diagram it looks to be more than three times as much. The reason is that the diagram was drawn as a line diagram, but the eye sees the area as well as the lines and the area embraced by the enveloping lines increases as the points become farther from the center. ESSENTIAL FEATURES OP A DIAGRAM 63 Other fallacies connected with the choice of scales will be pointed out in the consideration of that subject. Essential features of a diagram. — Every diagram, save the very simplest, should have a title; one or more scales, plainly indicated; a background of cross-section, or co- ordinate lines; the points, lines or areas representing the data plotted, marked for identification; and any necessary notes or explanations. As a rule diagrams should be self- contained, that is, they should tell the facts without regard to the accompanying text. The title may be entirely outside of the frame of coor- dinate lines, with the idea that if the diagram is published the printer will set up the title in type. This simpUfies somewhat the construction of the diagram, but if a lantern shde is made it may be that the printer's type will be found to appear disproportionately small. If the title is placed within the frame of coordinate Unes these lines must be dis- continued and not allowed to run through the letters of the title. On machine-ruled paper this rule cannot hold as the coordinate lines cannot be erased. It is possible to place the title on a piece of white paper and paste it over the cross- section Unes. In the case of machine-ruled tracing cloth, the lines may be removed by the use of xylol, or gasolene, and a clear background obtained for the title. In designing the title it is not necessary to use the words " Diagram showing the . . . " any more than it is necessary to say " Table showing the . . . ." The size and shape of the diagram will depend in great measure upon the scales chosen, but as diagrams are very often reproduced, even though not drawn primarily for publication, it is always well to prepare them as if for publication. For the purposes of a typewritten report, diagrams should be kept within the limits of a rectangle 7 by 9| in. 64 STATISTICAL GRAPHICS The standard typewritten paper is 8| X 11 in., but there should be margins of 1 in. on the top and left and J in. on the bottom and right for binding and trimming. The paper containing the diagram should be cut 8| by 11 in. Larger diagrams may of course be desirable or necessarj'. For reproduction most diagrams have to be reduced in size. When this is done the diagram as a whole is not only made smaller but the letters are made smaller and every line made thinner. Care should be taken therefore that the letters and figures used are not too small and that the lines are not too thin. As a rule letters and figures should be so placed that they can be easily read from the bottom or the right-hand edge. The coordinate lines are used to guide the eye and to enable one to read from the scale with accuracy and minute- ness. For display purposes, however, no more coordinate lines should be used than are necessary, as too many are confusing. The coordinate lines should be lighter in weight than the plotted points or lines in order that the latter may stand out conspicuously. Too many plotted lines should not be used in the same diagram as confusion may result. If there is more than one plotted line each should be clearly marked. This is especially important if the lines cross or meet at any point. Often it is desirable to have the diagram include within its boundaries not only the graphic representation of the figures, but the figures themselves. One-scale diagrams. — The simplest diagram is one where the magnitudes of the different items are represented by the relative lengths of Imes or by narrow rectangles of con- stant width. They are easy to understand and are useful for many purposes. The magnitudes represented by the lines may be stated in figures or there may be a scale shown ONE-SCALE DIAGRAMS 65 for comparison. See Figs. 10 and 11. The lines may be drawn horizontally or vertically. An important principle in Hne diagrams is that all of the lines should- start from the same base. If this is not done comparison is difficult. In the case of Fig. 11, which shows the birth-rates and death-rates for two European countries, 200- ■' - 100- ' s & a 3 1 O 1 1 o 3 1 1 0- _ c _ H <1LJ Fig. 10. — Numbers Of Deaths from Five Most Important Causes. Cambridge, Mass., 1915. it is easy to compare the births, shown by the total lengths, and the deaths, shown by the black, because they start from the left-hand line, but it is difficult to compare the natural increase of population in the two countries, shown by the white, because they have no common base. If the natural rate of increase is important it is better to use sepa- rate hues for births, deaths and increase as shown in Fig. 11, b and c. 66 STATISTICAL GRAPHICS It is also difficult to compare two lines which, though they have a common base, extend in opposite directions from the base. This, however, is often done with a fair degree of satisfaction. See Fig. 42. I ENGLAND Fig. 11. — Comparison of Birth-rates, Death-rates and Rates of Natural Increase. Diagrams with rectangular coordinates. — Most of the diagrams used to illustrate statistics are of the two-scale type. There is a horizontal scale with magnitudes increas- ing from left to right and a vertical scale with magnitudes increasing from bottom to top.^ It is customary also to rule in a sort of checker-board consisting of parallel ver- tical and horizontal lines to guide the eye in following the scales across the paper. To further assist the eye heavy lines are used for the round numbers of the scale and finer lines for sub-divisions. It is good practice also to always use for the zero hne a Hne as heavy as the plotted line. Usually this would be the bottom line and the left-hand DIAGRAMS WITH RECTANGULAR COORDINATES 67 line. If there be no zero, as in the case of a scale of years; the heavy line would not be used. In the case of percent- age diagrams both the zero per cent line and the hundred per cent line should be heavy. The numerical values for the sub-divisions of the scale are shown in figures, prefer- ably at the bottom and left side of the diagram. Sometimes they are placed also at the top and right. Thus the zeros of both scales are supposed to be at or near the lower left- hand corner; but circumstances may compel some different arrangement. In diagrams of this kind time, whether in years, months or days, is generally expressed by the horizontal scale and always runs from left to right. Such diagrams are sometimes called historigrams, sometimes merely graphs. The distances measured along the vertical scale are known to mathematicians as ordinates, the distances on the hori- zontal scale as abscissce. There are several ways of plotting with two scales. One' way is to use the vertical scale as a measure of the length of certain vertical lines, each of which represents the magnitude of an item, and to use the horizontal scale to indicate the occurrence of the item. Thus in Fig. 12 we have a daily record of the rainfall forgone month. Each rainfall is represented by a line of appropriate length, the position of the line showing when the rain occurred. This method is especially adapted to events which occur intermit- tently, and without regular gradations, that is to discrete series. The rainfall data might have been indicated by dots, or crosses placed at the tops of the lines, the latter being left out. This would be misleading, however, unless similar dots or crosses were placed on the zero line for the days of no rainfall. This would not look well, and it is never done. The vertical line method or ordinate plotting is sometimes 68 STATISTICAL GRAPHICS used for plotting data in series, the horizontal scale repre- senting time. Thus we may compare the death-rates for different years by a diagram such as that shown in Fig. 13 .4. This, however, is a continuous series and may be plotted 3 ; s . & ( \ / ( ) 1 II \ 1 1 II II 1 1 %l Fig. 12 ^° Jul., mr^^ — Example of Plotting a Record of Rainfall. \ \, Iq0 A V B s, c \ ^ S, \ 1 S ^ \ ■*- ^ 02468 10 12 02468 10 12 02468 10 12 Ordinates Troflle Curve Fig. 13. — Example of Simple Plottings. as a broken line, known as a profile line, which shows continuity. See Fig. 13 B. For most purposes this profile method is to be preferred to the vertical line method, but the latter is perhaps understood better by persons not familiar with graphic methods. USE OP THE HORIZONTAL SCALE 69 Still another way would be to plot the data as dots, or crosses, and draw a smooth curve through them to show the trend of events. This implies that the data are subject to errors and that the smooth curve gives a better picture of the true events. See Fig. 13 C. The art of smoothing curves is described in most books on statistical technique. In general it may be said thatHhe rules usually laid down are based on the laws of probability. Use of the horizontal scale. — In the illustrations just given the divisions of the horizontal scale were taken to be definite points of time, namely days and years, each point being plotted directly on a vertical line. This does very well for plotting yearly records which run on continuously, and there is no objection to the method for practical pur- poses. It is not, however, strictly accurate, for a year is not a point of time, but an interval of time. It is the space between the lines, which represents the year, the vertical lines marking the boundaries. Graphs are sometimes made on this basis. j Let us plot the following numbers of deaths which oc- curred in the different months of a single year. TABLE 13 NUMBER OF DEATHS: EXAMPLE FOR PLOTTDjrG Month. Deaths. Month. Deaths. Month. Deaths. Month. Deaths. (1) (2) 0) (2) (1) (2) (1) (2) Jan. Feb. Mar. 40 30 25 Apr. May June 27 25 July Aug. Sept. 20 17 15 Oct. Nov. Dec. 17 20 25 Here the problem is to divide the horizontal scale, which represents a year, into twelve parts, each of which represents a month, and plot one point for each month. Now we get 70 STATISTICAL GRAPHICS V Quanliity plolltea]at \ Be Bio iini of Month s ^ s. A s ^ ^^ / ">s V y i^ "5 «an t{«7 pli>ttea( at Eiao^Jf jmth k, y s. B s y N / "^N V ,^ ^ ar ' ' 2 < S < U5 O Z D ->"-S / — ^+ '^-..-'^ J FMAMJJASOND Tear Fig. 14. — Examples of Time Plotting. JFMAMJJASOND Tear into trouble if we plot the data on the hnes, for we might do this in two Ways, as in Fig. 14, A and B. In one case we plot the point at the beginning of the month, in the other, at the end of the month. Of the two the latter is to be preferred. It would be more logical to let each month' be represented by the space between the lines and to plot the points in the middle of the spaces as in Fig. 14, C or D. If the figures plotted represent the monthly averages of PLOTTING FIGURES BY GROUPS 71 several items occurring in each month the method of plot- ting shown in Fig. 14 i? is a proper one. Fig. 14 F shows how one may plot the mean as well as the maximum and minimum item for each month. At present there is no well-established custom in regard to these methods. Plot- ting 'on the line is usually followed simply because it is easier and makes a neater diagram. Its illogical character seldom causes serious misunderstandings. Plotting figures by groups. — The plotting of individual observations is comparatively easy; but it is difficult to decide how to plot the totals and means of groups, and still more difficult if the groups are irregular. This can best be appreciated by an example. Let us undertake to plot the following data: TABLE 14 DATA TO BE PLOTTED Age (last birthday). Number of cases. Age group. Number of cases in group. Average number of cases for each year. (1) (2) (3) . (4) (5) 1 1 2 2 2 0-4 12 2.4 3 4 4 3 5 1 6 4 7 3 5-9 15 3.0 8 5 9 2 10 6 11 4 12 7 10-14 25 5.0 13 5 14 3 15 4 16 6 17 5 15-19 20 4.0 18 3 19 2 72 STATISTICAL GRAPHICS If we plot the individual items we have the result shown in Fig. 15 A. If we plot the total numbers of cases in each group we may do so by the methods B, C, or D. In these the horizontal scale represents not individual ages, but groups. We may indicate this fact by using the hyphens as shown. In B we have plotted the figure 12 on the line which indicates the maximum limit of the group 0-4, 15 on the line which indicates the maximum Umit of group 5-9, etc. In C we have plotted 12, 15, etc., in the middle of the spaces which represent the groups. In D the height of the horizontal line above the base is taken to represent the total and extends across the group limits. If we wish to show both the individual observations and the means for the groups we may plot as in E. In plotting by groups care should be taken to make it clear that the horizontal scale stands for groups and that the vertical scale stands for the number in the group. Plotting irregular groups. — Let us now take the case of irregular groupings. Assume the following data: TABLE 15 DATA TO BE PLOTTED Age group. Number of cases in group. Average for each year in group. (1) (2) (3) 0- 4 5- 9 10-14 15-19 20-29 30-39 40-59 60-79 80-99 4 6 8 6 7 5 8 6 3 0.8 1.2 1.6 1.2 0.7 0.5 0.4 0.3 0.15 PLOTTING IRREGULAR GROUPS 73 I* 53 ^ M-{-K ^ riliQ ^M ^ K J-ALl \ (V 30 ,20 10 Age 15 B. 1 — ^ ^ V *■' <«SS s# _J ■10- .15 ■ -20, Age Group Age Qioup 20 c I 10 c - 5 10 15 20 Age Group Fig. 15. — Examples of Age Plotting. 74 STATISTICAL GRAPHICS 7 / / /' / / 05 s, \ - ^ ^ ■^ ^ ^ ^ dnojg uj jaqran^ si 5 g & *«' § /_ / 1 Y 1 f 1 -! / S ^ \ z J7 \ x I^^ ^^^ ■^, Sg. ' bo ~ I — — I i ^i - i i 'M M m q 11 ^^ MM ^,11 mm rSma, WMWM mmmm '/MMM/mm imm jBajS. jod jsqcani^ 3J9CJ3AV .a -•J ■■8 O. 3 O T S Pi C3 dnoao uj .laqiunx anoJB U! aaquiux SUMMATION DIAGRAMS 75 In the first place we must find some way to indicate to the eye the varying intervals of the group. The first four groups cover five years, the next two ten years and the last three twenty years each. We might do this as in Fig. 16 A, in which the heavy vertical lines indicate the group limits. In B the coordinate lines are regular and the group limits are shown by the emphasized horizontal scale. In C the blocks indicate the group limits. Not one of these, however, gives an adequate picture of the distribution of the cases according to age, because the groups are not uniform. All three diagrams are fallacious because the ordinates are not strictly comparable. The best way to show distribution by age is to make the groups comparable by reducing all to a common denominator. This can be done by finding the average number of cases for each year in the group. The results are shown in Fig. 16 D. Here the irregular grouping on the horizontal scale is maintained, yet a good idea is given of the distribution of the cases according to age. Summation diagrams. — For many purposes it is desir- able to plot the results obtained by the successive summa- tion of the items in preceding groups. This gives what are called summation diagrams, cumulative plots, mass plots or mass curves. This may be illustrated by the data on p. 77. These data are plotted in Fig. 17. Sometimes instead of connecting the plotted points by straight lines a curved line passing approximately through them is sketched in. It should, be noticed that in this diagram the horizontal scale stands for age and not for age-groups. One use which can be made of a plot of this kind is to find the median of the series. There are 53 cases in all. The middle one is the 27th. From the scale this item has a value of 24 years, as shown by the cross. In. the same way the quartiles may be found and the decentiles. 76 STA'f'ISTICAL GRAPHICS ^ ^^'^ it: 7 ^^ 7 / ~/' y jr 7_ / T~ ' t 4. L A 1 f _j 7 I^ / / I r 7 L 10 BO 30 40 50 60 TO 80 90 , 100 Age Fig. 17. — Example of Cumulative, or Summation Plotting. CHOICE OF SCALES 77 TABLE 16 DATA TO BE PLOTTED Age-group. Number ot cases. Summation groiip. Number ot cases. Leas than age. (1) (2) (3) -<^^. \ ^ H2 ■--> 15 A v^ s^ 1 10 g 25 SO .a 15 bIO \^ k^ \ -- - B """ Ti^B, '^JSSia 06 20 15 „ Fig. 19. — Comparison of Deaths from Tuberculosis with Deaths from all Causes: Boston, Mass. A, Incorrect Method. B, Correct Method. 80 STATISTICAL GRAPHICS LUU 90 80 70 60 60 40 80. \ \ A \ \ ^ s. \ N^ k U ? u ? 100 90 80 TO 60 50 40 30, \, \ c \J V \ \ S, \ N ^ ? «? "? & 100 I' « 90 S 80 R to . ■§ TO 50 40 u 30 20 10 \ \ \ B \ \ \ s. \ \, D u I " r S S S JlJ s s s s Fig. 20. — Example of Not Carrying Scale to Base Line, culosis Death-rate: Boston, Mass. Tuber- DOUBLE COORDINATE PAPER 81 Fig. 20 shows the reduction of the tuberculosis death- rate in Boston expressed in terms of the percentage which the death-rate of each period was of that for the period 1881 to 1885. In B the vertical scale is carried down to per cent at the base line. This gives a true picture of the re- duction which has taken place and the 4eath-rate remaining. In A the vertical scale is not carried to the base line and the diagram gives the optical impression that the reduction has been greater than it actually has been and that the rate at the end of the period was very much less than at the beginning. Brinton has suggested that when the base line does not represent the zero of the vertical scale it should be drawn as a wavy line instead of a straight line, and this idea has much merit. Where two different vertical scales are used, and one goes to zero at the base line while the other does not, the wavy line may extend only half way across the diagram from that side of the diagram where the scale does not go to zero. C in Fig. 20 illustrates the appear- ance of a diagram drawn in this way. The wavy line implies that the lower part of the diagram is omitted. Diagrams with polar coordinates. — Fig. 21 illustrates a diagram with the. ordinates represented by distances from a central point along radial lines, the abscissae, if we may use the term out of its place, being represented by the angle which the ordinate makes with the vertical measured clockwise around the circle. This form of plotting has a limited application and because of its inherent fallacious character should be abandoned. Double coordinate paper. — Sometimes it is convenient to use what may be called double coordinate paper. This is illustrated by Fig. 22. Here the plotted line may be read against either set of coordinates. The horizontal lines give the number of deaths from typhoid, fever, the scale being at the left. The inclined lines give the death- 82 STATISTICAL GRAPHICS rate per 100,000. - ^hus in 1900 the number of deaths was about 305, the death-rate about 27 per 100,000. The slope of the inclined lines depends upon the increase in population. The black inclined line represents popula- tion and this may Tae read for the censal years from the right-hand scale. It will be seen that the ratio between / < 1 ^V\ A \ ^^\ / Oct. ^^k., APr.\ , ^^^m "" / W / ^^vW \ I \/ Fig. 21. — Example of Radial Plotting. the right-hand and left-hand scale for any horizontal line gives the rate for the heavy line, i.e., 200 -5- 1,000,000 = ^" , or 20 per hundred thousand. So also 100 -H 500,000 = 20 per hundred thousand. Any point on the heavy line, therefore, gives a rate of 20 per hundred thousand. The rate Une for 10 per 100,000 is one-half way to the line between the heavy hne and the zero or base line, on each vertical Une which represents a census. The rate line of 30 is, on each vertical, as far above the black line as the'rate line of 10 is below it. And so on. In the example chosen the typhoid fever rate in Brooklyn has fallen since the date of the last plotting, i.e., 1906. RATIO CROSS-SECTION PAPER 83 Nouvindod SOEl 0061 9681 06Bt S881 0881 S^8l «r3Aad oioHdAJ. wouj shxvbq m uaatMnN Ratio cross-section paper. — Thus far we have been dealing with regular scales in which the intervals are uni- form from one end to the other. It is possible to construct scales with intervals which are not uniform, but which vary- in a systematic way. These are used for special purposes. The most common scale of this kind is the logarithmic scale. 84 STATISTICAL GRAPHICS Diagrams in which the vertical scale is logarithmic and the horizontal scale uniform are sometimes called " ratio charts." These have been used by engineers for many years, but they are only beginning to be appreciated by statisticians. [_It wiU be recalled that the logarithms of the decimal numbers are as follows: TABLE 17 LOGAMTHMS OF NUMBERS Number. Logarithm. (1) (2) 1 0.000 10 1.000 100 2. coo 1,000 3.000 10,000 4.000 100,000 5.000 1,000,000 6,000 As each number increases tenfold the logarithm increases by one; and in general it may be said that as numbers increase at a regular rate the logarithms increase by a regular increment. From the logarithm tables ^ it may be seen that the log of 10 is 1.0000, and that if 10 is increased by 25 per cent and becomes 12.5 the log of 12.5 is 1.0969, an increment of 0.0969. The log of 50 is 1.6990. 50 in- creased by 25 per cent is 62.5. The log of 62.5 is 1.7959, an increment of 0.0969 as before. The log of 1570 is 3.1959. 1570 increased by 25 per cent is 1962.5 and the log of this is 3.2928, an increment of 0.0969 as before. If, using a uniform scale, we plot figures which increase at a constant rate we shall get a curve as shown in Fig. 23 A. Let us ' See Appendix. RATIO CROSS-SECTION PAPER 85 Fig. 23. — Example of Logarithmic Plotting. 86 STATISTICAL GRAPHICS start with a population of 100 in 1870 and assume an in- crease of 20 per cent each decade. We then have the following: TABLE 18 DATA TO BE PLOTTED Year. Population. Log of popu- lation. (1) (2) (3) 1870 1880 1890 1900 1910 1920 1930 100 120 144 173 207 248 299 2.0000 2.0792 2.1584 2.2380 2.3160 2.3945 2.4757 The figures in column (2) are plotted in A. If we plot the logarithms of the numbers in column (2) we have a straight line as in B. This being so, why not label the horizontal lines with the numbers in column (2) instead of their logarithms? This is done at the right of the diagram. It wUl be seen that the vertical scale is not made up of uni- form intervals, but aside from that fact it is a perfectly good scale. In C we have a diagram in which the vertical scale (represented by the horizontal lines) is drawn on this basis, and it will be seen that the figures in column (2) plotted on it fall in a straight line. This is a single loga- rithmic, or in simpler words, a ratio chart. Figures increas- ing at a constant rate plot out as a straight line on paper thus ruled, i.e., with a uniform horizontal scale and a logarithmic vertical scale. There are two uses for single logarithmic paper. One is to show variations in rate. If we plot the population of the United States on ordinary cross-section paper with RULED PAPER 87 uniform scales we obtain an ascending curve, but from this we get no idea of the constancy of the rate of increase. This is shown in Fig. 24 A. But if we use ratio cross- section paper, as in B, we find that the rate of increase was constant from] 1790 to 1860, but that since the Civil War the rate has been nearly constant yet not as great as before. On this paper equal slopes mean equal rates of in- cre*ie, -while on uniform paper equal slopes mean equal in- crements. Another use is that of enabling us to plot on one sheet observations which cover a very wide range. If we were using a uniform scale to plot such figures we should have to make the scale so small that individual differences between the small numbers could not be discerned. It will be noticed that on the ratio paper the intervals for the small numbers are larger than for the high numbers, so that if plotted on this paper we can still read differences in the lower part of the scale. The upper part of the scale is foreshortened. In fact we can discern the same percent- age differences in all parts of the scale. Logarithmic cross-siection paper. — By logarithmic cross- section paper we usually mean paper on which both the horizontal and the vertical scales are" logarithmic. Here the ratios are in both directions. It will be observed that the interval from 1 to 10 is the same as that from 10 to 100, from 100 to 1000 and so on. One objection to the loga- rithmic scale is that it does not go to zero. The interval below 1 runs from 1 to 0.1, the next from 0.1 to 0.01, the next from 0.01 to 0.001 and so on. This paper is very largely used in scientific work, but its use for statistical purposes is somewhat limited. Ruled paper. — It is not difficult to rule your own. cross- section paper, although it is tedious work. Many sorts of ruled papers are on the market and can be purchased 88 STATISTICAL GRAPHICS / / ■ / / y / / • / ^ — Dire ot Sea e ', • _,*> — ^ *-^ ,.^ ^ ^ -- ^ ^ y- ^ / ' Lo rarith mlo Si aJe a 9 s a s s Fig. 24. — Population of the United States shown by Direct and Logarithmic Plotting. MECHANICS OF DIAGRAM MAKING 89 from dealers in engineering drawing materials. The fol- lowing scales are convenient for ordinary work: (a) Inches subdivided into tenths in both directions. (6) Half inches subdivided into tenths in both directions. (c) Inches subdivided into tenths in one direction and into twelfths in the other direction, — -useful for plotting data for the twelve months of a year. (d) Ratio paper, with inches subdivided into tenths in one direction, and with a Jogarithmic scale from 1 to 10,000 in the other direction. (e) Arithmetical probability paper. - (/) Logarithmic probability paper. {g) Paper with horizontal scale ruled for the calendar year, and vertical scale in inches subdivided to tenths. It is possible to buy tracing cloth ruled iii cross-section form, but the kinds of ruling are limited. Such cross- section tracing cloth is sold by the yard, width about 26 in., and may be cut to sheets of. desired size. Mechanics of diagram making. — For making diagrams it is advisable to provide a regular draughtsman's equip- ment. This should include : (a) A drawing board of appropriate size. For small diagrams a size of about 12 in. by 17 in. is satis- factory. (6) A tee-square long enough to extend across the drawing board. (c) A 30-degree triangle, 10 in. long, celluloid. (d) A 45-degree triangle, 6 in. long, celluloid. (e) A lettering triangle, to give slopes for letters. (/) A ruling pen. (g) One or more scales, steel, celluloid or boxwood, variously ruled in tenths, quarters, etc. (h) Black drawing ink (Higgins). 90 STATISTICAL GRAPHICS D Jan. F Fig. 25. — Examples of Plotting Paper. Sheets 8| X 11 inches. LETTERlNa 91 (i) Thumb tacks. 0) Brown " detail " paper. (fc) Tracing cloth. Other equipment may be needed according to the nature of the work. Lettering. — There is much truth in the statement that good letter ers are bom and not made. Yet it is surprising how much one can improve in lettering by giving attention to a few guiding principles. For most diagrams it is best to adopt a very simple style of letter. Shaded letters look well on maps, but are out of place on hne diagrams. The two styles shown in Fig. 26 are suitable for ordinary work. The choice of a vertical letter or a sloping letter is largely a matter of taste. Most people are more successful with sloping letters. They can be made a httle more rapidly, but they are perhaps a Uttle more informal than vertical letters. It is important that letters appear to be uniform in height and slope. It is weU to use guides both as to height and slope. Letters should also appear to be spaced uni- formly. The curves of such letters as C, G, and S should extend shghtly above and below the horizontal guide lines. Adjacent straight-line letters such as N, I, U, M, etc., should be spaced a little farther apart than curved letters. Attention should be given to the manner of making the strokes as shown in the plate. The student should consult a book on lettering such, for example, as that of Reinhardt. If the title is inset it should be carefully placed. In general the lower right-hand corner is the best place for it, but often its location is governed by available space. The sizes of letters used should follow the important words. Each line should be centered. Write each line on a scrap of paper: count the letters in it: find the middle letter: 92 Statistical graphics E N s - 5» 1- Y X 1 :< •\ s i; - > ' > UJ - : 3 ■ -1 < o V m a. LlJ u L :c c c- 1 u C. ! IL Q c ' i: : c ■ ;? 13 [^ cm ^ 2i 5 5 ■) i '^ *w, UJ "'IP'" O h V) ■^, : VI o z < a: O L. a o I h u Q h (0 U o o 3 (0 Dl' I .1 . ill" = ' put that down first and then letter backwards and forwards. Capitals may be used for the principal lines of a title. In a general sort of way try to arrange the lines so that a line circumscribing the title will be approximately an ellipse. Label each scale, except that it is unnecessary -to do so in the case of months and years. Do not use abbreviations. THE USE OP COLOR IN DIAGRAMS 93 If there is more than one plotted line label each one. Be free in the use of explanatory notes. A diagram should tell its own story. In doing this use letters of readable size. It is a good rule never to make a letter or a figure less than J inch in height. Somewhere on the sheet, but outside of the diagram itself, should be plkced the initials of the person who made the diagram and the date. This is valuable for identifica- tion, but it need not be published. Wall charts. — Wall charts are much used nowadays in the display of vital statistics. It is not difficult to prepare these, but certain general principles should be kept in mind. They should be simple and clear, of aftiple size and plainly lettered. If intended to be seen from- a dis- tance the letters should be large and the lines heavy. As lettering forms an important part of a wall diagram it is well to know that gummed letters of all sizes can be pur- chased. Examples of these letters are shown in Fig. 27. The use of color in diagrams. — • Colored lines should be used sparingly if the diagrams are to be pubhshed.' A sheet must go through the press once for each color and this adds to the cost. The most effective use of color is where a single colored line is made to stand out in contrast to other black lines, and for this purpose red is the best. Color on plotted lines may be avoided by using black lines made in different ways. The following are easily dis- tinguishable: 1. Heavy full line 2. Light full line 3. Heavy broken line 4. Light broken line 5. Dotted line 6. Dot-dash line 94 STATISTICAL GRAPHICS For wall charts or posters intended to be viewed from a distance, colors are justifiable. The cross-section lines on the ruled paper ordinarily sold are colored green or brown or light red. Very bright colors 1234567890 BC Fig. 27. — Examples of Gmnmed Letters, Useful for Wall Diagrams. used for this purpose are exceedingly trying on the eyes. It is desirable however to have a color' which can be pho- tographed and also blue-printed. Green is not satisfac- tory from these points of view. Dull red is much better. Vermilion red should be used, not carmine. COMPONENT PART DIAGRAMS 95 Component part diagrams. — In order to show the com- ponent parts of a total number we may subdivide a Une or a long rectangle and label each part, or we may subdivide an area, as a square or a circle, indicating differences by ^ Earalysis^.8 Eijflfflreiia. ;i5^ ti-». ^^ >^ J^, ^j*/ # .^' ,«^' «!.** ..^ P^ 8.6 Heart Disease *«, ■<% Fig. 28. -Proportion of Deaths from Each Specified Cause in the U. S. Registration Area: 1907. colors, shades or patterns as in cartography. A circle properly subdivided is perhaps the best type of diagram to show percentages. Here the sectors plainly show the de- sired differences. This sort of a diagram is not to be con- fused with plotting by polar coordinates. (See Fig. 28.) 96 STATISTICAL GEAPHICS Statistical maps. — The object of statistical maps is to display classes and groups of statistics for different areas. It will be remembered that statistical classes involve differ- ences which cannot be expressed in figm'es, but that statisti- cal groups contain facts similar in kind but which differ from each other numerically. This difference should be kept in mind in preparing statistical maps. The statistical data are shown on maps by different colors, by different patterns of lines and dots or by sur- face shadings. In the display of data arranged in groups, that is, in accordance with magnitude, it is well to indicate the differences by variations in shade from light to dark. In the display of data arranged by classes it is "well to use different patterns or colors. Different shades may be ob- tained by successive washes of color applied with a brush, or by the use of cross-hatching in which the proportion of surface covered with ink regularly increases. The so-called " Ben Day " system of indicating shades by the use of special devices is well known to printers and engravers.^ Sometimes the figures themselves are placed on the maps. If this is done care' should be taken to make sure that the boundaries of the areas to which the figures apply are prop- erly defined. Blue prints and other prints. — It is often desirable to obtain several copies of the diagrams made, and the quickest and cheapest method is that of making blue prints. The process is the same as that of making photographic prints from a negative. Blue-print paper can be purchased; in fact, it can be easily made. A large photographic printing frame is required. The diagram is placed in the frame over the blue-print paper and exposed to the sunlight for a few minutes, after which the paper is washed in water and dried. It is necessary, of course, to have the paper on ' See Brinton's Graphic Methods, pp. 216, 233. REPRODUCTION OP DIAGRAMS 97 which the diagram is made fairly thin and transparent. Paper should be selected with blue-printing in mind. The transparency of paper can be greatly increased by oiling it on the back after the diagram is made. A liquid sold under the name of " transparantine " is satisfactory. The best blue prints of diagrams are obtained by the use of trac- ing cloth. This has many advantages. It is easy to ink on and erasures may be made. The lines are sharp and photograph well. The cloth does not tear. The cloth is oiled on one side. The drawing should be done on the other. A httle powdered chalk should be dusted on and rubbed off before using ink. Pencil lines may be used as guide lines and erased before blue-printing. In the ordinary blue print the lines are white and the background blue. Additional white lines can be drawn on the blue by using a weak solution of caustic soda in a pen as ink. ^ It is possible to obtain prints in which blue or brown lines appear on a white ground. This requires the making of a negative, from which subsequent prints are made. Reproduction of diagrams. — The common method of reproducing diagrams for publication is to photograph them and print from a zinc plate. This is the cheapest and most available method. It is necessary that the original draw- ing be well made, with lines of the right weight and the letters of the right size. All imperfections are of course reproduced. Usually the drawing should be made at least fifty per cent larger than the published plate, that is, the size is reduced one-third. To have diagrams made by a draughtsman costs something, but, if the photographic process is to be used, it is worth while. The draughtsman should know what the size of the published plate is to be. Those not skilled in making diagrams ought to know that there is another process of reproduction which does not 98 STATISTICAL GRAPHICS require a carefully 'drawn original, namely, that of wax engraving. In this process the engraver does the work of the draughtsman. A copper plate is used. The lettering in this process can be put in with type. This results in per- fect legibility, which is often not the case with photographic work. Reproduction by the wax process costs almost twice that by the photographic process, but if to the latter is added the time and expense of preparing a perfect original the wax process costs no more. Most of the plates in this book were made by the wax process by the L. L. Poates Company of New York. Unfortunately there are not many wax engravers in this country. Equation of a curve. — Having plotted certain data on rectangular coordinate paper, that is, using a horizontal and a vertical scale, and finding that the points fall on a straight line or on a regular curve, it is sometimes desirable to find the equation of the straight line or curve. This is ftot difficult, but it requires the use of mathematical prin- ciples not considered in this book. The reader is referred to such books as Saxelby's "A Course in Practical Mathe- matics" ^ or Peddles' " Construction of Graphical Charts." ^ EXERCISES AND QUESTIONS 1. Describe Ripley's method of preparing statistical maps with different shadings. [Pub. Am. Sta. Asso., Sept. 1899, pp. 319-322.] 2. Construct a graph of the birth-rates and death-rates of Sweden from 1749 to 1900. (See p. 203.) 3. Construct a graph of the natural rate of increase of the population of Sweden from 1749 to 1900. 4. Show by suitable diagrams the data in Tables 100, 106 and 110. 5. Find diagrams in this book which do not conform to the principles described in Chapter III. ' Pub. by Longmans, Green & Co., 1908. 2 Pub. by McGraw-Hill Book Co,, 1910. EXERCISES AND QUESTIONS 99 6. Construct a "devil's checker-board," as follows: • o. Take a piece of cardboard or heavy drawing paper and rule in black ink a rectangle 8j" wide and 11" high. Rule also a horizontal line 1" below the top, and a vertical line 1" from left-hand edge, in order to leave suitable margins at top and left. b. Subdivide the 7|" on the horizontal line into 15 haH-inch spaces and rule vertical lines. Subdivide the 10" on the vertical line into 40 quarter-inch spaces and rule horizontal lines. c. Draw in red inclined lines sloping downward to the left, being J" apart in a horizontal line and Ij" apart in a vertical direction. If the work is done accurately certain of these diagonals wiU intersect corners of the small rectangles; if the work is not accurate the name of the problem is justified. These guide lines will be found convenient in the construction of tables. The sloping lines will serve as guides for sloping letters. 7. Construct a colored wall chart showing the death-rates from several diseases for some city, using the one-scale type of diagram. Assume the chart is to be read from a distance of twenty feet. 8. Describe the method of construction and the varied uses of ratio cross-section paper. (Quar. Pub. Am. Sta. Asso. June, 1917, p. 577.) 9. Plot the population of some city (assigned by the instructor) using ordinary cross-section paper and ratio paper. 10. Construct a colored component-part diagram (subdivided circle), showing the composition of the population of some city or state (data assigned by the instructor). CHAPTER IV ENUMERATION AND REGISTRATION All civilized nations at regular periods enumerate their populations, that is, take a census. There are various governmental reasons for doing this, two important ones being the adjustment of representation in legislative bodies and the levying of taxes. There are also business, social and sanitary uses to which .the figures are put. In consid- ering a census several questions immediately arise; when was it made, what area was included, how were the data obtained, what were the results and where may they be found? The United States census. — The first general census of the United States was made in 1790, the first year divisible by ten after the founding of the new republic, and a census has been taken every ten years since that date, the census of 1910 being the thirteenth. The first twelve censuses were made by special commis- sions created for the purpose and which went out of exist- ence as soon as the task had been accomplished. A per- manent Bureau of the Census was created in 1902. At first it was under the Department of the Interior, but in 1903 was transferred to the Department of Commerce and Labor. Its head is known as the Director of the Census. Besides taking the general census of the country every ten years this bureau is charged with the collection of sta- tistics of many kinds relating to the people, vital statistics, financial statistics, municipal statistics, statistics of agri- 100 THE United states census 101 culture, fishing, manufacture, transportation, mining, and others. The census data prior to 1910 were pubhshed as a series of special volumes by the commission having the work in charge. Many of the older volumes are out of print, but may be found in large libraries. In 1900 there were three volumes on population and two volumes on vital statistics obtainable by purchase from the U. S. Publication Office at Washington. Bulletins of the census of 1910 may be ob- tained from the " Director of the Census, Washington, D. C." Lists of available reports and bulletins may be obtained without charge by writing to the director. In 1910 the report of population comprised four large volumes. The first contained the general data for the coun- try, classified and grouped in many ways; the second and third gave the population subdivided by civil divisions; the fourth, occupations. For some time it has been cus- tomary to include in eacft census report the populations for the two censuses preceding. This is for comparison and to enable estimates of population to be made. Thus, in the thirteenth census will be found the populations for 1910, 1900 and 1890. A table often consulted was that on page 430 of Vol. I, Part I, of the U. S. Census of 1900, which gave the popula- tions of all cities which were larger than 25,000 in 1900, for every census since 1790. In the 1910 census these figures are given in the second and third volumes mentioned under the head of each state. See also pages 80-97 of the first volume. These census reports should be in every public library, and in the library of every city government, as they con- ■ tain a vast amount of important information relative to the growth and condition of our country. Every student of demography should become thoroughly familiar with the U. S. Census reports. 102 ENUMERATION AND REGISTRATION The census date. — For most purposes it is sufficiently accurate to say that the census was taken in a certain year, but for the more exact computations a definite day must be named. The population of the country is con- stantly changing, even from hour to hour. If we wish to use the figure which best represents the population for any year we should naturally choose the population as it was' at the middle of the year, namely July 1st. But it is not practicable to enumerate all of the people on a single day, and July 1st is not the best time to make the enumer- ation because being in the vacation season many people are likely to be away from home. For practical reasons another day is chosen as the ofiicial day for taking the census. In 1910 this day was April 15th. It took several weeks to make the enumeration, but the data were adjusted to this day so that the statistics are stated " as of April 15th." But it should be noted that in 1900, in 1890, and back to 1830 the official date was June 1. Hence between the census of 1900 and 1910 the interval was not 10 years, but ten years less 1^ months (April 15 to June 1) or IJ per cent less than ten years. In some computations this introduces an appreciable error and a correction must be made. From 1820 back to 1790 the day of the census was the first Mon- day in August. In Great Britain, including Canada and Australia, the national census is taken every ten years, but one year later than in the United States, that is, in 1901 and 1911. This has been so since 1801. The time of the census is " at mid- night before the first Monday in April." It is quite possible to adjust the population of the census year, 1910, so as to find what it was on July 1st of that year, and this has been done by the U. S. Census Bureau and the figures used for the computation of mortality statistics for THE ENUMERATION SCHEDULE OF 1910 103 that year. The method used is described in the next chapter. Civil divisions. — The population of the United States is given in the census reports by minor civil divisions. The total population of the nation is subdivided into continen- tal and " non-contiguous territory," the latter including Alaska, the Hawaiian Islands, Porto Rico, and persons in naval and miUtary service stationed abroad. The con- tinental population is subdivided into states; the states into counties; the counties into cities, boroughs or towns; the cities into wards; the boroughs and towns into villages and rural regions. These civil divisions differ somewhat in different parts of the country. I In comparing the figures for different decades it must be remembered that the boundaries of the civil divisions are subject to change. State boundaries are quite permanent, but cities frequently increase by annexation of suburbs, and ward Unes change still more frequently according to poUtical exigencies. In most cases changes of bound- aries are indicated in the census reports by explanatory notes. In sending to the Director of the Census for reports of populations by states or for the whole country, the request should be made for that report which gives the facts by " minor civil divisions." The enumeration schedule of 1910. — In taking the census of 1910 the country was divided into 329 supervisor's districts each under the charge of a supervisor appointed by the President. About 70,000 enumerators were selected by the supervisors, or one for about every 1600 persons. The enumerators were required to visit each dwelling and collect the various statistics included in the schedule. The enumerators began their work throughout the country on April 15, 1910. The law provided that this 104 ENUMERATION AND REGISTRATION should be completed within two weeks in cities of 5000 or more inhabitants, and within 30 days elsewhere. The schedule of f&cts to be collected was printed on sheets of paper, 16 by 23 in., on which were 100 horizontal lines, 50 on each side, and numbered from 1 to 100. The facts for each person occupied one line.^ The schedule corresponded closely to those used in the censuses from 1850 to 1880 and 1900. The schedule used in 1890 was somewhat different, a separate schedule sheet 15 by 11 in. being employed for each family.^ For purposes of compilation the facts for each person were transferred to a separate punched card; These cards were then sorted by machine. The data collected by the enumerators for each person were as follows: At the top of each sheet were given the state, county, township or other division of county, name of incorporated place, name of institution (if any), ward of city, number of supervisor's district, number of enumerator's district, name of enumerator and date of enumeration. Schedule Location. Street, avenue, road, etc. House number (in cities or towns). 1. Number of dwelling-house in order of visitation. 2. Nimiber of family in order of visitation. 3. Name of each person whose place of abode on Apr. 15, 1910 was in this family. [Enter surname first, then the given name and middle initial, if any. Include every person Uving on Apr. 15, 1910. Omit children born since Apr. 15, 1910]. 4. Relation. Relationship of this person to the head of the family. ' IT. S. Census, 1910, Population, Vol. I, p. 1368. « U. S. Census, 1890, Population, Part I, CCIV. THE ENUMERATION SCHEDULE OF 1910 105 Personai Description. 5. Sex. 6. Color or race. 7. Age at last birthday. 8. Whether single, married, widowed or divorced. 9. Number of years of present marriage. Mother of how many children? 10. Number born. 11. Number now living. Nativity. Place of birth of each person and parents of each person enumerated. If born in tbe United States give the State or Territory. If of foreign birth give the country. 12. Place of birth of this person (including mother tongue). 13. Place of birth of father of this person (including mother tongue). 14. Place of birth of mother of this person (including mother tongue) . Citizenship. 15. Year of immigration to the United States. 16. Whether naturalized or alien. 17. Language. Whether able to speak English; or, if not, give language spoken. Occupation. 18. Trade or profession of, or particular kind of work done by, this person, as spinner, salesman, laborer, etc. 19. General nature of industry, business or establishment in which this person works, as cotton mill, dry-goods, store, farm, etc. 20. Whether an employer, employee, or working on own account. If an employee, 21. Whether out of work on Apr. 15, 1910. 22. Number of weeks out of work during year 1909. Ectv^ation. 23. Whether able to read. 24. Whether able to write. 25. Attended school any time since Sept. 1, 1909. Ovmership of Home 26. Owned or rented. 27. Owned free or mortgaged. 28. Farm or house. 29. Number of farm schedule. 106 ENUMERATION AND REGISTRATION Miscellaneous. 30. Whether a survivor of the Union or Confederate Army or Navy. 31. Whether bUnd (both eyes). 32. Whether deaf or dumb. One has only to read over this list to see the importance of statistical definitions. What, for example, 'is meant by the " usual place of abode"? This is the place where he "lives" or "belongs" or "the place which is his home." As a rule it is where he regularly sleeps. And then what about those persons who have no place of abode, lodgers in one-night lodging houses, tramps, laborers in construction camps, etc.? Such persons have to be enumerated where found. It required a formidable book of instructions to make all these things plain to the enumerators. Bowley's rules for enumeration. — The English statis- tician, Bowley, has laid down the following rules in regard to the collection of statistical data by the method of enu- meration. " In practice the enumerator is usually furnished with blanks to be filled out and with questions to be answered. These questions should be : 1. Comparatively few in number. 2. Require an answer of a number or of a "yes" or "no." 3. Simple enough to be readily understood. 4. Such as will be answered witliout bias. 5. Not unnecessarily inquisitorial. 6. As far as possible corroboratory. 7. Such as directly and unmistakably cover the point of information desired. These rules apply equally well to the collection of data by registration." Credibility of census returns. — It is not to be expected that the census figures are strictly accurate. Errors are bound to be made by the enumerators; some persons are COLLECTION OF FACTS 107 sure to be omitted from the count, especially those travel- ing; some may be counted twice; and in rare instances the lists have been thought to be padded. Taken as a whole, however, the results may be considered as reliable, and it should be noted that the pubUshed data of the U. S. Census are accepted as evidence which may be introduced without proof in courts of record. Unless there is good reason for doing otherwise they should be used instead of local estimates as the basis of computing vital rates. As a rule also they should be used in place of state censuses, but there are some exceptions to this. Collection of facts by registration and notification. — If it is difficult to secure accurate statistics of population obtained by enimierators hired for the purpose and properly instructed, how much greater the difficulty to obtain com- plete and accurate statistics by the method of registration, when the returns are made by large numbers of physicians, undertakers, clergymen, nurses and laymen not properly instructed, not interested in the proceedings and not always understanding the law, with inadequate laws, and with governments too easy-going to insist on the enforcement of such laws as exist! And yet most of the vital statistics of the country are collected in this way. Worst of all, the people at large do not appreciate the personal importance _ of having the most important events in their lives, — birth, marriage and death, — made matters of public record. By registration is meant the reporting of certain events and associated facts to a governmental authority and the ofiicial filing or recording of such facts. The reports are made in accordance with prescribed rules and usually on a blank designed for the purposes. Most nations in one way or another have endeavored to preserve their history by keeping these personal records. In England the registration of baptisms, marriages and 108 ENUMERATION AND REGISTRATION deaths dates back to 1538 when Thomas Cromwell, Vicar General under Henry VIII, issued injunctions to all parishes in England and Wales reqTiiring the clergy to enter every Sunday, in a book kept for the purpose, a record of all baptisms, marriages and burials of the preceding week. In 1653 this work was assigned to " parish registers." It was not until 1837 that registration of births, marriages and deaths became a civil function. In 1870 it was made compulsory. In parts of Canada the registration of births and deaths is still on a parish instead of a civil basis. In the early American colonies the practice of recording births, marriages and deaths was instituted. In New England the town clerk figured largely. In Massachusetts a fairly definite law was passed in 1692, according to which the town clerk was required to keep such records, and there were fees to be paid him for so doing, and penalties for those persons who withheld the desired information. This act was altered in 1795. In 1842 a registration act was passed in Massachusetts which made the Secretary of the Commonwealth the custodian of these records. This act, together with an amplifying act in 1844, forms the basis of registration in Massachusetts to this day. It was brought about largely through the activities of Lemuel Shattuck.' The story of the registration of vital statistics is too long to be told here. Many physicians, Uke Dr. Edward Jarvis, of Boston, and many committees of such organizations as the American Medical Association and the American Public Health Associations have played prominent parts in the movement. At the present time the United States Bureau of the Census is taking the lead in urging necessary reforms in the registration of vital statistics. The laws relating to the registration of vital statistics are not the same in all states. In Massachusetts a State Reg- ' State Sanitation, by George C. Whipple, Vol. I, p. 56. REGISTRATION OF BIRTHS 109 istrar in the office of the Secretary of the Commonwealth has charge of the matter, but in many states the State Board (or Department) of Health' has charge. In order to bring about uniformity a model law was drafted and en- dorsed by a number of national organizations and this has been adopted by a number of states. Some of the older states, however, still maintain their old arrangement. This model law should be carefully studied. It may be found in the Appendix. Registration of births. — It is important that the birth of each and every child born be duly registered. The information desired for the legal, social and sanitary purposes, according to the United States standard certifi- cate approved by the Bureau of the Census, and in use since 1906, is as follows : 1. Place of birth, including State, county, township or town, village, or city. If in a city, the ward, street and house number; if in a hospital or other institution, the name of the same to be given, instead of the street and house number. 2. Full name of child. If the child dies without a name, before the certificate is filed, enter the words "Died unnamed.-". If the living child has not yet been named at the date of filing certificate of birth, the space for "Full name of child" is to be left blank, to be filled out subsequently by a supplemental report, as hereinafter provided. 3. Sex of child. 4. Whether a twin, triplet, or other plural birth. A separate cer- tificate shall be required for each child in case of plural births. 5. For plural births, number of each child in order of birth. 6. Whether legitimate or illegitimate. (This question may be omit- ted if desired, or pro.vision may be made so that the identity of parents win not be disclosed.) 7. Date of birth, inSSiding the year, month and day. 8. Full name of father. 9 Residence of father. 10. Color or race of father. 11. Age of father at last birthday, in years. 12. Birthplace of father; at least State or foreign country, if known. 110 ENUMERATION AND REGISTRATION 13. Occupation of father. The occupation to be reported if engaged in any remunerative employment, with the stat«ment of (a) trade, profession, or particular kind of work; (b) general nature of industry, biisiness, or establishment in which employed (or employer). 14. Maiden name of mother. 15. Residence of mother. 16. Color or race of mother. 17. Age of mother at last birthday, in years. 18. Birthplace of mother; at least State or foreign country, if known. 19. Occupation of mother. The occupation to be reported if en- gaged in any remunerative employment, with the statement of (a) trade, profession, or particular kind of work; (b) general nature of industry, business, or establishment in which employed (or employer). 20. Number of children born to this mother, including present birth. 21. Number of children of this mother living. The duty of making out this certificate rests upon the attending physician, mid-wife or person acting as such, or in their absence upon the father or mother of the child, the householder or owner of- the premises where the birth occurred or the manager or superintendent of the institu- tion, pubhc or private, where the birth occurred, each in the order named. This certificate must be filed with the local registrar within ten days after the date of the birth. A supplemental blank is provided in case the child has not been named when the first report is submitted. The local registrar,, or a sub-registrar, must examine this certificate as to completeness and probable accuracy, secure correc- tions if necessary, keep a record of the birth certificates received, numbered serially as received, and once a month transmit the original certificates to the State Registrar, for permanent preservation. Small fees to local registrars for the recording of births are provided and likewise penalties for failure. Provision is made for giving certified copies of the birth records to persons entitled to receive them. The period of time within which a birth must be recorded may with advantage be less than the ten days above men- ENFORCEMENT OF THE REGISTRATION LAW 111 tioned, especially in cities, in fact it is best that the birth be reported within twenty-four hours. If, as should be the case, the local registrar is connected or closely associ- ated with the local board of health, the prompt information that a birth has occurred enables the health officer to send a visiting nurse to offer advice and assistance in caring for the child. Infant mortaUty cannot be greatly reduced in cities unless this prompt report is made. Advantages to individuals of having births publicly recorded. — Legal evidence is thus made available as to: — Place of Birth, useful to prove citizenship (necessary for pass-ports), to prove residence, to acquire a legal " settle- ment." Time of Birth, useful to prove age, to obtain admission to school, to establish right to go to work (legal age), to prove liabiUty for military service, to establish right to vote, to obtain pensions. ,^ Parentage, to prove legitimacy, to inherit property, to obtain settlement of insurance, to establish citizenship. What are some of the evidences of incomplete birth registration? — Dr. Louis I. Dublin has suggested three simple tests. First. The number of births registered in a calendar year should be greater than the number of living children under one year of age. Second. The birth-rate does not usually vary greatly from year to year. Wide and erratic variations indicate probable deficiencies in reporting. Third. Birth-rates less than 20 per thousand (or less than 25 per thousand in cities which have large foreign populations) are uncommon where registration is complete. Enforcement of the registration law. — - The persons most concerned in the enforcement of the birth registration law are (1) the state registrar, who should be associated with the state department of health; (2) the local registrar, who 112 ENUMERATION AND REGISTRATION should be associated with the local board of health; (3) the physician, whose duty it is to make the report; and (4) the parents of the child and the child himself or herself. In order that better registration be obtained parents and physicians should be made to understand the benefits which result to individuals and to the community. Facili- ties in the form of suitable blanks, etc., should be provided, so as not to make the matter of reporting a burden to busy physicians. It might well be that a simple post-card notification, stating that a birth occurred at such and such a place, sent on the day of birth, with a complete certificate filed at a later date would help to solve the problem. No fee should be given to a physician who does not report within the statutory time limit. What is most needed however is a rigid enforcement of the penalty clause. A local registrar once gave the author as' the reason for not imposing fines on physicians .for failure to report, — ^ " I am too good natured." This spirit is fatal to good govern- ment. Registrars are not without opportunity to obtain evidence of neglect. In the case of reported infant deaths the local registrar should ascertain if the child's birth had been recorded. Church records of baptisms may be compared with birth returns. The checks are not as complete as in the case of death returns, but an ingenious local registrar will have little difficulty in getting good returns if he takes his task seriously. In Cambridge, Mass., the birth records are so incomplete that annually a house to house canvass is mad^ to ascer- tain the births for the year. This is a disgraceful admis- sion of incompetence on the part of the local registrar and of the negligence of all concerned. No fines are imposed and some of the payments of fees are, with a proper inter- pretation of the law, of questionable legality. Unfortu- REGISTRATION OF DEATHS 113 nately Cambridge is not alone in this, but is typical of hundreds of other cities. Registration of deaths. — ■ The facts desired in connection with deaths are as follows, according to the United States Standard Certificate. 1. Place of death, including State, county, township, village, or city. If in a city, the ward, street, and house number; if in a hospital or other institution, the name of the same to be given instead of the street and house number. If in an industrial camp, the name of the camp to be given. 2. Full name of decedent. If an unnamed child, the surname pre- ceded by "Unnamed." 2a. Residence at usual place of abode (ward, street and number), and length of residence in city or town where death occurred in years and months. Also how long in United States if of foreign birth. 3. Sex. 4. Color or race, as white, black, mulatto (or other negro descent), Indian, Chinese, Japanese, or other. 5. Conjugal condition, as single, married, widowed, or divorced. 5a. If married, widowed, or divorced. Name of husband or wife. 6. Date of birth, including the year, month, and day. 7. Age, in years, months, and days. If less than one day, the hours or minutes. 8. Occupation. The occupation to be reported of any person, male or female, who had any remunerative employment, with the statement of (a) trade, profession or particular kind of work; (b) general nature of industry, business, or estabUshment in which employed (or employer); (c) name of employer. 9. Birthplace; at least State or foreign country, if known. 10. Name of father. 11. Birthplace of father; at least State or foreign country, if known. 12. Maiden name of mother. 13. Birthplace of mother; at least State or foreign country, if known. 14. Signature and address of informant. 15. Official signature of registrar, with the date when certificate was filed, and registered number. 16. Date of death, year, month, and day. 17. Certification as to medical attendance on decedent, fact and time of death, time last seen alive, and the cause of death, with contribu- 114 ENUMERATION AND REGISTRATION tory (secondary) cause of complication, if any, and duration of each, and whether attributed to dangerous or insanitary conditions of em- ployment; signature and address of physician or official making the medical certificate. 18. Where was the disease contracted if not at place of birth ? Did an operation precede death ? If so give date. Was there an autopsy ? What test confirmed diagnosis ? 19. Place of burial or removal; date of bmial. 20. Signature and address of undertaker or person acting as such. The first thirteen items are chiefly personal and these facts may be signed by any competent person acquainted with the facts. Items 16 and 17 comprise the medical certificate, which must be made out by the physician, if any, last in attendance. In the absence of medical attendance the undertaker must notify the local registrar who may not issue a burial permit until the case is referred to the local health ofiicer for investigation and certifi- cation. In case there is suspicion of neglect or unlawful act the coroner, medical examiner, or other proper officer must conduct an investigation. There are various provisos, differing in different states, which should be known by every physician and nurse and, of course, by every health officer. Finally items 19 and 20 must be signed by the undertaker. The certificate of death thus made out and duly signed must be filed by the undertaker with the local registrar (in some states the local board of health), and a burial permit or removal permit obtained prior to the disposition of the body. This permit must be delivered before burial to the person in charge of the place of burial. If the body is transported the undertaker must attach a removal permit to the box containing the corpse in order that it may reach the person in charge of the place of burial. Thus the undertaker is primarily responsible for filing the certificate with the local registrar (or local board of MARRIAGE REGISTRATION 115 health), but the physician is responsible for making out certain very essential parts of the certificate. Records of death certificates and burial permits are of course kept by the local registrar (or local board of health). Thus there is a check on the death certificate, and partly for this reason the registration of deaths is more complete than the registration of births. It is easier to come into the world without public notice than it is to leave it. The data regarding the deaths are transmitted by the local registrar to the state registrar. Uses of death registration. — The uses of death regis- tration are legal, economic, and -social. It assists in the prevention and detection of crime. It is invaluable in the settlement of life insurance and property inheritance cases. It furnishes the basis of genealogical studies. The sta- tistics based upon these records have been a powerful weapon in studying disease, and therefore in improving the health of the race and lengthening human life. The records may be of great local value in the study and sup- pression of epidemics and outbreaks of communicable dis- eases. " Marriage registration. — There "is no uniform or " model " marriage- law in the United States; state laws differ from each other. The custom is that persons desiring to marry must first obtain a civil license from a designated local official and present it to the authorized person who performs the ceremony. The person officiating is required to register the marriage. The persons responsible for mar- riage registration are therefore the clergymen and the justices of the peace. The facts required in the registration of marriages are commonly as follows : 116 ENUMERATION AND REGISTRATION 1. Date of the marriage. 2. Place of the marriage. 3. Names of the persons married. 4. Their places of birth. 5. Their residences. 6. Their ages. 7. Their color. 8. The nmnber of the marriage (as the first or second). 9. If previously married, whether widowed or divorced. 10. Their occupations. 11. The names of their parents. 12. The maiden names of their mothers. 13. The date of the record. 14. The signature of the officiating person. 15. His residence scad official station. Morbidity registration. — The compulsory registration of cases of disease dangerous to the public health is com- paratively modern. It is true that many years ago such dreaded diseases as smallpox had to be reported, but it is since the organization of modern health departments and the general understanding of the manner in which com- municable diseases are spread that compulsory notification has become widespread. In 1874 the State Board of EEealth of Massachusfetts took the lead by arranging a plan for the weekly voluntary notification of prevalent diseases. Over a hundred physicians agreed to make this report. Ten years later, in 1884, the state passed a law requiring householders and physicians to report immediately to the selectmen or board of health of the town all ca'tees of small- pox, diphtheria, scarlet fever, or any other disease danger- ous to the public health. Other states followed suit. The requirement of notification of diseases is an act of police power and authority for it resides in the state gov- ernments. In Massachusetts legislative authority has been delegated to the State Board (now Department) of Health to determine what diseases are dangerous to the public MORBIDITY REGISTRATION 117 health, and such diseases must be reported according to prescribed rules. Power is often delegated to local com- munities to supplement the state requirements for local reports. At the present time the regulations in the several states differ greatly from each other. In 1913 a model law for morbidity reports was adopted by a conference of state and territorial health authorities and the U. S. Pubhc Health service. According to this law the state boards (or departments) of health are re- quired to provide machinery for keeping informed as to current diseases dangerous to the public health; physi- cians are required to report cases of such diseases imme- diately to the local health authorities having jurisdiction; teachers in schools must do the same; these records must be promptly sent to the state authorities, There are vari- ous provisos and provisions for keeping records, and for penalties. The data inquired are the following: 1. The date when the report is made. 2. The name of the disease or siispected disease. 3. Patient's ndme, age, sex, color, and address. (This is largely for purposes of identification and location.) 4. Patient's occupation. (This serves to show both the possible origin of the disease and the probability that others have been or may be exposed.) 5. School attended by or place of employment of patient. (Serves same purpose as the preceding.) 6. Number of persons in the household, number of adults and number of children. (To indicate the nature of the household and the prob- able danger of the spread of the disease.) 7. The physician's opinion of the probable source of infection or origin of the.disease. (This gives important information and frequently reveals unreported cases. It is of particular value in occupational dis- eases.) 8. If the disease is smallpox, the type (whether the mild or virulent strain) and the number of times the patient has been successfully vac- cinated, and the approximate dates. (This gives the vaccination status and history.) 118 ENUMERATION AND REGISTRATION 9. If the disease is typhoid fever, scarlet fever, diphtheria, or septic sore throat, whether the patient had been or whether any member of the household is engaged in the production or handUng of milk. (These diseases being frequently spread through milk, this information is im- portant to indicate measures to prevent further spread.) 10. Address and signature of the physician making the report. Notifiable diseases. — The following was the list of dis- eases made notifiable by the model law of 1913. Obviously this cannot be a permanent one. It is being continually revised chiefly by addition. In many states influenza has been added to the Ust dm-ing the last few months (1918). Under present conditions the lists vary in different states. Group I. — Infectiotts Diseases. Actinomycosis. Anthrax. Chicken-pox. Cholera. Asiatic (also cholera nostras when Asiatic cholera is present or its importation threatened). Continued fever lasting seven days Dengue. Diphtheria. Dysentery: (o) Amebic. (6) Bacillary. Favus. German measles. Glanders. Hookworm disease. Leprosy. Malaria. Measles. Meningitis: (a) Epidemic cerebrospinal. (b) Tuljerculous. Mumps. Ophthalmia neonatorum (con- j unctivitis of new-born infants) . Paragonimiasis (endemic hemop- tysis). Paratyphoid fever. Plague. Pneumonia (acute). PoHomyehtis (acute infectious). Rabies. Rocky Mountain spotted, or tick, fever. Scarlet fever. Septic sore throat. SmaUpo?. Tetanus. Trachoma. Trichinosis. Tuberculosis (all forms, the organ or part affected in each case to be specified). Typhoid fever. Typhus fever. Whooping cough. Yellow fever. INCOMPLETENESS OF MORBIDITY STATISTICS 119 GROtrp II. — Occupational Diseases and Injuries. Arsenic poisoning. Bisulphide of carbon poisomng. Brass poisoning. Dinitrobenzine poisoning. Carbon monoxide poisomng. ' Caisson disease (compressed-air Lead poisoning. iUness). Mercury poisomng. Any other disease or disability Np,tural gas poisoning. contracted as a result of the Phosphorus poisoning. nature of the person's employ- Wood alcohol poisoning. ment. Naphtha poisomng. Group III. ^-Venereal Diseases. Gonococcus infection. Syphilis. Group IV. — Diseases of Unknown Origin. Pellagra. " Cancer. Incompleteness of morbidity statistics. — Complete ac- curacy in securing records of morbidity under any law is impossible. All of the cases existing are not seen by physi- cians, of the cases seen not- all are recognized or correctly diagnosed, of those recognized not all are reported within the required time and some not at all. The chief error is that of incompleteness. Conservative physicians wait until sure of their diagnosis before reporting. A vast number of physicians are careless; a few deliberately shield their patients from possible inconvenience by withholding re- ports. More and more, however, physicians are coming to realize that in dealing with communicable diseases they have a public as well as a private duty. Death certificates give a partial check on morbidity reports. The ratios be- tween statistics of sickness and death from reportable dis- eases furnishes a measure of the incompleteness of the re- ports. Trask has noted this difference between morbidity and mortality returns; death records are usually com- 120 ENUMERATION AND REGISTRATION plete but the cause of death often incorrectly diagnosed, morbidity records are incomplete, but the diagnosis usu- ally correct. This must be kept in mind in deahng with fatality ratios. Morbidity from non-reportable diseases. — It is much to be regretted that at the present time there is no adequate way of getting the facts in regard to sickness in the com- munity due to diseases which are non-reportable. Sick- ness surveys are sometimes made, but they give only the facts at a given date, and are, moreover, very expensive to make. Hospital records help us a little, the examinations made by the hfe insurance companies help a Httle, the re- cent examinations of men for the army have helped a good deal, but some day a more universal method must be de- vised. Reporting venereal diseases. — ; For a number of years the matter of requiring physicians to report, cases of vene- real diseases as diseases dangerous to the pubUc health has been under consideration by public health officials; in a few places it has been attempted. The present war has emphasized the need of such reports and these are now required in many states. For social reasons it is un- desirable to have the names of the victims reported, yet under some conditions it is desirable and necessary in the control of disease. The following system was adopted by the Massachusetts State Department of Health in 1918 as a war measure. 1. Gonorrhoea and syphUis are declared diseases dan- gerous to the pubUc health and shall be reported in the manner provided by these regulations promulgated under the authority of chapter 670, Acts of 1913. 2. Gonorrhoea and syphilis are to be reported (in the manner provided by these regulations) on and after Feb. 1, 1918. REPORTING VENEREAL DISEASES 121 3. At the time of the first visit or consultation the physi- cian shall furnish to each person examined or treated by him a numbered circular of information and advice con- cerning the disease in question, furnished by the State Department of Health for that purpose. 4. The physician shall at the same time fill out the num- bered report blank attached to the circular of advice, and forthwith mail the same to the State Department of Health. On this blank he shall report the following facts: Name of the disease. Age. Sex. Color. Marital condition and occupation of the patient. Previous duration of disease and degree of infectiousness/ The report shall not contain name or address of patient. 5. Whenever a person suffering from gonorrhoea or syphiUs in an infective stage applies to a physician for ad- vice or treatment, the physician shall ascertain from the person in question whether or not such person has pre- .viously consulted with or been treated by any other physi- cian within the Commonwealth. If not, the physician shall give and explain to the patient the numbered circular of advice, as provided in the previous regulation. If the patient has consulted with or been treated by another physician within the Commonwealth and has re- ceived the numbered circular of advice, the physician last consulted shall not report the case to the State Department of Health, but shall ask the patient to give him the name and address of the physician last previously treating said patient. 6. In case the person seeking treatment for gonorrhoea or syphilis gives the name and address of the physician last previously consulted, the physician then being consulted 122 ENUMERATION AND REGISTRATION shall notify immediately by mail the physician last pre- viously consulted of thepatient's change of medical adviser. 7. Whenever any person suffering from gonorrhoea or syphihs in an infective stage shall fail to return to the physician treating such person for a period of six weeks later than the time last appointed by the physician for such consultation or treatment, and the physician also fails to receive a notification of change of medical advisers as pro- vided in the previous section, the physician shall then notify the State Department of Health, giving name, ad- dress of patient, name of the disease and serial number, date of report and name of physician originally reporting the case by said serial number, if known. 8. Upon receipt of a report giving name and address of a person suffering from gonorrhoea or syphilis in an infective stage, as provided in the previous section, the State De- partment of Health will report name and address of the person as a person suffering from a disease dangerous to the public health, and presumably not under proper medi- cal advice and care sufficient to protect others from infec- tion, to the board of health of the city or town of patient's residence or last known address. The State Department of Health shall not divulge the name of the physician making said report. Sickness surveys. — A new method of securing data in regard to disease has been recently applied in an experi- mental way in a nmnber of cities, namely that of making a house to house canvas to determine the number of persons ill at the time. The Metropolitan Life Insurance Com- pany has been foremost in this undertaking under the direction of Dr. Lee K. Frankel and Dr. Louis I. Dublin. Spring and fall surveys have been made in several cities, the enumerator for the most part being the collecting agents of the insurance company. UNITED STATES REGiSTRATION AREA FOR DEATHS 123 The data sheet used included the age, sex, and occupa- tion of each member of the family; and if sick the disease or cause of disability, its duration and extent, i.e., whether confined to bed, and the kind of treatment, i.e., by physi- cian at home, hospital, or dispensary. Surveys have been made for Rochester, N. Y., September, 1915; Trenton, N. J., October, 1915; North Carolina (sample districts throughout the state), April, 1916; Bos- ton, Mass., July, 1916; Chelsea neighborhood of New York City, April, 1917; Pittsburg and other cities of Pennsylvania and West Virginia, March, 1917; Kansas City, Mo., April, 1917. This method obviously has its advantages and disad- vantages. Within its natural limitations the data secured ought to be of value and should furnish an excellent check on the results obtained by registration of communicable diseases. Other methods of securing data. — It will riot be pos- sible to describe here all of the many ways in which data bearing on the health of a community may be secured, but mention should be made of the importance of hospital records, life insurance records, records of physical exami- nations made by the U. S. Army and Navy, records of physical examinations of school children. More and more the systematic physical examination of the people will be extended, until it becomes universal and compulsory. All of this will wonderfully increase our knowledge of vital statistics. United States registration area for deaths. — ■ The Bureau of the Census keeps records and publishes reports of the mortality of those parts of the United States where the statistics are suflaciently accurate to make it worth while to do so. A so-called registration area for deaths was es- tablished in 1880. This included those states and cities 124 ENUMERATION AND REGISTRATION in which satisfactory registration laws were being effec- tively enforced and where there was good reason to believe that more than 90 per cent of all deaths were being regis- tered. At first the registration area included only two states, Massachusetts and New Jersey, and certain cities in other states. The area has gradually expanded as shown by the following tables. In studying the mortality rates of the country in the published reports it is important to keep in mind this addition of new territory, new populations, from year to year. TABLE 19 REGISTRATION AREA FOR DEATHS Population. Land irea. Year. Number. Per cent of total. Square miles. Per cent of total. 0) (2) (3) (4) (5) 1880 8,538,366 17.0 16,481 0.6 1890 19,659,440 31.4 90,695 3.0 1900 30,765,618 40.5 212,621 7.1 1901 31,370,952 40.3 212,770 7.2 2 32,029,815 40.4 212,762 7.2 3 32,701,083 40.4 212,762 7.2 4 33,345,163 40.4 212,744 7.2 5 34,052,201 . 40.4 212,744 7.2 6 41,983,419 48.9 603,066 20.3 7 43,016,990 49.2 603,151 20.3 8 46,789,913 52.5 725,117 24.4 9 50,870,518 66.1 765,738 25.7 1910 53,843,896 58.3 997,978 33.6 11 59,275,977 63.1 1,106,734 37.2 12 60,427,247 63.2 1,106,777 37.2 13 63 298,718 65.1 1,147,039 38.6 14 65,989,295 66.8 1,228,644 41.3 15 67,336,992 67.1 1,228,704 41.3 16 71,621,632 70 2 1,307,819 44.0 17 75,306,588 72.7 1,349,506 45.4 18 81,786,052 77.7 1,546,166 52.0 UNITED STATES REGISTRATION AREA FOR DEATHS 125 TABLE 20 LIST OF STATES IN THE REGISTRATION AREA FOR DEATHS Year of Entrance. State. Year of Entrance. State. (I) (2) (1) (2) 1880 Massachusetts 1906 South Dakota (drop- New Jersey ped in 1910) District of Columbia 1908 Washington 1890 Connecticut Wisconsin Delaware (dropped in 1909 Ohio 1900) 1910 Minnesota New Hampshire Montana New York Utah Rhode Island 1911 Kentucky Vermont Missouri 1900 Maine 1913 Virginia Michigan 1914 Kansas Indiana 1916 North Carolina 1906 California South Carolina Colorado 1917 Tennessee Maryland 1918 Illinois Pennsylvania Oregon Louisiana As a result of a test of the completeness of the registra- tion of deaths in Hawaii the territory was admitted to the registration area for deaths for 1917, thus extending be- yond the Continental United States the area from which the Bureau of the Census annually collects and pubUshes mortaUty statistics. The population and land area of Hawaii are not included in the figures of the above table. The states in which the registration of deaths is still too unsatisfactory to warrant inclusion in the registration area are: Alabama, Arizona, Arkansas, Delaware, Florida, Georgia, Idaho, Iowa, Mississippi, Nebraska, Nevada, New Mexico, North Dakota, Oklahoma, South Dakota, Texas, West Virginia, and Wyoming. (1918.) 126 ENUMERATION AND REGISTRATION f A C-T^'f I C NEED OF NATIONAL STATISTICS 127 United States registration area for births. — A regis- tration area for births was not. established until 1915. For this year the Bureau of the Census published its first annual report of birth statistics based on registration records. The birth statistics published in connection with the regular decennial reports from 1850 to 1900 inclusive were based on enumerator's returns. The registration area in 1915 included only ten states — Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, Pennsylvania, Michigan, Minnesota, and the District of Columbia. In these states the registration of births is believed to include upwards of ninety per cent of the actual ntunbers. This registrati6n area includes only 10 per cent of the area and 31 per cent of the population of the country. In spite of this unfavor- able showing a beginning has been made, and inasmuch as the standard birth certificate has been adopted for 85 per cent of the population and as public sentiment in regard to the importance of vital statistics is rapidly gaining ground, it is likely that the registration area for births will rapidly extend. No state is admitted until the accuracy of its records have been submitted to test. In 1916 Maryland was added. In 1917, Virginia, North Carolina, Kentucky, Indiana, Ohio, Wisconsin, Washington, Utah and Kansas were added, bringing the population included up to 53.1 per cent. Need of national statistics. — More and more it becomes obvious that there is need of a national system of keeping records of vital statistics, with uniform state laws, and with proper provision for the local use of the data regis- tered. The excellent work done by the Bureau of the Census has done much to emphasize this need. Likewise interstate barriers must be broken down in the interest of suppressing diseases dangerous to the public health. The 128 ENUMERATION AND REGISTRATION U. S. Public Health Service keeps a record of cases of diseases from data furnished by the states and publishes the same in its weekly Public Health Reports. This is only a part of what is needed. If the time ever comes when the United States establishes a real National Health Department the maintenance of an adequate system of vital records will be one of supreme importance. EXERCISES AKD QUESTIONS 1. Compare the methods of numeration used in taking the U. S. census of 1910, with those used in 1900, 1890, 1880, etc. 2. How do these methods compare with those used in England, France, Sweden? 3. Would there be any advantage in making the census date, "as of January first "? I 4." What advantages would come from the adoption of a uniform census date for ^he entire world? 5. How accurately is the population of China known? 6. To what extent is the keeping of accurate census records and records of vital statistics an index of national progress? 7. How can improvements be made in ascertaining the facts con- cerning morbidity? CHAPTER V POPULATION Estimation of population. — It is only for the census years that populations can be known with certainty. For the intercensal years, the years between two censuses, it is necessary to depend upon estimates. This is also the case for the postcensal years, namely, the years following the last census. These estimates are only approximately true, a fact which must not be forgotten, but they are sufficiently near the truth for many practical uses. Estimations of population may be made in various ways. The natural growth of population is like that of money at compound interest except that the interest is being added constantly instead of semi-annually or quarterly. J^IaUlS- TWjpiang pall tiji''" g eometrical progressi on. Wit h a give n pnnqfgn+. rqfp nf mt.prPjaf. nr ionev in the bank increases m ore and more each year. It is the same with population. In geometrical progression the basis of our population estimates is the annual rate of increase. When dealing with very large populations, and especially when dealing with popu- lations not influenced by emigration or immigration, this method is the most accurate one to use. It has several practical disadvantages, however, and in the present shift- ing condition of the world's population there are not many places where the natural growth of population is the only factor to be considered. A simpler method is that of arithmetical progression, which assumes a constant annual increment between two 129 130 POPULATION census years. The increase in ten years divided by ten gives the annual increase. This is practically the method by which money increases by simple interest. The arguments in favor of this method of estimating population are that it is simple and easily understood; that in view of the various disturbing factors due to migration and other caftses it gives results practically as near the truth as those obtained by geometrical progression; that the estimates for the whole area of a given district wiQ be equal to the simi of the estimates for all the parts of the district, which would not be the case with the geometrical method. The U. S. Bureau of the Census has adopted this method, and in the interest of uni- formity all cities and states should do the same. The method is one which should not be extended far into the future. In vital statistics it is not necessary to extend it beyond ten years from the last census, for ten years always brings another census. Another method is that of using local data as indices — such as the number of registered voters, the niunber of new building permits, the number of school children, the^number of names in the directory, the bank clearings, the number of passengers carried by the trolley cars, etc. These facts are often obtainable for each year and serve as valuable checks on the census method, but as a rule they should not be depended upon alone. Common sense must be used. WMt jg^gntpH qra iho fanis,^ fj, nd rip ;id adherence t o a rule when the result i s manifestly unfair is absur d. When deviations from accepted practice are made, however, a statement of the method of making the estimates of the population should always accompany the result. Even the U. S. Census utilizes local data to modify its estimates where plainly necessary.. Estimates of population might be made from records of births and deaths if these were accurately kept and if the ADJUSTMENT OF POPULATION TO MID-YEAR 131 migrations of the people were known. Practically this method is useless. One item in connection with the estimation of the popular tion of cities should not be lost sight of, namely, that of changing boundaries. Cities often grow by extending their area. Increases of population from this cause should not be mistaken for natural increase in population. Arithmetical increase. — Let us assume that the popu- lation of a place in 1900 was 70,000 and in 1910, 100,000. The increase was, by the arithmetical method, 30,000 in ten years, or 3000 in each year. For 1904, therefore, the esti- mated population would be 70,000 plus four times 3000 or 82,000; and for 1915 it would be 100,000 plus five times 3000 or 115,000. It is assiuned that within the ten years following the last census the annual increase will be the same as the average annual increase between the last two censuses. This is the simple and customary way of making the estimates. It must be remembered that between these particular censuses the interval was not exactly ten years. The census of 1900 was "as of Junalst," that of 1910 "as of April 15th." Consequently, the interval was ten years less a month and a haK or 9| years ( = 9.875 years) . The average increase was not, therefore, 3000 per year, but 30,000 -i- 9.875 or 3038. This would make the estimated population 82,152 for 1904 and 115,190 for 1915. It will be seen that this difference is, not great. Nevertheless, it is a correction which in some cases is of importance. Whether it will have to be made after the next census will depend upon the date decided upon. Strictly speaking, the populations of the census years should be adjusted to the middle of the year before the average annual increments are computed. Adjustment of population to mid-year. — The census of 1910 was "as of April 15th." What then was the population •on July 1st ? 132 POPULATION On June 1, 1900, the population was 70,000. The av- erage annual increase was 3038 per year, or 3038 4- 12 = 253 per month. On July 1, 1900, the population was, therefore, 70,000 + 253 = 70,253. On July 1, 1910, it was 100,000 + 253 X 2i months or 100,633. The increase in ten years was, therefore, 100,633 - 70,253 = 30,880, or 3038 per year, as before. This arithmetical method, therefore, is used in adjusting the population for the census years from the day on which the census was actually taken to the mid-year. For example, on Jxme 1, 1900, the population of the state of Indiana was 2,516,462; on Apr. 15, 1910, it was 2,700,876, an increase of 184,414 in 118.5 months. On July 1, 1910, i.e., 2.5 months later than the census date, the estimated 2 5 population would therefore be 2,700,876 + -rk-^ X 184,414 or 2,704,767. This is the figure used -by the U. S. Census in the Mortality Report of that year. Geometrical increase. — A simple rule for computing populations by the geometrical method is to use the loga- rithms of the populations concerned in the same way that the populations are used in computing by the arithmetical method. Let us assume, as before, that the population was 70,000 in 1900 and 100,000 in 1910. The logarithm of 100,000 is 5.0000, that of 70,000 is 4.8451. Instead of sub- tracting 70,000 from 100,000 we subtract 4.8451 from 5.0000 and get 0.1549. Instead of dividing 30,000 by 10 we divide 0.1549 by 10 and get 0.01549. Then we multiply this by 4 and get 0.0620. Finally, we add this to 4.8451, which is the log of 70,000, and get 4.9071. This is the log of the answer, which is 80,750. The following comparison ought to make this clear : Example. — The population of a city in 1900 was 70,000 and in 1910, 100,000. What was the population in 1904, in 1915 and in 1925? FORMULA FOR GEOMETRICAL INCREASE 133 TABLE 21 Arithmet- ical method. Geometrical method. (1) (2) (3) Population in 1910. . " 1900.. 100,000 70,000 log of 100,000 = 5.0000 " " 70,000 = 4.8451 Increase in 10 years- Increase in 1 year.- 30,000 3,000 0.1549 0.0155 Increase in 4 years . . 12,000 0620 Population in 1900. . " 1904.. 70,000 82,000 4.8451 log of 80,750 = 4 9071 Increase in 5 years. . Population in 1900. . " 1915.. 15,000 100,000 115,000 1 0.0775 '-,5.0000 log of 119,600 = 5.0775 Increase in 15 years. Population in 1900. . " ■ " 1925.. 45,000 100,000 145,000 0.2325 5.0000 log of 170,800 = 5.2325 It will be noticed that for intercensal years the arithmet- ical method gives higher estimates than the geometrical, but that for postcensal years the geometrical results are higher. This is illustrated graphically by Fig. 30. Fonnula for geometrical increase. — The mathematical formula for geometrical increase is P„ = Fc (1 + rY, in which Pc is the population at one census, P„ is the population n years after Pc, r is the annual rate of increase and n is the niunber of years. * Let us apply this to the case abeady considered. Here we know the two populations P. and P„, 70,000 and 100,000, 134 POPtTLA'tlON 170 160 150 140 |» •^120 i 100 90 BO i7o,8ocry ' / / J ;> f / 119,500^/ / //^v&fm ^ensus / 82,000 ^ //^80,7i50 ^ensua 60 _ 1900 1910 1920 1930 Fig. 30. — Example of Arithmetical and Geometrical Methods of Estimating Population. FORMULA FOR GEOMETRICAL INCREASE 135 and we know that n is 10 years; first we need to find r, the annual rate of increase. According to algebra we naay rewrite the above formula, thus: logP„ — logPc = nlog (1 + r). Substituting the values of the logarithms of 100,000 and 70,000 and the value of n we have 5.0000 - 4.8451 = 10 log (1 + r) 0.1549 = 101og(l+r) 0.01549 = log (1 + r) and from the tables of logarithms (1 + r) is found to be 1.036, hence r = 1.036 - 1 = 0.036, or 3.6 per cent. There- fore, the average annual rate of increase between 1900 and 1910 was 3.6 per cent. Knowing this rate and assuming it to be constant we can find the population in any other year. Suppose we try 1925, 15 years after 1910. Then we have: P„ = 100,000 (1 + 0.036)15, log P„ = log 100,000 +' 15 log 1.036 = 5.0000 + 15 X 0.01549, logPn = 5.23245, .". P„ = 17,079 (according to the log. tables.) By the use of this formula many interesting problems can be solved. Fot example, how many years would it take the population in our now familiar example to reach 200,000? We know that the average rate of increase between 1900 and 1910 was 3.6 per cent. Therefore, we have in the formula 200,000 = 100,000 (1 + 0.036)". We want to find the value of n. We have log 2000,00 = log 100,000 + n log 1.036, 5.30103 = 5.0000 + nX 0.01549, 0.30103 =nX 0.01549, 0.30103 ,„,. " = o:oi549 = ^^■^^y"^^• 136 POPULATION Strictly speaking, we have no reason to use a year or even a month as the basis of compounding, as the population is increasing from day to day and from hour to hour. A more accurate formula may be found in books on calculus. We do not need to use it in this work. Rate of increase. — The population of the United States on June 10, 1900, was 75,994,575; on Apr. 15, 1910, it was 91,972,266. The increase in 9| years was 15,977,691 or, 134,833 per month, assuming the increase to have been constant. We might divide this still further and say that the average increase was 4494 per day, or about 3.12 persons per minute. On this basis we might also by computation ascertain that the population of the United States passed the one hundred million mark at 4 o'clock on Apr. 3, 1915. Such statements as this have a fascination for certain people, but they are of idle moment. They merely serve to illustrate the method of computation by the arithmetical method. Had the geometrical method been used the result would have been different. As a matter of fact no one will ever know just when the population passed the hundred million mark. If we take the above figures for 1900 and 1910 and regard them as representing a ten year period (instead of 9.875 , ,, . , , 15,977,691 „, , years), the increase amounts to „. ,„ . -__ , or 21 per cent. ^ " 75,994,575' ^ We may divide this by 10 and say the annual increment was 2.1 per cent, or more accurately by 9.875 and say that it was 2.13. But we ought not to use the word rate in this connec- tion. As a matter of fact, if the rate of increase in 10 years was 21 per cent, the average annual rate would not be 2.1 per cent. If in the formula for geometrical increase we let Pc = 100 and P„ = 121, which would represent an increase of 21 per cent in 10 years, then log 121 - log 100 = 10 log (1 + r), 2.08278 - 2.00000 = 10 log (1 + r). DIFFERENCE BETWEEN ESTIMATE AND FACT 137 from which r = 1.92 per cent, not 2.1 per cent. This assumes that, as we might say, the interest is com- pounded annually. This error of dividing the percentage increase in 10 years by 10 to find the annual increase is sometimes made in using the geometrical method of estimating increase. Obviously with compound interest a lower rate sufiices to produce a given increase in 10 years than with simple interest. The proper way to find the annual rate is by the use of the formula. Decreasing rate of growth. — It seems to be generally true that as cities become larger their annual rate of growth decreases. A study of six American cities gave the following annual rates of increase when -the populations were as indicated. TABLE 22 DECREASING RATE OF GROWTH OF CITIES stage of Annual percent- Population age Increase. CD (2) 100,000 4.85 200,000 3.59 300,000 2.91 400,000 2.48 500,000 2.02 600,000 1.75 700,000 1.66 800,000 1.58 Difference between estimate and fact. — In estimating the population either by the arithmetical or geometrical method we are assuming something which is almost never true, i.e., that the population is increasing regularly. As a 138 POPULATION matter of fact the increase is not regular from year to year. Therefore, any estimate may be erroneous. In the absence of the facts, however, we are compelled to resort to the method of estimation. Also when we assume that the growth in the present decade is the same as in the last, decade we assume a uniformity of conditions which seldom obtains. Let us check a few of our estimates by actual census returns. In Cambridge, Mass., the census population was 70,028 in 1890 and 91,886 in 1900, a gain of 21,858 in the decade. If the same increase had continued during the next decade the population would have been 113,744. The census of 1910 was, however, only 104,839. In Detroit, Michigan, the population in 1890 was 205,876 in 1900 it was 287,704, the increase being 79,828. If this increment continued regularly the population in 1910 would have been 365,532; actually it was 465,766. This of course is an extreme case. In most cities the estimates agree fairly well with the facts. Let us take the case of a larger population, say that of the UniteH States. In 1890 the population was 62,947,714, in 1900, 75,994,575, the decadal increase, 1,304,861. The esti- mate for 1910 based on these figures would have been 89,041,436 by arithmetrical, or 91,723,000 by geometrical increase. Actually the population in 1910 was 91,972,266. For large populations like this the geometrical method gives closer results. Revised estimates. — Suppose, however, that as in Cambridge, Mass., the census of 1910 showed that the city had not grown as fast as in the decade from 1890 to 1900, what shall be done with the estimates already made for the years 1901 to 1909, inclusive? Obviously they were not correct even on the theory of steady increase. Yet they have been used as the basis of computing birth-rates and death-rates. The answer is that if the discrepancy is large POPULATION FROM ACCESSIONS AND LOSSES 139 the populations for those years should be reestimated and the birth-rates and death-rates recomputed. Let us see what differences would result. TABLE 23 REVISION OF POPULATION ESTIMATES Year. Census. Postcensal estimate based on 1890-1900. Intercensal estimate based on 1900-1910. (1) (2) (3) (4) 1890 1900 1 2 3 4 5 6 7 8 9 10 70,028 91,886 104,839 94,072 96,258 98,444 100,630 102,816 105,002 107,188 109,374 111,560 93,181 94,476 95,771 97,066 98,361 99,656 100,951 102,246 103,541 Ordinarily the errors are not as great as this and no correction need be made, but the chance of error is so great that old published figures for death-rates should not be accepted at their face value until the population estimates have .been carefully examined for errors of this sort. It would be sound practice to revise all rates based on postcensal population estimates every ten years, i.e., after each new census. ' Estimation of population from accessions and losses. — In a place where records of the births and deaths are accu- rately kept it would be possible to use them in estimating population, but emigration and immigration enter as dis- turbing factors. Two examples of this method wUl illustrate the way in which this method works out. 140 POPULATION In England and Wales the data were as follows: Population in 1891 29,000,000 Births, 1891 to 1901 9,160,000 38,160,000 Deaths, 1891 to 1901 5,560,000 Computed population in 1901 32,600,000 Census gave, for the year 1901 32,530,000 Difference representing excess of emigration over immigration 70,000 In Massachusetts the population for 1910 computed in this way was 3,092,349, but the census gave 3,366,416, an excess of 274,067, which represented in part the excess of inunigration over emigration and in part, no doubt, incom- plete registration of births. Estimation of future population. — For some purposes, as, for example, in planning for sewerage or water supply systems, it is necessary to estimate the population of a city for half a century or more in the future. This cannot be safely done by mathematical methods alone, for much depends upon other things not subject to definite analysis. Bound- aries may change, business and manufacturing may expand or contract in ways unforeseen, changes in transportation or in methods of housing may influence the problem. Mathe- matical analyses are helpful, but the conclusions miist be tempered with judgment based on a study of local conditions and on the history of other cities similar in size and conditions. A few examples of unfulfilled estimates may be mentioned. In 1865 Jas. P. Kirkwood, a well known civil engineer, estimated that the population of Cincinnati would be 431,644 in 1890; actually it proved to be 297,000. At Rochester an estimate made in 1889 claimed that the population in 1910 would be 283,459; actually this city grew to 218,149. At Winnipeg in 1897 a certain estimate of the GRAPHICAL METHOD OF ESTIMATING POPULATION 141 probable population in 1907 was made, but when 1907 arrived the population was double the estimated figure. For long-time estimates the methods already described may be used, but with this difference that the rate of past increase is best obtained, not by taking the results of the last two censuses only, but by considering a longer period. To look farther ahead than 10 years you must begin farther back. This is an important principle which appHes to many things in Ufe. It means the use of experience. The pubUc health student who desires to project himself forcefully into the coming era needs to study the past history of the health of the human race. It is equally true in the fields of science, philosophy and religion. As a rule in United States cities the arithmetical method gives results which are too low, and the geometrical method gives results which are too high. All things considered the graphical method is the most serviceable for long term esti- mates as it enables data for various cities to be brought together. Immigration. — The irregular effect of immigration in the United States may be inferred from Fig. 31, which shows the immigration by years from 1820 to 1909. Immi- gration has occurred in a series of waves, resulting from the relative economic conditions in this country and abroad. When this incoming population has been concentrated in manufacturing cities, as has periodically been the case, it has been followed by an increased prevalence of disease. The subject is, therefore, an important one for sanitarians to consider. The data for immigration are published in the annual reports of the U. S. Commissioner General of Immigration. Graphical method of estimating population. — The simp- lest method of estimating future populations graphically is to plot the populations on cross-section paper using all past 142 POPULATION records available, and then sweep the curve forward accord- ing to its general trend. It is easy to use poor judgment in doing this. Local conditions should be kept in mind and especially additions of area should be considered. 1,200,000 1,100,000 1,000,000 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 Fig. 31. — Immigration to the United States: 1820-1917. (Prom report of Commissioner of Immigration.) A safer way is to plot not only the populations for the city being considered, but for other cities where the conditions are near enough to warrant them being taken as guides. GRAPHICAL METHOD OF ESTIMATING POPULATION 143 These cities must be larger than the one for which the esti- mate is to be made. A good way is to plot them all on cross-section paper on the same scale and then trace the lines upon a single sheet, adjusting the time scale so that all of the curves meet and cross on some selected year, usually the last census year. In this way there will be a number of population lines extending ahead and these may be used as guides in sweeping in the curve of the city being considered. Judgment inevitably plays a large part in long-term esti- mates and statistics are used merely as an aid to that judgment. Example. — Estimate the future population of Springfield, Mass., using for comparison the cities of Worcester, Mass., Syracuse, N. Y., Rochester, N. Y., and Providence, R. I. From the census reports we have the following data: TABLE 24 POPULATION OF CITIES Year. Springfield. Worcester. Syracuse. Rochester. - Providence. CD (2) (3) (4) (5) t6) 1860 15,199 24,960 28,119 48,204 50,666 1870 26,703 41,105 43,051 62,386 68,904 1880 33,340 58,291 51,792 89,366 104,857 1890 44,179 84,655 88,143 133,896 132,146 • 1900 62,059 118,421 108,374 162,608 175,597 1910 88,926 145,986 137,249 218,149 224,326 These data are first plotted as in the upper part of Fig. 32. They are afterwards brought together as in the lower part of the figure, the lines being made to cross on the line of 1910. The estimate for Springfield is made by sweeping the ciu-ve forward as shown. 144 POPULATION ^ .-Vt o 150,000 1 §" 100,000 56,000 jr .;.-' ".^ ^, k [y] l^ ^ ^5**" 250,000 o 200,000 o 130,000 100.000 50,000 c r r9 GRAPHICAL METHOD OF ESTIMATING THE FUTURE POPULATION OF SPRINGFIELD, MASS. / ^»^^> M r /- -9 ^ <^ f^' ' Lines c of Spri xrasatPc ifffleld, 1 pnlatlon e. 88926 ^- ■"t^^^" jet 1 \ -1 I- a H r s c > c a H r C H r 3 ? n c 3 C 3 % -1 r 3 o 1 U3 H iH Fig. 32. — Example of Graphical Method of Estimating Future Population. ACCURACY OF STATE CENSUSES 145 Accuracy of state censuses. — The U. S. Bureau of the Census does not recognize as generally acceptable the results obtained by those states which enumerate their populations in the years which end in 5, on the ground that it does not control such intermediate censuses and has no way of assur- ing itself of their accuracy. On the whole this position is probably sound. In Massachusetts, the last federal census in 1910 was made by the same state authority, namely the Director of the Massachusetts Bureau of Statistics, which has made the state census, and one census is presumably as accurate as the other. In the past, however, the state censuses have evidently not been as accurate as the federal censuses. If the results of the federal censuses for Massachusetts are plotted the points fall on quite a smooth and regular curve froni 1820 to 1910, the only important departure being during the decade of the Civil War. The figures for the state censuses do not aU fall on this line, but rise and fall irregularly. This is presumptive, though not conclusive, proof of the inaccuracy of some of the figures (Fig. 33). The Massachusetts state census was taken on May 1 from 1855 to 1905, inclusive; in 1915 it was taken on April 1. The question often comes up for decision, shall the state censuses be used in estimating populations for the years in the ■ last half of each decade ? For the sake of uniformity it is best to use the federal figures only. But these figures should, of course, be modified if the state census reveals that there have been important changes in conditions. The state figures should be used, therefore, as a check on the estimates based on the federal results. Should glaring differences be noticed their cause should be investigated. If state figures are used this fact should be stated in connection with the estimate. 146 POPULATION Urban and rural population. — It is common to classify the population of a country into "urban" and "rural." This is done for purposes of discussion, the idea being to separate the people living in sparsely settled regions and small villages from those living in cities, on the theory that 4,000,000 3,000,000 1 2,000,000 a o P4 1,000,000 1830 1840 1850 1860 1870 1880 1890 1900 1910 Years Fig. 33. — Popiilation of Massachusetts according to Federal and State Censuses. (The effect of the Civil War should be noticed.) the former lead a more individualistic life, while the latter lead a more communal life. In cities for example, water supplies, sewerage systems, food supplies, methods of trans- portation and various public utilities are used in common by all, while in the country each household has its own well, its own garden, its own cesspool, its own means of transporta- tion. Thus urban and rural populations are supposed to hve and work under different conditions. URBAN AND RURAL POPULATION 147 Obviously the separation of the two classes must be an arbitrary one. In the United States prior to the Census of 1880 the limit of 8000 inhabitants was used. In 1880 it became ^recognized that many communities of less than 8000 inhabitants possessed "the distinctive features of urban life," and accordingly the hmit was dropped to 4000, although the old limit was used in many of the tabulations of the census of that year, and also of the years 1890 and 1900. In 1900 some comparisons of the two limits were made. It was found, for example, that 32.9 per cent of the population of the United States would be classed as urban on the basis of the 8000 limit, and 37.3 per cent, on the basis of the 4000 limit. In 1910 the limit was reduced by the Census Bureau to 2500. The reason for this probably lay in the extension of various public utilitieSj once existing only in the cities of larger size, to the smaller communities. In 1910, 46.3 per cent of the population were classed as urban on the basis of the 2500 limit, but only 38.8 were in cities larger than 8000. One must be careful in drawing conclusions from "urban and rural statistics." In the first place, of necessity they relate to civil divisions. "Outside of New England," says the Census Report for 1900, "there is not much difficulty in distinguishing between the urban and rural elements of the population, as only dense bodies of population are chartered. But in New England a town, which is the usual division of the county, is chartered bodily as a city when certain con- ditions of population are fulfilled, so that a city may contain a considerable proportion of rural population, and, conversely, a town may contain a compact body of population of magni- tude sufficient to be classed as urban." Evidently then, rural population does not necessarily mean people living in isolation, as on a farm. Almost every incorporated town or 148 POPULATION borough has some center, and here people may live under communal conditions which may be quite as insanitary as those found in cities, with houses close together, with board- ing houses, saloons, stables, numerous cesspools, and even sewers and public water supphes. Attempts have been made by various writers to make a triple separation of the population into "rural," "village," and "urban," using populations of 1000 and 4000 as de- markations. These add but little to the value of the statis- tics and usually it is best to follow the practice of the Bureau of the Census. Populations of 3000 and 5000 have also been used as hmits between rural and urban. Whatever limits are used the possible fallacies inherent in an arbitrary classi- fication should be kept in mind. In comparing conditions as shown by censuses ten years apart there is always likely to be some confusion caused by communities which have populations near the limit changing from one side to the other. The Bureau of the Census has followed this practice: "In order to contrast the proportion of the total population living in urban or rural territory the territory is classified according to the conditions as they existed at each census; but in order to contrast between the rate of growth of urban and rural communities it is necessary to consider the changes of population for the same territory, which have occurred between censuses, and the places in- cluded in the urban class are those which have populations above the limit at the last census, even though they were below the limit at the time of the previous census. Since about 1820 the urban population of the country has been rapidly increasing, the rural population becoming relatively less. This is well shown by the following figures : URBAN AND RURAL POPULATION 149 TABLE 25 TOTAL AND URBAN POPULATION AT EACH CENSUS: 1790-1910 (From U. S. Census, 1900, Vol. 1, Pt. 1, p. LXXXIII.) Per cent of Census year. Total population. Urban population.* Number of places. mban of total popu- lation. (1) (2) (3) w (5) 1790 3,929,214 131,472 6 3.3 1800 5,308,483 210,873 6 4.0 1810 7,239,881 356,920 11 4.9 1820 9,638,453 475,135 13 4.9 1830 12,866,020 864,509 26 6.7 1840 17,069,453 1,453,994 44 8.5 1850 23,191,876 2,897,586 85 12.6 1860 31,443,321 5,072,256 141 16.1 1870 38,558,371 8,071,875 226 20.9 1880 50,155,783 11,450,894 291 22.8 1890 62,947,714 18,327,987 449 29.1 1900 75,994,575 25,142,978 556 33.1 1910 91,972,266 35,726,720 778 38.8 * Population of places of 8000 or more at each census. This is also shown by the increase in the number of large cities since 1860. TABLE 26 TABLE SHOWING THE INCREASE IN NUMBER OF LARGE CITIES IN THE UNITED STATES BETWEEN i860 AND 1910 Number of cities with population above. 1360. 1870. 1880. 1890. 1900. 1910. (1) (2) (3) W) (5) (6) (71 25,000 50,000 100,000 500,000 1,000,000 32 15 8 2 50 24 13 2 77 35 20 4 1 125 58 28 4 3 161 79 38 6 3 229 109 50 8 3 150 POPULATION Density of population. — By the density of population we usually mean the niunber of persons dwelling upon a unit area of land, as a square mile or an acre. It is not to be supposed that the persons within this unit area are uniformly distributed over it. Usually they are not. The ratio is one of convenience, however, and variations of density within the area under consideration are tacitly assmned. On the catchment area of the Croton river (331 square miles) which supplied New York with unfiltered water the population in 1903 was on an average about 52 per square mile, while on the catchment areas of many German streams, where the water is filtered before being used the population per square mile is often 500 or 800. Thus the average density expressed in this way is a valuable means of comparing the relative liability of the water to be contaminated, even though both in Germany and on the Croton catchment area the popula- tion consists of villages and farms irregularly scattered. The average density of the population of the United States js steadily increasing. In 1790 it was only 4.5 persons per square mile; in 1860 it was 10.6; in 1910 it was 30.9. The density varies greatly in the different states. Rhode Island has the greatest density. In 1910 it was 508.5 per square mile, Massachusetts came next with 418.8, then New Jersey Aisjth 337.7, Connecticut, 231.3, New York, 191.2, Pennsylvania, 171, Maryland, 130.3, Ohio, 117,' Delaware, 103, and Illinois, 100.6. These were the only states above 100 per square mile. In Nevada the density was .only 0.7 per square mile. The density of population of the United States by counties is shown in Fig. 34. When we need to know the variations in density more accurately we take a smaller unit of area. For the purpose of calculating the size of sewers required in a district, or for studying the congestion of population in a city the density DENSITY OF POPULATION 151 152 POPULATION per acre . is computed. The population density in cities usually increases with their population. In the congested portions of cities the density may be several hundred per acre, sometimes over a thousand. Fig. 35 shows the den- sities of population in the different wards of Boston and Cambridge in the year 1910. There are two ways in which the density of population of a city may be computed. The first and most com- 100,000 200,000 300,000 400,000 500,000 600,000 Population Fig. 36. — Density of Population by Wards in Boston and Cam- bridge, Mass.: 1910. " mon way is to divide the population by the area in acres. This gives the actual density per acre. In Boston, for example, in 1910 the population was 686,092, the acreage 27,674, and the number of persons on the average acre -^as 24.8. But if we look at the density from the standpoint of the people we find that the median person fives where the density is about 50 per acre and that 10 per cent of the population live where the density is 125 per acre, 5 per cent where it is 150. In POPULATION OF UNITED STATES CITIES 153 Cambridge, Mass., the average density per acre is 25.1, or practically the same as in Boston. The density for the median person is also about the same, i.e., 50 per acre; but 10 per cent of the population live where it is less than 60 per acre, and 5 per cent where it is only 100. In no ward of Cambridge is the density as great as in five large pop- ulous wards of Boston. For some purposes, as when we are providing a sewerage system, the density per acre is what is wanted, but when we are considering the crowded condition of the people it is the median density based on population which is needed, and the proportion of people living under conditions of different congestion. We need also to consider areas as small as single blocks. Population of United States Cities. — The figures in Table 27 will be found useful in computing vital rates. They are based on published reports of the U. S. Bureau of the Census. 154 POPULATION TABLE 27 POPTTLATION OF UNITED STATES CITIES HAVING, IN 1910, 25,000 INHABITANTS OR MORE (1) Alabama Birmingham Mobile Montgomery Arkansas Little Rock.. . ., . California Berkeley Los Angeles Oakland Pasadena Sacramento San Diego San Francisco . . . San Jos6 Colorado Colorado Springs Denver Pueblo Connecticut Bridgeport Hartford Meriden (town) . . Meriden (city) . . . New Britain New Haven Norwich (town) . Stamford (town). Stamford (city) . . Waterbury Delaware Wilmington District of Columbia Washington Florida Jacksonville Tampa Georgia Atlanta Augusta 1900. 1910. 1916 (estimate). (2) (3) H) 38,415 132,685 181,762 38,469 51,521 58,221 30,346 38,136 43,285 38,307 45,941 57,343 13,214 40,434 57,653 102,479 319,198 603,812 66,960 150,174 198,604 .9,117 30,291 46,450 29,282 44,696 66,895 17,700 39,578 53,330 342,782 416,912 463,516 21,500 28,946 38,902 21,085 29,078 32,971 133,859 213,381 260,800 28,157 44,395 54,462 70,996 102,054 121,579 79,850 98,915 110,900 28,695 32,066 34,183 24,296 27,265 29,130 25,998 43,916 53,794 108,027 133,605 149,685 24,637 28,219 29,419 18,839 28,836 35,119 15,997 25,138 30,884 45,859 73,141 86,973. 76,508 87,411 94,265 278,718 331,069 363,980 28,429 57,699 76,101 15,839 37,782 53,886 89,872 154,839 190,558 39,441 41,040 50,245 POPULATION OF UNITED STATES CITIES 155 TABLE 27 POPULATION OF UNITED STATES CITIES HAVING, IN 1910, 25,000 INHABITANTS OR MOKE — (Continued) (1) Georgia — (Continued) Macon Savannah Illinois Aurora Bloomington Chicago Danville Decatur East St. Louis Elgin Joliet Peoria Quincy Rockf ord Springfield Ivdiana Evansville Fort Wayne Indianapolis South Bend Terre Haute Iowa Cedar Rapids Clinton Council Bluffs Davenport Des Moines Dubuque Sioux City Waterloo Kansas Kansas City Topeka Wichita Kentucky Covington Lexington Louisville Newport '. . . . 1900.- 1910. 1916 (estimate). (2) (3) (41 23,272 40,665 45,757 54,244 65,064 68,805 24,147 29,807 34,204 23,286 25,768 27 258 1,698,575 2,185,283 2,497,722 16,354 27,871 32,261 • 20,754 31,140 39,631 29,655 58,547 74,708 22,433 25,976 28,203 29,353 34,670 38,010 56,100 66,950 71,458 36,252 36,587 36,798 31,051 45,401 55,185 34,159 51,678 61,120 59,077 • 69,647 76,078 45,115 63,933 76,183 169,164 233,650 271,708 35,999 53,684 68,946 36,673 58,157 66,093 25,656 32,811 37,308 22,698 25,577 27,386 25,802 29,292 31,484 35,254 43,028 48,811 62,139 86,368 101,598 .36,297 38,494 39,873 33,111 47,828 57,078 12,580 26,693 35,559 51,418 82,331 99,437 33,6t)8 43,684 48,726 24,671 52,450 70,722 42,938 53,270 57,144 26,369 35,099 41,097 204,731 223,928 238,910 28,301 30,309 31,927 156 POPULATION TABLE 27 POPULATION OF UNITED STATES CITIES HAVING, IN 1910, 25,000 INHABITANTS OR MOKE — {Continued) (1) Louisiana New Orleans Shreveport Maine Lewiston Portland Maryland Baltimore Massachusetts Boston Brockton Brookline (town) Cambridge Chelsea Chicopee Everett Fall River Fitchburg Haverhill Holyoke Lawrence Lowell Lynn Maiden New Bedford . . . . Newton Pittsfield Quincy Salem Somerville Springfield Taunton Waltham Worcester Michigan Battle Creek Bay City Detroit Flint Grand Rapids • 1900. 287,104 16,013 23,761 50,145 508,957 560,892 40,063 19,935 91,886 34,072 19,167 24,336 104,863 31,531 37,175 45,712 62,559 94,969 68,513 33,664 62,442 33,587 2i,766 23,899 35,956 61,643 62,059 31,036 23,481- tl8,421 18,563 27,628 285,704 13,103 87,565 1910. (3) 339,075 28,015 26,247 58,571 558,485 670,585 56,878 27,792 104,839 32,452 25,401 33,484 119,295 37,826 44,115 57,730 85,892 106,294 89,336 44,404 96,652 39,806 32,121 32,642 43,697 77,236 88,926 34,259 27,834 145,986 25,267 45,166 465,766 38,550 112,571 1916 (estimate). (4) 371,747 35,230 27,809 63,867 589,621 756,476 67,449 32,730 112,981 46,192 29,319 39,233 128,366 41,781 48,477 65,286 100,560 113,245 102,425 51,155 118,158 43,715 38,629 38,136 48,562 87,039 105,942 36,283 30,570 163,314 29,480 47,942 571,784 54,772 128,291 POPULATION OF UNITED STATES CITIES 157 TABLE 27 POPULATION OF UNITED STATES CITIES HAVING, IN iQio, 25,000 INHABITANTS OR MORE ~ (Cmtimied) T (1) 1900. (2) 1010. (3) 1916 (estimate). W Michigan — (Continued) Jackson Kalamazoo Lansing Saginaw Minnesota Duluth Minneapolis St. Paul Missouri Joplin. . . .• .Kansas City St. Joseph St. Louis Springfield Montana Butte Nebraska Lincoln Omaha South Omaha New Hampshire Manchester Nashua New Jersey Atlantic City Bayonne Camden East Orange Elizabeth Hoboken Jersey City Newark Orange Passaic Paterson Perth Amboy Trenton West Hoboken (town) 25,180 24,404 16,485 42,345 52,969 202,718 163,065 26,023 163,752 102,979 575,238 23,267 "30,470 40,169 102,555 26,001 56,987 23,898 27,838 32,722 75,935 • 21,506 52,130 59,364 206,433 246,070 24,141 27,777 105,171 17,699 73,307 23,094 31,433 39,437 31,229 50,510 78,466 301,408 214,744 32,073 248,381 77,403 687,029 35,201 39,165 43,973 124,096 26,259 70,063 26,005 46,150 55,545 94,538 34,371 73,409 70,324 267,779 347,469 29,630 54,773 125,600 32,121 96,815 35,403 35,363 48,886 41,698 55,642 94,495 363,454 247,232 33,216 297,847 85,236 757,309 40,341 43,425 46,515 165,470 78,283 27,327 57,660 69,893 106,233 42,458 86,690 77,214 306,345 408,894 33,080 71,744 138,443 41,185 111,593 43,139 158 POPULATION TABLE 27 POPULATION OF UNITED STATES CITIES HAVING, IN igio, 25,000 INHABITANTS OR MORE— (Continued) New York Albany , Amsterdam Auburn Binghamton Buffalo Elmira Jamestown Kingston Mount Vernon: New Rochelle New York Manhattan Borough Bronx Borough Brooklyn Borough . . Queen's Borough Richmond Borough. Newburgh Niagara Falls Poughkeepsie Rochester Schenectady Syracuse Troy Utica Watertown Yonkers North Carolina Charlotte Wilmington Ohio Akron Canton Cincinnati... Cleveland Columbus Dayton Hamilton Lima Lorain 1900. (2) 94,151 20,929 30,345 39,647 352,387 35,672 22,892 24,535 21,288 14,720 3,437,202 1,850,093 200,507 1,166,582 152,999 67,021 24,943 19,457 24,029 162,608 31,682 108,374 60,651 66,383 21,696 47,931 18,091 20,976 42,728 30,667 381,768 381,768 125,560 85,333 23,914 21,723 16,028 1910. (3) 100,253 31,267 34,668 48,443 423,715 37,176 31,297 25,908 30,919 28,867 4,766,883 2,331,542 430,980 1,634,351 284,041 85,969 27,805 30,445 27,936 218,149 72,826 137,249 76,813 74,419 26,730 79,803 34,014 25,748 69,067 50,217 560,663 560,663 181,511 116,577 35,279 30,508 28,883 1916 (estimate). (4) 106,003 37,103 37,385 53,973 468,558 38,120 36,580 26,771 37,009 37,759 5,602,841 575,876 . 1,928,734 2,634,224 366,126 97,881 29,603 37,353 30,390 256,417 99,519 155,624 77,916 87,401 29,894 99,838 39,823 29,892 85,625 60,852 410,476 674,073 214,878 127,224 40,496 35,384 36,964 POPULATION OF UNITED -STATES CITIES 159 TABLE 27 POPULATION OF UNITED STATES CITIES HAVING, IN 1910, 25,000 INHABITANTS OR M.O'RE — (Continued) (1) Ohio — (Continued) , Newark Springfield Toledo Youngstown Zanesville Oklahoma Muskogee Oklahoma City Oregon Portland Pennsylvania Allentown Altoona Chester Easton Erie -. Harrisburg Hazleton Johnstown Lancaster McKeesport Newcastle Norristown (borough). Philadelphia Pittsburgh Reading Scranton Shenandoah (borough) Wilkes-Barre Williamsport York Rhode Island Newport Pawtucket Providence Warwick (town) Woonsocket South Carolina Charleston 1900. (2) 1910. (3) 1916 (estimate). (4) 18,157 38,253 131,822 44,885 23,538 4,254 10,037 90,426 35,416 38,973 33,988 25,238 52,733 50,167 . 14,230 35,936 41,459 34,227 28,339 22,265 ,293,697 451,512 78,961 102,026 20,321 51,721 28,757 33,708 22,441 39,231 175,597 21,316 28,204 55,807 25,404 46,921 1-68,497 79,066 28,026 25,278 64,205 207,214 51,913. 52,127 38,537 28,523 66,525 64,186 25,452 55,482 47,227 42,694 36,280 27,875 1,549,008 533,905 96,071 129,867 25,774 67,105 31,860 44,750 27,149 51,622 224,326 26,629 38,125 58,833 29,635 51,550 191,554 108,385- 30,863 44,218 92,943 295,463 63,505 58,659 41,396 30,530 75,195 72,015 28,491 68,529 50,853 47,521 41,133 31,401 1,709,518 579,090 109,381 146,811 29,201 76,776 33,809 51,656 30,108 59,411 254,960 29,969 44,360 60,734 160 POPULATION TABLE 27 POPULATION OF UNITED STATES CITIES HAVING, IN igio, 25,000 INHABITANTS OR MORE— (Concluded) (1) SouthCarolina — (Continued) Columbia 7'ennessee Chattanooga , Knoxville Memphis Nashville Texas Austin Dallas El Paso Fort Worth Galveston Houston San Antonio Waco Utah Ogden Salt Lake City Virginia Lynchburg Norfolk Portsmouth Richmond Roanoke Washington Seattle Spokane Tacoma West Virginia Huntington Wheeling Wisconsin Green Bay La Crosse Madison Milwaukee Oshkosh Racine Sheboygan Superior (2) (3) 1916 (estimate). (4) 21,108 30,154 32,637 102,320 80,865 22,258 42,638 15,906 . 26,688 37,789 44,633 53,321 20,686 1Q,313 53,531 18,891 46,624 17,427 85,050 21,495 80,671 36,848 37,714 11,923 38,878 18,684 28,895 19,164 285,315 28,284 29,102 22,962 31,091 26,319 44,604 36,346 131,105 110,364 29,860 92,104 39,279 73,312 36,981 78,800 96,614 26,425 25,580 92,777 29,494 67,452 33,190 127,628 34,874 237,194 104,402 83,743 31,161 41,641 25,236 30,417 25,531 373,857 33,062 38,002 26,398 40,384 34,611 60,075 38,676 148,995 117,057 34,814 124,527 63,705 104,562 41,863 112,307 123,831 33,385 31,404 117,399 32,940 89,612 39,651 156,687 43,284 348,639 150,323 112,770 45,629 43,377 29,353 31,677 30,699 436,535 36,065 46,486 28,559 46,266 COLOR OR RACE, NATIVITY AND PARENTAGE 161 » Metropolitan districts. — For some purposes the popula- tion of a city plus its adjacent suburbs is of more importance than that of the city itself. During recent years the growth of the suburbs has often been much greater than that of the city itself. This subject is discussed in U. S. Census, 1910, Population, Vol. I, p. 74. In 1910, New York City had a population of 4,766,883, the adjacent territory, 1,863,716; or 39 per cent of the city's population. During the last decade the city increased 38.7 per cent and the adjacent territory 45.5 per cent. In Boston the city's population was 560,892, that of the adjacent territory, 708,492, or 126 per cent of the city's population. Classification of population. — One of the greatest mis- takes which health officers make is failure, to take into account the make-up of the population. Two places cannot be fairly compared as to death-rate or birth-rate, unless the composition of the population in the places is substan- tially the same. This point will be emphasized again in Chapter VII: In many demographic studies it is necessary to take into account age, sex, and nationality as primary factors; and at times also such matters as marital condition, school attend- ance, ilHteracy, ownership of homes, occupation, and so on. It will not be possible in this volume to go into all of these classifications. They should be carefully studied, however, from the census reports themselves. Every health officer should know the composition of the people in the city or district under his jurisdiction. I Color or race, nativity and parentage. — The racial composition of the United States has changed materially in fifty years. This is well illustrated by Fig. 36. In 1850 about three-quarters of the people were native whites, now 162 POPULATION 1860 1870 Fig. 36. — Racial Composition of Population of the United States. SEX DISTRIBUTION 163 only about one-half. There are^reat differences in different cities and states. According to the U. S. Bureau of the Census the popula- tion is divided into six classes: (1) white, (2) negro, (3) Indian, (4) Chinese, (5) Japanese and (6) "all others." The white population is subdivided into : a. Native, native parentage, having both parents born in the United States. b. Native, foreign parentage, having both parents born in foreign countries. c. Native, mixed parentage, having one native parent and the other foreign born. d. Foreign born. It is often desirable to subdivide the foreign born accord- ing to the country from which they came. This is true also of the parents. Sex distribution. — There are two ways in which the sexes are compared, — one is to compute the percentage which the number of each sex is of the total population, the other is to compute the ratio of males to females. Thus, we have the following figures for 1910: TABLE 28 COMPARISON OF SEXES IN THE UNITED STATES Per cent. Males to Male. Female. 100 females. (!)• (2) (3) (4) Total population Native white, native parentage Native white, mixed parentage Native white, foreign parentage Foreign born white 51.5 51.0 49.6 50.0 56.4 48.5 49.0 50.4 50.0 43.6 106.2 104.1 98.4 100,0 129.3 164 POPULATION In most parts of the country males are in excess, and gen- erally speaking the ratio of males to females increases from east to west. In only a few states do we find females in excess. One of these is Massachusetts, where in 1910 the ratio was only 96.6. In Nevada, on the other hand, the ratio was- 181.5, not very far from two men to one woman. Sex distribution ought to be studied in connection with age distribution. Dwellings and families. — A knowledge of the number of persons in a dwelling or a family is of sociological interest, and it may be of practical use in estimating the population of an area the boundaries of which are not coincident with any civil division. Here we come again to the difficulty of definition. What is a dweUing? What is a family? A dwelling-house is considered to be "a place where one or more persons regularly sleep." A family is "a household or group of persons who live together, usually sharing the same table." This includes both private families, consisting of persons related by blood, and economic families. The ideal family has been said to consist of a father and mother and three children with an occasional grandfather or grandmother, aunt or uncle. In the United States in 1910 the average number of persons to a family was only 4.5, — ■ apparently much smaller than the ideal. The average number of persons to a dwelling was 5.2. Figures for differ- ent parts of the country are given in Table 29. For housing problems it is not enough to know that the average number of persons per dwelling is 5.2. This extra two-tenths of a person is difficult to place. We need to know how many dwellings contain one person, how many two persons, and how many three, four, five, six, and so on. It is difficult to secure these data. Age distribution 165 TABLE 29 SIZE OF FAMILIES AND HOUSEHOLDS Place. Persona per ' dwelling. Persons per family. Families per dwelling. (1) (2) C3) (4) United States. . . 5.2 5.9 4.7 6.0 6.5 4.2 15.6 30.9 9.1 7.2 4.6 5.1 4.5 4.5 4.6 4.5 4.6 4.0 4.7 4.7 4.8 4.6 4.1 4.6 1 15 Urban " 1.31 Rural 1.02 New England .... 1.33 Urban 1.41 Rural ... 1.05 New York City 3.32 Borough of Manhattan, . . . Boston . . 6.58 1.90 1.57 1.12 Spokane, Wash 1.11 Age distribution. — We now come to what is a most important division of the population, namely separation into age-groups. In connection with a study of death-rates and causes of death a knowledge of age distribution is funda- mental. As a factor in vital statistics it is more important than sex or nationality or parentage or occupation or any other particular characteristic. In taking a census it is impossible to find the exact age of every person in a community, and even if this could be done it would be impracticable to arrange the people in groups, varying by short intervals of time. Infants and young children may be grouped by their age in weeks or months, but'older persons are seldom divided into groups for which the time interval is less than one year. Five-year and ten- year groups are even more commonly used. In this chapter we shall not consider smaller subdivisions than one year. The ages of infants will be taken up in the chapter which treats of infant mortality. 166 POPULATION Census meaning of age. — If we wish to state a person's age in years, using a whole number, we may do so in one of two ways; we may give the age as that of the last birthday or as that of the nearest birthday. The difference is by no means insignificant in the case of children, for the difference of half a year would represent a large percentage of the age. In some parts of the world the next birthday is often stated as the age, an infant being regarded as one year of age even though he had been bom only an hour. In the Orient age has to do also with the calendar year in which the child was born. A child born in November might in December be called a year old, but after January first might be called two years. These curious customs ought to be known by Grouping by last Birthdays 0+ 1+ 2+ 3+ 4 + —A ^- is „ A A ^^ ^f^ 2 3 4 6 Grouping by nearest Birthdays Fig. 37. — Age-Grouping by Years. those enumerating the ages of persons in the foreign quarters of our cities and justify the check question asked by census enumerators, namely, the date of birth. The last birthday method was used in the United States census of 1910, 1900 and 1880; it is the method used in Eng- land. In 1890, however, the nearest birthday was used. The effect of the definition of age on the age-grouping will be ap- parent from the following diagram: The nearest birthday method creates confusion in the ages of infants and children one year old. If infants include children up to the age of one year, then the "one-year" group must be limited to half a year or else there is duplication of those between six months ERRORS IN AGES OF CHILDREN 167 and one year. The discrepancies in the 1890 figures are plainly shown by the following table which gives the per- centage distribution of the population under five years of age. TABLE 30 PER CENT DISTRIBUTION OF POPULATION UNDER 5 YEARS OF AGE Age in years. " Nearest birthday." "Last birthday.'' 1S90. 1880. 1900. 1910. (1) (2) (3) (4) C5) Under 1 year 1 + 2+ 3+ 4+ Per cent. 20.5 14.1 22.7 21.4 21.3 Per cent. 20.9 18 2 20 6 20.0 20.3 Per cent. 20.9 19.3 20.0 19.9 20.0 Per cent. 20.9 18 6 20.4 20.3 19.9 Total under 5 years 100.0 100.0 100.0 100.0 The small nvunber in the one-year group and the large number in the two-year group in 1890 should be noticed. Errors in ages of children. — The above table shows that even by the last-birthday method the age distribution of children in one-year groups was unsatisfactory. Normally there are more children under one year of age than between one and two years, more between one and two than between two and three and more between three and four than between four and five. Yet in 1910 the one-year group contained fewer than the two-year group, and in 1900 the 3+ year group contained fewer than the 4-|- year group. These discrepancies are due to errors. They are greatest in populations where there is much illiteracy , and where no attempt is made to check the age returns by asking the date of birth. Thus we may compare the data for Germany (1900) and the negro population of the United States (1910). 168 POPULATION TABLE 31 PERCENTAGE DISTRIBUTION OF POPULATION UNDER 5 YEARS Age. Germany. United States (Negro population.) (1) (2) (3) 0+ 1+ 2+ 3+ 4+ Under 5 20.6 20.3 20.2 19.5 19.3 100.0 20.0 17.4 20.6 20.9 21.1 100.0 Errors due to use of round numbers. — An important source of error in age statistics is that of mixing round numbers with more accurate figures. In replying to the enumerator's questions concerning age most persons will state their age accurately, but some will give the nearest round number. An ignorant or careless person who may be 39 or 41 years old may give his age as 40, a figure which in his mind is near enough. This habit is encouraged by ask- ing for the "nearest birthday" as was done in 1890. In most censuses there are enough instances of this sort to produce noticeable concentrations around the ages ending in or 5. This is well illustrated by Fig. 38, which shows the popula- tion of Massachusetts males in 1905 distributed by groups. This error of round numbers is by no means confined to the subject of age. It is met with in all sorts of statistical work. Dates are often stated as "the first of the month," or the tenth or the fifteenth. These, mixed with more accurate statements, may produce abnormal concentrations. Methods of adjusting data troubled with these concentrations on the round numbers are used by statisticians and are referred to in Chapter XIV. ERRORS DUE TO USE OF ROUND NUMBERS 169 The U. S. Census Bureau in studying the error due to the abnormal use of round numbers has made use of a measure termed the "Index of Concentration." This was taken to be the "per cent which the number reported as multiples of 50 40 30 20 ll HH LD AGE DISTRIBUTION IN MASSACHUSETTS FROM 1905 STATE CENSUS VOLUME 1, POPULATION AND SOCIAL STATISTICS, P. 555 u \ IN ta X 10 20 30 «) 50 60 Age in Years Fig. 38. — Age Distribution in Massachusetts. 70 5 forms of one-fifth of the total number between ages 23 to 62 years, inclusive." Thus in the U. S. there were 43 million persons aged 23 to 62 years. One-fifth of these would be 8.6 million. The total number of persons aged 23 to 62 whose age was reported as a multiple of 5 was 10.3 million. Hence the index of concentration was 10.3 -f- 8.6, or 120. 170 POPULATION It was found that the mdex' of concentration increased directly with the ignorance and illiteracy. For the native white persons it was 112; for foreign born, whites, 129; for colored persons, 153. It is interesting to compare these figures for those of certain other countries. TABLE 32 ERRORS OF REPORTING AGE Country. Date. Index of concen- tration. (1) (2) (3) Belgium England and Wales Sweden German Empire France Canada Hungary Russian Empire Bulgaria 1900 1901 1900 1900 1901 1881 1900 1897 1905 100 100 101 102 106 110 133 182 245 Other sources of error. ' — Besides ignorance as to age there are other sources of error. One of these is deUberate under-estimate of age, most conspicuous among middle-aged women. Another is over-estimate, most conspicuous among the aged. The latter is of relatively Uttle weight, but the former tends to overload the early ages of adult life. Age groups. — The primary tabulations of the census give the ages of the people by single years. For practical use and for application to particular localities it is necessary to combine them into groups of five, ten, or twenty years, or other groups suitable to particular needs. There appears to be no recognized standard of age grouping, and perhaps this is not desirable as there are many different uses to which the figures are put. PERSONS OF UNKNOWN AGE 171 The U. S. Census states the boundaries of the groups in inclusive numbers, such as 0-4; 5-9; 10-14; etc., and not in round numbers, as 0-5; 5-10; 10-15. With the original age records given in years it is undoubtedly the most exact method. A grouping largely used in the 1910 census was the fol- lowing: Under 5 Years (Under 1 Year) 5-9 10-14 15-19 20-24 25-34 35-44 45-64 65 and over Age unknown In this arrangement -we have one-year groups from ages one to five, 5-year groups from ages five to twenty-five, 10-year groups from twenty-five to forty-five, and above that twenty-year groups. Persons of unknown age. — One of the puzzling things about age distribution is to know how to treat the "age unknown." Usually this number is not large, but in par- ticular cases it may be. In 1910 only 0.18 per cent of the people of the United States were included in this group, and m 1900 only 0.26 per cent. One-way is to place them in a group by themselves, letting the size of the group stand as a sort of test of the accuracy of the investigation. On the whole this is probably the best thing to do. Another way would be to distribute the unknowns pro rata through the other groups. But there is really no justi- 172 POPULATION fication for doing so, because the persons of unknown age may be confined to certain selected ages, as the very old. Redistribution of population. — If the ages of the people are tabulated by years it is of course easy to combine them into any desired age groups- but if the data are tabulated according to one age-grouping and it is desired to ascertain the numbers in other age-groups the problem is more difficult. Approximate results only c'an be expected and these can be obtained by graphical methods or by computation. For this purpose the summation diagram is most convenient. In 1910 the population of Cambridge was as follows: TABLE 33 POPULATION OF CAMBRIDGE, MASS., BY AGE-GROUPS Persona leas than stated age. Age-group. Affe Number. Per cent. (1) (2) (3) (4) (5) 0-1 2,323 1 2,323 2.3 1-A 8,479 5 10,802 10.4 5-9 9,471 10 20,273 19.4 10-14 8,892 15 29,165 27.9 15-19 8,930 20 37,095 36.4 20-24 10,408 25 47,503 46.4 25-34 19,175 35 66,678 64.6 35-44 15,726 45 82,404 79.6 45-64 16,732 65 99,136 95.6 65-99 4,642 100 104,778 99.4 Unknown 61 61 0.6 ToUl 104,839 104,839 iqp.o The figures in' column (4) are plotted in Fig. 39. Let i^s suppose that we desire to obtain the number of persons in age-group 23-27 inclusive. The diagram shows that about 43,500 were less than 23 years old and about ,53, .500 less than REDISTRIBUTION OF POPULATION 173 100 — - -^ — / 90 / / 80 > / / |:o / 1 [/ 60 / f / / ;5o / ;ii] h f (1- !; ■ 'i I. / ij'1 j ( 1 30 / / 20 / / \ I 10 / / a / 10 20 40 50 6C Age in. Years 70 90 100 Fig. 39. •Age Distribution of Population shown by Summation Curve, Cambridge, Mass. : 1910. 28 years old. The group, therefore, contains 53,500 — 43,500, or 10,000. In making a complete redistribution of the population in new age-groups it is well to check the results by adding them together to see that they equal the total. The accuracy of the result will depend upon the scale used for plotting and the smoothness of the curve. 174 POPULATION We might compute the number of persons in age-group 23-27 as follows: 10,408 X f = 4163 19,175 X tV = 5753 9916 This assumes a uniform age distribution within each age- group, which is not strictly correct. Redistribution of population for non-censal years. — In the case of non-censal years the method of redistribution of population is essentially the same as that just described but there are three steps to the process. The first step is to estimate the total population for the year in question by methods already described. The second step is to find the percentage distribution of the population as it was at the time of the nearest census. As a rule the percentage composition of a population by age- groups does not change rapidly from year to year. For an intercensal year it would be possible to find the percentage distribution for both the preceding and following census and by interpolation obtain more accurate percentages for the intercensal years. The use of the summation curve is the most convenient method however. The third step is to multiply the estimated total popu- lation by the percentage obtained in the second step. The feature of this problem obviously lies in the second step. Let us try to find the age distribution of the population of Cambridge in the year 1906. In addition to the above figures for 1910 we have also from the census records the following figures for 1900: PROGRESSIVE CHARACTER OP AGE DISTRIBUTION 175 TABLE 34 ESTIMATES OF POPULATION BY AGE-GROUPS FOR A NON-CENSAL YEAR: CAMBRIDGE, MASS. Persona less than stated age. Age. Number. Per cent. (1) (2) (3) (4) (6) 0-1 2,123 1 2,123 2.3 1-i 7,519 5 9,642 10.5 5-9 8,343 10 17,985 19.6 10-14 7,331 15 25,316 27.5 15-19 7,781 20 33,097 36.0 20-24 10,588 25 43,685 47.5 25-29 9,973 30 53,658 58.4 30-34 8,157 35 61,815 67.3 35-^ 12,377 45 74,192 78.5 45-54 8,561 56 82,753 90.0 55-64 5,028 65 87,781 95.5 65-99 3,652 100 91,433 99.4 Unknown 453 453 Total 91,886 91,886 The percentage distribution for 1900 and 1910 are both shown on Fig. 40. It will be noticed that the two curves coincide for the upper and lower ages, but not for the middle ages. For the year 1906 the percentages to be used would naturally lie somewhere between the two. Progressive character of age distribution. — Among the causes of the variation of death-rates from year to year is the progressive change in age distribution. We often overlook this. We know that individuals grow old, but we forget that the 10 year old children of today wUl be 20 years old ten years hence, and 30 years old ten years later and so on. We are less wise than the motley fool who said: "It is ten o'clock: 'Tis but an hour ago since it was nine. And after one hour more 'twill be eleven; And so from hour to hour, we ripe and ripe, And then, from hour to hour, we rot and rot; And thereby hangs a tale." 176 POPULATION While the age distribution of a population does not change rapidly from year to year yet it does change. This is strik- ingly shown by the statistics of Sweden from 1750 to 1900. 100 90 80 70 iso 40 30 20 10 r — ^ / ^ / / / r /? / r-^ ^/ f'/ I /# / 7 1 1 ,! I / N ; ( / • / / / • / 10 20 30 90 JO 50 60 70 8 Age in Years Fig. 40. — Percentage Age Distribution of Population, Cambridge, Mass., showing slight differences in ten years. 100 During this interval there was but little emigration or immi- gration, but the birth-rate varied considerably. In Fig. 41, the population data are plotted for five-year groups and for five-year intervals of time; consequently the persons who PROGRESSIVE CHARACTER OF AGE DISTRIBUTION 177 appeared in the 0-4-group at one date would appear in the 5-9-group five years later, except as losses by death occurred. It is interesting to see how the influences which increase or decrease the numbers of children produce results which flow u.o Fig. 41. — Age Distribution of the People of Sweden by Five- Year Groups: 1750-1900. as waves throughout a long life-term. For example, the high birthTrate between 1820 and 1825, which caused a peak in the (>-4-group in 1825, caused a peak in the 5-9-group in 1830 and this could be traced for three-score years and ten. In the same way the trough in the 0-4 curve in 1810 can be followed for sixty years. 178 POPULATION This same progressive change in age distribution can be observed in Massachusetts inx spite of the fact that the curves are confused by accessions due to immigration. The peak in the 0^-group in 1860 can be followed for fifteen years, but after that immigration appears to control. The immigration peak seen in the 20-24-group in 1880 can hke-. wise be traced almost to 1910. This progressive change of age is very important, for with constant specific death-rates for each age it would auto- matically control the general death-rate. It shows too that a loss of milHons of young men in the present Great War will profoundly affect the age distribution of the nations of Europe for half a century to come. There is much food for reflection in this study. Types of age distxibution. — According to Sundbarg one of the striking features of normal age distribution is the fact that about one-half of the population are between 15 and 50 years of age. He distinguishes three types of age distribu- tion. The first is the Progressive Type, the second the Stationary Type, and the third, the Regressive Type. These are illustrated by the following-typical groupings: TABLE 35 TYPES OF POPULATION Age-group, years. Per cent of population. Progressive type. Stationary type. Regressive type. (1) (2) (3) (4) 0-14 15-49 50- 40 50 10 33 50 17 • 20 50 30 TYPES OF AGE DISTRIBUTION 179 It will be noticed that in all cases, the proportion of middle- aged persons is the same, and that the classification depends upon the proportion of persons under 15 years of age to those more than 50 years of age. To these classes might be added two more, one in which a population has lost many of its middle-aged persons by emigration and one in which a population has gained by accessions of middle-aged persons. If the percentage of persons between 15 and 50 years of age is much less than 50 it indicates that the place has lost by emigration and this may be termed the secessive type; while if the percentage of per- sons between 15 and 50 years of age is greater than 50 it may be termed the accessive type. The following are examples of age distribution on the basis of this classification: TABLE 36 TYPES OF POPULATION BASED ON AGE-GROUPING Per cent of population. 0-U years. 15-49 years. 50 years and over. (1) (2) (3) (4) Sweden (1751-1900) United States (1910) Massachusetts Minnesota New York State ., Washington State Maine Mass., native white of native parentage ■ Mass., native white of foreign or mixed par- entage Mass., foreign-born white 33 32 27 32 27 26 27 28 46 6 50 54 57 54 58 61 51 50 48 74 17 15" 16 14 15 13 22 22 6 20 180 POPULATION It will be seen that Sweden has a normal stationary popu- lation, Massachusetts has an accessive population with 57 per cent between 15 and 50 years. Washington is even more accessive. Maine tends to be regressive, as it has an abnor- mally large number of persons over 50 years of age. This is also the case with the population of native-white parentage of Massachusetts. The native-white population of foreign or mixed parentage, however, is decidedly progressive. Standards of age distribution. — For purposes of com- putation and comparison it is often convenient to have some standard of age distribution which can be used as a basis of reference. Several have been suggested. A simple one was the actual population of Sweden in 1890. This was suggested because the country was not much in- fluenced by emigration or immigration. This standard had only five groups. It was this: TABLE 37 AGE DISTRIBUTION OF SWEDEN, 1890 Age-group. Per cent. (1) (2) 0-1 1-19 20-39 40-59 60- 2.55 39.80 26.96 19.23 11.46 100.00 STANDARD MILLION 181 The "Standard Million," iiamely the population of Eng- land and Wales in 1901, has been much used in adjusting birth-rates and death-rates. It is as follows: TABLE 38 ENGLAND AND WALES STANDARD MILLION OF 1901 Age-group. Males. Females. Persons. (1) (2) (3) (4) 0-5 57,039 57,223 114,262 5-9 53,462 53,747 107,209 10-14 61,370 51,365 102,735 15-19 49.420 50,376 99,796 20-24 45,273 50,673 95,946 25-34 76,425 85,154 161,579 35^4 59,394 63,455 122,849 4^-54 42,924 46,298 89,222 55-64 27,913 31,828 59,741 65-74 14,691 18,389 33,080 75- 5,632 7,949 13,581 G. H. Knibbs and C. H. Wickens,' statisticians of the Commonwealth of Australia have worked out in a very- elaborate way the probable normal age distribution of the people of Europe for the year 1900 or thereabouts. Eleven countries are considered- The results were as follows: 1 The Determination and Uses of Population Norms representing the Constitution of Populations according to Age and Sex, and accord- ing to Age only. Transactions, 15th International Congress on Hygiene and Demography, Vol. VI, p. 352. 182 POPULATION TABLE 39 PER CENT OF POPULATION AT EACH AGE (Eleven Countries of Europe) Age. Per cent. Age. Per cent. Age. Per cent. Age. Per cent. Age. Per cent. (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) 2.46 19 1.90 38 1.25 57 0.67 76 0.20 1 2.43 20 1.86 39 1.21 58 0.64 77 0.18 2 2.41 21 1.83 40 1.18 59 0.62 78 0.16 3 2.38 22 1.80 41 1.15 60 0.59 79 0.13 4 2.35 23 1.76 42 1.11 61 0.57 80 0.11 5 2.33 24 1.73 43 1.08 62 0.54 81 0.10 6 2.30 25 1.69 44 1.05 63 0.51 82 0.08 7 2.27 26 1.66 45 1.02 64 0.49 83 0.07 8 2.24 27 1.62 46 0.99 65 0.46 84 0.05 9 2.21 28 1.59 47' 0.96 66 0.44 85 0.04 10 2.19 29 1.56 48 0.93 67 0.42 86 0.03 11 2.15 30 1.52 49 0.89 68 0.39 87 0.02 12 2.12 31 1.49 50 0.86 69 0.37 88 0.02 13 2.09 32 1.45 51 0.84 70 0.34 89 0.01 14 2.06 33 1.41 52 0.81 71 0.32 90 15 2.03 34 1.38 53 0.78 72 0.29 91 16 2.00 35 1.35 54 0.75 73 0.27 92 0.02 17 1.96 36 1.31 55 0.73 74 0.24 93 18 1.93 37 1.28 56 0.70 75 0.22 94 All ages 100.0 Age distribution of the population of the United States. — On account of the heterogeneous character of the people of the United States, due to immigration and to internal migrations, we find that states and cities vary widely in the age composition of their inhabitants. In the older parts of the coimtry we find a more normal age distribution of the people, one that approaches that of Sweden and Switzerland, but in the newer sections, especially in the west, we find an abnormally large number of persons of middle-age. This is also true of cities to which persons of middle-age are drawn. On the other hand the rural districts are relatively low in the middle-age groups. There are also important differences AGE DISTRIBUTION MALES FEMALES 1 JlZ ^ ^ F - — \ 1 ^ ^ pl^ ^ ^ ^ n. -" — 1 ^ ^ 1 1 — ii 3 ^ < 1 — 1 — n 3 r [=3 r^ r=i l: — _i 1=; 3 r^ L t= 3 ^ ^^ -H= =i=H *■ ^ dp ^ =^ r^ =^ nFH =^ ] r^ =^ 1 ::r-r b 13 10 Fig. 42. 6 18 2 4 Hundreds of Thousands 8 10 18 ■Distribution of Population by Age and Sex, United States, 1910. 184 POPULATION between native whites, foreign bom whites and negroes; and between males and females. The student is urged to study in the census reports these differences among differ- ent classes of populations and in different sections of the country. The following table shows the percentages of total popula- tion in 1910 arranged by years: TABLE 40 PER CENT OF TOTAL POPULATION, BY SINGLE YEARS, 1910 (United States) Age 10 20 30 40 50 60 70 so 90 2.4 2.0 2.0 2.0 1.7 1.2 0.7 0.4 1 2.1 1.9 1.9 1.2 0.9 0.7 0.4 0.2 2 2.4 2.1 2.0 1.6 1.2 0.9 0.5 0.2 0.3 4: 3 2.3 1.9 1.9 1.4 1.0 0.7 0.4 0.2 4 2.3 2.0 1.9 1.4 0.9 0.7 0.4 0.2 5 2.2 1.9 2,0 1.7 1.2 0.7 0.5 0.21 6 2.2 2.0 1.8 1.4 0.9 0.7 0.3 0.2 7 2.1 1.9 1.7 1.2 0.9 0.5 0.3 0.1 0.1 t 8 2.1 2.1 1.9 1.5 1.0 0.6 0.3 0.1 9 2.0 1.9 . 1.5 1.2 0.9 0.5 0.3 0.1 * Less than 0.1%. t Age unknown = 0.2% The concentrations around the years ending in and 5 should be noticed. The differences between the percentages for males and females in the whole population are relatively slight. EXERCISES AND QUESTIONS 1. What were the points in the Washington' controversy in regard to death-rates and population? [See Am. J. P. H., Apr., 1917, June, 1917, Feb., 1918.] 2. From the data given in Table 3, 13th Census, Population, Vol. I., p. 24, estimate by three methods the probable population of the United States in 1950. EXERCISES AND QUESTIONS 185 3. What was the average annual percentage rate of increase of the population of the United States between 1790 and 1800, assuming a geometrical rate of increase? Between 1900 and 1910? 4. Under what temperature conditions do the people of the United States live? (See 11th Census, page ix.) 6. Under what rainfall conditions do the people of the United States live? (See 11th Census, page ix.) 6. From data given on page 314 of the 13th Census, Population, Vol. I, make a table giving the age distribution by single years of the entire population of the United States, the native white of native parentage and the foreign born white. 7. Make a plot of the last two. 8. Assuming the age distribution of the United States native white population of native parentage (both sexes) as given below, find by graphical methods the age distribution as indicated. Given Wanted Age Per cent Age Per cent 6-4 13.2 0-4 ? &-9 11.8 5-14 7 10-29 21.1 15-24 ? 20-29 17.7 25-34 ? 30-39 13.1 35-44 ? 40-49 9.2 45-64 ? 50-59 6.9 65-84 ? 60-69 4.4 70-79 2.1 ■ 80-89 0.5 Check the result by computation from figures given in previous problems. 9. Look up the "Incremental Increase Method" of estimating future populations. (Jour. Am. Water Works A-sso., March, 1915,) 10. What is meant by the "Center of Population?" Where was the centre of population in the United States in 1790? In 1910? [U.S. Census, 1910, Population, Vol. I, p. 45.] 11. What is the "median point " ? 12. Which states have the largest per cents of urban population? 13. Describe Moore's " Expectancy Curve," for estimating future populations. (Engineering News, Nov. 2, 1916, p. 844.) CHAPTER VI GENERAL DEATH-RATES, BIRTH-RATES AND MAR- RIAGE-RATES Gross death-rates (general death-rates.) — Stated sim- ply, the death-rate is the rate at which a population dies. It is the ratio between the number of persons who die in a given interval of time and the median number of persons alive during the interyal. Unless otherwise specified the interval -of time is considered to be one year. For the sake of comparison the ratio mentioned is reduced to the basis of some round number of population, generally 1000. Not until such reduction is made may we consider this ratio as a " rate." The computation is, of course, very simple. If in the year 1917 the number of deaths in a given city was 5710 and the population on July 1 of that year was 390,000, then the death-rate was: 5710 H- 390,000, or 14.6 for each thousand. The death-rate for 1917 was therefore 14.6. We sometimes call this the " general " death-rate because it refers to the general population. Sometimes it is called th e " crude " death-rate to distinguish it from rates corrected and ad- justed in various ways. Or it may be called the " annual " death-rate. This is unnecessary, however, as death-rates are always assumed to refer to a year as the basis unless stated to the contrary. Perhaps the best term of all would be the " Gross death-rate," but this term is not as common. 186 PRECISION OF DEATH-RATES 187 Death-rates may be based on 10,000 or 100,000 or 1,000,000 of population, but 1000 is the common base for all general rates. The higher numbers, however, are often used for special rates, as described in the next chapter. The method of estimating mid-year population was fully described, in the-preceding chapter. Precision of death-rates. — The accuracy of a death- rate depends upon the accuracy of the number of deaths and the correctness of the estimated population. One or both of these may be in error. Only in a census year can the death-rate be computed from actual facts, because only in a census year is the population known by actual count. In other years, the population is estimated, and hence the death-rate based upon it must also be regarded as an estimate. Incorrect estimates of population obviously must produce incorrect death-rates. If this fact be kept in mind it will prevent one from drawing unwarranted conclusions in comparing rates which differ from each other by small amounts. It is quite common to see the gross death-rate, referred to 1000 persons as a basis, expressed to the second place of decimals. This is warranted in the case of large popula- tions for then the figures in the second decimal place have a significant value. It is hot warranted for small popu- lations. This, it wUl be remembered, was discussed in Chapter II, but the following figures will further illustrate the point. In A) with a population of 1000, the number of deaths was 16 and, of course, the death-rate was 16. An error of one death, the smallest possible error, would have made the deaths 17 (or 15). In B, with a population of 10,000, an error of one death would have- changed the rate from 16.0 to 16.1; in C, population 100,000, from 16.00 to 16.01, and in D, population 1,000,000, from 16.000 to 16.001. In a 188 DEATH-, BIRTH- AND MAHRIAGE-RATES TABLE 41 PRECISION OF DEATH-RATES City. Population. Number of deaths. Death-rate. (1) (2) (3) (4) A 1 1,000 1,000 16 17 16.00 17,00 B 10,000 10,000 160 161 16.00 16.10 C ! 100,000 100,000 1,600 1,601 16.00 16.01 D 1 1,000,000 1,000,000 16,000 16,001 16.00 16.001 city of less than 10,000 population it would obviously be unreasonable to use two decimal places. Similarly the following figures show the differences in population required to change the death-rate from 16.00 to 16.10 in cities of different size, the actual numbers of deaths remaining the same. TABLE 42 PRECISION OF DEATH-RATES City. Death-rate. Number of deaths. Population. Difference in population. (1) (2) (3) (4) (5) A 1 16.00 16.10 16 16 1,000 ) 994 i 6 B ! 16.00 16.10 160 160 10,000 ) 9,938 1 62 C .: 16.00 16.10 1,600 1,600 100,000 1 99,378 ) 621 D 16.00 16.10 16,000 16,000 1,000,000 f 993,789 ) 6211 CORRECTED DEATH-RATES 189 It will be noticed that in all cases the percentage differ- ence in population is the same, i.e., 0.62 per cent. This percentage varies] according to the death-rate. To alter the death-rate from 12.00 to 12.10, for example, if the num- ber of deaths remained the same, would require a change of population of 0.83 per cent. The following figures show the percentage change in population required to alter the death-rate by 0.10 per 1000 from certain given death- rates. TABLE 43 Percentage Change of rate from change of population. (1) C2) 20.00 to 20.10 0.50 19.00 to 19.10 0.62 18.00 to 18.10 0.55 17.00 to 17.10 0.58 16.00 to .16. 10 0.62 15.00 to 15. 10 0.66 14.00 to 14. 10 0.71 13.00 to 13.10 0.76 12.00 to 12. 10 0.83 11. 00 to 11.10 0.90 10.00 to 10.10 0.99 As a rough and ready rule we may therefore decide that for places smaller than 1000 the death-rate shall be stated in whole numbers; for places between 1000 and 100,000 one decimal shall be used; for places above 100,000 two decimal places shall be used. Corrected death-rates. — What shall be taken as the number of deaths in a community? Shall non-residents who die within the geographical hmits be included? Shall residents who die away from home be referred back to the place where they live? In other words shall the place for which the death-rate is computed be considered as a geo- 190 DEATH-, BIRTH- AND MARRIAGE-RATES graphical area or as a community of persons? The answer must depend upon the use which is to be made of the facts. The Bureau of the Census, looking at the matter in a broad way, takes the geographical point of view. It can hardly do otherwise. By recording deaths in the place where the deaths actually occur there is far less danger that all deaths will not be recorded and that no death will be counted twice than if a process of distribution by actual residence were attempted. It may be laid down as a general rule that in computing gross death-rates all deaths within the defined area shall be included and no others; that is, gross death-rates shall have a geographical basis. This does not prevent the making of corrections to allow for local conditions. Often such corrections are desirable. If a hospital is located in a suburban town near a large city the deaths in that hospital should be included in the gen- eral death-rate of the town; but this- figure could not be taken as an index of the hygienic or sanitary condition of the town. For such a purpose another rate — ■ a corrected rate — should be computed, leaving out the hospital deaths. This might be called the local death-rate. This rate should not be used in place of the gross death-rate, but in addition to it. If, besides the omission of non-resident deaths in insti- tutions, the attempt is made to find and include the deaths of residents who have died away from home we might caU the result the " resident death-rate." The gross death-rate, or general rate, is best for pur- poses of national or state record. The local rate is best for environmental studies. The resident rate is useful for social and political studies. In New York city the health department publishes a general death-rate and also a " corrected " death-rate in which the deaths are redistributed among the five boroughs CORRECTED DEATH-RATES 191 on the basis of residence. This is because so many persons residing in one borough are talien to hospitals in other boroughs. In some cases this makes an important differ- ,ence. For the week ending Mar. 23, 1918, the death- rates for the five boroughs were as follows:' TABLE 44 DEATH-RATES IN NEW YORK CITY Borough. General death- rate. Resident death- rate. (1) (2) (3) Manhattan Bronx Brooklyn Queens Richmond 20.32 20.20 18.98 20.71 25.13 20.30 17.68 20.04 20.98 18.98 On the basis of the gross death-rate Richmond is seen to have a death-rate much higher than Manhattan, but its resident, or " corrected," rate is lower than that of Manhattan. At the end of a year a preliminary death-rate is often computed and published. Afterwards delayed reports of deaths are received and this necessitates a correction. The term " corrected " death-rate is sometimes apphed to the new result. This of course is a proper use of the adjective, but a better term would be "fined." The term " corrected death-rate " has been used by some writers as synonymous with the " standardized death- rate," described on page 240. This use. of the term is unfortunate and should be avoided. Properly the word " corrected " should be applied only to death-rates in which changes are made in the number of deaths. 192 DEATH-, BIRTH- AND MARRIAGE-RATES Revised death-rates. — Inasmuch as death-rates are based on estimated populations in post-censal years, and as these estimates are usually less accurate than intercensal estimates, it is always wise after each new census to re- compute the death-rates for the preceding intercensal years if it is found that the new census is different from the estimated population. Sometimes the " resulting changes are slight, but they may be considerable. The rates based on these revised estimates of population should be called " revised death-^ates." Variations in death-rates in places of different size. — Wide fluctuations in the general death-rates from year to year are to be expected in small places. Having a small population a change of one death in a year may consider- ably alter the rate. In larger populations the fluctuations are less marked. This is well illustrated by the death- rates of three places in Massachusetts, — Boston (popu- lation 686,092 in 1910), Springfield (88,926) and Yarmouth (1420). Fig. 43 shows that the death-rate for Boston changed slowly, that of Springfield, although lower, fluc- tuated more, while that of Yarmouth varied through wide limits. This very well illustrates what is sometimes called the principle of large numbers. Errors in published death-rates. — • It is necessary to use published death-rates and birth-rates with great caution. The old reports especially contain many unsuspected errors. For example, it was not at all uncommon ten or twenty years ago for the population of one census to be used year after year as the basis of death-rates, or until a new census was taken; that is, no intercensal estimates were made. Even the registration reports of Massachusetts are full of inconsist- encies and cases of disagreements. In the following table the general death-rates are given in the second column as VARIATION IN DEATH-RATES 193 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 Fig. 43. — Comparison of Death-rates in a Large City, a City of Moderate Size and a Small Town. 194 DEATH-, BIRTH- AND MARRIAGE-RATES they appeared originally in successive annual reports. In the third column the rates for the same years are given as published in the annual report for 1915, the rates having been recomputed. TABLE 45 DEATH-RATES IN MASSACHUSETTS Year. As given originally in successive annual reports. As given in report of 1915 (recomputed). (1) (2) (3) 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 16.8 16.9 18.1 17.2 , 17.0 16.2 15.8 15.6 15.9 14.5 16.7 16.4 17.2 16.0 15.5 16.1 15.8 14.9 14.9 14.5 Rates for short periods. — The general death-rate is always computed on the basis of a year. Strictly speaking the monthly death-rate would be the number of deaths occurring in the month divided by the estimated population for the middle of the month; and the weekly death-rate would be the number of deaths in a week divided by the estimated Wednesday population for that week. This practice would reduce population estimates to an absurd degree of precision. The months moreover do not all have the same number of days. On account of the varjdng estimates of population the sum of the monthly rates would not equal the annual rates. It is much better for many reasons to reduce all rates for short periods to the basis of a year, and to use the popu- RELATIONS BETWEEN BIRTH- AND DEATH-RATES 195 lation estimated for July 1 for all months and weeks of the same year. Account must be taken, too, of the varying length of the months, and of the fact that a year is- not exactly fifty-two weeks. To find the death-rate for January we therefore multiply the number of deaths in January by -V/-, and divide by the estimated population for July 1. For the months of thirty days the multiplier is %y^-; for February it is V/ in ordi- nary years, and V/ in leap years. , To find the death-rate for any week in the year we mul- tiply the number of deaths in the week by ^^ and divide by the population estimated for July 1st. Birth-rates. — • Birth-rates are computed in the same way as death-rates. We may have general rates, local rates, and resident ratesf preliminary rates and final rates; cor- rected rates and revised rates. Weekly and monthly rates are reduced to a yearly basis. One thing should be always remembered. If a child is born dead, that is if it is a " still-birth," it is not consid- ered by statisticians as a birth. Births include only living births. StUl-births are placed in a class by themselves. In some places, still-births have been included with the living births, and in comparing old birth-rates with present rates this must be kept in mind. It must be remembered also that birth registration is less complete than the registration of deaths. Relations between birth-rates and death-rates. — The relations which exist between general birth-rates and gen- eral death-rates are very complicated. It is easy to say that because of a naturally high infant mortality, which until recently has seldom been less than 10 per cent and which in some countries is more than 25 per cent, the birth of many children means many deaths and hence a high birth-rate means a high death-rate. To a certain extent this is true. 196 DEATH-, BIRTH- AND MARRIAGE-RATES It is true for a sudden increase in the birth-rate and its effect may last for five or ten years if the high birth-rate keeps up. But a tiigh birth-rate adds to the population, and this increases the denominator of the birth-rate. Also most of the babies will within a few years become - children and enter age groups where the specific death-rates are low. If a high birth-rate is long continued it may actually reduce the general death-rate. Fifty or sixty years after a high birth-rate there should be an excess of persons living within the advanced age groups when the specific death- rates are high and rapidly increasing. Instead of becoming confused by trying to think out these puzzling relations, and especially so because wars and migrations upset aU such reasonings, it is better to regard the birth-rate as something which togetBer with deaths and migrations controls the age composition of the people. Conversely the age composition of the people influences both the given birth-rate and the general death-rate. One cannot think clearly on this subject without cutting loose from general rates and studying specific rates both for births and deaths. Fecundity. — From a social standpoint the birth-rates computed in the usual way give an inadequate idea of some of the most important matters concerning the increase of population. They are ratios between births and total populations, and not all of the population included are child producers. If we are to follow the statistical prin- ciple of comparing things which are logically comparable we shall compute other ratios, that between births and women of child bearing age and that between births and married women of child bearing age, and we shall separate legitimate from illegitmate births, and take into account still births, though always keeping them separate from living, or true statistical births. FECtJNDlTY 197 What are the chief factors which control the number of children born? The number of marriages; the effective duration of these marriages, that is the number of years be- tween the age of the bride at marriage and the natural age when child-bearing ceases; and the frequency with which conception occurs. The number of marriages depends up- on the age and sex composition of the population and upon economic and social conditions. The effective duration of marriage depends upon the age at marriage, especially the age of the bride. Obviously if marriage occurs late in life the effective duration of marriage is shortened. The frequency of conception depends to some extent upon the iof ant m ortality as, a shortening of the period of suckling reHuces the child-bearing interval; but to a considerable extent this is a matter which is, or may be, controlled by the husband and wife. The number of still births also has an influence on the intervals between living children. Korosi 1 and others have attempted to compute tables of natahty, similar to the Ufe tables described in Chapter XIV. Statistics for Budapest indicated that the age of maximum fecundity for females reached its maximum between the eighteenth and nineteenth years, falling steadily to age fifty when it practically ceased. Males attain their maxi- mum fecundity at the age of about twenty-five, after which there is a steady decline to age sixty-five or thereabouts. It is understood that these figures are not physiological limits necessarily, but include social and economical con-; siderations. Late marriages therefore- reduce the number of resulting children. Combinations of brides and grooms'" of different ages results in different pr6Babiiities"rf^births. The following figures given by Korosi illustrate this. The percentages refer to the probability of a birth occurring in a year. 1 1899, Newsholme, Vital Statistics, p. 667, 198 DEATH-, BIRTH- AND MARKIAGE-RATES TABLE 46 RELATION OF AGE TO FECUNDITY Fecundity of mothers. Fecundity of fathers. Age of Age of mother. Age of mother. Age of father. father. 25yr3. 30 yrs. 35 yrs. 25yi3. 35 yra. 45 yrs. 65 yrs. (1) (2) (3) (4) (5) (6) (7) (7) (9) 25-29 Per cent 36 31 27 Per cent 25 24 22 17 14 Per cent 21 20 19 14 11 11 ' 20 20-24 25-29 30-34 35-39 40-44 Per cent 49 43 31 33 Per cent Per cent Per cent 30-34 35-39 40^4 45^9 50-54 si 27 24 19 7 16 18 14 12 6 "s" 7 3 Nationalities differ considerably in the number of chil- dren per marriage. For example, in Russia, the number of children per marriage in 1894 averaged as high as 5.7, while in France it was only 3.0. During recent years in most countries the birth-rates have fallen considerably. In studying this subject in its social relations, these natural conditions of fecundity as influenced by the age composi- tion of the people, the age of marriage and the influence of nationality must be taken into account. Illegitimate births. — Children born to unmarried women are called illegitimate. In computing general birth-rates they are included, but in the study of social problems they should be considered by themselves. The illegitimate birth- rate is the ratio between illegitimate births and the total population expressed in thousands. The percentage of ille- gitimacy is sometimes computed, that is the ratio between illegitimate and total births, but this ratio may be mislead- ing as the total number of births depends on the marriage- ILLEGITIMATE BIRTHS 19D rate, which fluctuates more or less according to economic conditions. As a measure of morality a more ugeful ratio is that between illegitimate births and unmarried women of child-bearing age. It is just as important to consider the age and sex composition of a population in studying illegiti- mate, births as in studying all births. Newsholme has given th'e following interesting compari- sons between two sections of London, Kensington, an aristocratic fashionable districb, and Whitechapel, a poor industrial parish. TABLE 47 BIRTH-RATES IN KENSINGTON AND WHITECHHAPEL, 1891 Birth-rate. Legitimate. Illegitimate. Ken- sington. White- chapel. Excess in White- chapel. Ken- sington. White- chapel. Excess in White- chapel. (1) (2) (3) (4) (5) (6) (7) A Per thousand of popula- 21.8 61.6 215.4 39.9 172.1 328.3 Per cent. 83 177 53 1.2 3.4 4.7 1.3 5.4 11.4' Per cent. 6 B Per thousand of women, aged 15-44 years C Per thousand married women, aged 15-44 years D Per thousand, unmar- ried women, aged 15-44 years. 62 136 We see from this table that on the basis of married women of child-bearing age the birth-rate in the industrial district of Whitechapel was only 53 per cent greater than in the fashionable district of Kensington. On the basis of the general birth-rate or the rate computed for all women of child-bearing age the difference between the two districts 200 DEATH-, BIRTH- AND MARRIAGE-RATES would have been said to be much greater. In Kensington there were many unmarried servants. The illegitimate birth-rate computed on the basis of total population was only 6 per cent greater in Whitechapel than in Kensington, but on the basis of unmarried women of child-bearing age it was 136 per cent greater. This is an excellent example of the necessity of considering specific rates in the study of illegitimacy. Fallacious conclusions in regard to the relative moraUty of different nationaUties, of urban and rural districts, of different states and cities have resulted from failure to take the proper ratios as a basis of study. Marriage-rates. — The marriage-rate is foimd by dividing the number of persona- married in a year by the estimated mid-year population, expressed in thousands. The wed- ding-rate would be one-half of the marriage-rate. In some places this wedding-rate is called the marriage-rate, but this is not according to present-day practice. To prevent misunderstanding it is a good plan to use the expression " persons married per 1000 population." Divorce-rates. — ■ Similarly the divorce-rate is found by dividing the number of persons divorced in a year by the mid-year population. Divorce in the United States is becoming more and more important as a social problem. The conditions are dif- ferent -in different states. In Massachusetts the data, ob- tained originally from court records, are published in the State Registration Report. The following figures are from the report of 1914. The divorce-rate, based on an average for five years of which the census year was the median, has increased as follows. DIVORCE-RATES 201 TABLE 48 DIVORCE-RATE, MASSACHUSETTS Median year. Average rate per 100,000 ' population. Average per 100,000 of mar- ried population. (1) (2) (3) 1880 1890 1900 1905 1910 1914 30 32 46 58 56 60 86 123 153 146 156 The relative number of divorces granted to wives is larger than the number granted to husbands. At present the ratio is in round numbers 7:3. The percentage distribution of divorces according to cause has been as follows: TABLE 49 CAUSES OF DIVORCE, MASSACHUSETTS, i860 to 1914 Cause. (1) Desertion Adultery Intoxication Cruel and abusive treatment Nullity of marriage Extreme cruelty Impotency Neglect to provide T Imprisonment -. Total Percentage. Granted to husband. (2) Per cent. 56.7 34.8 5.8 1.5 0.7 0.2 0.2 100.0% Granted to wife. (3) Per cent. 41.5 14.8 14.4 19.8 0.4 4.1 0.2 4.2 0.5 100.0% 1 Less than 0.1 per cent. 202 DEATH-, BIRTH- AND MAKRIAGE-RATES About three out of every four applications for divorce in Massachusetts are granted. About nine out of ten are not contested. The distribution of divorces according to the duration of marriage is interesting. In 1914 the average duration of the marriage at the time apphcation for divorce was made 10.9 years. The 2963 applications were distributed as follows: TABLE 50 DURATION OF MARRIAGES ENDING IN DIVORCE Duration of marriage. Per cent of applications. (1) (2) 0- 6 months 6-11 " 1-4 years 5-9 " 10-19 20-29 30 Total 0.7 27.'4 30.7 28.7 10.3 2.2 100.0 In discussions of the divorce problem comparison is sometimes made between marriage-rates and divorce-rates. This is not a logical comparison. Why? The student must begin to answer such questions as this on the basis of his own reasoning. In 1910 in Massachusetts divorce was dissolving each year about 3 marriages out of every 1000 in existence, or, more exactly, one out of every 342; in 1897 one out of every 580. The U. S. Bureau of the Census has estimated the prob- ability of divorce ' as not less than 1 in 16, and probably 1 in 12. This figure was based on the statistics of 1900, and ■ Marriage and Divorce, 1867-1906, Vol. I, pp. 23, 24. NATURAL RATE OF INCREASE 203 means that one marriage in every 16 would probably be ended by divorce instead of continuing until "death do us part." This general figure must not be taken too seriously, as it includes all classes of people living under many different con- ditions and represents past rather than present conditions. Divorce statistics ought to be studied specifically, just as much as births and deaths. Natural rate of increase. — The difference between the birth-rate and the death-rate gives the natural rate of increase (or decrease) in population per 1000 inhabitants. In the absence of immigration and emigration, and if the data are correct, the excess of births over deaths will cor- respond with the increase of population as revealed by the census counts. This may be illustrated by the statistics of Sweden from 1750 to 1900. TABLE 51 INCREASE OF POPULATION IN SWEDEN Per 1000 of population at middle of period. Population at end Year. of given year (thousands). Increase as shown by census. Excess of births over deaths. Emigration (com- puted from last two columns). (1) (2) (3) (4) (5) 1750 1781 8.89 8.89 0.00 1760 1925 7.76 8.43 0.67 1770 2043 5.92 6.60 0.68 1780 2118 3.71 4.14 0.43 1790 2188 3.22 4.03 0.81 1800 2347 6.99 7.96 0.97 1810 2396 2.04 2,63 0.59 1820 2584 7.60 7.52 -0.08 1830 2888 11.02 11.00 -0.02 1840 3139 8.32 8.69 0.37 1850 3482 10.39 10.51 0.12 1860 3860 10.36 11.10 0.74 1870 4169 7.57 11.24 3.67 1880 4566 9.05 12.21 3.16 1890 4785 4.69 12.12 7.43 1900 5136 7.13 10.78 3.65 204 DEATH-, BIRTH- AND MARRIAGE-RATES The figures in the last column show that there was very little emigration before 1870, but that since then the losses by emigration have been considerable. It is quite likely, however, that some of the early birth-rates were not as accurate as the. more recent ones. > Comparison of general rates. — The object of computing gross death-rates is to enable us to compare the general mortality in places of different population and of different years in the same place; and yet, as will be demonstrated in the next chapter, such comparisons are very apt to be mis- leading unless the percentage composition of the popu- lation remains substantially constant in all the places and in all the years which are compared. One naturally asks, " Why, if such is the case, should we compute it at all? " The answer is that in a general and crude way the gross rate does show differences in the mortality of different places, and that in any given place the composition of the population changes slowly from year to year. Large differ- ences in general death-rates may be significant, but small differences are usually not significant. What is true of general death-rates is also true of birth- rates and marriage-rates. Far too much attention in studies of vital statistics is given to comparisons of general rates. Such comparisons are Ukely to be superficial and sterile of results. Nevertheless one should have a general appreciation of the changes which have taken place in birth-rates and death-rates throughout the world during the last fifty years. A few examples will be given, but the reader should consult more extended works on the subject and compile for himself tables of rates taken from official reports. Marriage-rates, birth-rates and death-rates in Sweden. — One of the longest records of birth-rates, marriage-rates and death-rates is that of Sweden. Table 48 shows these VITAL STATISTICS OF SWEDEN 205 oon oesT 088T OMX 09BT § 0S81 o o (mi oesT OBBT 0T8t 03 0081 06il 08:i out oan osii 206 DEATH-, BIRTH- AND MARRIAGE-RATES rates from 1749 to 1900. The death-rates and birth-rates are also shown in Fig. 44. It will be seen that the birth- rate has had a general downward trend for a long time, but especially during the last fifty years. The death-rate has fallen more than the birth-rate so that the natural in- crease has risen. Of course, there have been fluctuations and some very abnormal rates will be found. As one would naturally expect the birth-rate has fluctuated synchro- nously with the marriage-rate. At intervals great epi- demics have occurred which carried the death-rate far above the birth-rate. As a statistical series this diagram is de- serving of careful study. The dotted line shows the " mov- ing average " referred to in Chapter II. MARRIAGE-, BIRTH- AND DEATH-RATES, SWEDEN 207 TABLE 48 MARSIAGE-RATES, BIRTH-RATES, AND DEATH-RATES Sweden, 1 749-1 goo (After Sundbarg) Year. Mar- riage- rate. Birth- rate. Death- rate. Natiiral in- crease. Year. Mar- riage- rate. Birth- rate. Death- rate. Natural increase. (1) (2) (3) (4) (5) (1) (2) (3) (4) (6) 1749 17.10 33.82 28.13 5.69 1750 18.48 36.40 28.83 9.57 1780 17.06 35.70 21.74 13.96 1751 18.54 38.63 26.18 12.45 1781 14.66 33.46 25.55 7.91 1752 18.52 35.91 27.34 8,57 1782 15.36 32.05 27.26 4.79 1753 17.42 36.12 24.03 12.09 1783 15.98 30,33 28.11 2.22 1754 18.90 37.22 26.33 10.89 1784 14.96 31.53 29.75 1.78 1755 18.32 37.52 27.38 10.14 1785 15,64 31.43 28.30 3.13 1756 17.00 36.12 27.66 8.46 1786 16,04 32,89 25.94 6.95 1757 15.94 32.61 29.92 2.69 1787 15,90 31,47 23.95 7.52 1758 16.14 33.42 32.37 1.05 1788 15,78 33,87 26.68 7.19 1759 19.50 33.62 26.27 7.35 1789 15.86 32,01 33.13 -1.12 - 1760 19.52 35.70 24.78 10.92 1790 16.50 30,48 30.43 0.05 1761 18.88 34.82 25.80 9.02 1791 21.68 32.63 25.49 7.14 1762 17.92 35.08 31.22 3.86 1792 20.02 36.58 23.90 12.68 1763 17.28 34.98 32.90 2.08 1793 17.80 34,39 24,27 10.12 1764 17.58 34.70 27.24 7.46 1794 16.36 33,79 23,60 10.19 1765 16.30 33.41 27,68 5.73 1796 15,18 32,04 27.94 4.10 1766 16.54 35.36 25,06 10.30 1796 17.24 34.68 24.65 10.03 1767 16.54 35.36 25.63 9.73 1797 16.88 34.77 23.81 10.96 1768 16.92 33.61 27.17 6.44 1798 16.58 33.68 23.08 10.60 1769 16.26 33.06 27.15 5.91 1799 14,70 32.02 25.18 6.84 1770 16.24 32,98 26.06 6.92 1800 14.90 28.72 31.43 0.9 1771 15.52 32.24 27.77 4.47 1801 14.50 30.04 26,08 3.96 1772 13.64 28.89 37.41 -8.52 1802 15,66 31.72 23.71 8.01 1773 15.52 25.52 52.45 -26,93 1803 16.38 31.36 23.77 7,59 1774 8.77 34.45 22.36 12.09 1804 16.14 31.90 24.87 7.03 1775 18.90 35.63 24.84 10.79 1805 16.74 31.73 23.48 8.25 1776 18.02 32.92 22.50 10.42 1806 16.08 30.75 27.51 3.24 1777 18.14 33.03 24.93 8.12 1807 16.40 31.16 26.22 5.94 1778 18.10 34.82 26.65 8.17 1808 16,24 30.39 34.85 5.54 1779 17.34 36.70 28.50 8.20 1809 15.62 26.67 40.04 13.37 208 DEATH-, BIRTH- AND MARRIAGE-RATES TABLE 48 MARRIAGE-RATES, BIRTH-RATES, AND DEATH-RATES Sweden, 1749-1900 (After Sundbarg) Year. Mar- nage- rate. Birth- rate. Death- rate. ^Jatural in- crease. Year. Mar- riage- rate. Birth- rate. Death- rate. Natural increase. (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) 1810 21.52 32.95 31.57 1.38 1840 14.14 31.43 20.35 11.08 1811 21.32 35.30 28.81 6.49 1841 14.34 30.33 19.42 10.91 1812 18.26 33.57 30.27 3.30 1842 14.22 31.65 21.06 10.59 1813 15.48 29.74 27.37 2.37 1843 14.38 30.78 21.45 9.33 1814 15.04 31.19 25.07 6.12 1844 14.88 32.15 20.27 11.88 1815 19.22 34.77 23.59 11.18 1845 14.58 31.45 18.83 12.62 1816 19.60 35.32 22.66 12.66 1846 13.80 29.94 21.83 8.11 1817 16.68 33.40 24.25 9.15 1847 13.64 29.58 23.69 5.89 1818 16.92 33.83 24.37 9.46 1848 14.64 30.33 19.68 10.65 1819 16.28 32.99 27.36 5.63 1849 15.66 32.84 19.84 13.00 1820 16.88 32.97 24.46 8.51 1850 15.18 31.89 19-. 79 12.10 1821 17.62 35.44 25.57 9.87 1851 14.72 31.74 20.72 11.02 1822 18.58 35.88 22.59 13.29 1852 13.68 30.69 22.70 7.99 1823 17.98 36.83 21.02 15.81 1853 14.40 31.37 23.66 7.71 1824 17.66 34.56 20.77 13.79 1854 15.38 33.50 19.76 13.74 1825 17.20 36.49 20.54 15.95 1855 15.04 31.75 21.45 10.30 1826 16.16 34.84 22.61 12.23 1856 14.88 31.47 21.77 9.70 1827 14.44 31.30 23.05 8.25 1857 15.50 32.43 27.58 4.85 1828 15.82 33.61 26.74 6.87 1858 16.22 34.77 21.69 13.08 1829 15.82 34.85 28.97 5.88 1859 16.56 34.99 20.13 14.86 1830 15.46 32.91 24.08 8.83 1860 15.60 34.83 17.65 17.18 1831 13.80 30.49 26.00 4.49 1861 14.54 32.57 18.47 14.10 1832 14.38 30.86 23.38 7.48 1862 14.52 33.38 21.40 11.98 1833 15.66 34.11 21.74 12.37 1863 14.52 33.62 19.33 14.29 1834 16.02 33.74 25.68 8.06 1864 13.96 33.61 20.25 13.36 1835 15.00 32.67 18.55 14.12 1865 14.14 32.81 19.36 13.45 1836 14.34 31.84 19.97 11.87 1866 13.44 33.11 19.98 13.13 1837 ,13.80 30.84 24.65 6.19 1867 12.18 30.83 19.64 11.19 1838 12.18 29.37 24.10 5.27 1868 10.92 27.47 20.98 6.49 1839 13.54 29.49 23.56 5.93 1869 11.28 28.25 22.27 5.98 MARRIAGE-, BIRTH- AND DEATH-RATES, SWEDEN 209 TABLE 48 MARRIAGE-RATES, BIRTH-RATES, AND DEATH-RATES Sweden, 1749-1900 (After Sundbarg) Year. Mar- riage- rate. Birth- rate. Death- rate. Natural in- crease. Year. Mar- riage . rate. Birth- rate. Death- rate. Natural increase. CD (2) (3) (3) (5) CD C2) C3) C4) C5) 1870 12.04 28.78 19.80 8.98 1871 12.98 30.42 17.21 13.21 1872 13.86 30.04 16.28 13.76 1873 14.62 30.80 17.20 13.60 1874 14.54 30.85 20.32 10.53 1875 14.10 31.17 20.27 10.90 1876 14.16 30.84 19.59 11.25 1877 13.66 31.07 18.66 12.41 1878 12.94 29.83 18.06 11.77 1879 12.58 30.52 16.94 13.58 1880 12.64 29.36 18.10 11.26 . 1881 12.38 29.07 17.68 11.39 1882 12.66 29.35 17.35 12.00 ' 1883 12.86 28.94 17.31 11.63 1884 12.06 30.01 17.53 12.48 1885 13.26 29.44 17.75 11.69 1886 12.82 29.76 16.61 13.15 1887 12.50 29.66 16.13 13.53 1888 11.84 28.78 15.99 12,79 1889 11.98 27.74 15.99 11.75 1890 11.98 27.95 17.12 10.83 1891 11.66 28.27 16.81 11.46 1892 11.38 26.98 17.88 9.10 1893 11.30 27.36 16.83 10.53 1894^ 11.48 27.10 16.38 10.72 1895 11.74 27.49 15.19 12.30 1896 11.90 27.18 15.64 11.54 1897 12.12 26.67 15.35 11.32 1898 12.28 27.11 15.08 12.03 1899 12.48 26.35 17.65 8.70 1900 12.30 27.00 16.84 10.16 210 DEATH-, BIRTH- AND MARRIAGE-RATES Downward trend in birth-rates and death-rates. — For nearly half a century there has been a general down- ward trend in the birth-rates and death-rates of almost all civilized countries. There is space here for only a few figures which represent averages for quinquennial periods. They .are taken from the reports of the Registrar-General of England. TABLE 49 CHRONOLOGICAL CHANGES IN VITAL RATES Country. Quinquennial averages. 1881-5 1886-90 1891-5 1896-00 1901-5 1906-10 1911-15 (1) (2) (3) (4) (5) (6) (7) (8) Birth-rates. England and Wales Germany France Hungary 33.5 31.4 30.5 29.3 28.1 26.3 37.0 36-. 5 36.3 36.0 34.3 32.7 24.7 23.1 22.3 21.9 21.2 19.9 44.6 43.7 41.7 39.4 37.2 37.0 23.6 Death-rates. England and Wales Germany France Hungary 19.4 18.9 18.7 17.7 16.0 14.7 25.3 24.4 23.3 21.2 19.9 17.5 22.2 22.0 22.3 20.7 19.6 19.2 33.1 32.1 31.8 27.9 26.2 25.0 14.3 Rates of natural increase. England and Wales Germany France Hungary 14.1 12.5 11.8 11.6 12.1 11.6 11.7 12.1 13.0 14.8 14.4 15.2 2.5 1.1 0.0 1-2 1.6 0.7 11.5 11.6 9.9 11.5 11.0 12.0 9.3 In most countries the natural rate of increase tends to lie between the limits of 8 and 14 per 1000, i.e., between 0.8 and 1.4 per cent, but sometimes it runs above 1.4 per cent or below 0.8 per cent per year. France is an example of VARIATIONS DUE TO POPULATION ESTIMATES 211 an extremely low rate of natural increase. In Germany both the birth-rates and death-rates have been higher than in England. In Hungary both rates have been much higher than in Germany, yet the rate of natural increase has been lower. The student should seek to explain all of these facts. 3,400,000 1900 1905 1910 Fig. 45. — Estimated Death-rates and Populations, Massachu- setts, 1900-1910. Variations due to population estimates. — ■ Some of the variations in the general death-rates from year to year are due to the use of incorrect population estimates. The following comparison is interesting. Fig. 45 shows the populations and death-rates for the state of Massachusetts from 1900 to 1910, based on the following data:' ' Registration Report, 1914, p. 176, 212 DEATH-, BIRTH- A^fD MARRIAGE-RATES TABLE 50 DEATH-RATES: MASSACHUSETTS Year. Population. Deaths. Death-rates. (1) f2) (3) (4) 1900 2,806,346 (census) 51,156 18.2 1901 2,849,047 48,275 16.9 1902 2,889,386 47,491 16.4 1903 2,929,725 49,054 16.7 1904 2,970,064 48,482 16.3 1905 3,016,872 (census) 50,486 16.7 1906 3,089,029 50,624 16.4 1907 3,162,186 64,234 17.2 1908 3,235,343 51,788 16.0 1909 3,308,500 51,236 15.5 1910 3,380,161 (census) 54,407 16.1 The upper diagram shows the estimated population as a uniform change from 1900 to 1905 and again from 1905 to 1910. The death-rates computed from the actual deaths and estimated populations are seen to vary irregularly. But suppose we assume that the changes in death-rates between 1900 and 1905 and 1905 and 1910 are uniform. Then we can compute the changes in population from these estimated rates and the actual deaths. The results are shown in the lower diagram. Do these irregular fluc- tuations seem to be reasonable? There is no way of telling exactly how much of the in- crease or decrease in the general death-rate is due to actual increase in mortality and how much to error in the esti- mated population. Both factors are involved. Birth-rates and death-rates in Massachusetts. — Fig. 46 shows the annual variations in birth-rates and death- rates from 1850 to 1915. The stars indicate the so-called panic years, or years of business depression. The tendency has been for the marriagfe-rate and the birth-rate to fall for a number of years after a period of depression. Since BIRTH- AND DEATH-RATES IN MASSACHUSETTS 213 / ; ,' ( y ^ ^ ^ f \ / -J 1 w ' •^_ ^ s / fl ^, s ►< .? rl / s ? ^ D^ ^ 7 ?-2- ^ ^ S r' C^H s v^ ■^s- cj y 4t -^ -r*= IS ■^i-L —^ — ^ — " - — ■g > , ^, n „f, ^- V 03" s fs. \ T / U3 s s A'v Si aj V * JfV rh •?^ '^i' 1^^^^ ^^ "=7 ~; ^ / .'' — -- J* I 1 i«=: 1 1 '■*^ 1 1 — s 7 \ ^^;^ ■^ — -X • CO. in'xoiij r-t i-t i-f iH ^ ajn-B^Hq^iini ooo I ^^3. 214 DEATH-, BIRTH- AND MARRIAGE-RATES 1892 the death-rate has decreased considerably. The general synchronism between the birth-rate and the death- rate should be noticed, — and also the numerous excep- tions to the rule. In recent years there has been a marked tendency towards uniformity in the death-rate, not only in the state as a whole from year to year, but among the subdivisions of the state in any given year. The fluctuations from year to year are due in part to incorrect estimates of population. Monthly death-rates in Massachusetts. — ^ The general death-rate is not constant throughout the year, but varies seasonally. There are several ways in which this may be shown. The following figures are for the state of Massa- chusetts for the year 1915. TABLE 51 MONTHLY DEATH-RATES: MASSACHUSETTS, 1915 Month. Rate. Per cent of annxial rate. (1) (2) (3) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Year 14.65 13.60 16.80 17.45 13.95 12.35 12.55 13.10 13.75 13.40 13.10 16.00 14.40 102 94 117 121 97 86 87 91 96 93 91 111 100 MARRIAGE-RATES IN MASSACHUSETTS 215 Monthly rates vary considerably from year to year in the same place and are different for different places. Climatic conditions have an influence on these -short term rates. The chance occurrence of communicable diseases also has its effect. Weekly rates fluctuate even more widely than monthly rates, and' daily rates d fortiori. The ten year average for Massachusetts for 1905-14 gave the highest winter rate for February and not for April as in 1915; and the highest summer rate was in August, not September as in 1915. The student should compute and study monthly rates for places where the climatic conditions are different. Marriage-rates in Massachusetts. — Marriage-rates rise and fall periodically. The rate is influenced by social and economic conditions, by the age distribution of the popu- lation, the ratio of the sexes at marriageable age, by nation- ality, and by many causes. There has been no steady downward trend in the marriage-rate as in the case of the death-rate and birth-rate. There is, however, a seasonal variation. June and October are the most popular months for weddings. In 1915 the Massachusetts marriage-rate for the year was 17.0; in June it was 27.5, in October, 23.9, but in March only 6.6. There were four times as many weddings in June as in March. Since 1870. the median marriage-rate in Massachusetts has been 18.0. After the panic of 1873 the annual rates for several years ranged between 15 and 16.5, and after other periods, of business depression they have been below 17. The highest annual rate in nearly flfty years was during 1871 and 1872, when it was 21.1 per thousand. The published statistics of marriages generally include tables classified according to the age and nativity of the bride and groom; the number of the marriage (whether first, 216 DEATH-, BIRTH- AND MARRIAGE-RATES second, third, etc.); and the previous state of the persons wed (whether bachelors, maids, widowers, or widows). Divorce-rate in Massachusetts. — In 1915 the number of persons divorced was 1.22 per 1000 papulation; in 1914 the rate was 1.21; in 1910, 1.15; in 1890, 0.58; in 1870, 0.52. Limited use of general death-rates (gross rates). — General death-rates are composite figures. They cover the entire population, both sexes, all ages and nationali- ties, all occupations, all causes of death, while the estimates of population are often inaccurate. Fluctuations from year to year depend in part on the size of the population, in part upon the composition of the population, as well as upon causes of death. Under these conditions it is evident that they cannot be safely used as an index of mortality condi- tions in different places and for long periods of time in any one place. A general death-rate, or gross death-rate, is of little use until it has been analyzed. The " total solids " in a water analysis gives the chemist almost no idea of the quality of the water : it is necessary to separate the " solids " into their constituent parts. In the same way a general death-rate must be broken up into its constituent parts. At the present time the analysis of death-rates is practiced but little. Death-rate analysis today is in about the same condition that water analysis was in fifty years ago. The. necessary analysis cannot be made until the im- portant subject of specific death-rates has been considered in the next chapter. The ideal death-rate. — Is there such a thing as an ideal death-rate? At present our general death-rates are falling. They cannot continue to fall forever, for man is mortal and all must die? A large part of the decrease in the THE IDEAL DEATH-RATE 217 death-rate can be traced to sanitary, hygienic and medical improvements. Another part may be due to a lowering birth-rate following a relatively high birth-rate, or in other words to an increasing ratio of persons in the young and middle-aged groups. This condition will not continue permanently. In due. course the young will become middle aged and the middle aged will become old, the excess of population will enter those age-groups where the specific death-rates are high and this will cause the general death- rate to rise. Or the birth-rate will rise and temporarily this will raise the general death-rate. Unless public health officials learn how to view general death-rates in a proper light — p. good way being not to • view them at all — they may be surprised and discouraged some day to find that the death-rate is rising. The Great War in a most horrible and pitiful way cut out a large number of males in the middle-aged groups in many countries. Temporarily this will increase the gen- eral death-rate. On the other hand these young men will not five to enter the old-age groups where the specific death-rates are high. What effect will this have on the future trend of the death-rate? What effect will it have on the birth-rate? Perhaps it may be for the best interest of the race that the genera] death-rate be higher than it now is. This would be the case if there should be more babies and more grandfathers and grandmothers. To answer the ques- tion as to what is the lowest practicable death-rate we must first decide what is an ideal distribution of popula- tion as to age and sex, and then consider what diseases at the different ages we can reasonably expect 'to eliminate. It is an interesting problem for thought and discussion. 218 DEATH-, BIRTH- AND MARRIAGE-RATES EXERCISES AND QUESTIONS 1. Plot the general death-rates of Massachusetts by years from 1850 to date. Connect the points with straight lines. Then draw straight lines connecting the death-rates for the years divisible by ten. Why is the resulting curve so regular? Connect the points for years ending in 9. Why is the resulting curve so irregular? 2. Compare the published statistics for tuberculosis as given by local, state and federal authorities. Explain the differences. [See Am. J. P. H., May 1913, p. 431.] 3. Compute the following death-rates, carrying the results only as far as accuracy warrants. Population Deaths per year 5,461,200 70,210 261,500 2,913 35,000 421 5,260 98 897 17 4. How does the marriage-rate ordinarily compare with the ratio of marriages to persons eligible to marriage (bachelors, spinsters, widowers, widows and divorced persons, all of marriageable age)? [Newsholme's "Vital Statistics," p. 58.] 5. How do the marriage-rates in cities compare with those in rural districts? 6. Is the. marriage-rate a reliable "barometer of prosperity," as Dr. Farr called it? 7. What effect has war on the marriage-rate? 8. What proportion of marriages are remarriages? 9. Are remarriages more common among widowers or widows? ^ ' 10. Prepare a table showing the marriage state (single, married, widowed, divorced) of the population of some civil division for each sex and for different age-groups above age fifteen. [Consult census reports.] 11. At what ages do people in different social positions marry? EXERCISES -AND QUESTIONS 219 12. What changes, if any, have taken place in the age of marriage among people of different social position during recent years? 13. How do the general birth-rates for urban and rural districts compare with each other? 14. How do the birth-rates for urban and rural districts compare with each other if based on the number of married women of child- bearing age? 16. What relation is there between birth-rates based on married women of child-bearing age and the social position of these women? 16. What relation is there between the birth-rate thus computed and the age of marriage? 17. What influence has war on the general birth-rate? 18. What influence has national prosperity on fecundity? 19. How do the general birth-rates compare for different political coimtries, such as England, Ireland, France, Germany, Austria, Bel- gium, etc. 20. How do the birth-rates for different nationalities in the United States compare with each other? 21. How does the birth-rate for the Irish in Ireland compare with that of the Irish in Massachusetts? 22. How do the birth-rates among CathoUcs compare With that among Protestants? Consult the statistics of Canada, especially the provinces of Ontario and Quebec. 23. What is the ratio of males to females among births? 24. What is the ratio of males to females among still-births? 25. What is the ratio of males to females among illegitimate 'births? CHAPTER VII SPECIFIC DEATH-RATES Although general death-rates have their uses, something more is needed if statistics of mortality are to be used to their best advantage. The tendencies of hmnan beings to die are not constant; diseases differ] in their fatality; persons of different age differ Hn susceptibility to disease; sex, nationality, connubial condition are likewise variable factors. One cannot properly use mortaUty statistics in public health work without taking these factors into ac- count, at least without considering the most important of them. This brings us to a consideration of specific death- rates. General death-rates are ratios between the entire population of a given place and all deaths which occur in a year. We may restrict these rates in several ways. Restrictions of death-rates. — We may consider a shorter period than a year, and compute the rate for a month or a week and thus obtain a partial rate or a short-term rate as described in the previous chapter. This, however, is not usually classed as a specific rate. We may restrict the computation to a special class or group of the population; that is, we may take into account only males or only females and compute the death-rate for them alone. These would be specific death-rates by sex. We may consider each age-group by itself and find the death-rate for it alone. This would be to compute specific death-rates by age-groups. Or we may take only persons of the same nationality or occupation and com- pute specific death-rates for them. 220 AGE 221 Again we may consider separately the different causes of death, and compute specific death-rates for tuberculosis, for scarlet fever, or for cancer. Finally we may consider particular diseases and at the same time restrict the computation to certain classes or groups of people; thus we may compute the " typhoid fever death-rate for males in age group 15-19 years." It has been suggested that these various modes of re- striction might be designated by such expressions as "special death-rates," "particular" rates, "limited" rates, etc., but apparently the common expression " specific " death-rate serves every useful purpose. It is the purpose of the present chapter to describe the methods of computing specific rates and to call attention to their importance. It is not too much to say that an understanding of specific rates is the key to the interpretation of vital statistics. Failure to appreciate the important influ- ences of age is alone responsible for scores of fallacious conclusions derived from tables of vital statistics. Age. — The span of human Ufe has been divided into age periods in many different ways. Shakespeare' vividly describes the seven ages of man. Jagvjes: All the world's a stage, And all the men and women merely players: They have their exits and their entrances; And each man in his time plays many parts, His acts being seven ages. At first the infant, Mewling and puking in the nurse's arms; Then the whining school-boy, with his satchel And shining morning face, creeping like snaU Unwillingly to school; and then the lover. Sighing like furnace, with a woeful ballad Made to his mistress' eyebrow; then a soldier. Pull of strange oaths and bearded like the pard, 1 Jaques in As You Like It, Act II, Scene VII. 222 SPECIFIC DEATH-RATES Jealous in honour, sudden and quick in quarirel, Seeking the bubble reputation Even in the cannon's mouth; and then the justice, In fair round belly with good capon lin'd, With eyes severe and beard of formal cut, Full of wise saws and modem instances; And so he plays his part; the sixth age shifts Into the lean and sUpper'd pantaloon. With spectacles on nose and pouch on side, His youthful hose well sav'd, a world too wide For his shrunk shank; and his big manly voice. Turning again toward childish treble, pipes And whistles in his sound; last scene of all. That ends this strange eventful history. Is second childishness and mere obUvion, Sans teeth, sans eyes, sans taste, sans every thing. Just where to draw the age hnes between Shakespeare's seven ages is a most difficult matter and it would be hard to get any two people to agree. The divisions suggested in Fig. 47 are merely for provoking discussion. Physiologically seven fairly distinct states may be recog- nized — the pre-natal state, infancy, childhood, youth (maidenhood), early manhood and manhood (child-bear- ing age and maturity), and finally old age, or seniUty. The age limits of the early groups are fairly well marked. The later groups are more indistinct. He would be a bold person who would undertake to establish an age limit for senility. Every one knows what was said about Dr. Osier when he attempted to do. something of that sort. In Fig. 47 the biblical limit of " three score years and ten " has been used. The author believes that he may safely hide behind that. The division between childhood and youth in boys is perhaps not quite the same as the division between childhood and maidenhood in girls. From the standpoint of environment there are several fairly distinct age periods. Infancy in this case means the AGES OF MAN 223 Envlroment Physiological State Sbakespearea Seven Ages of Man Occarence^ oi Diseases Per cent per year (After Pearson) Specific deatli rate, according to age. 10 20 ■ 30 40 50 60 70 • Fig, 47. — Ages of Man. 224 SPECIFIC DEATH-RATES earliest period, in which the environment is maternal. It terminates when the child is weaned. Then follows the period of home environment. Later the school environ- ment controls. After that the work place comes in as an important factor. Of course the home influence continues through life, and in the case of most women it predominates after the school age. Indeed after the school age the environment becomes complex. Karl Pearson has analyzed the curve which shows the age distribution of deaths in an interesting way. He con- cludes that there are five groups of diseases, those of in- fancy, childhood, youth, middle age and old age. All of these extend over wide limits, but culminate at the ages shown in Fig. 47. One may die of an old age disease at thirty, or one may have a children's disease at forty. Endless complications exist in special cases, yet in the main the distinctions between the five classes of diseases are well known. At the bottom of the diagram we see the curve which shows the specific death-rate in its characteristic variations through the span of life. This curve in its general form is the same for both sexes, for all nationalities, for all climates. There are differences, of course, but over all the other factors which influence death, age predominates. This curve, it should be observed, is based on deaths from all causes. It would not necessarily apply to particular diseases. The student should study this curve of specific death- rates according to age until he can reproduce it with ap- proximate accuracy from memory. Vision of Mirza. — Those who do not enjoy studying statistics may appreciate the following paragraph taken from Addison's " Vision of Mirza." " The bridge thou seest, said he, is Human Life; con- sider it attentively. Upon a more leisurely survey of it, HOW TO COMPUTE SPECIFIC DEATH-RATES 225 I found that it consisted of threescore and ten entire arches, with several broken arches, which, added to those that were entire, made up the number about an hundred. As I was counting the arches, the Genius told me that this bridge consisted at first of a thousand arches; but that a great flood swept away the rest, and left the bridge in the ruinous con- dition I now beheld it. But tell me further, said he, what thou disco verest on it. I see multitudes of people passing over it, said I, and a black cloud hanging on each end of it. As I looked more attentively, I saw several of the passengers dropping through the bridge into the great tide that flowed underneath it: and upon further exami- nation perceived that there were innumerable trap-doors that lay concealed in the bridge which the passengers no sooner trod upon, but they fell through them into the tide, and immediately disappeared. These hidden pit-falls were set very thick at the entrance of the bridge, so that throngs of people no sooner break through the cloud, but many of them fell into them. They grew thinner towards the middle, but multiplied and laid closer together towards the end of the arches that were entire. There were, in- deed, persons, but their number was very small, that con- tinued a kind of hobbling march of the broken arches, but fell through one after another, being quite tired and spent with so long a walk." How to compute specific death-rates. — The specific death-rate for any age-group is found by dividing the number of deaths of persons whose ages lie within, the group limits by the number of thousands of persons in the same group alive at mid-year. The computation is pre- cisely the same as that for the general death-rate except that both deaths and population &re confined to specific age-groups. If both quantities are known the process is merely arithmetical. 226 SPECIFIC DEATH-RA'riES Example: — Given the following data for New South Wales, 1901' (Columns 1, 2, 3). TABLE 52 Age-group. Population. Deaths. Specific death- rate. (1) (2) (3) (4) 0-1 1-19 20-39 40-59 60- Total 40,500 704,000 514,900 256,600 89,800 1,605,800 3,234 1,960 2,251 2,965 5,400 15,810 79.9 2.8 4.4 11.6 60.1 9.85 To find the specific death-rate for the age-group 1-19 years, divide the number of deaths in that group, i.e., 1960 by 704, the number of thousands of population. The result is 2.8 per 1000. Similarly the specific death-rate for age- group 20-39 is 2251 ^ 515 = 4.4 per 1000. The figures in Column 4 were thus computed. The total deaths di'^ vided by the total population, in thousands, gives the gen- eral death-rate, i.e., 15810 -=- 1605.8 = 9.85 per 1000. If the number of deaths within the age-group is known but the population is unknown, it is necessary to estimate the population in the group. This can usually be done with sufficient accuracy from the data provided by the censuses. The methods of making these estimates both for censal and non-censal years has been already described. This may ■ involve a redistribution of the population from those given in the census to those corresponding to the death statistics. If the population in the group is known but the number of deaths is unknown tlie computation cannot be made with accuracy. It might be possible to redistribute the deaths into age-groups corresponding to the population, but DEATH-RATES BY AGES FOR MALES AND FEMALES 227 zw SPECIFIC DEATH RATES OF MALES AND FEMALES IN ORIGINAL REGISTRATION STATES 1910 FROM U.S. LIFE TABLES PREPARED BY PROF. JAMES. W. GLOVER, FOR THE BUREAU OF THE CENSUS, 1916 aoo 180 i 1 160 / // // l:i2o 4) j 1 i 100 // ' / 80 , f fii S 60 ■^ fl / «N 40 {/ / S 20 n ^ 1 f, — ?= ^ ^ >k» •f~ 6= != S= 6= B=^ 10 go 30 10 SO 61 Age in Years 70 80 90 100 Fig. 48. — Specific Death-rates. Specific death-rates obtained in this way would in most cases be unreliable. Specific death-rates by ages for males and females. — ■ Looking at the two curves for the specific death-rates of males and females shown in Fig. 48 one would say at first that they were much alike, but that the rates at all ages were 228 SPECIFIC DEATH-RATES higher for males than for females. In a general way this is true, but a closer study shows that the differences are not the same for all ages. The table from which these curves were plotted gave data from which the following figures were obtained. TABLE 53 PER CENT BY WHICH THE SPECIFIC DEATH-RATES FOR MALES EXCEEDED THOSE FOR FEMALES IN VARIOUS AGE INTERVALS (Based on the original registration states; population in 1910, and deaths in 1909, 1910 and 1911). Age interval. Per cent (approximate). Age interval. Per cent (approximate). (1) (2) (3) (4) yr. 0-1 5-6 10-11 15-16 20-21 25-26 30-31 35-36 40-41 45-46 50-51 20 5 15 5 15 6 10 20 35 27 23 yr. 55-56 60-61 65-66 70-71 75-76 80-81 85-86 90-91 95-100 100-101 14 19 14 10 12 8 7 3 -2 3 In infancy the death-rate for males exceeds that for females by 20 per cent. Between five and twenty-five years of age the differences vary considerably in successive years but average about 10 per cent.' Above age twenty-five the male death-rate begins to exceed the female death-rate by considerable amounts and this continues to the age of forty, when the excess is 35 per cent. After that it steadily decreases. In old age the two rates are much alike. It must be remembered that these figures are for a certain ' The error of population due to concentration on round numbers probably accounts for some of these differences. EFFECT OF MARITAL CONDITION ON DEATH-RATES 229 limited area and for a short interval of time and for a par- ticular composition of people with respect to nationality, birth-rate, and so on. They are to be regarded merely as illustrative of the differences between males and females. What are the reasons for the differenceshere shown? Effect of marital condition on specific death-rates. — Students will find it interesting to compute specific death- rates for males and females according to their marital con- dition. It will be found that the rates for single men are considerably higher than for married men. Between thirty and forty years of age they may be nearly twice as high; at higher ages the percentage differences become less. The death-rates of single females are higher than those of married females except that during part of the child-bearing period, — say from twenty to forty-five, — the rates are higher for married women. Professor Walter F. Willcox, of Cornell University, has computed the following specific death-rates for New York State, the cities of New York and Buffalo excluded, for 1909-1911, arranged by age-groups and by classes corre- sponding to marital condition, as follows: TABLE 54 SPECIFIC DEATH-RATES ACCORDING TO AGE AND MARITAL CONDITIONS, NEW YORK, 1909-11 Males. Females. Age-group. Single. Married. Widowed or divorced. Single. Married. Widowed or divorced. (1) (2) (3) (4) (5) (6) (7) 20-29 30-39 40-49 50-59 60-69 70-79 80- 6.6 12.9 19.5 28.7 51.0 101.4 204.2 4.2 5.9 9.5 17.0 31.9 72.7 205.1 12.0 14.1 17.8 30.5 - 48.6 96.0 315.7 4.7 7.4 10.0 19.9 37.1 82.2 279.8 5.7 6.3 8.2 14.5 28.1 61.4 194.8 9.4 9.5 12.1 18.8 38.2 87.2 269.8 230 SPECIFIC DEATH-RATES Among the theories suggested in explanation of these differences is the effect of leading a better supervised and more restrained life among married persons, the better economic conditions of the married, the effect of marriage selection and the effect of the marriage relation itself. Nationality and specific death-rates. — Specific death- rates for different ages and sexes are not the same for all nationalities. It is very difficult, however, to say how much of this is due to racial difference and how much is due to environmental conditions; that is, it is hard to separate the physiological from the social and economic factors. Practically, however, these factors must be considered together in discussing nationalities in the United States. We see these differences well marked between the negro and the white populations of the original registration states. The figures in Table 55, taken from Professor Glover's re- port, will show this. The figures in this table are carried to an unnecessary degree of precision so far as this particular point is concerned and in the case of the advanced ages for negroes probably not even the whole numbers are accurate. The rate for male negroes is almost double that for male whites up to the age of sixty or thereabouts; above eighty the rate for negroes is lower than for whites. Substantially the same relations hold for white and colored females. It should be noticed that in these various comparisons the effect of age is a factor which must never be left out of account. EFFECT OF AGE COMPOSITION ON DEATH-RATE 231 TABLE 55 SPECIFIC DEATH-RATES FOR WHITE AND NEGRO MALES United States, Original Registration States, ipio Ratea per 1000. Age interval. White. Negro. ■ (1) (2) (3) 0-1 123.26 219.35 5-6 4.71 8.56 10-11 2.38 5.02- 15-16 2.83 7.87 20-21 4.89 11.96 25-26 5.54, 12.28 30-31 6.60 14.96 35-36 8.52 17.28 40-41 10.22 21.03 45-46 12.64 23.99 50-51 15.53 31.42 55-56 21.50 39.50 60-61 30.75 50.79 65-66 43.79 64.33 70-71 62.14 83.98 75-76 92.53 112.77 80-81 135.75' 131.27 85-86 191.11 179.82 90-91 255.17 201.01 95-96 324.86 227.76 100-101 427.46 336.29 Effect of the age composition of a population on the death-rate. — It is evident also, from our acquired knowl- edge of speciiic death-rates, that the general death-rates of two places cannot be reasonably compared unless the age composition of the population is substantially the same in the two places. The following simple example will make this plain: Two places, A and B, have the sanie total population, i.e., 50,000; and they have the same specific death-rates at 232 specific; DEATH-RATES different ages. The ages of the people, however, differ as shown in the table. From these figures we may compute the general death-rate for each place. TABLE 56 EFFECT OF AGE COMPOSITION OF POPULATION ON THE GENERAL DEATH-RATE Age. Population. Specific death-rate per 1000. Computed deaths. Computed death-rates per 1000. A B A B .■1 B (l) (2) (3) (♦) (5) (6) (7) (8) 0-4 5-59 60-79 10,000 35,000 5,000 20,000 20,000 10,000 25 10 60 250 350 300 500 200 600 Total 50,000 50,000 900 1300 18 26 In B, a place with a large number of children and old people, the rate is 26 per 1000, while in A, a place~with a large middle-aged population, the rate is only 18. This is, of course, an exaggerated case, but slight differences in age distribution make a greater difference in the general death-rate than one would suppose. In 1899, according to a report of the U. S. Secretary of War, the annual death-rate of soldiers in the Philippines was 17.20, while the death-rate of Boston was 20.09, of Washington 20.74 and of San Francisco 19.41. The ob- vious inference was that the mortaUty in the^army com- pared favorably with the mortaUties of the cities mentioned. The facts unstated were that soldiers are picked men in a limited age-group while the cities contain a conglomerate population. A better comparison would have been one between the soldiers and males between 20 and 40 years of age in the United States, the usual death-rate for which is EFFECT OF AGE COMPOSITION ON DEATH-RATE 233 less than 10 per 1000. Hence the mortality among the troops in the Philippines was nearly twice as high as that of males of similar age in the United States. In 1911 the general death-rate of Chicago was 14.5 and that of Cambridge, Mass., was 15.2. Was Chicago the healthier city? No, indeed! The following figures show that the specific death-rates were lower in Cambridge for all ages except the age-intervals of 10-19 years and 65 years and over. The reason for Chicago's lower rate was because there were relatively more people in Chicago at those middle ages where the specific death-rates are naturally low. TABLE 57 COMPARISON OF DEATH-RATES IN CAMBRIDGE, MASS., AND CHICAGO Per cent of population in age-groups. Both sexes. Specific death-rates per 1000, in 1911. Age in years. Cambridge. Chiicago. Cambridge. Chicago. (1) (3) (3) w (5) Under 5 10,3 10.2 39.1 39.5 5-9 9.1 8.8 4.3 4,7 10-14 8.5 8.6 3.5 2,6 15-19 8.5 9.6 4.6 3,7 20-24 9.9 11.5 3.8 5.3 25-34 18.2 19.7 5.5 6.9 35-44 15.0 14.5 9.0 11.4 45-54 16.0 9.6 16,0 19.3 55-64 4.5 29,4 35.1 65-74 4.5 2.0 64,0 63.6 75 and over (in- cluding unlinown) 1.0 148,8 144.2 Total 100.0 100.0 15.2 14.5 Obviously the two general death-rates tell us very little that we want to know — that is, not until they have been analyzed. 234 SPECIFIC DEATH-RATES Effect of race composition on death-rates. — If differ- ent races have different specific death-rates then the general death-rates of two places which have different percentages of various races cannot be fairly compared. The general death-rates of southern cities cannot be fairly com- pared with those of northern cities. In 1911 the general death-rate in New York City was 15.2; in Washington it was 18.7; in New Orleans, 20.4. The death-rate for the white population in Washington, however, was only 15.5 and in New Orleans only 16.6. Even these figures are not strictly comparable as they do not take into account age distribution. Changes in specific death-rates through long periods. — We have seen that the general, or gross, death-rates have been falling for a long time. Are the same changes occur- ring in the specific death-rates at different ages and for dif- ferent classes of the population? This is a most important question. If we can answer it we shall have come close to measuring the effect of our sanitary, hygienic and med- ical improvements during recent years. Far too little effort has been made to compile statistics of this sort. Let us see what we can learn from Massachusetts records. In 1830 Lemuel Shattuck computed specific death-rates for Boston. It will be interesting to compare these with figures for the year 1911, published in the U. S. Mortality Statistics by the Bureau of the Census and recast to make the age-groups correspond. CHANGES IN SPECIFIC DEATH-RATES 235 TABLE 58 SPECIFIC DEATH-RATES, BOTH SEXES, FOR BOSTON Age inter- val. Rate per 1000. 1830. 1911. (1) (2) (3) 0-1 1-5 0-5 5-9 10-14 15-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90- "59.6 8.1 . 5.5 4.9 10.4 20.1 22.4 29.3 45.8 92.4 162.1 321.4 (approximate) 161 17 "■■4" 2.4 4 6 10 15 27 52 102 During the 81 years there has been a marked reduction in the specific death-rates at all ages below sixty. In the :r case of children and youths the reduction was as much as one half. In 1898 Dr. Samuel W. Abbott, then Secretary of the Massachusetts State Board of Health, computed a life table for the State ' for the years 1893-7 in which the spe- cific death-rates were given for certain age-groups. It is interesting to compare these with the figures given for Massachusetts in the U. S. Life Tables for 1910. 1 Ann. Rept. 1898, p. 810. 236 SPECIFIC DEATH-RATES TABLE 59 SPECIFIC DEATH-RATES FOR MASSACHUSETTS Rate per 1000 Rate per 1000 1893-7 1910 Age-group. Age-group. Males. Females. Males. Females. (1) (2) (3) W (5i (6) 0-4 60.12 52.22 5-9 5.69 5.82 7-8 3.37 3.13 10-14 3.11 3.40 12-13 2.27 2.05 15-19 5.29 5.68 17-18 3.43 3.17 20-24 7.48 7.32 22-23 5.16 4.30 25-34 9.33 8.78 30-31 6.60 5.97 35-44 11.19 10.74 40-41 10.00 8.14 45-54 16.67 14.88 50-51 16.05 12.58 55-64 30.42 26.00 60-61 33.15 27.03 65-74 59.67 51.37 70-71 67.91 56.47 75-84 116.20 99.88 80-81 137.43 123.49 85-94 223.50 184.81 90-91 251.53 244.90 95- 429.20 367.07 100-101 483.90 392.91 Here we see the specific death-rates still falling up to age sixty. For the later ages there has been a slight tend- ency to increase. It should be noticed, however, that the age-groups are not quite the same for the two periods. In 1830 and also in 1893-7 the specific rates at ages five to twenty, or thereabouts, were higher for females than for males, but in 1910 the opposite was true. If we should make similar comparisons of specific death- rates for other places and for different periods we should almost always find that in recent years the rates have been falling for all ages below fifty or sixty. What have been the reasons for this reduction? Un- doubtedly improved sanitary and hygienic conditions, advances in medical and surgical science and the arts of preventive mecUcine have tended to reduce the number of CHANGES lisr SPECIFIC DEATH-RATES 237 1870 1880 1890 1900 1910 1910 FiQ. 49. — Specific Death-rates by Age-Groups, Massachusetts, 1870-1910. 238 SPECIFIC DEATH-KATES -cases of sickness and to increase the percentage of recoveriea of those who are taken sick. This has been especially true in the earlier ages. But it must not be forgotten that changes in the relative numbers of married and single persons in each sex, and of persons of different national- ity, have also their influence. A reason for the increase in the specific death-rates above fifty or sixty years of age has been frequently discussed of late, namely an increase in cer- tain degenerative and organic diseases. This is important, if true, but it is a difficult thing to prove. The fallacy of concealed classification. — Now that we have come to appreciate the effect of age, sex, nationality, and such factors on death-rates, but especially the factor of age, we can better understand what may be called the fallacy of concealed classification. If we classify males according to occupation we might find that the death- rate of bank presidents was higher than that of newsboys; but this would not be because of different occupation but because of different ages. In classifying by occupation we have concealed a grouping by age. If, in classifying the employees of the city of Boston or New York by occupation we distinguish between policemen and street cleaners, we might find that we had concealed a classification by nation- ality, the street cleaners being Italians and the pohcemen Irishmen. Similarly in classifying railroad employees into conductors and brakemen, we might conceal age differences, and under the class of Pullman porters we might conceal a nationahty difference. When we consider stenographers as a separate class we conceal a classification by sex. These concealed classifications and groupings are sometimes very illusive; they creep into our statistics unawares and upset what might otherwise be sound reasoning. Illustrations may be found on every hand. Every one who uses statis- tics should be continually on the watch for them. USE OF SPECIFIC DEATH-RATES 23D Use of specific death-rates. — It must be evident from - what has been said that in order to compare the mortahty conditions in various places the best way is to compare age with age, sex with sex, nationality with nationality, or in other words to compare the various places, classes and groups on the basis of their specific death-rates. To do this in great detail involves labor and the use of many figures. Hence there has always been a fascination in combining these figures so as to obtain a single figure which may be regarded as an index of mortality. There are at least two ways of do- ing this. If there were such a thing as a standard population — and several such standards have been suggested, notably the Standard Million (see page 181) — and if we knew the specific death-rates by ages and sex for any place, we could apply these rates to the standard population and find what the general death-rate would have been in the given place if the population had been standard. And we might do the same for another place and thus obtain figures for the death-rates which could be compared with some degree of justice. When general death-rates are adjusted to a standard population in this way the results are called " Standardized death-^ates." Sometimes they have been referred to as " corrected " death-rates, but this is a poor use of the word, for the process is not one of correcting errors or mistakes and the final result is not " (jorrect," for it does not take into account all differences in population. Nor is the expression " standardized " a good one, because it is not the death- rate which is standardized, but only the population. A better term is " Death-rates adjusted to a Standard Pop- ulation." In the annual report of the Massachusetts State Board of Health for 1902 may be found another method of " cor- recting " death-rates, used by Dr. Samuel W. Abbott. He 240 SPECIFIC DEATH-RATES • took as a standard the specific death-rates of Massachusetts by age and sex. He then apphed these to the age and sex groups of the cities of the state, to obtain what he called the standard death-rate for each place. Then he found the ratio between the " standard death-rate " for each place and the general death-rate of the state, and called this the " fac- tor of correction." Finally he multiplied the actual general death-rate of each place by this factor to obtain his " cor- rected death-rate." The advantage of this method was that he did not need to use the age distribution of deaths for each place. The method is interesting, but is not one for general adoption, because it would be hard to decide on a standard of specific death-rates. Another way of using specific death-rates is that of con- structing what are called life tables. These will be de- scribed in Chapter XIV. But the best way of using specific death-rates is to use them directly. To be sure it means that one must carry more figures in one's mind. • Instead of having to think of one figure for the general death-rate it is necessary to think of figures for infant deaths, for the deaths of children, of adults and of the aged — but, after all, are not these the really important figures? Statistics are worthless unless they can be used. If specific death-rates are more usable than general death-rates, we should make the specific rates more prominent and educate peeple to think in terms of them. Death-rates adjusted to a standard population. — r A few examples will now be given to show how general rates may be adjusted to a standard population. For the sake of simplicity age differences only will be considered. The data required are (a) the number of deaths by age-groups in the given place; (b) the number of persons living at mid-year in the corresponding age-groups; (c) an assumed ADJUSTED DEATH-RATES 241 standard population for the same age- grouping. First of all, therefore, some system of age-grouping must be decided upon. Let us take first a simple case, that is, one where there are only a few groups. On page 226 were given data for New South Wales, from which the specific death-rates were computed. Let us apply these specific death-rates to the population of Sweden in 1890 which we will take as a standard. This is given in column (5) of Table 60. For age-group 1-19 years the spe- cific rate was 2.78 per 1000; hence, among 398 persons the number of deaths would be 0.398 X 2.78 or 1.11 as given in column (6). And so for the other age-groups. The figures in column (6), therefore, give the number of deaths in each group of the standard thousand of population, and their sum is the total number of deaths in the stanjdard thousand. Hence the death-rate of New South Wales ad- justed to the standard population was 13.44. This is much higher than the general death-rate, which was only 9.85. TABLE 60 ADJUSTED DEATH-RATE FOR NEW SOUTH WALES, 1901 Age-.!roupin years. Population. Number of deaths in one year. Specific death-rate per 1000. Standard age distribution per 1000. Computed deaths per 1000 of total population. (1) (2) (3) (4) (6) (6) 0-1 1-19 20-39 40-59 60 and over 40,500 704,000 614,900 . 256,600 89,800 3,234 1,960 2,251 2,965 5,400 79.88 2.78 4.37 11.56 60.13 25.5 398.0 269.6 192.3 114.6 2.04 1.11 1.18 2.22 6.89 Total 1,605,800 15,810 9.85 1000.0 13.44 Why this difference? The answer is found by comparing the age distribution of the people of New South Wales with the assumed standard population. 242 SPECIFIC DEATH-RATES TABLE 61 COMPARISON OF POPULATION DISTRIBUTION OF NEW SOUTH WALES WITH THAT OF SWEDEN IN 1890 New South Wales. Sweden. Number. Per thousand. Per thousand. (1) (2) (3) (4) 0-1 1-19 30-39 40-59 60- 40,500 704,000 514,900 256,600 89,800 24.9 439.0 320.0 160.5 55.6 25.5 398.0 269.6 192.3 114.6 AU Ages 1,605,800 1000.0 1000.0 It will be seen that in New South Wales there were fewer old persons, for whom the specific death-rates are naturally high, but more persons in middle life, for whom the specific death-rates are naturally low. This is an extreme case, but characteristic of a new population built up by immigration. Let us now take a more complicated situation. In 1914 there were 1452 deaths in Cambridge,^ Mass., distributed by age as follows: TABLE 62 DISTRIBUTION OF DEATHS: CAMBRIDGE, MASS., 1914 Age. Num- ber. Age. Num- ber. Age. Num- ber. Age. Num- ber. (1) (2) (1) (2) (1) (2) (1) (2) [0-1] 0-5 5-9 10-14 15-19 [243] 340 20 26 33 20-24 25-29 30-34 35-39 40-44 43 49 62 58 56 45-49 50-54 55-59 60-64 65-69 90 83 73 107 109 70-74 75-79 80-84 85-89 90-94 95-99 110 72 66 33 18 4 » U. S. Mortality Statistics, 1914, p. 264. ADJUSTED DEATH-RATES 243 The Standard Million' will be taken as the standard of population. It is necessary to take an age-grouping which will correspond to this, and find the number of persons in Cambridge in 1914 in each of these groups. There was no census in Cambridge in 1914, but in 1910 the population was 104,839, in 1900 it was 91,886. The estimated popu- lation July 1, 1914, was 110,357. In 1910 the age distri- bution of the people of Cambridge was given by the census. It was as follows (columns 1, 2 and 3) : TABLE 63 PERSONS LESS THAN STATED AGE: CAMBRTOGE, MASS. Age. Actual number of persons in 1910 Per cent. Computed number of persons in 1914. (1) (2) (3) w 1 • 5 10 15 20 25 35 45 65 100 Unknown 2,323 10,802 20,273 29,165 37,095 47,503 66,678 82,404 99,136 104,778 61 2.3 10.4 19.4 27.9 36.4 46.4 64.6 79.6 :95.6 • 99.4 0.6 2,430 11,500 21,400 30,800 40,200 51,200 70,500 88,000 105,700 110,280 77 Total 104,839 100.0 110,357 It may be fairly assumed that the percentages of column 3 for 1910 apply also with no great change to 1914. By multiplying 110,357, therefore, by these percentages we get the following numbers of persons in each group for 1914 (column 4). The figures in column (4) may be redistributed in any 1 See p. 181. 244 SPECIFIC DEATH-RATES desired age-grouping as described on p. 172. In this way the figures in column (2) of the following table were ob- tained : TABLE 64 ADJUSTED DEATH-RATES FOR CAMBRIDGE, MASS. Age-jroup. Estimated ' population in 19H (approximate). Number of deaths in 1914. Specific death-rate per 1000. Standard age distribution per 1000. Computed deaths. (1) (2) (3) (4) (5) (6) 0-4 5-9 10^14 15-19 20-24 25-34 35-44 45-54 55-64 65-74 75- 11,500 9,900. 9,400 9,400 11,000 19,200 17,400 11,600 5,-800 3,100 2,100 340 20 26 33 43 111 114 173 180 219 193 29.5 2.02 2.76 3.51 3.91 5.78 6.53 14.9 31.1 70.6 91.8 114.262 107.209 102.735 99.796 95.946 161.579- 122.849 89.222 59.741 33.080 13.681 0.380 0.217 0.284 0.350 0.374 0.935 0.803 ■ 1.330 ■1.856 2.330 1.246 Total 110,400 1452 13.15 1000.000 13.105 From columns (2) and (3) the specific death-rates are obtained (column 4), and these apphed to the standard age distribution (column 5) give the number of computed deaths in each age- group (column 6). Their sum gives 13.1, which is the death-rate adjusted to the. standard age distribution. We have done all this work to get a result which differs but fractionally from the general, or crude death-rate, i.e., 13.15. Not worth while? Yes, it is if we are to use a death-rate at all. It was only because the age distribution of the Cambridge population happened to be so near that of the standard million that the two death-rates came so close together. In another case the result might be very different. ADJUSTED DEATH-RATES 245 A fair criticism of this last computation would be that the age-groupings below age five and above middle age are too wide, for it is in these groups where the specific death- rates are highest. Dr. Wm. L. Holt, C.P.H. (School of Pubhc Health, Harvard University and Mass. Inst, of Tech.), investigated this subject of grouping and concluded that seven properly selected groups would give results which compared well with those obtained by using the eleven groups of the Standard Million. The author be- lieves that even five well-chosen groups would suffice, but the matter is one which needs free discussion. Certainly something more convenient than the Standard Million is possible. TABLE 65 COMPUTED DEATH-RATES IN BOSTON AND CAM- BRIDGE, 1905 (Computations by Dr. Wm. L. Holt) Boston. Age- Popula- tion. Deatha. Specific deatli-rate. Adjusted rates per 1000. group. Eleven groups. Nine groups. Seven groups. Six groups. (1) (2) (3) w (5) (6) (7) (8) 0-4 5-9 10-14 15-19 20-24 25-34 35-44 45-54 55-64 65-74 75- 52,152 54,091 48,694 47,608 57,421 119,632 95,946 58,810 33,602 16,711 6,413 3128 253 157 218 ,380 1070 1081 1255 1308 1213 937 60.1 4.68 3.22 4.58 6.61 8.95 11.28 21.4 38.9 72.6 146.0 6.850 0.501 0.331 I 0.457 ( 0.634 1.441 1.388 1.910 2.325 2.403 f 1.980) 6.850 0.501 0.785 ■ '0.634 1.441 1 1.388 f 1.910 2.325 4.802 6.850 1.963 2.840 1.9101 2.325S 2.403 1.980 6.850 1.963 2.840 4.135 2.403 1.980 Total 20.220 20.636 20.271 20.171 (Continued on next page.) 246 SPECIFIC DEATH-RATES Cambridge. Age- Popula- tion. Deaths. Specific death-rate. Adjusted rates per 1000. group. Eleven groups. Seven groups. (1) (2) (3) (4) (5) (6) 0-4 5-9 10-14 15-19 20-24 25-34 35-44 45-54 55-64 65-74 75- 9,088 9,096 8,078 8,512 10,789 18,671 14,148 9,267 5,628 2,864 1,251 412 27 20 34 51 130 130 133 165 155 179 45.3 2.96 2.48 4.00 4.72 6.97 9.19 14.35 29.4 54.1 143.2 5.176 0.317-1 0.255 1 0.399 ( 0.452 J 1.125 1 1.127 i 1.280 1.755 1.790 1.950 5.176 : 1.468 2.253 1.280 1.755 1.790 1.950 Total 15.626 15.672 Examples of death-rates adjusted to a standard popu- lation. — The U. S. Mortality Statistics give numerous examples of death-rates adjusted to the Standard Million. , Let us first of all compare Cambridge, Mass., and Chicago, lU. TABLE 66 City. Death-rate, 1911. Gross. Adjusted. (1) (2) (3) Cambridge, Mass. Chicago, 111. 15.2 14.5 15.4 16.4 Here again we see that adjustment of the Cambridge rate changes it but little, '^ while that of Chicago was increased by 1.9, making the adjusted rate higher than that of Cambridge. Why? ' In this computation sex as well as age was considered. EXAMPLES OF ADJUSTED DEATH-RATES 247 In every instance in the following table the adjusted death-rate exceeded the gross death-rate, the excesses ranging from 1 to 18 per cent and averaging 8.4 per cent. As would naturally be expected the differences were less in the older cities of the East than in the newer cities of the West, but New York, Pittsburgh and a few others witih large numbers of recent immigrants were exceptions to this rule. The following figures illustrate this: TABLE 67 COMPARISON OF GROSS AND ADJUSTED DEATH-RATES FOR CERTAIN CITIES Death-rates per 1000. City. Gross. Adjusted. Difference. (1) (2) (3) (4) New Haven, Conn. 16.7 17.7 1.0 Boston, Mass. 17.1 17.9 0.8 New York, N. Y. 15.2 17.2 2.0 Pittsburgh, Pa. 14.9 16.9 2.0 Cleveland, Ohio 13.8 15.3 1.5 Chicago, 111. 14.5 16.4 1.9 Spokane, Wash. 11.6 13.7 2.1 Seattle, Wash. 8.8 10.4 1.6 Adjustment to a standard population tends to equalize the death-rates in different places. The rural districts of New England contain a large percentage of persons of ad- vanced age. This tends to cause the adjusted rate to be lower than the gross rate. Taking figures for entire states we find this to be true, as the following figures show. In the western 'states this difference is not as marked, as they have not suffered by emigration as have the New England States. 248 SPECIFIC DEATH-RATES TABLE 68 COMPARISON OF GROSS AND ADJUSTED DEATH-RATES FOR CERTAIN STATES Death-rates per 1000. state. . Gross. Adjusted. Dilference. (1) (2) (3) (4) Massachusetts 15.3 15.0 -0.3 New Hampshire 17.1 14.2 -2.9 Maine 16.1 13.0 -3.1 Connecticut 15.4 14.8 -0.6 Indiana 12.9 12.3 -0.6 Kentucky 13.2 13.4 0.2 Michigan 13.2 12.4 -0.8 Minnesota 10.5 10.8 0.3 Missouri 13.1 13.1 0.0 Montana 10.2 11.6 1.4 The following figures show the relation between the crude and adjusted death-rates for various countries: ADJUSTMENT FOR RACIAL DIFFERENCES 249 TABLE 69 COMPARISON OF GROSS AND ADJUSTED DEATH-RATES FOR CERTAIN COUNTRIES Hatio of Death-rates per 000. adjusted Country. Year. rate to that of Grosa. Adjusted. Difference. England and Wales. (1) (2) (3) w (5) (6) Russia 1896-1898 32.80 28.61 -4.19 166.7 Spain 1900-1902 27.63 26.63 -1.10 154.6 Austria 1899-1901 24.83 23.12 -1.71 134.7 Italy 1900-1902 22.72 20.23 -2.49 117.9 Germany 1901 20.84 19.52 -1.32 113.8 U. S. (Registra- 1900 17.55 18.05 0,50 105.2 tion area) Scotland 1900-1902 17.91 17.61 -0.30 102.6 France 1900-1902 20.80 17.50 -3.30 102.0 England & Wales 1900-1902 17.16 17.16 0.00 100.0 Switzerland 1899-1901 18.22 16.86 -1.36 98.3 Belgium 1899-1901 18.53 16.78 -1.75 97.8 Ireland 1900-1902 18:27 16.59 -1.68 96.7 Netherlands 1898-1900 17.32 15.40 -1.92 89.7 Sweden 1899-1901 16.78 13.88 -2.90 80.9 New South Wales 1900-1902 11.72 13.10 1.38 76.3 Victoria 1900-1902 13.12 13.08 -0.04 76.2 South Australia 1900-1902 11.02 11.73 0.71 68.4 Adjustment for racial differences. — In certain parts of the United States, especially in the South, the crude death-rates are absolutely useless for purposes of com- parison unless allowance is made for the number of colored persons at different ages. The specific death-rates for col- ored persons are higher at all ages than for white persons, as the following figures for the U. S. registration states in 1900 show: 250 SPECIFIC DEATH-RATES TABLE 70 COMPARISON OF SPECIFIC DEATH-RATES FOR WHITE AND COLORED PERSONS Death-rates per 1000 (exclusive of still-births). Ratio of colored Age-group (both sexes)-. to white death- rate. Native white. Colored. > (1) (2) (3) (4) 0-4 49.1 106.4 2.17 5-9 4.5 8.9 1.98 10-14 2.9 9.0 3.10 15-19 4.7 11.4 2.43 20-24 6.8 11.6 1.71 25-34 8.2 12.2 1.49 35-44 9.6 15.0 1.56 45-54 12.7 24.5 1.93 55-64 22.6 42.5 1.88 65-74 50.4 69.5 1.38 75 138.5 143.3 1.03 Crude death-rate 16.5 25.0 1.52 The following figures for the cities of Washington, Balti- more and New Orleans show the necessity of taking into ac- count these striking differences between the white and colored people: DEATH-RATES FOR PARTICULAR DISEASES 251 TABLE 71 ADJUSTED DEATH-RATES FOR CITIES HAVING LARGE COLORED POPULATIONS Death-rates per 1000 (both sexes), 1911. Gross. Adjusted. Difference. (1) (2) • (3) (4) Washington, D. C. White Colored Total Baltimore, Md. White Colored Total New Orleans, La. White Colored Total 15.5 26.6 18.7 16.2 30.9 18.4 16.6 31.2 20.4 14.6 30.5 18.9 16.7 35.4 19.4 17.5 34.0 21.8 -0.9 3.9 0.2 0.5 4.5 1.0 0.9 2.8 1.4 Death-rates for particular diseases. — Death-rates for particular diseases are computed in the same way as other specific death-rates. The numerator of the ratio is limited to the disease in question. The denominator may be the entire population, oi^it may be confined to some specific part of it. In order to avoid the use of too many decimals it is well to express the death-rates for particular diseases as so many per 100,000 instead of so many per 1000. This practice is becoming universal. The use of 10,000 as a base should be avoided. If all of the deaths from typhoid fever be compared with the total mid-year population, we have the general typhoid fever death-rate of the place. General rates for particular diseases are much used and have practical value. Specific 252 SPECIFIC DEATH-RATES rates in which" deaths from typhoid fever in a given age- group are compared with the population in the same age- group are sometimes computed, but are useful only when the numbers involved are large. Special death-rates. — In epidemiological studies it is necessary to compute death-rates in all sorts of ways, to separate the people into classes according to where and how they Uve, according to their occupation or their exposure to certain risks. This causes us to deal with many special rates. In studying birth statistics we may find the general birth-rate, by taking the ratio between the number of births and the total population. But we may also desire to find the ratio between births and women of child- bearing age, or between births and married women of child-bearing age. In interpreting all of these many sorts of rates and ratios the principles already outlined hold good. We must see that the data compared are logically comparable, that there are no concealed classifications and that the rules of, pre- cision are not violated. EXERCISES AND QUESTIONS 1. Are the changes in age-composition from decade to decade in Massachusetts sufficient to explain a considerable part of the faUing general death-rate of the state, assuming the specific death-rates by ages to remain constant? 2. Compute the specific death-rates by sex and age-groups for three Massachusetts cities for 1910, obtaining data from the census and registration reports. 3. Compare the specific death-rates by age-groups for white and colored persons in some southern city for some selected year. 4. Adjust the death-rate of some western city in 1910 to the Swedish standard of population. EXERCISES AND QUESTIONS 253 6. Repeat this computation using the standard million as a basis of adjustment. 6. Select from the Mortality Reports examples of the need of adjust- ment of death-rates of cities for purposes of comparison. 7. Adjust the death-rates of some selected city to the basis of the Standard Million for 1915, 1910, 1905, 1900 and as far back as record can be obtained. CHAPTER VIII CAUSES OF DEATH Nosography. — The description and systematic classifi- cation of disease is called nosography. The word is derived from the Greek word nosos, which means sickness, or disease. (The word is pronounced noss'ography, not noze-ography.) Nosology. — The science of classifying disease is similarly called nosology. The purpose of nosology. — ■ At one time it was thought that a knowledge of nosology was necessary for the practical treatment of disease. Many systems were proposed and abandoned. Today the idea has few, if any, supporters. Nosology is of great importance as one of the foimdation stones of our modem structure of vital statistics. Without uniform definitions of disease which furnish us with adequate statistical units our statistics would be worthless. It is because of changes in our definitions of disease that we fall into so many errors in comparing past conditions with those of the present day. Such changes are inevitable as medical science advances, but they ought to be universally recognized when they are made. Dr. WilUam Farr was one of the first to recognize the importance of "statistical nosology." History of nosography. — Nosography emerged from its former chaotic condition in 1893 when the use of the Inter- national Classification of Diseases and Causes of Death was begun. This was due chiefly to the labors of Dr. Jacques Bertillon of France. 254 INTERNATIONAL LIST OF THE CAUSES OF DEATH 255 In 1853 Dr. William Farr and Dr. Marc d'Espine, of Geneva, had been selected by the First Statistical Congress, which met at Brussels, to present a report on the subject. The list of diseases reported by them was adopted in Paris in 1855, in Vienna in 1857, and was translated into six languages. It was revised several times between 1864 and 1886. In 1893 the International Statistical Institute, the successor of the Statistical Congress, met in Chicago and adopted this list with some changes. Provision was made for decennial revisions by an International Commission, and such revisions were made in Paris in 1900 and again in 1909, the latter a year earlier in order that the new list might be used in the censuses of 1910. The present list is intended to stand un- changed until 1919. In 1898 the International List was endorsed by the American Public Health Association. Eng- land adopted the Hst in 1911. It is used by all English and Spanish speaking countries, but it is not yet universal. A few of our own states do not follow it exactly, namely: " Alabama, New Hampshire, New Mexico, Rhode Island and West Virginia. International list of the causes of death. — In 1911 the L . S. Bureau of the Census published a Manual of 297 pages, being a revision of a former manual published in 1902. This list is the present standard for the United States and has come to be almost universally used. This manual is very complete. It gives the standard list of the causes of death, with synonyms, and is indexed alphabetically as weU as according to the chosen classification. The Bureau of the Census also publishes a Physician's Pocket Reference to the International List of the Causes of Death, whicli can be obtained without charge by anyone who makes request of the Director of the Census, Washington, D. C. This is a small pamphlet of 28 pages, vest pocket size. 256 CAUSES OF DEATH Classification of diseases in 1830. — Dr. Farr classified diseases as follows: Class I. Epidemic, Endemic and Contagious diseases (Zymotici). Order 1 . Miasmatic diseases, — ■ small-pox, ague, etc. Order 2. Enthenic diseases, — syphilis, glanders. Order 3. Dietetic diseases, — scurvy, ergotism. Order 4. Parasitic diseases. Class II. Constitutional Diseases (Cachectici) . Order 1. Diathetic diseases, — gout, dropsy, cancer, etc. Order 2. Tubercular diseases, — scrofula, consumption. Class III. Local Diseases (Monorganici). Order 1. Diseases of the brain. Order 2. Diseases of the circulation. Order 3. Diseases of respiration. Order 4. Diseases of digestion. Order 5. Diseases of the urinary system. Order 6. Diseases of reproduction. Order 7. Diseases of locomo'.ive system. Order 8. Diseases of integumentary system. Class IV. Developmental Diseases (Metamorphid). Class V. Violent Deaths or Diseases (Thanatici). It is extremely interesting to study this list in detail as given in the 16th Annual Report of the Registrar General of England, Appendix, pp. 71-79. Present classification. — The list recognizes 189 causes of death, which are divided into fourteen classes. It is not claimed that these are all of the possible causes. For con- venience of reference and tabulation each of these diseases is given a number. The following is the list as given in the Physician's Pocket Reference. It is recommended that only the names printed in heavy type be used. The terms in italics are indefinite or otherwise undesirable. An abridged list of causes of death useful for annual reports of health departments may be found on page PRESENT CLASSIFICATION 257 INTERNATIONAL LIST OF CAUSES OF DEATH (I. — General Diseases) 1. Typhoid fever. 2. Typhus fever. 3. Relapsing fever. [Insert "(spirillum)."] 4. Malaria. 5. Smallpox. 6. Measles. 7. Scarlet fever. 8. Whooping cough. 9. Diphtheria and crou-p. 10. Influenza. 11. Miliary fever. [True Febris miliaris only.] 12. Asiatic cholera. 13. Cholera nostras. 14. Dysentery. [Amebic? Bacillary? Do not report ordinary diarrhea and enteritis (104, 105) as dysentery.] 15. Plague. 16. Yellow fever. 17. Leprosy. 18. Erysipelas. [State also cause; see Class XIII.] 19. Other epidemic diseases: Mumps, German measles, Chicken-pox, Rocky Mountain spotted (tick) fever. Glandular fever, etc. 20. Purulent infection and septicemia. [State also cause; see Classes VII and XIII especiaUy.] 21. Glanders. 22. Anthrax. 23. Rabies. 24. Tetanus. [State also cause; see Class XIII.] 25. Mycoses. [Specify, as Actinomycosis of lung, etc.] 36. Pellagra. 27. Beriberi. 28. Tuberculosis of the lungs. 29. Acute miliary tuberculosis. 30. Tuberculous meningitis. 258 CAUSES OF DEATH 31. Abdominal tuberculosis. 32. Pott's disease. [Preferably Tuberculosis of spine.] 33. White sweUings. [Preferably Tuberculosis of joint.] 34. Tuberculosis of other organs. [Specify organ.] 35. Disseminated tuberculosis. [Specify organs affected.] 36. Rickets. 37. Syphilis. 38. Gonococcus infection. 39. Cancer i of the buccal cavity. [State part.] 40. Cancer ' of the stomach, liver. 41. Cancer ' of the peritoneum, intestines, rectum. 42. Cancer ' of the female genital organs. [State organ.] 43. Cancer ' of the breast. 44. Cancer ' of the skin. [State part.] 45. Cancer ' of other or unspecified organs. [State organ.] 46. Other tumors (tumors of the female genital organs excepted.) [Name kind of tumor and organ affected. Malignant?] 47. Acute articular rheumatism. [Always state " rheumatism " as acute or chronic] 48. Chronic rheumatism [preferably Arthritis deformans] and gout. 49. Scurvy. 50. Diabetes. [Diabetes mellitus.] 51. Exophthalmic goiter. 52. Addison's disease. 53. Leukemia. 54. Anemia, chlorosis. [State form or cause. Pernicious?] 65. Other general diseases: Diabetes insipidus, Purpura haemorrhagica, etc. 56. Alcoholism (acute or chronic). 57. Clironic lead poisoning. [State cause. Occupational?] 68. Other chronic occupational poisonings. [State exact name of poison, whether the poisoning was chronic and due to oc- cupation, and also please be particularly careful to see that the Special Occupation and Industry are fiilly stated. If ' " Cancer and other malignant tumors." Preferably reported as Carcinoma of , Sarcoma of , Epithelioma of , etc., stating the exact nature of the neoplasm and the organ or part of the body first affected. PRESENT CLASSIFICATION 259 the occupation stated on the certificate is not that in which the poisoning occurred, add the latter in connection with the statement [of cause of death, e.g., " Chronic occupational phosphorus necrosis (dipper, match factory, white phos- phorus).'' Give full details, including pathologic conditions contributory to death. Following is a List of Industrial Poisons (BuU. Bureau of Labor, May, 1912) to which the attention of physicians practicing in industrial communities should be especially directed: Acetaldehyde, Acridine, Acrolein, Ammonia, Amyl acetate, Amyl alcohol, Aniline, Aniline dyestuffs [name], Antimony compounds [name], Arsenic compounds [name], Arseniureted hydrogen. Benzine, Benzol, Carbon dioxide. Carbon disulphide, Carbon monoxide (coal vapor, il- luminating water gas, producer gas), Chloride of lime, Chlorine, Chlorodinitrobenzol, Chloronitrobenzol, Chromium compounds [name], Cyanogen compounds [name], Diazomethane, Dimethyl sulphate, Dinitrobenzol, Formaldehyde, Hydrochloric acid, Hydrofluoric acid, Lead (57), Manganese dioxide, Mercury, Methyl alcohol, Methyl bromide, Nitraniline, Nitrobenzol, Nitroglycerin, Nitronaphthalene, Nitrous gases, Oxalic acid. Petroleum, Phenol, Phenylhydrazine, Phosgene, Phosphorus (yellow or white), Phosphorus sesquisulphide, Phosphureted hydrogen, Picric acid. Pyridine, Sulphur chloride, Sulphur dioxide, Sulphureted hydrogen. Sulphuric acid, Tar, Turpentine oil. Not aU substances in the preceding Ust are likely to be reported as causes of death, but the physician should be familiar with it in order to recognize, and to report, if required, oases of illness, and 260 CAUSES OF DEATH should also be on the alert to discover new forms of industrial poi- soning not heretofore recognized. In the Bulletin cited full details may be found as to the branches of industry in which the poisoning occurs, mode of entrance mto the body, and the symptoms of poi- soning. Attention should also be called to industrial infection, e.g., Anthrax (22), and the influence of gases and vapors, dust, or unhygienic industrial environment. 59. Other chronic poisonings: Chronic morphinism, Chronic cocainism, etc. (II. — Diseases op the Nervous System and of the Organs op Special Sense) 60. Encephalitis. 61. Meningitis: Cerebrospinal fever or Epidemic cerebrospinal meningitis, Simple meningitis. [State cause;] 62. Locomotor ataxia. 63. Other diseases of the spinal cord: Acute anterior poliomyelitis. Paralysis agitans. Chronic spinal muscular atrophy, Primary lateral sclerosis of spinal cord. Syringomyelia, etc. 64. Cerebral hemorrhage, apoplexy. 65. Softening of the brain. [State cause.] 66. Paralysis without specified cause. [State form or cause.] 67. General paralysis of the insane. 68. Other forms of mental alienation. [Name disease causing death. Form of insanity should be named as contributory cause only, unless it is actually the disease causing death.] 69. Epilepsy. 70. Convulsions (nonpuerperal). [State cause.] 71. Convulsions of infants. [State cause.] 72. Chorea. 73. Neuralgia and neuritis. [State cause.] 74. Other diseases of the nervous system. [Name the disease.] 75. Diseases of the eyes and their annexa. [Name the disease.] 76. Diseases of the ears. [Name the disease.] PRESENT CLASSIFICATION 261 (III. — Diseases of the Circulatory System) 77. Pericarditis. [Acute or chronic; rheumatic (47), etc.] 78. Acute endocarditis. [Cause? Always report " endocarditis " or " myocarditis " as acute or chronic. Do not report when mere terminal condition.] Acute myocarditis. 79. Organic diseases of the heart: [Name the disease.] Chronic valvular disease, [Name the disease.] Aortic insufficiency, Chronic endocarditis, [See note on (78).] Chronic myocarditis, [See note on (78).] Fatty degeneration of heart, etc. 80. Angina pectoris. 81. Diseases of the arteries, atheroma, aneurism, etc. 82. Embolism and thrombosis. [State organ. Puerperal (139)7] 83. Diseases of the veins (varices, hemorrhoids, phlebitis, etc.). 84. Diseases of the lymphatic system (lymphangitis, etc.). [Cause? Puerperal?] 85. Hemorrhage; other diseases of the circulatory system. [Cause? Pulmonary hemorrhage from Tuberculosis' of limgs (28)? Puer- peral?] (IV. — Diseases op the Respiratory System) 86. Diseases of the nasal fossae. [Name disease.] 87. Diseases of the larynx. [Name disease. Diphtheritic?] 88. Diseases of .the thyroid body. [Name disease.] 89. Acute bronchitis. 1 [Always state as acute or chronic. Was it 90. Chronic bronchitis. J tuberculous?] 91. Bronchopneumonia. [If secondary, give primary cause.] 92. Pneumonia. [If lobar, report as Lobar pneumonia.] 93. Pleurisy. [Cause? If tuberculous, so report (28).] 94. Pulmonary congestion, pulmonary apoplexy. [Cause?] 95. Gangrene of the lung. 96. Asthma. [Tuberculosis?] 97. Pulmonary emphysema. 98. Other diseases of the respiratory system (tuberculosis excepted). [Such indefinite returns as " Lung trouble," " Pulmonary hem- orrhage," etc., compiled here, vitiate statistics. Tuberculosis of lungs (28)? Name the disease.] 262 CAUSES OF DEATH (V. — Diseases of the Digestive System) 99. Diseases of the mouth and annexa. [Name disease.] 100. Diseases of the pharynx. [Name disease.' Diphtheritic?] Streptococcus sore throat. 101. Diseases of the esophagus. [Name disease.] 102. Ulcer of the stomach. 103. Other diseases of the stomach (cancer excepted). [Name disease. Avoid such indefinite terms as " Stomach trouble," " Dyspepsia," " Indigestion," " Gastritis,'' etc., when used vaguely.] 104. Diarrhea and enteritis (under 2 years). 105. Diarrhea and enteritis (2 years and over). 106. Ankylostomiasis. [Better, for the United States, Hookworm disease or Uncinariasis.] 107. Intestinal parasites. [Name species.] 108. Appendicitis and typhlitis. 109. Hernia, intestinal obstruction. [State form and whether stran- gulated.] Strangulated inguinal hernia (operation), Intussusception, Volvulus, fete. 110. Other diseases of the intestines. [Name disease.] 111. Acute yellow atrophy of the liver. 112. Hydatid tumor of the liver. 113. Cirrhosis of the liver. 114. Biliary calculi. 115. Other diseases of the liver. [" lAver complaint " is not a satis- factory return. ] 116. Diseases of the spleen. [Name disease.] 117. Simple peritonitis (nonpuerperal). [Give cause.] 118. Other diseases of the digestive system (cancer and tuberculosis excepted). [NamS disease.] (Yl. — NONVENEREAL DISEASES OF THE GeNITO-UrINART SySTEM AND AnTIIIXA) 119. Acute nephritis. [State primary cause, especially Scarlet fever, etc. Always state " nephritis " as acute or chronic] 120. Bright's disease. [Better, Chronic interstitial nephritis, Chronic parenchymatous nephritis, etc. Never report mere names of symptoms, as " Uremia," " Uremic coma," etc. See also note on (119).] PRESENT CLASSIFICATION 263 121. Chyluria. 122. Other diseases of the kidneys and annexa. [Name disease.] 123. Calculi of the urinary passages. [Name bladder, kidney.] 124. Diseases of the bladder. [Name disease.] Cystitis. [Cause?] , 125. Diseases of the urethra, urinary abscess, etc. [Name disease. Gonorrheal (38)?] 126. Diseases of the prostate. [Name disease.] 127. Nonvenereal diseases ofthe male genital organs. [Name disease.] 128. Uterine hemorrhage (nonpuerperal). [Cause?] 129. Uterine tumor (noncancerous). [State kind.] 130. Other diseases of the uterus. [Name disease.] Endometritis. [Cause? Puerperal (137)?] 131. Cysts and other tumors of the ovary. [State kind.] 132. Salpingitis and other diseases of the female genital organs. [Name disease. Gonorrheal (38)? Puerperal (137)?] 133. Nonpuerperal diseases of the breast (cancer excepted). [Name disease.] (VII. — The Puerperal State) Note. — The term puerperal is intended to include pregnancy, part\irition, and lactation. Whenever parturition or miscarriage has occurred within one month before the death of the patient, the fact should be certified, even though childbirth may not have contributed to the fatal issue. Whenever a woman of childbearing age, especially if married, is reported to have died from a disease which might have been puerperal, the local registrar should require an expUcit statement from the reporting physician as to whether the disease was or was not puerperal ' in character. The following diseases and symptoms are of this class: Abicess of the breast, Albuminuria, Metrorrhagia, Cellulitis, Nephritis, Coma, Pelviperitonitis, Convulsions, Peritonitis, Eclampsia, Phlegmasia alba dolens. Embolism, Phlebitis, Endometritis, Pyemia, Gastritis, Septicemia, Hemmorrhage (uterine or Sudden death, unqualified), Tetanus, Lymphangitis, Thrombosis, Metritis, Uremia. 264 CAUSES OF DEATH Physicians are requested always to write Puerperal before the above terms and others that might be puerperal in character, or to add in parentheses (Not puerperal), so that there may be no possibility of error in the compilation of the mortality statistics; also to respond to the requests of the local registrars for additional information when, inad- vertently, the desired data are omitted. The value of such statistics can be greatly improved by cordial cooperation between the medical profession'^and the registration officials. If a physician will not write the true statement of puerperal character on the certificate, he may privately communicate that fact to the local or state registrar, or write the number of the International List under which the death should be compiled, e.g., " Peritonitis (137)." 134. Accidents ' of pregnancy: [Name the condition.] Abortion, [Term not used in invidious sense; Criminal abor- tion should be so specified (184).] Miscarriage. Ectopic gestation. Tubal pregnancy, etc. 135. Puerperal hemorrhage. 136. Other accidents ' of labor: [Name the condition.] Caesarean section, Forceps application, Breech presentation, Symphyseotomy, Difficult labor, Rupture of uterus in labor, etc. 137. Puerperal septicemia. 138. Puerperal albtuoinuria and convulsions. 139. Puerperal phlegmasia alba dolens, embolus, sudden death. 140. Following childbirth (not otherwise defined). [Define.] 141. Puerperal diseases of the breast. [Name disease.] (VIII. — Diseases of the Skin and Cellular Tissue) 142. Gangrene. [State part affected. Diabetic (50), etc.] 143. Furuncle. 144. Acute abscess. [Name part affected, nature,- or cause.] 145. Other diseases of the skin and annexa. [Name disease.] 1 In the sense of conditions or operations dependent upon pregnancy or labor, not " accidents " from external causes. ' In the sense of conditions or operations dependent upon pregnancy or labor, not " accidents " from external causes. PRESENT CLASSIFICATION 265 (IX. — Diseases of the Bones and of the Obqans of Locomotion) 146. Diseases of the bones (tuberculosis excepted) : [Name disease.] Osteoperiostitis, [Give cause.] Osteomyelitis, Necrosis, [Give cause.] Mastoiditis, etc. [Following Otitis media (76)?] ■ 147. Diseases of the joints (tuberculosis and rheumatism excepted). [Name disease; always specify Acute articular rheumatism (47), Arthritis deformans (48), Tuberculosis of — joint (33), etc., when cause is known.] 148. Amputations. [Name disease or injury requiring amputation, thus permitting proper assignment elsewhere.] 149. Other diseases of the organs of locomotion. [Name disease.] (X. — Malformations) 150. Congenital malformations (stillbirths not included) : [Do not " include Acquired hydrocephalus (74) or Tuberculous hydro- cephalus (Tuberculous meningitis) (30) under this head.) Congenital hydrocephalus. Congenital malformation of heart. Spina bifida, etc. (XI. — Diseases op Early Infanct) 151. Congenital debility, icterus, and sclerema: [Give cause of debility.] Premature birth, Atrophy, [Give cause.]. Marasmus, [Give cause.] Inanition, etc. [Give cause.] 152. Other diseases peculiar to early infancy: Umbilical hemorrhage, Atelectasis, Injury by forceps at birth, etc. 153. Lack of care. (XII. — Old Age) 154. Senility. [Name the disease causing the death of the old person.] 266 CAUSES OF DEATH (XIII. — Affections Produced by External Causes) Note. — Coroners, medical examiners, and physicians who certify to deaths from violent causes, should always clearly indicate the funda- mental distinction of whether a death was due to Accident, Suicide, or Homicide; and then state the Means or instrument of death. The qualification " probably " may be added when necessary. 155. -Suicide by poison. [Name poison.] 156. Suicide by asphyxia. [Name means of death.] 157. Suicide by hanging or strangulation. [Name means of stran- gulation.] 158. Suicide by drowning. 159. Suicide by firearms. 160. Suicide by cutting or piercing instruments. [Name instrument.] 161. Suicide by jumping from high places. [Name place.] 162. Suicide by crushing. [Name means.] 163. Other suicides. [Name means.] 164. Poisoning by food. [Name kind of food.] 165. Other acute poisonings. [Name poison; specify Accidental.] 166. Conflagration. [State fully, as Jumped from Window of burning dwelUng, Smothered — biuning of theater, Forest fire, etc.] 167. Bums (conflagration excepted). [Includes Scalding.] 168. Absorption of deleterious gases (conflagration excepted) : Asphyxia by illimiinating gas (accidental). Inhalation of (accidental), [Name gas.] Asphyxia (accidental), [Name gas.] Suffocation (accidental),- etc. [Name gas.] 169. Accidental drowning. 170. Traumatism by firearms. [Specify Accidental.] 171. Traumatism by cutting or piercing instruments. [Name instru- ment. Specify Accidental.] 172. Traumatism by fall. [For example. Accidental fall from window.] 173. Traumatism in mines and quarries: Fall of rock in coal mine. Injury by blasting, slate quarry, etc. 174. Traumatism by machines. [Specify kind of machine, and if the Occupation is not fully given under that head, add sufficient to show the exact industrial character of the fatal injury. Thus, Crushed by passenger elevator; Struck by piece of emery wheel (knife grinder) ; Elevator accident (pile driver), etc.] ir-KKSKJNT UbASSlFlUATION ^iOV 175. Traumatism by other crushing: Railway collision, Struck by street car, Automobile accident, Rim ove by dray. Crushed by earth in sewer excavation, etc. 176. Injuriesby animals. [Name animal.] 177. Starvation. [Not " inanition " from disease.] 178. Excessive cold. [Freezing.] 179. Excessive heat. [Sunstroke.] 180. Lightning. 181. Electricity (Ughtning excepted). [How? Occupational?] 182. Homicide by firearms. 183. Homicide by cutting or piercing instruments. [Name instru- ment.] 184. Homicide by other means. [Name means.] 185. Fractures {cause not specified). [State means of injury. The nature of the lesion is necessary for hospital statistics but not for general mortality statistics.] 186. Other external causes: Legal hanging, Legal electrocution. Accident, injury, or froMraaJisml (unqualified). [State Means of injiuTT.] (XIV. — Ill-Defined Diseases) Note. — If physicians will familiarize themselves with the nature and purposes of the International List, and will cooperate with the registration authorities in giving additional inform^ion so that returns can be properly classified, the number of deaths compiled under this group will rapidly diminish, and the statistics will be more creditable to the office that compiles them and more useful to the medical pro- fession and for sanitary purposes. 187. Ill-defined organic disease: Dropsy, Ascites, etc. [Name the disease of the heart, liver, or kidneys in which the dropsy occurred.] 188. Sudden death. [Give cause. Puerperal?] 268 CAUSES OF DEATH 189. Cause of death not specified or ill-defined. [It may be extremely difficult or impossible to determine definitely the cause of death in some cases, even if a post-mortem be granted. If the physi- cian is absolutely unable to satisfy himself in this respect, it is better for him to write Unknown than merely to guess at the cause. It will be helpful if he can specify a Uttle further, as Unknown disease (which excludes ejrtemal causes), or Unknown chronic disease (which excludes the acute infective diseases), etc. Even the ill-defined causes included under this head are at least useful to a hmited degree, and are preferable to no attempt at statement. Some of the old "chronics," which well-informed physicians are coming less and less -to use, are the following: Asphyxia; Asthenia; Bilious fever; Cachexia; Catarrhal fever; Collapse; Coma; Congestion; Cyanosis; De- bility ; Delirium; Dentition; Dyspnea; Exhaustion; Fever; Gastric fever; HEART FAILURE; Laparotomy; Marasmus; Paralysis of the heart; Surgical shock; and Teething. In many cases so reported the physician could state the disease (not mere symptom or condition) causing death.] PRESENT CLASSIFICATION 269 LIST OF UNDESIRABLE TERMS Undesibable Term. (It is understood that the term criticised is in the exact form. given below, without further ex- planation or qualification.) Reason Why Undesirable, and SuGGEsxiON fob More Definite Statement of Cause of Death.. (1) (2) ' Abscess," '* Abscess of brain,' " Abscess of lung," etc. * Accident,*' " Injury," '* External causes," " Violence." Also more specific terms, as " Drown- ing," " GuThshot," which might be either accidental, suicidal, or homicidal. * Anasarca" " Ascites." * Atrophy," " Asthenia," " Debil- ity," " Decline," " Exhaustion," " Inanition," " Weakness," and other vague terms. * Blood poisoning " . ' Cancer," " Carcinoma," cornea," etc. ' Sar- ' Catarrh " , ' Cardiac insufficiency," " Cardiac degeneration," " Cardiac weak- ness," etc. ' Cardiac dilatation " ' Cellulitis " * Cerebrospinal meningitis." ' Congestion,"" Congestion of bow- els," " Congestion of the brain," " Congestion of kidneys," " Con- gestion of lungs," etc. WiEis it tuberculous or due to other infection? Trau- matic? The return of " Abscess," unqualified, is worthless. State cause (in which case the fact of " abscess " may be quite unimportant) and loca- tion. Impossible to classify satisfactorily. Always state (1) whether Accidental, Suicidal, or Homicidal; and (2) Means of injury {e.g., Railroad accident). The lesion (e.g.. Fracture of skull) may be added, but is of secondary importance for general mortal- ity statUtics. See '* Dropsy." Frequently cover tuberculosis and other definite causes. Name the disease causing the condition. See "Septicemia." Syphilis? In all cases the organ or part first affected by cancer should be specified. Term best avoided, if possible. See " Heart disease " and " Heart failure. Do not report when a mere terminal condition. State cause. See " Abscess," " Septicemia." See "Meningitis." Alone, the word " congestion " is worthless, and in combination it is almost equally undesirable. If the disease amounted to inflammation, use the proper term (lobar pneumonia, chronic nephritis, enteritis, etc.); merely passive congestion should not be reported as a. cause of death. State the primary cause. 270 CAUSES OF DEATH LIST OF UNDESIRABLE TERMS (Continued) Undesirable Term. Reason Why Undesirable, and Suggestion for More Definite Statement of Cause of Death. (1) (2) * Convulsions," " Eclampsia," " Fit," or " Fits." ' Ctouv " - * Dentition" " Teething " . ' Disease," " TrotAle," or " Com- plaint " of [any organ], e.g., " Lung troi^le," " Kidney com- plaint," " Disease of brain," etc. ' Dropsy ' ' Edema of IxtngB ' ''Fever" ' Fracture," " Fracture of skull,' etc. * Gastritis," " Gastric catarrh,^ *' Acute indigestion." ' It is hoped that this indefinite term [" Convul- sions "] will henceforth be restricted to those cases in which the true cause of that symptom can not be ascertained. At present more than eleven per cent of the total deaths of infants under one year old are referred to ' convulsions ' merely." — Reg- istrar-General. "Fit. — This ia an objectionable t«rm; it is indiscriminately applied to epilepsy, convulsions, and apoplexy in difTerent parts of the country." — Dr. Farr, in First Rep. Reg.-Gen.,lSZ9. " Croup " is a most pernicious term from a public health point of view, is not contained in any form in the London or Bellevue Nomenclatures, and should be entirely disused. Write Diphtheria when this disease is the cause of death. State disease causing death. Name the disease, e.g.. Lobar pneumonia, Tuber- culosis of lungs. Chronic interstitial nephritis. Syphilitic gumma of brain, etc. " ' Dropsy ' should never be returned as the cause of death without particulars as toits probable origin, e.g., in disease of the heart, liver, kidneys, etc.'* — Registrar-General. Name the disease causing (the dropsy and) death. Usually terminal. condition. Name the disease causing the Name the disease, as Typhoid fever. Lobar pneu- monia, Malaiia, etc., in which the " fever " occurs. Indefinite; the principle of classification for general mortality statistics is not the lesion but (1) the nature of the violence that produced it (Acciden- tal, Suicidal, flomiddal), and (2) the Means of injury. Frequently worthless as a statement of the actual cause of death; the terms should not be loosely used to cover almost any fatal affection with irri- tation of stomach. Gastroenteritis? Acute or chronic, and cause? PRESENT CLASSIFICATION 271 LIST OF UNDESIRABLE TERMS (Continued) Undesirable Tehm, Reason Wht Undesirable, and Suooestion for More Definite Statement of Cahstc op Death. (1) (2) 'General decay, etc.. ' Heart disease," " Heart trouble," even " Organic heart trouble." ' Heart failure,'' " Cardiac weak- ness," " Cardiac asthenia,' •* Cardiac exhaustion," " Paraly- sis of the heart, ' etc. ' Hemorrhage," " Hemoptysis," " Hemorrhage of lungs." * Hydrocephalus ' ' Hysterectomy *' ' Infantile asthenia," *' Infantile atrophy," '* Infantile debility," " Infantile marasmus," etc. * Infantile paralysis " * Inflammation * * Laparotomy " . See " Old age." The exact form of the cardiac afifection, bs Mitral legurgitationj Aoitic stenosiS; or, less precjsely, as Valvular heart disease, should be stated. " Heart failure " is a recognized synonym, even among the laity, for ignoranceof the cause of death on the part of the physician. Such a return is for- bidden by law in Connecticut. If the physician can make no more definite statement, it must be compiled among the class of ill-defined diseases {not under Organic heart diseased . Frequently mask tuberculosis or deaths from in- juries (traumatic hemorrhage), Puerperal hem- orrhage, or heniorrha.g,e after operation for various conditions. What was the cause and location of the hemorrhage? If from violence, state fully (p. U). "It is desirable that deaths from hydrocephalus of tuberculous origin should be definitely assigned in the certificate to Tuberculous meningitis, so as to distinguish them from deaths caused by simple infiammation or other disease of the brain or its membranes. Congenital hydrocephalus shonid always be returned as such." General. See "Operation." See *'Atrophy.'' This term is sometimes used for paralysis of infants caused by i strumental delivery, etc. The im- portance of the disease in its recent endemic and epidemic prevalence in the United States makes the exact and unmistakable expressions Acute an- terior poliomyelitis or Infantile paralysis (acute anterior poliomyelitis) desirftble. Of what organ or part of the body? Cause? See "Operation." 272 CAUSES OF DEATH LIST OF UNDESIRABLE TERMS (Continued) Undesir\ble Term. Reason Why Undesirable, and Suggestion for More Definite Statement op Cause of Death. (1) (2) ' Malignant,' ' Malnutrition ' ' Malignant dis- * Marasmus " * Meningitis,** " Cereal meningv- tia," " Cerebrospinal meningi- tis," " Spinal meningitis." * Natural causes " ' Old age," " Senility," etc.. ' Operation," " Surgical opera- tion," " Surgical shock," " Am- putation," " Hysterectomy," " Laparotomy " etc. Should be restricted to use as qualification for neo- plasms; see Tumor. See " Atrophy" This term covers a multitude of worthless returns, many of which could be made definite and useful by giving the name of the disease causing the ' ' ma- rasmus " or wasting. It has been dropped from the English Nomenclature since 1885 (" Maras- mus, term no longer used "). The Bellevue Hos- pital Nomenclature also omits this term. Only two terms should ever be used to report deaths from Cerebrospinal fever, synonym. Epidemic ceiebrospinal meningitis, and they should be written as above and in no other way. It matters not in the use of the latter term whether the disease be actually epidemic or not in the locality. A single sporadic case should be ao reported. The first term (Cerebrospinal fever) is preferable be- cause there is no apparent objection to its use for any number of cases. No one can intelligently classify such returns as are given in the margin. Mere terminal or symptomatic meningitis should not be entered at all as a cause of death; name the disease in which it occurred. Tuberculous men- ingitis should be reported as such. This statement eliminates external causes, but is otherwise of little value. What disease (prob- ably) caused death ? Too often used for deaths of elderly persons who suc- cumbed to a definite disease. Name the disease causing death. All these are entirely indefinite and unsatisfactory — unless the surgeon desires his work to be held primarily responsible for the death. Name the disease, abnormal condition, or form of 'eternal violence (Means of death; accidental, suicidal, or homicidal?), for which the operation was per- formed. If death was due to an anesthetic (chlo- roform, ether, etc.), state that fact and the name of the anesthetic. PRESENT CLASSIFICATION LIST OF UNDESIRABLE TERMS (Continued) 273 Undesirable Term. Reason Why Undesirable, and Suggestion fob More Definite Statement of Cause of Death. (1) (2) ' Paralysis,^* " General paralysis," " Paresis," *' General paresis," * etc. ' Peritonitis *\ ' Pneumonia/ monia." " Typhoid pneu- The vague use of these terms should be avoided, and the precise form stated, as Acute ascending paral- ysis. Paralysis agitans. Bulbar par^ysis, etc. Write GenerEil paralysis of the insane in full, not omitting any part of the name; this is essential for satisfactory compilation of this cause. Distin^ guish Paraplegia and Hemiplegia; and in the latter, when a sequel of Apoplexy or Cerebral hemorrhage, report the primary cause. " Whenever this condition occurs — either as a con- sequence of Hernia, Perforating ulcer of the stomach or bowel [Typhoid fever?!. Appendicitis, or] Metritis (puerperal or otherwise), or else as an extension of morbid processes from other organs [Name the disease], the fact should be mentioned in the certificate." — Registrar-General. Always specify Puerperal peritonitis in cases re- sulting from abortion, miscarriage, or labor at full term. Always state if due to tuberculosis or cancer. When traumatic, report means of injury. and whether accidental, suicidal, or homicidal. " Pneumonia," without qualification, is indefinite; it should be clearly stated either as Bronchopneu- monia or Lobar pneumonia. The term Croup- ous pneumonia is also clear. " The term ' Ty- phoid pneumonia ' should never be employed, as it may mean either Enteric fever [Typhoid tegrei] with pulmonary complications, on the one hand or Pneumonia with so-called typhoid symptoms on the other. ' '. — Registrar-General. When lobar pneu- monia or bronchopneumonia occurs in the course of or following a disease the primary cause should be entered first, with duration, and the lobar pneumonia or bronchopneumonia be entered be- neath as the contributory cause, with, duration. Do not report " Hypostatic pneumonia " or other mere terminal conditions as causes of death when the disease causing death can be ascertained. 274 CAUSES OF DEATH LIST OF UNDESIRABLE TERMS (Continued) Undesirable Term. Reason Why Undesirable, and Suggestion fob More Definite Statement of Cause of Death. (1) ' Ptomain poisoning " *' Autoin- toxication" " Toxemia,*' etc. ' Pulmonary congestion,*' ** Pul- monary hemorrhage," ^Pyemia " . ' Septviemia," " Sepsis," " Sep- tic infection," etc. ' Shock " (poat-operative) . ' Specific " ' Tabes meeenterica" " Tabes ' 'Teething"... * Toxemia" . . ' Tuberculosis (2) These terms are used \ery loosely and it is impos- sible to compile statistics of value unless greater precision can be obtained. They should not be used when merely descriptive of symptoms or con- ditions arising in the course of diseases, but the disease causing death should alone be named. " Ptomain poisoning " should be restricted to deaths resulting from the development of putre- factive alkaloids or other poisons in food, and the food should be named, as Ptomain poisoning (mussels), etc. See " Congestion" " Hemorrhage." See " Septicemia." Always state cause of this condition, and, if local- ized, pait affected. Puerperal? Traumatic (see p. ID? See "Operation." The word specific should never be used without further explanation. It may signify syphilitic, tuberculous, gonorrheal, diphtheritic, etc. Name the disease. " The use of this term [" Tabes mesenterica "] to de- scribe tuberculous disease of the peritoneum or in- testines should be discontinued, as it is frequently used to denote various other wasting diseases which are not tuberculous. Tuberculous perito- nitis is the better term to employ when the condi- tion is due to tubercle." — Registrar-General, Tabes dorsalis should not be abbreviated to " Tabes." See "Dentition." See "Ptomain poisoning." The organ or part of the body affected shoiild always be stated, as Tuberculosis of the lungs, Tuber- culosis of the spine, Tuberculous meningitiSi Acute general miliary tuberculosis, etc. SYNONYMS USED FOR "TYPHOID FEVER" 275 LIST OF UNDESIRABLE TERMS (Concluded) Undesirable Term. Reason Why Undesirable, ajtd Suggestion for More Definite Statement of Cause of Death. (1) (2) '* TwnoT** " Neoplasm,'' groiath." " Uremia" " New These terms should never be used without the qual- fyiD€ words Malignant, Nonmalignant, or Be- nign. If malignant, they belong under Cancer, and should preferably be so reported, or under the more exact terms Carcinoma, Sarcoma, etc. In all cases the oigan or part affected should be specified. Name the disease causing death, i.e., the primary cause, not the mere terminal conditions or symp- toms, and state the duration of the primary cause. See " Hemorrhage.^' " Uterine hemorrhage" . Some of the synonyms used for " t3rphoid fever." — The foUowing is a partial list of terms which have been used to describe typhoid fever: Abdominal fever, Abdominal typhoid, Abdominal tj^hus. Abortive typhoid. Ambulant typhoid, Cerebral typhoid. Cerebral typhus Continued fever, Enteric fever, Enterica, Gastroenteric fever Hapmorrhagic typhoid fever, Ileotyphus, Intermittent tsrphoid fever. Malignant typhoid fever. Mountain fever, Paratyphoid fever. Paratyphus, Posttyphoid abscess Rheumatic typhoid fever, Typhobilious fever, Typhoenteritis, Typhogastric fever, Typhoid fever. Typhoid malaria, Typhoid meningitis, Typhoid stupor, Typhoid ulcer Typhomalaria, Typhomalarial fever, Typhoperitonitis, Typhus Typhus abdominalis. This shows the great need of standardization. 276 CAUSES OP DEATH Joint causes of death. — The Bureau of the Census in 1914 published an "Index of Joint Causes of Death," which shows the proper method of assignment to the preferred title of causes of death when two causes are simultaneously reported. This index, alphabetically arranged, is very useful. Physicians sometimes report two or more causes of death upon the death-certificate. This may be histori- cally true as one disease may be a complication of the other. For statistical purposes, however, only one cause can be tabulated for each death. Out of the two or more causes given one must be selected, and it is a matter of great impor- tance how this is done. For some years the attempt has been made to separate the diseases reported into the primary cause and secondary cause. As this gave rise to some uncer- tainty as to which was which, the form of the Revised U. S. Standard Certificate of Death asks for " The Cause of Death " and for "The Contributory Cause (Secondary)." The Eng- hsh, French and Germans have laid down certain rules for making the proper selections. In general, it may be said that the primary cause is the real, or underlying, cause of death (the primary affection with respect to time and causation). The following are the American instructions as printed on the back of the standard death-certificate. STANDARD CERTIFICATE OF DEATH Statement of occupation. — Precise statement of occupation is very important, so that the relative healthf ulness of various pursuits can be known. The question applies to each and every person, irrespective of age. For many occupations a single word or term on the first line will be sufficient, e.g., Farmer or Planter, Physician, Compositor, Architect, Locomotive engineer, Civil engineer, stationary fireman, etc. But in many cases, especially in indiistrial employments, it is necessary to know (a) the kind of work and also (6) the nature of the business or industry, and therefore an additional line is orovided for the latter statement; it should be used only when needed. As examples: (o) JOINT CAUSES OF DEATH 277 Spinner, (6) Cotton mill, (a) Salesman, (b) Grocery, (a) Foreman, (6) Automobile factory. The material worked on may form part of the second statement. Never return " Laborer,". " Foreman," " Manager," " Dealer," etc., without more precise specification, as Day laborer. Farm laborer, Laborer — Coal mine, etc. Women at home who are engaged in the duties of the household only (not paid Housekeepers who receive a definite salary) may be entered as Houseioife, Housework, or At home, and children, not gainfully employed, as At school or At home. Care should be taken to report specifically the occupations of persons engaged in domestic service for wages, as Servant, Cook, Housemaid, etc. If the occupation has been changed or given up on account of the Disease Causing Death, state occupation at beginning of illness. If retired from business, that fact may be indicated thus: Farmer (retired, 6 yrs.). For persons who have no occupation whatever, write None. Statement of cause of death. — Name, first, the Disease Causing Death (the primary affection with respect to time and causation), using always the same accepted term for the same disease. Examples: Cerebrospinal fever (the only definite synonym is " Epidemic cerebro- spinal meningitis"); Diphtheria (avoid use of "Croup"); Typhoid /ewer (never report " Typhoid pneumonia "); Lobar pneumonia ; Bron- chopnfiurnonia ("Pneumonia," unqualified, is indefinite); Tuber- culosis of lungs, meninges, peritoneum, etc.. Carcinoma, Sarcoma, etc., of (name origin: " Cancer " is less definite; avoid use of ",Tumor" for malignant neoplasms); Measles; Whooping cough; Chronic valvular heart disease; Chronic interstitial nephritis, etc. The contributory (secondary or intercurrent) affection need not be stated unless important. Example: Measles (disease causing death), 29 ds.; Broncho-pneumonia (secondary), 10 ds. Never report mere symptoms or terminal conditions, such as " Asthenia," " Anemia," (merely symptomatic), " Atrophy," " Collapse," " Coma," " Convulsions," "Debility" ("Congenital," "Senile," etc.), "Dropsy," "Exhaus- tion," " Heart failure," " Hemorrhage," " Inanition," " Marasmus," " Old age," " Shock," " Uremia," " Weakness," etc., when a definite disease can be ascertained as the cause. Always qualify all diseases resulting from childbirth or miscarriage, as " Puerperal septicemia," " Puerperal peritonitis," etc. State cause for which surgical operation was undertaken. For violent deaths state means or injury and qualify as acci- dental, SUICIDAL, or homicidal, or as probably such, if impossible to determine definitely. Example.s : Accidenlal drowning; Struck by railway 278 CAUSES OF DEATH train — accident; Revolver wound of head — homicide; Poisoned by carbolic acid — probably suicide. The nature of the injury, as fracture of skull, and consequences (e. g., sepsis tetanus) maybe stated under the head of " Contributory." (Recommendations on statement of cause of death approved by Committee on Nomenclature of the American Medical Association.) Cases for the Medical Examiners. — Under the provisions of chapter 24 of the Revised Laws deaths under the following conditions must be referred to the Medical Examiners: 1. Deaths following injury or violence, as Bums, Falls, Drowning, Gas poisoning, Suicide, Homicide, etc. 2. Deaths supposedly caused by violence, as Criminal abortion. Poisoning, Starvation, Suffocation, Exposure, etc. 3. Sudden deaths of persons not disabled by recognized disease, as A death upon the street, or one supposed to be due to Alcoholism, etc. 4. Deaths under circumstances unknown, as A person found dead, etc. The following supplementary suggestions are also useful.' yl. Select the primary cause, that is, the real or under- lying cause of death. This is usually — (a) The cause firsb in order. (6) The cause of longer duration. If the physician writes the cause of shorter duration first, in- quiry may be made whether it is not a mere symptom, complication, or terminal condition. (c) The cause of which the contributory (secondary) cause is a frequent complication. See lists of " Frequent complications " under the various titles of the Tabular List. (d) The physician may indicate the relation of the causes by words, although this is a departure from the way in which the blank was in- tended to be filled out. For example, " Bronchopneumonia following measles " (primary cause last) or " measles followed by brochopneumonia " (primary cause first). 1 Manual, 1911, 1, p. 23. JOINT CAUSES OF DEATH 279 2. If the relation of primary and secondairy is not clear, prefer general diseases, and especially dangerous infective or epidemic diseases, to local diseases. 3. Prefer severe or usually fatal diseases to niild dis- eases. 4. Disregard ill-defined causes (Class XIV), and also indefinite and ill-defined terms {e.g., " debility," 'f atro- phy ") in Classes XI and XII that are referred, for certain ages, to Class XIV, as compared with definite causes. Neglect mere modes of death (failure of heart or respira- tion) and terminal symptoms or conditions {e.g., hypostatic congestion of lungs). 5. Select homicide and suicide in preference to any con- sequences, and severe accidental injuries, sufficient in themselves to cause death, to all ordinary consequences. Tetanus is preferred to any accidental injury and ery- sipelas, septicaemia, pyaemia, peritonitis, etc., are pre- ferred to less serious accidental injuries. Prefer definite means of accidental injury {e.g., railway accident, explosion in coal mine, etc.) to vague statements or statement of the nature of the injury only {e.g., accident, fracture of skull). 6. Physical diseases {e.g., tuberculosis of lungs, diabetes) are preferred to mental diseases as causes of death {e.g., manic depressive psychosis), but general paralysis of the ■ insane is a preferred term. 7. Prefer puerperal causes except when a serious dis- ease {e.g., cancer, chronic Bright's disease) _was_the inde- pendent cause. 8. Disregard indefinite terms and titles generally in favor of definite terms and titles. The precise line of demarcation is difficult to lay- down, but may be indicated broadly by the kinds of type employed in the International List presented on page 35. The List in this form has been distributed by the Census to all physicians in the United 280 CAUSES OF DEATH States/ so that the proportion of indefinite returns should become less. Occupation. — During recent years the study of the rela- tion between occupation and disease has received much attention, and this study has shown the very great impor- tance of the industrial hazard. Fundamental to such a study is a proper classification of occupations. The Ust which follows was pubUshed by the Bureau of the Census in 1915. It is taken from a report entitled "Index to Occupa- tions, alphabetical and classified," a book of 414 pages. This classification contains 215 main groups, 84 of which are subdivided; making a total of 428 separate groups. The industrial field is divided into eight general divisions, and each occupation has been "classified in that part of the industrial field in which it is most commonly pursued." Clerical occupations are classified apart. The classification is along occupational rather than industrial lines. In the table each occupation is indicated by a symbol consisting of three figures, the first of which indicates one of the following main divisions: 0. Agricultiu'e, forestry and animal husbandry. 1. Extraction of minerals. 2. 3. Manufacturing and mechanical industries. 4. 5. Transportation. 6. Trade. 1 Pubhc Service. ■J Professional Service, 8. Domestic and Personal Service. 9. Clerical Occupations. ^ See Physicians' Pocket Reference to the International List of Causes of Death. OCCUPATIONS 281 The second and third figures of each symbol are used in combination and indicate the occupation under the given main division. Thus in the symbol 529, 5 stands for " Trans- portation" and 29 for "Brakeman-steam railroad." The report emphasizes the need of great care in distinguish- ing between occupations and gives the following as examples of distinctions which must be made : — An iron foundry and a brass foundry. A felt hat factory and a straw hat factory. A steam railroad and a street railway. A paper box and a wooden box factory. A locomotive engineer and a stationary engineer. A wholesale and a retail merchant or dealer. A clerk in a store and a salesman, A machinist and a machine tender. A paid housekeeper and a housewife in her own home. A paid housekeeper and a servant girl. A cook and a servant. A proprietor and an employee, etc. LIST OF OCCUPATIONS AND OCCUPATION GROUPS WITH THEIR SYMBOLS Symbol. Occupation and occupation group. Agriculture, Forestry, and Animal Husbandry 1 . . . . Dairy farmers 1 2 . . . . Dairy farm laborers 1 4. . . . Farmers' Farm laborers 2 1 . . . . Farm laborers (home farm) 2 2. . . . Farm laborers (working out) 2 3 . . . . Turpentine farm laborers Farm, dairy farm, garden, orchard, etc., foremen 2 5 . . . . Dairy farm foremen 2 6 Farm foremen^ 2 7 . . . . Garden and greenhouse foremen 2 8. . . . Orchard, nursery, etc., foremen > Includes turpentine farmers. ' Includes turpentine farm foremen. 282 CAUSES OF DEATH Symbol Occupation and occupation group. Agriculture. Forestry, and Animal Husbandry — Continued 3 3 . . . . Fishermen and oystermen 3 5. 6 5. 6 6. 6 7. 6 8. 7 5. 7 7. 7 9. 8 5. 8 6. 8 7. 8 8. 8 9. Foresters Gardeners, florists, fruit growers, and nurserymen Florists Fruit growers and nurserymen Gardeners Landscape gardeners Garden, greenhouse, orchard, and nursery laborers Cranberry bog laborers Garden laborers Greenhouse laborers Orchard and nursery laborers Lumbermen, jaftsmen, and woodchoppera Foremen and overseers Lumbermen and raftsmen Teamsters and haulers Woodchoppers and tie cutters Owners and managers of log and timber canjps Stock herders, drovers, and feeders Stock raisers Other agricultural and animal husbandry pursuits Apiarists Corn shellers, hay balers, grain threshers, etc. Ditchers (farm) Poultry raisers and poultry yard laborers Other and not specified pursuits Extraction of Minerals Foremen, overseers, and inspectors 1 0. . . . Foremen and overseers 1 1 . . . . Inspectors Operators, officials, and managers 1 1 0. . . . Managers 1 1 1 . . . . Officials 1 1 2. . . . Operators OCCUPATIONS 283 Symbol. 12 2. 13 3. 14 4. 15 5. 16 6. 16 7. 17 7. 1 8 8. 1 8 9. 2 2 1 2 2 2 10.... 2 1 1 2 12 2 13.... 2 14.... 2 15.... 2 16.... 2 17.... 2 18.... 2 19.... 2 2 0.... 2 2 1.... 2 2 2.... 2 2 3.... ] ] 2 2 4.... 2 2 5.... Occuoation and occupation group. Extraction of Minerals — Continued Coal mine operatives Copper mine operatives Gold and silver mine operatives Iron mine operatives Operatives in other and not specified mines . Lead and zinc mine operatives . All other mine operatives Quarry operatives Oil, gas, and salt well operatives . Oil and gas well operatives . Salt well and works operatives Manufacturing and Mechanical Industries Apprentices Apprentices to building and hand trades Dressmakers' and milliners' apprentices Other apprentices Bakers Blacksmiths, forgemen, and hammermen Blacksmiths Forgemen, hammermen, and welders Boiler makers Brick and stone masons Builders and building contractors Butchers and dressers (slaughterhouse) Cabinetmakers Carpenters Compositors, linotypers, and typesetters Coopers Dressmakers and seamstresses (not in factory) Dyers Electricians and electrical engineers Electrotypers, stereotypers, and lithographers Electrotypers and stereotypers Lithographers 284 CAUSES OF DEATH Symbol. Occupation and occupation group. Manufacturing and Mechanical Industries — Continued 2 2 6. . . . Engineers (mechanical) 2 2 7 . . . . Engineers (stationary) 2 2 8 . . . . Engravers Filers, grinders, buffers, and polishers (metal) 2 3 Buffers and polishers 2 3 1 Filers 2 3 2 Grinders 2 3 3 . . . . Firemen (except locomotive and fire department) 2 3 4 . . . . Foremen and overseers (manufacturing) Furnace men, smelter men, heaters, pourers, etc. 2 3 5 . . . . Furnace men and smelter men 2 3 6 Heaters 2 3 7 . . . . Ladlers and poiu-ers 2 3 8 Puddlers 2 3 9 . . . . Glass blowers Jewelers, watchmakers, goldsmiths, and silversmiths 2 4 . . .^ Goldsmiths and silversmiths 2 4 1 . . . . Jeweler J and lapidaries (factory) 2 4 2. . . . Jewelers and watchmakers (not in factory) Laborers (n. o. s.') Building and hand trades 2 4 3 . . . . General and not specified laborers 2 4 4. . . . Helpers in building and hand trades Chemical industries 2 4 5. . . . FertiUzer factories 2 4 6 . . . . Paint factories 2 4 7 . . . . Powder, cartridge, fireworks, etc., factories 2 4 8 . . . . Other chemical factories Clay, glass, and stone industries 2 5 . . . . Brick, tile, and terra-cotta factories 2 5 1 . . . . Glass factories 2 5 2 . . . . Lime, cement, and gypsum factories 2 5 3 . . . . Marble and stone yards 2 5 4 Potteries 1 Not otherwise specified. OCCUPATIONS 285 Symbol. 2 5 5. 2 5 6. 2 5 7. '2 5 8. 2 5 9. 2 6 3. 2 6 4. 2 6 5. 2 6 6. 2 6 7. 2 8 0. 2 8 1. 2 8 2. 2 8 3. 2 8 4. 9 0. 9 1. 9 2. 9 3. 9 4. 9 5. 9 6. 9 7. Occupation and occupation group. Manufacturing and Mechanical Industries — Continued Iron and steel industries Automobile factories Blast furnaces and rolling mills ' Car and railroad shops Wagon and carriage factories Other iron and steel works Other metal industries Brass mills Copper factories Lead and zinc factories Tinware and enamelware factories Other metal factories Lumber .and furniture industries Furniture, piano, and organ factories Saw and planing mills ^ Other woodworking factories Tesctile industries Cotton mills Silk mills Woolen and worsted mills Other textile mills Other industries Charcoal and coke works Cigar and tobacco factories Clothing industries Electric light and power plants Electrical supply factories Food industries — Bakeries Butter and cheese factories Fish curing and packing Flour and grain mills Fruit and vegetable canning, etc. Slaughter and packing houses Sugar factories and refineries Other food factories 1 Includes tinpiate mills. ' Includes wooden box factories. 286 CAUSES OF DEATH Symbol. , Occupation and occupation group. Manufacturing and Mechanical Industries — Continued 0. . . . Gas works 1 . . . . Liquor and beverage industries 2. . . . Oil refineries 3 . . . . Paper and pulp mills 4 . . . . Printing and publishing 5. . . . Rubber factories 6. . . . Shoe factories 7. . . . Tanneries 8. . . . Turpentine distilleries 9 . . . . Other factories 3 1 . . . . Loom fixers Machinists, millwrights, and toolmakers 3 1 1 . . . . Machinists and miUwrights 3"1 2. . . . Toolmakers and die setters and sinkers 3 1 3 . . . . Managers and superintendents (manufacturing) Manufacturers and officials 3 1 4. . . . Manufacturers 3 15.... Officials Mechanics (n. o. s.') 3 1 6 . . . . Gunsmiths, locksmiths, and beUhangers 3 1 7 Wheelwrights 3 1 8 . . . . Other mechanics * 3 2 0.... Millers (grain, flour, feed, etc.) 3 2 1 . . . . Milliners and millinery dealers Molders, founders, and casters (metal) 3 2 2 . . . . Brass molders, founders, and casters 3 2 3. . . . Iron molders, founders, and casters 3 2 4. . . . Other molders, founders, and casters 3 2 6. . . . Oilers of machinery Painters, glaziers, varnishers, enamelers, etc. 3 2 7. . . . Enamelers, lacquerers, and japanners 3 2 8. . . . Painters, glaziers, and varnishers (building) 3 2 9 . . . . Painters, glaziers, and varnishers (factory) ^ Not otherwise specified. OCCUPATIONS 287 Symbol. Occupation and occupation group. Manufacturing and Mechanical Industries — (Continued) 3 3 . . . . Paper hangers 3 3 1 . . . . Pattern and model makers 3 3 2 Plasterers 3 3 3 . . . . Plumbers and gas and steam fitters 3 3 4. . . . Pressmen (printing) 3 3 5 . . . . Rollers and roll hands (metal) 3 3 ,6. . . . Roofers and slaters 3 3 7...,. Sawyers Semiskilled operatives (n. o. s.^) Chemical industries 3 4 0.... Paint factories 3 '4 1 . . . . Powder, cartridge, fireworks, etc., factories 3 4 2. . . . Other chemical factories 3 4 4. . . . Cigar and tobacco factories Clay, glass, and stone industries 3 4 5 . . . . Brick, tUe, and terra-cotta factories 3 4 6. . . . Glass factories 3 4 7 . . . . Lime, cement, and gypsum factories 3 4 8. . . . Marble and stone yards 3 4 9 Potteries Clothing industries 3 5 5. . . . Hat factories (felt) 3 3 6. . . . Suit, coat, cloak, and overall factories 3 5 7 . . . . Other clothing factories Food industries 3 6 0. . . . Bakeries 3 6 1 . . . . Butter and cheese factories 3 6 2 . . . . Candy factories 3 6 3 . . . . Flour and grain mills 3 6 4 Fruit and vegetable canning, etc. 3 6 5 . . . . Slaughter and packing houses S 6 6 . . . . Other food factories 3 6 9 Harness and saddle industries 1 Not otherwise soecified. 288 CAUSES OF DEATH Symbol. Occupation and occupation group. 3 7 0.... 3 7 1.... 3 7 2.... 3 7 3.... 3 7 4.... 3 8 0.... 3 8 1.... 3 8 2.... 3 8 3.... 3 8 4.... 3 8 5.... 3 9 0.... 3 9 1.... 3 9 2.... 3 9 4.... 3 9 5.... 3 9 6.... 4 0.... 4 1.... 4 2... 4 3.... 4 5.... 4 6... 4 7... 4 8... 4 10... 4 1 1... 4 12... 4 13... Manvjacturing and Mechanical Industries — (Continued) Iron and steel industries Automobile factories Blast furnaces and rolling mills' Car and railroad shops '' Wagon and carriage factories Other iron and steel works Other metal industries Brass milla Clock and watch factories Gold and silver and jewelry factories Lead and zinc factories Tinware and enamelware factories Other metal factories Liquor and beverage industries Breweries Distilleries Other Uquor and beverage factories Lumber and furniture industries Furniture, piano, and organ factories Saw and planing mills ' Other woodworking factories Paper and pulp mills Printing and publishing Shoe factories Tanneries Textile industries — Beamers, warpers, and slashers Cotton mills Silk mills Woolen and worsted mills Other textile mills Bobbin boys, doffers, and carriers Cotton miEs Silk mills Woolen and worsted mills Other textile miUs 1 Includes tinplate mills. ^ Includes car repairers for street and steam railroads. 3 Includes wooden box factories. OCCUPATIONS 289 Symbol. Occupation and occupation group. Manufacturing and Mechanical Industries — (Continued) Carders, combers, and lappers 4 1 5 . . . . Cotton mills 4 1 6 Silk mills 4 1 7 . . . . Woolen and worsted mills 4 1 8 Other textile mUls Drawers, rovers, and twisters 4 2 . . . . Cotton mills 4 2 1 Silk mills 4 2 2 . . . . Woolen and worsted mills 4 2 3 Other textile mills Spinners 4 2 5. . . . Cotton mills 4 2 6 Silk mills 4 2 7 . . . . Woolen and worsted mills 4 2 8.... Other textile mills Weavers 4 3 Cotton mills 4 3 1 Silk mills 4 3 2. . . . Woolen and worsted mills 4 3 3 Other textile inills Winders, reelers, and spoolers 4 3 5... Cotton mills 4 3 6 Silk mills 4 3 7 . . . . Woolen and worsted mills 4 3 8 . . . . Other textile mills Other occupations 4 4 Cotton mills 4 4 1.... Silk mills 4 4 2.... Woolen and worsted mills 4 4 3 Other textile mills Other industries 4 6 . . . . Electrical supply factories 4 6 1... Paper box factories 4 6 2 . , . . Rubber factories 4 6 3 . . . . Other factories 290 CAUSES OF DEATH Symbol. 4 7 0.... 4 7 1.... 4 7 2.... 4 7 3.... 4 7 4.... 4 7 5.... 4 8 0.... 4 8 1... 4 8 2.... 4 8 3.... 4 8 4.... 4 8 5.... 5 0.... 5 2 ... 5 4.... 5 6.... 5 8.... 5 1 0.... 5 12.... 5 1 4.... 5 16... 5 18.... 5 2 0.... 5 2 2.... 5 2 4.... 5 2 5.... Occupation and occupation group. Manufacturing and Mechanical Industries — (Continued) Sewers and sewing machine operators (factory) ' Shoemakers and cobblers (not in factory) Skilled occupations (n. o. s.^) Annealers and temperers (metal) Piano and organ tuners Wood carvers Other skilled occupations Stonecutters Structural iron workers (building) Tailors and taUoresses Tinsmiths and coppersmiths Coppersmiths Tinsmiths Upholsterers Transportation Water transportation (selected occupations) Boatmen, canal men, and lock keepers Captains, masters, mates, and pilots Longshoremen and stevedores Sailors and deck hands Road and street transportation (selected occupations) Carriage and hack drivers Chauffeurs Draymen, teamsters, and expressmen' Foremen of livery and transfer companies Garage keepers and managers Hostlers and stable hands Livery stable keepers and managers Proprietors and managers of transfer companies Railroad transportation (selected occupations) Baggagemen and freight agents Freight agents 1 Includes sewers and sewing machine operators in all factories except shoe and harness factories, and sack sewers in fertilizer, salt, and sugar factories, and cement, flour, and grain mills. ^ Not otherwise specified. 3 Teamsters in agriculture, forestry, and the extraction of minerals are classified with the other workers in those industries, respectively; and drivers for bakeries and laundries are classified with deliverymen in trade. OCCUPATIONS 291 Symbol. Occupation and occupation group. Transportation — (Continued) 5 2 7 . . . . Boiler washers and engine hostlers 5 2 9. . . . Brakemen 5 3 . . . . Conductors (steam railroad) 5 3 2 . . . . Conductors (street railroad) 5 3 4. . . . Foremen and overseers Laborers 5 3 6 . . . . Steam railroad 5 3 7 . . . . Street railroad 5 3 9 . . . . Locomotive engineers 6 4 0. . . . Locomotive firemen 5 4 2 Motormen Officials and superintendents 5 4 4. . . . Steam railroad 5 4 5 . . . . Street railroad Switchmen, flagmen, and yardmen 5 4 7 . . . . Switchmen and flagmen (steam railroad) 5 4 8. . . . Switchmen and flagmen (Street railroad) 5 4 9. . . . Yardmen (steam railroad) 5 5 . . . . Ticket and station agents Express, post, telegraph, and telephone (selected oc- cupations) 5 5 2 . . . . Agents (express companies) Express messengers and railway mail clerks 5 5 4. . . . Express messengers 5 5 5. . . . Railway mail clerks 5 5 7. . . . Mail carriers 5 5 9 . . . . Telegraph and telephone linemen 5 6 . . . . Telegraph messengers 5 6 2. . . . Telegraph operators 5 6 4 . . . . Telephone operators Other transportation pursuits Foremen and overseers (n. o. s.') 5 6 6. . . . Road and street building and repairing 5 6 7 . . . . Telegraph and telephone companies 5 6 8. . . . Water transportation 5 6 9 . . . . Other transportation 1 Not otherwise specified. 292 CAUSES OF DEATH Symbol. Occupation and occupation group. Transportation — (Continued) Inspectors 5 7 . . . . Steam railroad 5 7 1 Street railroad 5 7 2 . . . . Other transportation Laborers (n o. s.>) 5 7 5 . . . . Road and street building and repairing 5 7 6 Street cleaning 5 7 7.... Other transportation Proprietors, officials, and managers (n. o. s.^) 8 . . . . Telegraph and telephone companies 8 1 . . . . Other transportation Other occupations (semiskilled) 8 5 . . . . Steam railroad 8 6 . . . . Street railroad 8 7 . . . . Other transportation 6 6 1 6 6 6 6 6 1 6 1 6 1 6 2 0. 6 2 2. 6 2 4. 6 2 5. Trade Bankers, brokers, and money lenders Bankers and bank officials Commercial brokers and commission men Loan brokers and loan company officials Pawnbrokers Stockbrokers Brokers not specified and promoters Clerks in stores Commercial travelers Decorators, drapers, and window dressers Deliverymen Bakeries and laundries Stores Floorwalkers, foremen, and overseers Floorwalkers and foremen in stores Foremen, warehouses, stockyards, etc. ^ Not otherwise specified. OCCUtATIONS 293 Svrabol Occupation and occupation group. Trade — (Continued) 6 2 7 Inspectors, gaugers, and samplers Insurance agents and officials 6 3 0. . . . Insurance agents 6 3 1 . . . . Officials of insurance companies Laborers in coal and lumberyards, warehouses, etc. 6 3 3 . . . . Coal yards 6 3 4 Elevators 6 3 5 . . . . Lumberyards 6 3 6. . . . Stockyards 6 3 7. . . . Warehouses 6 4 0.... Laborers, porters, and helpers in stores 6 4 2. . . . Newsboys Proprietors, officials, and managers (n. o. s.') 6 4 4. . . . Employment office keepers 6 4 5. . . . Proprietors, etc., elevators 6 4 6. . . . Proprietors, etc., warehouses 6 4 7 . . . . Other proprietors, officials, and managers 6 5 . . . . Real estate agents and officials 6 5 5. . . . Retail dealers Salesmen and saleswomen 6 6 3. . . . Auctioneers 6 6 4. . . . Demonstrators 6 6 5. . . . Sales agents 6 6 6. . . . Salesmen and saleswomen (stores) 6 6 8 Undertakers 6 7 7 . . . . Wholesale dealers, importers, and exporters Other pursuits (semiskilled) 6 8 6. . . . Fruit graders and packers 6 8 7 Meat cutters 6 8 8 Other occupations 1 Not otherwise specified. 294 CAUSES OF DEATH Symbol. Occupation and occupation group. Public Service {not Elsewhere Classified) 7 0... Firemen (fire department) 7 2... . Guards, watchmen, and doorkeepers Laborers (public service) 7 6... Garbage men and scavengers 7 7... Other laborers Marshals, sheriffs, detectives, etc. 7 10... Detectives 7 11... Marshals and constables 7 12... Probation and truant oflScers 7 13... Sheriffs Officials and inspectors (city and county) 7 15... Officials and inspectors (city) 7 16... Officials and inspectors (county) Officials and inspectors (state and United States) 7 2 0... Officials and inspectors (state) 7 2 1... Officials and inspectors (United States) 7 2 5... Pohcemen 7 2 7... Soldiers, sailors, and marines Other pursuits 7 3 0... Life-savers 7 3 1... Lighthouse keepers 7 3 3... Other occupq,tions Professional Service 7 4 0... . Actors 7 4 2... . Architects 7 4 4... . Artists, sculptors, and teachers of art Authors, editors, and reporters 7 4 6... Authors 7 4 7... Editors and reporters 7 5 0... . Chemists, assayers, and metallurgists Civil and mining engineers and surveyors 7 5 2... Civil engineers and surveyors 7 5 3.. Mining engineers 7 5 5... . Clergymen 7 5 7... . College presidents and professors 7 5 9... . Dentists OCCUPATIONS Symbol. Occupation and occupation group. Professional Service — (Continued) Designers, draftsmen, and inventors 295 Draftsmen Inventors Lawyers, judges, and justices Musicians and teachers of music Photographers Physicians and surgeons Showmen Teachers Teachers (athletics, dancing, etc.) Teachers (school) , Trained nurses Veterinary surgeons Other professional pursuits Semiprofessional pursuits Abstractors, notaries, and justices of peace Fortune tellers, hypnotists, spiritualists, etc. Healers (except physicians and surgeons) Keepers of charitable and penal institutions Officials of lodges, societies, etc. Religious and charity workers Theatrical owners, managers, and officials Other occupations Attendants and helpers (professional service) Domestic and Personal Service Barbers, hairdressers, and manicurists Bartenders Billiard room, dance hall, skating rink, etc., keepers Billiard and pool room keepers Dance hall, skating rink, etc., keepers Boarding and lodging house keepers Bootblacks Charwomen and cleaners Elevator tenders Hotel keepers and managers 296 CAUSES OF DEATH Symbol. Occupation and occupation ^roup. Domestic and Personal Service — (Continued) 8 3 3 . . . . Housekeepers and stewards 8 3 5 . . . . Janitors and sextons 8 4 2 . , , . Laborers (domestic and professional service) 8 4 4 . . . . Launderers and laundresses (not in laundry) 8 4 6 . . . . Laundry operatives "8 4 8. . . . Laundry owners, officials, and managers Midwives and nurses (not trained) 8 5 4 Midwives 8 5 5. . . . Nurses (not trained) 8 6 6 . . . . Porters (except in stores) 8 6 8 . . . . Restaurant, cafe, and lunch room keepers 8 7 . . . . Saloon keepers Servants 8 7 3 . . . . Bell boys, chore boys, etc. 8 7 4. . . . Chambermaids 8 7 5 . . . . Coachmen and footmen 8 7 6,... Cooks 8 7 7 . . . . Other servants 8 8 8.... Waiters Other pursuits 8 9 5 . . . . Bathouse keepers and attendants 8 9 6. . . . Cemetery keepers 8 9 7 . . . . Cleaners and renovators (clothing, etc.) 8 9 8 . . . . UmbreUa menders and scissors grinders 8 9 9... ■ Other occupations Clerical Occupations Agents, canvassers, and collectors 9 5 5 . . . .- Agents 9 5 6. . . . Canvassers 9 5 7 Collectors 9 6 6 . . . . Bookkeepers, cashiers, and accountants Clerks (except clerks in stores) 9 7 6 . . . . Shipping clerks 9 7 7 Other clerks Messenger, bundle, and office boys '■ 9 8 7 . . . . Bifndle and cash boys and girls 9 8 8. . . . Messenger, errand, and office boys 9 9 9 Stenographers and tjTDewriters • Except telegraph and telephone messengers. EXERCISES AND QUESTIONS 297 Nosology not an exact science. — The following reported causes of death will enable the student to decide whether or not nosology is an exact science: "Went to bed feeling well, but woke up dead." "Died suddenly at the age of 103. To this time he bid fair to reach a ripe old age." "Deceased had never been fatally sick." ^"Last illness caused by chronic rheumatism, but was cured before death." " Died suddenly, nothing serious." " While cranking his automobile sustained what is technically known as a colles fracture of the right rib." "Kick by horse showed on left kidney." "Chronic disease." "Deceased died from blood poison caused by a broken ankle, which is remarkable, as the automobile struck him between the lamp and the radiator." , "Death caused by five doctors." "Dehcate from birth." "Artery lung busted." " Collocinphantum." "Typhoid fever, bronchitis, pneumonia and a miscarriage." — " Vital Statistics." EXERCISES AND QUESTIONS 1. What does Van Buren mean by the "Will-o'-the-wisp" of the statistics of causes of death? [See Am. J. P. H., Dec. 1917, p. 1016.] 2. What changes have taken place in the nordenclature of " Tuber- culosis," during the last century? • 3. Give ten examples of joint causes of death, indicating in each case which is primary and which secondary. 4. What preparations are being made to revise the present Inter- national List of Causes of Death? 5. Select the appropriate cause of death for statistical report from the following joint causes of death, and give reason for your selection, a. Broncho-pneumonia and measles. b. Infantile diarrhoea and convulsions. c. Scarlet fever and diphtheria. 298 CAUSES OF DEATH d. Nephritis and scarlet fever. e. Pulmonary tuberculosis and puerperal septicemia. /. Typhoid fever and pneumonia. g. Pericarditis and appendicitis. h. Cirrhosis and angina pectoris. / i. Saturnism and peritonitis. J. Old age and bronchitis. CHAPTER IX ANALYSIS OF DEATH-RATES Reasons for Analyzing a Death-rate. — We have now covered the principal methods used in the simpler forms of statistical study. We have seen the futility of using general death-rates for comparing the mortality of different places. We have learned how to compute specific rates for groups and classes, particular rates for different diseases and special- rates of various kinds. Let us now put these ideas together and say that the way to use a general death-rate is to analyze it. Taken by itself it means very little, but if properly analyzed it will yield us useful information. Two Methods of Analysis. — There are two methods of analyzing a general death-rate. ** One is to sub-divide the numerator of the fraction into classes and groups, leaving the denominator of the fraction unchanged. The total population at mid-year is taken as the denominator of the fraction. This is sometimes done in separating all of the deaths in a year according to months and dividing each by the total population. It has the ad- vantage that the sum of all the parts is equal to the whole. In the case mentioned the sum of all the monthly rates gives the yearly rate. It has the disadvantage that the figures cannot be compared or any standard easily carried in the mind. Another and better method is to sub-divide both the numerator and denominator into classes and groups, that is, tp find their specific rates. Here the sum of the rates 299 300 ANALYSIS OF DEATH-RATES resulting from the separation does not equal the whole. The weighted average of the constituent rates will, however, equal the whole. Let us take a simple example: In 1910 in Massachusetts there were the following popu- lations and deaths classified by sex. TABLE 72 POPULATION AND DEATHS: MASSACHUSETTS Population. Deaths. (1) (2) (3) Males 1,655,248 1,711,168 28,259 Females 26,148 Total 3,366,416 54,407 According to the first method of analysis the partial rates would be 28,259 -^ 3366 = 8.4 for males, and 26,148 h- 3366 = 7.7 for females, the sum being 16.1, which is the same as dividing 54,407 by 3366, i.e., 16.1 per 1000. According to the second method the specific rate for males is 28,259 4- 1655 = 17.1, and for females, 26,148 4- 1711 = 15.3. In this case the weighted average would be (17.1 X 1655 + 15.3 X 1711) H- 3366 = 16.1 per 1000. The ad- vantage of this second method is obvious, as one may readily compare the rate of 17.1 for males, and that of 15.3 for females, with 16.1, the death-rate for the entire popula- tion. In other words, this method of analysis gives us a chance to compare, and that is a prune object of statistical study. Useful subdivisions. — For the purpose of analyzing a general death-rate we may subdivide the area geographically, finding the specific death-rate for each part. A state may ANALYSIS OF A DEATH-RATE. FOR A STATE 301 be subdivided into counties, boroughs, cities and towns; or into urban and rural districts. A large city may be divided into wards, precincts or blocks. The subdivisions must be so chosen that both the population and the deaths may be obtained for each one. This often limits the comparison to political subdivisions. Those who take the census and those who keep the death records should get together and see that the geographical subdivisions correspond. Having made these subdivisions and obtained the rates for each, the results should be arrayed and studied by the statistical method described in a later chapter. We may subdivide the year into seasons, months, weeks, or even days and ascertain the specific death-rate for each sub- division. These results should be arranged for chronological study, and for comparing the results for similar seasons or months for different years. We may subdivide the population by sex, by nationality, by occupation, and in all sorts of ways. We may subdivide the deaths according to cause, using either individual causes or classes of causes. And finally we may use these various separations in com- bination with each other. Example of the analysis of a general death-rate for a state. — To give a complete example of an analysis of the general death-rate of a state would require a small volume. A few hints may be given by asking a number of questions in regard to Massachusetts for the year 1910. ! According to the 73d Registration Report the general death-rate for the state was 16.1. Q. Was the death-rate unifonn throughout the state? The answer is obtained by finding the rate for each county and placing them in array, that is, in order of magnitude. The result is as follows: 302 ANALYSIS OF DEATH-EATES TABLE 73 DEATH-RATES BY COUNTIES: MASSACHUSETTS, 1910 County. General death- rate. County. General death- rate. (1) (2) (1) (2) Norfolk 13.3 14.2 15.4 15.5 15.6 15.6 15.7 Essex 15.9 Plymouth Middlesex. . .* Bristol 16 3 Hampden 16.8 Franklin Suffolk 17.0 Worcester Barnstable Dukes . Nantucket 18.1 19.1 Hampshire 20.2 Q. What was the median death-rate for the different counties, that is, the rate for the county in the middle of the Hst? It was 15.8, i.e., between 15.7 and 15.9. Q. Why is this median rate lower than 16.1, the rate for the entire state? The more populous counties have death-rates relatively high and this brings up the average. An average of these county rates weighted according to their population would give 16.1. Q. Why was the rate for Nantucket county so much higher than that for Norfolk? : In order to answer this question intelligently we need to find out when the deaths occurred (seasonal distribution), where the deaths occurred (geographical distribution), who died (distribution by sex, age, nationahty), what was the cause of death. Knowing these facts we should then seek to correlate them with controllable conditions. As a rule a county is not a good geographical unit for such a study as it is diflScult to get the facts. A city is better. COMPARISON OF DEATH-RATES OF TWO CITIES 303 Comparison of the death-rates of two cities. — In 1910 the general death-rates of the cities of Massachusetts which had populations exceeding 50,000 were as follows: TABLE 74 DEATH-RATES OF CERTAIN CITIES IN MASSACHUSETTS 1910 City. General death- rate. City. General death- late. (1) (2) (1) (2) Brockton 12.3 13.1 13.4 15.0 16.6 16.9 Boston 17.2 Lynn Holyoke 17.7 Somerville Lawrence 17 7 Cambridge Fall River 18 4 Springfield New Bedford Lowell . . . 18.6 Worcester .... 19 7 Q. Why was the death-rate so much higher in Lowell than in Brockton ? We naturally look first to differences in age and sex dis- tribution. The U. S. Census gives us>the following infor- mation: TABLE 75 AGE AND SEX DISTRIBUTION OF POPULATION IN BROCKTON AND LOWELL, MASS. Brockton. Lowell. (1) (2) (3) Per cent of population under 10 years Male 8.8 8.6 10.1 10.6 9.3 Female 9.3 Per cent of population over 45 years Male 9.2 Female 10.8 304 ANALYSIS OF DEATH-RATES These differences are not striking, except that Lowell has a somewhat larger percentage of children under ten years of age. How about infants? There is not much difference. In Brockton the infant population was 2.15 per cent of the total, in Lowell, 2.19 per cent. The sex differences are not great except that in Lo^yell' in the age-group 15-44 years there are more females than males, while in Brockton the numbers are about alike. Let us next turn to nationality. Here we find a great difference. In Brockton, 72 per cent of the population were native white and 27 per cent foreign-born white, but in Lowell only 59 per cent were native white while 40 per cent were foreign-born white. Pursuing this further we find that in Lowell the foreign-born whites were made up of French Car>adians, 28.3 per cent; Irish, 23.0 per cent; Enghsh, 10.5 per cent; Canadians other than French, 9.3 per cent; Greek-s, 8.7 per cent. The corresponding figures for Brockton are not given in the census report. With these fundamental differences in mind we must next turn to industrial conditions, hving conditions, etc. Brock- ton is a shoe city, Lowell a textile city. The housing condi- tions of the working classes in Brockton are better than in Lowell. These matters should be studied in detail. But what of the causes of death? The annual report of the State Board of Health shows that the death-rate for pneu- monia was 118 per 100,000 in Brockton, but 210 in Lowell; tuberculosis 88 and 137 respectively, diarrhea and cholera morbus 23 and 184. This last is a very important difference. Turning to the age distribution of deaths we find that in Brockton 18.5 per cent of the deaths were infants, in Lowell 25.2 per cent. Evidently the large number of infant deaths, the large numbers of deaths from dysentery and the large foreign population in Lowell point to certain environmental conditions which influence mortality. "RATES" NOT THE ONLY METHOD OF COMPARISON 305 In order to get these facts it was necessary to consult the State Registration Report, the Annual Report of the State Board of Health and the Census Report. The annual reports of the local boards of health. should have contained these essential data; in fact they should have contained the following specific death-rates for 1910: TABLE 76 SPECIFIC DEATH-RATES BY AGE-GROUPS FOR BROCKTON AND LOWELL: igio Specific death-ratea per 1000. Age-group. Brockton. Lowell. Male. Female. Male. Female. (1) (2) (3) (4) C5) 0-1 123.0 101.0 286.0 237.0 1^ 8.0 13.0 31.0 35.0 5-9 3.5 6.5 5.2 4.6 10-14 2.1 3.0 1.6 2.7 15-19 4.0 3.2 4.7 3.1 20-24 3.1 2.6 5.2 5.0 25-34 3.9 6.0 7.5 6.8 35^ 4.7 4.3 9.8 10.7 45-64 18.4 11.8 24.0 23.0 65- 106.0 90.0 99.0 95.0 These figures show directly that the infant death-rate was much higher in Lowell than in Brockton, that the death-rate for young children was also higher. This would point at once to home environment. But the rates were also higher in Lowell for the middle-age groups, which would point to greater industrial hazards there. " Rates " not the only method of comparison. — So much has been said about rates and specific rates that there is danger that the student may come, to think of them as 306 ANALYSIS OF DEATH-RATES the only method of statistical comparison. That is far froin being the case. The seasonal changes in mortality may be shown in three ways, each of which has its use. In Massachusetts the general death-rate for 1910 was 16.1 per 1000. It varied seasonally as follows: TABLE 77 SEASONAL DISTRIBUTION OF MORTALITY Massachusetts, IQIO Ratio of monthly- Month. Death-rate. Percentage of total deaths. deaths to average number for each month. (1) (2) (3) (4) January 17.1 8.9 106 February 17.1 8.1 106 March 17.8 9.5 110 April 17.2 8.8 107 W ay 15.2 8.0 94 June 14.4 7.3 89 July 17.2 9.0 107 August 16.6 8.7 103 September 15.8 8.0 98 October 14.7 7.7 91 November 14.8 7.5 92 December 16.2 8.5 101 Year 16.1 100.0 100 Column (2) gives the death-rate for each month as compared with the yearly rate. Columns (3) and (4) are most useful in comparing one year with another. They do not involve population, an uncertain factor in all but the census years, but on the other hand a change in one month affects the figures in all the other months. EXERCISES AND QtlESTlONS 30? EXERCISES AND QUESTIONS 1. Make a statistical analysis of the general death-rates of Boston and Baltimore for the year 1910. 2. Make a statistical analysis of the general death-rates of Chicago and New Orleans for the year 1910. 3. Make a statistical analysis of the general death-rates of other cities to be assigned by instructor. 4. Find the median death-rate for the counties of New York state for 1910. 5. Compare the seasonal mortalities of San Francisco and Boston for 1910, using several different methods of statement. CHAPTER X STATISTICS OF PARTICULAR DISEASES In studying particular diseases we commonly use four ratios which, though described in different ways, may be distinguished by the terms, (a) mortahty rate; (6) propor- tionate mortaUty; (c) morbidity rate and (d) fatality or case fatahty. In addition to these ratios the number of cases of a particular disease may be arranged in groups and classes, by age, sex, nationality, occupation, date of onset and in other ways without using ratios; and the same is true of deaths from a particular disease. Mortality rate. — The mortality rate for a particular disease is obtained by dividing the number of deaths from that disease by the mid-year population expressed in hundred thousands. Proportionate Mortality. — The proportionate mortality of a particular disease is the per cent which the nmnber of deaths from that disease is of the total number of deaths from all causes. The interval of time is usually taken as one year, but shorter periods may be used. This method is sometimes spoken of as the percentage of mortality, or per cent distribution. Percentages of mortality are not as commonly published as they were some years ago. They do not involve the population, hence they are especially useful where the popu- lation is not known or cannot be correctly estimated. Since the custom of estimating population by a uniform system has become general there has been less need for considering 308 INACCURACY OF MORBIDITY AND FATALITY RATES 309 the percentage of mortality. A theoretical disadvantage of the method is the fact that the number of deaths from the particular disease appears in both the numerator and the denominator of the fraction; that is, the number of deaths from the particular disease helps to make up the total number of deaths. Morbidity rate. — The morbidity rate is the ratio between the number of cases of a particular disease in a year and the mid-year population expressed, in thousands, or better in hundred thousands. It is sometimes called the "case rate." The morbidity rate is very useful in epidemiological investi- gations. It is usually based on the entire population, but just as in the case of death-rates, or mortality rates, from particular diseases it may be computed for specific age-groups or classes. Fatality. — The fatahty of a disease is the ratio between the number of deaths and the number of cases. It is best expressed as a percentage. The fatality of any disease is far from being the same at all ages. Example. — In 1915 the population of Cambridge, Mass., was 108,822; the total number of deaths from all causes 1460; the number of cases and deaths from scarlet fever were 379 and 5, respectively. From these facts we have the following rates and ratios: General death-rate, 1460 + 108.822 = 13.45 per 1000. Scarlet-fever, mortality rate, 5 h- 1.08822 = 4.6 per 100,000. Scarlet-fever, proportionate mortality, 5 -i- 14.60 = 0.34 per cent, Scarlet-fever, morbidity rate, 379 4- 1.08822 = 347 per 100,000. Scarlet-fever, fatality, 5 ^ 379 = 1.32 per cent. Inaccuracy of morbidity and fatality rates. — It must not be forgotten that rates for morbidity are based on re- ported cases and that not all cases are reported. Nearly all morbidity rates, are too low. It follows therefore, that nearly all fatality percentages are too high. In the case of typhoid-fever, for example, a comparison of deaths and 310 STATISTICS OF PARTICULAR DISEASES reported cases, has led to the popular idea that the fatality is about 10 per cent, that is, one death for every ten cases. But in a number of epidemics, where the cases were accurately obtained by a house to house canvas, it has been found that there were from twelve to fifteen cases for each death, that is, the .fatality was only about 7 per cent. It is interesting to see how an epidemic of typhoid fever will result in an increased proportion of cases being reported. In Cleveland, Ohio, in the year 1902 there were but 3.7 times as many reported cases as deaths, but the following year, when a severe epidemic occurred, there were 7.3 times as many reported cases as deaths. If the figures for 1902 had been correct it would have meant a fatality of 27 per cent, which is most unlikely. Causes of death in Massachusetts. — In 1915 the prin- cipal causes of death in Massachusetts were as follows. They are arranged according to the Abridged International List. TABLE 78 PRINCIPAL CAUSES OF DEATH IN MASSACHUSETTS Rank. Cause of death. Per cent of mortality. (1) (2) (3) 10 Pneumonia (92) Tuberculosis of the lungs (28, 29) Organic diseases of the heart (79) Diarrhea and enteritis (104) Congenital debility and malformations (150, 151) . Cerebral hemorrhage and softening (64, 65) Cancer and other malignant tumors (39-45) Acute nephritis and Bright's disease (119, 120) . . . Other diseases of respiratory system (86-88, 91, 93-98) Violent deaths, suicide excepted (164r-186) 8.8 8.3 7.4 6.9 6.8 6.1 5.6 5.6 4.8 4.4 It will be seen that these ten causes account for nearly two- thirds of all the deaths. STUDY OF TUBERCULOSIS BY ^ AGE AND SEX 311 The ten most important causes of death for the U. S. registration area in 1914 were not placed in the same order, but were as follows: TABLE 79 PRINCIPAL CAUSES OF DEATH: UNITED STATES, 1915 Rank. Cause of death. (1) (2) 1 2 3 4 5 6 7 8 9 10 Organic diseases of the heart (79) Tuberculosis of the lungs (28, 29) Bright's disease (119, 120) Pneumonia (92) Violent deaths (164-186) Cancer (39-45) Cerebral hemorrhage (64, 65) Congenital debility and malformations (150, 151) Diarrhea and enteritis (104) Bronchitis (89, 90) The proportionate mortality differs more or less in different places. It is not the same for the two sexes. It differs greatly at different ages. It is not the same at all seasons. It is different to-day from what it was a generation ago. The control of communicable diseases has considerably altered the relative importance of the different causes of death. Study of tuberculosis by age and sex. — In attempting to study any particular disease in order to determine its,relation to age and sex one will be surprised to find how difficult it is to get a complete statement of the necessary facts for any given place. Obviously we need to have both the cases and deaths classified by age and sex, and we also need the population and the deaths from all causes arranged by sex and according to the same age grouping. If we attempt to use the U. S. Census reports we find that no data for eases are given; if we attempt to use the state board of health 312 STATISTICS 'OF PARTICULAR DISEASES reports we may find that the deaths are classified by age and sex, but that only the total numbers are given for cases; in some city board of health reports we may find cases and deaths duly classified but no populations given for the corresponding groups and classes. As an illustration of un- satisfactory current practice let us study the statistics of tuberculosis for the city of Cambridge, Mass., for the year 1915. The data in the following table were taken from the annual report of the local board of health, except the popu- lation statistics, which were taken from the state census of that year. These data are more than ordinarily complete, yet they are not satisfactory, due chiefly to incomplete reports of cases. It may be assumed that the numbers of deaths are reasonably precise, yet they do not strictly represent local conditions as they include deaths in hospitals. The nmnbers of cases and deaths are small and this also makes the derived rates subject to erratic fluctuations. The fundamental data are given in columns (2) to (9), the derived figures in the subsequent columns. Column (10) was obtained from columns (2) and (8); column (12) fropi column (8) ; column (14) from columns (6) and (2) ; column (16) from column (6); column (18) from columns (6) and (4); column (20) from columns (6) and (8). If we take the figures at their face value we notice first that both the morbidity and mortality rates are high in infancy and low in childhood. The male morbidity rate reaches its highest point in age group 30-39 years, but the male mortality rate is highest between 40 and 50. In females the morbidity rate rises earlier and is highest in age-group 20-29. The highest female mortality rate is also found in the same group. Forty per cent of all the cases and 37.9 per cent of all the deaths from tuberculosis among females oc- curred between the ages of twenty and thirty. If we study the figures for proportionate mortality we see STUDY OF TUBERCULOSIS BY AGE AND SEX 313 TABLE 80 CAMBRIDGE, MASS., 1915 Statistics of Tuberculosis (28-35) Cases and Death, Arranged by Age and Sex Population. Deatlis, all causes. Tuberculosis Deaths. Tuberculosis Cases. group. ^ oi V s c! 6 ■a 1, fe g 1 s fa S fa (1) (2) (3) (4) (5) (6) (7) (8) (9) 0-1 1,114 1,080 138 105 1 1 1 1-4 4,161 4,120 38 40 2 1 6 1 5-9 4,996 5,000 13 13 1 4 5 10-14 4,488 4,533 7 6 1 1 4 15-19 4,569 4,901 22 12 9 7 9 17 20-29 10,424 11,326 44 51 23 31 40 50 30-39 8,334 9,190 64 43 29 19 49 31 40-49 6,552 7,177 80 76 32 10 31 9 50-59 4,133 4,823 88 85 13 6 14 8 6O7 3,224 4,678 229 306 10 5 9 3 Total 51,995 56,808 723 737 - .119 82 167 125 Morbidity Percentage Mortality Percentage Proper tion- Fatality, rate per 100,000. distribution (death) distribution ate m ortal- Age- group. of cases. rate. of deaths. ity, per cent. •u m oj a d « a a © cA rt s ■3 i i£ a 1§ s iS i e fa d s a IS fa (1) (10) (11) (12) (13) (14) (15) (16) (17) (18) 09) (20) (21) 0-1 " 90 93 0,6 0.8 93 1.2 1 100 1-4 144 41 3.6 0.8 48 41 1.7 ,1.2 5 3 33 100 5-9 80 100 2.4 4.0 20 1.2 8 20 10-14 89 2.4 0.0 22 26 0.8 1.2 14 17 25 15-19 197 347 5.4 13.6 197 143 7.6 8.5 39 58 100 41 20-29 383 441 23.8 40.0 220 274 19.3 37.9 52 61 57 62 30-39 588 337 29.4 24.8 348 207 24.4 23.2 45 44 ,59 61 40-49 473 125 18.6 7.2 488 139 26.9 12.2 40 13 103 111 50-59 339 166 8.4 6.4 315 124 10.9 7.1 15 7 92 75 60- ^279 64 5.4 2.4 100.0 310 107 8.4 6.1 100.0 4 16.5 2 11.1 111 167 Total 321 220 100.0 229 144 100.0 71 66 314 STATISTICS OF PARTICULAR DISEASES that tuberculosis caused 16.5 per cent of aU deaths among males and 11.1 per cent of all deaths among females. In age- group 20-29 this disease caused nearly two-thirds of all deaths of females and more than half of all deaths of males. In comparing the figures for proportionate mortahty it should be observed that the age-groups are not of equal value throughout the table; some cover ten years, some five, one covers four years, and one only one year. The fatahty rates are practically worthless. . Sometimes the number of reported cases was less than the number of deaths, thus making the fatality rate higher than 100 per cent. This would be an absurdity, if we did not know that the tuber- culosis deaths of one year may represent cases of the year before or the year before that. Tuberculosis is a disease of long duration, sometimes several years. The fatality of such a disease as this cannot be computed in this way. Yet imperfect as these figures are we can gather from them the main facts. We can see that tuberculosis is essentially a disease of early manhood and womanhood, and at those ages we naturally look to working conditions as contributory factors. The disease continues as an important cause of death up to old age, especially among males. If we take the figures for the U. S. Registration Area as given in the Mortality Report for 1914 we obtain a more uniform set of figures, as they are based on 898,059 deaths instead of 1460 deaths. (Table 81.) Here the highest proportionate mortality for tuberculosis was for age-group 20-24 years; for males it was 34.3 per cent, for females 39.2. These figures are considerably lower than for Cambridge. The percentage distribution of tuberculosis deaths showed a maximum in age-group 20-24 for females, and in age-group 25-29 for males. The morbidity, mortality and fatahty could not be computed as no records of cases and no popula- tion by age-groups were given in the Mortality Report. DISTRIBUTION OF DEATHS FROM TUBERCULOSIS 31S TABLE 81 DEATHS FROM TXIBERCULOSIS OF THE LUNGS (28) U. S. Registration Area, 1914, by Age and Sex Age- Deaths, all causes. Deaths (28) Percentage distribution. Proportionate mortality. Male. Female. Male. Female. Male. Female. Male. Female. (1) (2) (3) (4) (5) C6) (7) (8) (9) 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 .75-79 80-84 85-89 90-94 95-99 100- 118,375 10,162 6,819 10,934 17,516 19,407 20,212 23,154 24,116 25,283 28,809 28,896 31,255 32,728 32,760 27,365 19,132 9,600 3,129 704 179 95,735 9,140 6,054 10,322 15,408 16,300 15,878 17,155 16,803 17,779 20,294 21,006 24,275 27,075 29,109 26,410 20,537 11,447 4,165 1,007 288 3,416 832 702 2,719 6,002 6,634 6,466 6,428 5.761 4,640 3,853 2,905 2,139 1,460 929 515 188 48 9 6 1 2,832 878 1,235 3,801 6,061 5,795 4,701 3,922 2,950 2,172 1,679 1,388 1,217 966 777 465 205 67 16 3 2 6.1 1.5 1.3 4.9 10.8 11.9 11.6 11.5 10.3 8.3 6.9 .6.2 3.8 2.6 1.6 0.9 0.3 o.r 6.9 2.1 3.0 9.2 14.7 14.1 11.4 9.5 7.2- 6.3 4.1 3.4 3.0 2.3 1.9 1.1 0.6 0.1 2.9 8.2 10.3 24.8 34.3 34.0 32.2 27.8 ' 23.8 18.3 13.4 10.1 6.8 4.5 2.8 1.9 1.0 0.5 0.3 3.0 - 9.6 20.3 36.8 39.2 36.6 29.7 22.9 17.6 12.2 8.3 6.6 5.0 3.6 2.7 1.8 1.0 0.5 0.4 Total 491,416 406,643 55,724 41,179 100.0 100.0 11.4 10.2 Seasonal Distribution of deaths from tuberculosis. — A natural way of studying the seasonal distribution of deaths from tuberculosis is to subdivide the annual number of deaths into the numbers which occurred each month and then find what per cent each is of the whole. It is common to arrange the results in a horizontal line thus: 316 STATISTICS 05' PARTICULAR DISEASiES TABLE 82 SEASONAL DISTRIBUTION OF DEATHS FROM TUBER- CULOSIS (28-35) U. S. Registration Area, 1914 1 1 1 i 0} t-9 i. O > 1 i a (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Number of deaths — Per cent of total for the year 7522 8.9 7524 8.9 8537 10 5 8238 9.8 7782 9.2 6901 8.1 6528 7.6 6209 7.4 6031 7.1 6009 7.1 6212 7.4 6873 8.0 84,366 100.0% These figures show that the largest numbers of deaths occur during the spring months, but the difference between winter and summer is not great. It must not be forgotten in such a_ comparison as this that the months are of unequal length. While the above figures show that 8.9 per cent of the deaths occurred in February and 10.5 per cent in March the average number of deaths per day was 269 per day in February and 275 per day in March. The U. S. MortaUty Report, frpm which these figures were taken, do not dis- tribute the deaths in each month according to age. Another way of studying the seasonal distribution is to find the proportionate mortaUty for tuberculosis for each month. TABLE 83 PROPORTIONATE MORTALITY FROM TUBERCULOSIS BY MONTHS (28-35) U. S. Registration Area, 1914 4 1 J3 i <0 § >-3 *-> < 1 > i 1 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 9.1 9.7 9.5 10.1 10.2 13.3 9.3 8.7 8.8 8.8 9.0 9.1 9.4% Here the highest per cent was found in June. These figures are influenced, of course, by the numbers of deaths from causes other than tuberculosis. CHRONOLOGICAL STUDY OF TUBERCULOSIS 317 Chronological study of tuberculosis. — The death-rate from tuberculosis has decreased steadily during the last generation in Massachusetts as shown by Fig. 50. This curve does not tell us many of the things which we desire to .7W V V, , £. eafh tpfjtp. snn \ r-x K nn fro \ Af^ iseitS- 'Tri \J \ /373-/ ?/■# ^ ?nn \ \ > 'V Vn V-x V ^ 'no "^ ^ AO ^ , /a7o /S7S /aeo /»3S /sso /<«ar /soo /90s /s/o /s/s . /s>2a Years Fig. 50. — Death-rates from Tuberculosis, Massachusetts, 1873-1914. know. It shows that prior to 1885 the death-rate exceeded 300 per 100,000 but that now it is in the vicinity of 100. It is not decreasing arithmetically, however. Tuberculosis will not disappear by 1940, or thereabouts as one might think by a hasty forward projection of the plottfed line. The curve is 318 STATISTICS OF PARTICULAR DISEASES losing slope. Even if the rate of decrease remained the same from year to year, it would take many, many years for the curve to reach the zero line. The curve does not tell us whether it is the lives of the young or the old which are being saved. It is not easy to obtain specific death-rates for tuberculosis by sex and age- groups which cover a long period of years. Even if we had the figures they would not be very reliable because of changes which are being made in the diagnosis of the disease. Tuberculosis and occupation. — Many misleading statis- tics relating to tuberculosis and occupation are continually being pubhshed. As statements of facts they may be correct, but they are often subject to the fallacy of concealed classification and therefore give false impressions. ' A recent report of the New Jersey State Department of Health gives statistics of deaths from tuberculosis in 1916 classified by age and occupation. This is a better arrange- ment than is sometimes used, but even in studying these figures, it is necessary to be on guard against wrong con- clusions because of inadequate data. Thus we find the following: TABLE 84 DEATHS FROM TUBERCULOSIS CLASSIFIED BY AGE AND OCCUPATION: NEW JERSEY, 1916 Class. Age. Total 10-19 20-29 30-39 40^9 50-59 60-69 70-79 80-89 90+ fl' (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) Farmers 47 11 110 858 364 19 2 2 11 34 12 6 2 45 276 61 1 3 31 269 96 2 9 1 20 158 115 4 11 .2 2 65 49 7 9 1 1 36 27 5 6 18 4 1 3 1 n Farm laborers Clerks... n Housekeepers and stewards 1 General laborers Stone cutters TUBERCULOSIS DEATH-RATE 319 Why is the number of deaths from tuberculosis so high among housekeepers? Not becaus.e housekeeping imposes a special hazard, but because there are so many housekeepers in the state. Obviously what is needed here are the specific rates for this particular disease by age-groups. But to compute them it is necessary to know how many housekeepers there are in the state in each age-group, and who knows these facts? Also are the " stewards " referred to male or female ? Why is the number of deaths among stone cutters so small? This occupation is certainly hazardous from the standpoint of tuberculosis, as the fine, sharp, stone dust tends to lacerate the lungs. We cannot draw any reliable conclusion from the figures because we do not know how many stone cutters there are in each group. We notice that the largest number of deaths from tuber- culosis among farmers occurred in age-group 50-59, but that among farm laborers in age-group 30-39. What is"a farmer and what is a farm laborer? We must know that. Also do farm laborers ultimately becpme farmers? Is there a shift- ing of individuals from one class to the other as they. grow older? So also in the case of clerks. The largest number of deaths is in age-group 20-29. Do the clerks die off at this early age or do they cease to be clerks? Are the clerks male or female? The student of statistics must persistently cultivate this critical faculty until it becomes a habit. It may/esult in a cynical and pessimistic frame of mind in regard to published vital statistics, but even this is better than an easy lapse into an unthinking acceptance of all statistics at their face value. Statistics should be used with truth or they had better not be used at all. Racial composition of population and tuberculosis death- rate. — The following interesting and at first puzzling 320 STATISTICS OF PARTICULAR DISEASES situation will serve to emphasize the importance of the careful analysis of death-rates and the necessity of taking into account not only specific death-rates but the composi- tion of the population. In 1910 the death-rate from tuberculosis of the lungs was 226 per 100,000 in Richmond, Va., and 187 in New York City, and yet the specific death-rates from this disease for both white and colored persons were greater in New York than in Richmond. The following figures were taken from the U. S. Census reports. TABLE 85 TUBERCULOSIS DEATH-RATES IN NEW YORK AND RICHMOND Claas. Population. Number of deaths. Death-rate per 100,000. New York. Rich- mond. New York. Rich- mond. New York. Rich- mond. (1) (2) (3) (4) (5) (6) (7) White Colored Total 4,675,174 91,709 4,766,883 80,895 46,733 127,628 8368 513 8881 131 155 286 179 560 187 162 332 226 The explanation of this anomaly Hes, of course, in the fact that in Richmond more than one-third of the population is colored, while in New York the colored population is less than two per cent. Many similar comparisons can be found between northern and southern cities. This is merely a striking case. Diphtheria in Cambridge, Mass. — Applying the same methods to the study of diphtheria we have the following figures: DIPHTHERIA IN CAMBRIDGE, MASS. 321 TABLE 86 CAMBRIDGE, MASS., 1916 Statistics of Diphtheria, Cases and Deaths Arranged by Age and Sex Deaths, all Deaths from Cases of Age- causes. diphtheria. diphtheria. Male. Female. Male. Female. Male. Female. Male. Female. „ (1) (2) (3) (4) (5) (6) (7) (8) (9) 0-1 1,114 1,080 138 105 1 3 7 4 1-^ 4,161 4,120 38 40 4 6 56 67 &-9 4,996 5,000 13 13 5 5 63 80 10-14 4,488 4,533 ■ 7 6 1 1 15 24 15-19 4,569 4,901 22 12 1 7 4 20-29 10,424 11,326 44 51 1 8 12 30-39 8,334 9,190 64 43 4 5 40-49 6,552 7,177 80 76 1 50-59 4,133 4,823 88 85 1 60- 3,224 4,678 229 306 Total 51,995 56,808 723 737 13 15 160 198 Age- Morbidity (case) rate per 10,000. Percentage" distribution of cases. Mortality (death) rate. Percentage distribution of deaths. Proportion- ate mortal- ity .percent. Fatality, per cent. group. 0} ■3 ■3 S i2 6 1 i 1 .2 a 6 1 ■1 i i a 1 (1) (2) (3) (4) C5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Number of cases 24 35 37 44 31 32 21 15 20 25 38 36 358 It will be noticed that the lowest numbers were reported during the summer vacation months. Knowing that the incidence of the disease was greatest during the school ages does this indicate that schools played an important part in spreading the infection? Do these statistics prove it? If not, what other statistics would be necessary to prove it? AGE SUSCEPTIBILITY TO DIPHTHERIA 323 Age susceptibility to diphtheria. — Dr. Charles V. Chapin the Superintendent of Health, of Proyidence, R. I., has been in the habit of computing what he calls the attack rate. This is a ratio between the number of cases and the number of persons exposed, that is, all the members of the family where the disease occurred, including the cases and those who were removed from home after the disease developed. The follow- ing figures, given in Dr. Chapin's report for the year 1915, are based on a studjs of 53,280 exposed persons during 1889- 1915. TABLE 88 DIPHTHERIA ATTACK RATE: PROVIDENCE, R. I., 1915 Age-group. Attack rate (per cent). Age-group. Attack rate (per cent). CD (2) (1) (2) 0-1 yr. 1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ 11+ 16,70 43.65 54,55 55.61 55.91 53.99 53.82 49.33 44.31 40.91 36.42 35.35 12+ yr. 13+ 14+ 15+ 16+ 17+ 18+ 19+ 20+ Adults Total 31.12 26.08 22.41 18.92 18.58 17.85 16.86 17.33 23.56 6,83 25.45 > These figures indicate that the chance of exposed persons acquiring the disease in recognizable form is highest at age four and decreases steadily as the age increases. At the most susceptible period more than half of those exposed came down with diphtheria. It was found that between the years 1889^ and 1915 out of 6822 families who lived in houses where the disease existed, in other families, only 474 of these exposed families were 324 STATISTICS OF PARTICULAB DISEASES attacked. This is only 6.9 per cent. In most of these cases of attacked famiUes there had been some sort of intercourse with the infected fanaiUes, that is enough to transmit the disease by contact. Fatality of diphtheria. — Dr. Chapin has also kept a careful record of the fatality of diphtheria in Providence. In 1884 it was 30 per cent, and a few years later it rose to 42 per cent. Between 1895 and 1896 it dropped from 20 per cent to 14 per cent, since which date it has fallen until now it is only about 8 per cent, that is, there is only one death for each 12 cases. The fataUty is not the same at all ages as the following table ' shows: TABLE 89 DIPHTHERIA CASE FATALITY AT DIFFERENT AGES Age. 1889-1914. 1915. Cases. Deaths. Fatality. Cases. Deaths. Fatality. (1) (2) (3) (4) (5) (6) (7) 0-1 280 96 34.28 21 2 9.52 1+ 706 247 34.99 43 6 1,3.95 2-4 .3,322 691' 20.98 181 24 13.26 5-9 4,541 460 10.13 219 15 6.85 10-14 1,801 83 4.61 9 3 3.79 15-19 616 26 4.22 20 1 5.00 20+ 1,670 40 2.39 62 2 3.23 Total 12,936 1649 12.74 625 53 8.48 The greatest decrease in the fatality of the disease has occurred among young children. To a large extent the decreased fatality has been due to the use of antitoxin, which decreased the number of deaths. To some extent it may have been due to better diagnosis by ' Ann. Report Providence Supt. of Health, 1915, p. 64. Urban and rOral distribution of diphtheria 325 culture. If this practice increased the number of recognized cases it would decrease the fataUty rates. Diphtheria is a short disease. Hence the fatahty can be computed far more accurately than in the case of tubercu- losis. Chronological study of diphtheria. — Fig. 51 1 shows the decrease in the death-rate from diphtheria in Massa- chusetts since 1873. In 1876 the rate was very high, about 195 per 100,000. It has decreased very greatly until now it is usually less than 20 per 100,000. Recurrences of diph- theria have occurred at intervals of five or six years. After the great epidemic of 1876 there was no important recurrence until 1889, but after that recurrences were noted in 1894 and 1900. Since then, thanks no doubt to preventive medicine, the recurrences have been so slight as to be almost un- noticed. What is the reason for these recurrences, for this periodic development of diphtheria? In a general way, whooping cough, scarlet fevef, measles, all children's diseases, have similar recurrences. It is commonly explained on the theory of susceptibility. It has already been seen that the rate of attack of exposed persons is very high among young children. It is known, too, that one attack usually makes the victim relatively immune against a second attack. After a period of relative quiescence during which the class of susceptible children has been annually recruited it is natural to expect that an epidemic may spread. This is apparently what happened Until the methods of preventive medicine came to be generally used. It probably still happens, but to a less extent than formerly. Urban and rural distribution of diphtheria. — It is not easy to obtain complete statements of the facts to show the differences betweeit the occurrence of diphtheria in cities and ' State Sanitation, Vol. I, p. 167. 326 STATISTICS OF PARTICULAR DISEASES K nprrtf 7 Pf^fl g D/d/7j r ZroLt^ \ M / 7 f,-! V \ /876 '-/3/4 « ^ j\ 1 h • VI \ j r \ , / \ V \, V \ ^-^^ v- /y7i' /«?^ /SSS /S30 /S9S /900 /90S /9/0 /9/S /SSO Fig. 51. — Death-rates from Diphtheria, Massachusetts, 1873-1914. STATISTICAL STUDY OF TYPHOID FEVER 327 rural districts. Occasionally partial statements are pub- lished. In the annual report of the Michigan State Board of Health for 1916-17'it is stated that for the period 1904^15 the morbidity rate was 213 per 100,000 in urban districts and 82 in rural districts; the mortality rates for 1908-1915 were 16.2 and 12.2 per 100,000 respectively. The fatality was 10.9 per cent for cities and 15.7 for urban districts. No separations were made according to age and sex and it is difficult to find these facts. There is, however, quite a difference in the age distribution of diphtheria between the city and the country. In general the average age of diph- theria cases, as well as of persons dying from this disease, is lower in the city. The following facts were taken almost at random from the Mortality Statistics of 1914: TABLE 90 PERCENTAGE AGE DISTRIBUTION OF DEATHS FROM DIPHTHERIA Cities. Rural states. Age. New York. Boston. Vermont. New Hampsliire. Maine. (1) (2) C3) (4) (5) (6) 0+ 10.7 7.7 0.0 6.7 9.3 -. 1+ 25.9 21.4 5.2 17.8 10.5 2+ 16.5 13.7 18.4 11.1 16.3 3+ 13.7 14.9 18.4 8,9 9.3 4+ 9.7 6.0 13.1 17,8 7.0 5-9 (per year) 3.7 5.3 6.3 4.0 7.0 10-19 0.26 0,6 0.52 1.55 0.7 20-29 0.14 0.12 0.0 0.0 0.23 30-39 0.05 0.06 0.0 0.0 0,23 Statistical study of typhoid fever. — Typhoid fever has been given a great deal of attention from the statistical point of view. Hundreds of scientific papers describing 328 STATISTICS OF PARTICULAR DISEASES local outbreaks of the disease, variations in the typhoid fever death-rate and so on have been published. For the most part these have been extensive and not intensive studies. It is rather surprising, when we view this enormous mass of statistics, how little we know about certain important points, such as the morbidity and fatality rates at different ages. Our interest has been engrossed by the more important matter of causation. There are many ways in which the disease may be communicated from one person to another and this question must be answered for each particular out- break or epidemic. The interest in statistical studies of typhoid fever has, therefore, centered around the subject of correlation, a phase of statistics which we shall consider in Chapter XIII. It will be useful to consider at this point some of the fundamental relations of this disease to human beings. Those who are interested in the epidemiology of the subject are referred to the author's book on Typhoid Fever. This book, it should be said, is to-day somewhat out of date, although its historical value remains. Age distribution of typhoid fever. — The largest number of deaths from typhoid fever is generally found in age-group 20-29 years. Table 91 shows the percentage distribution of deaths by ages according to the U. S. Census ^ for 1900. In the case of epidemics caused by a widely scattered in- fection, as through the public water-supply, the age dis- tribution of the deaths usually approximates these figures. If, however, the outbreak occurs in a school-house or is caused by infected milk, which is used more freely by children than by adults, the larger numbers of deaths may occur' in the lower ages ; in fact, this is a test often applied in the study of typhoid fever outbreaks. • Vital Statistics, Vol. Ill, Part I, page ojdTi. AGE DISTRIBUTION OF TYPHOID FEVER 329 TABLE 91 PERCENTAGE DISTRIBUTION OF DEATHS FROM TYPHOID FEVER; UNITED STATES: 1900 Age-group. Per cent of deaths. Age-group. Per cent of deaths. (1) (2) CD (2) 0-4 4.09 50-54 3.52 5-9 5.05 55-59 2.55 10-14 5.20 60-64 1.95 15-19 11.23 65-69 1.12 20-24 17.78 70-74 0.91 25-29 15.09 75-79 0.34 30-34 11.46 80-84 0.11 35-39 9.12 85-89 0.09 40-44 5.77 Total 100.00 45-49 4.62 If we take the specific death-rates by sex and ages we obtain the following figures: TABLE 92 SPECIFIC DEATH-RATES FOR TYPHOID FEVER United States: 1900 Age-group. Rate per 100,000. Age-group. Rate pel 100,000. Males. Females. Males. Females. (1) (2) (3) (1) (2) (3) 0-4 12 16 45-49 34 29 5-9 15 21 50-54 30 30 10-14 17 31 65-59 30 33 15-19 45 53 60-64 29 33 20-24 66 57 65-69 22 40 25-29 61 48 70-74 27 43 30-3^ 53 43 75-79 20 23 35-39 48 39 80-84 10 26 40-44 34 37 85-89 16 35 330 STATISTICS OF PARTICULAR DISEASES It will be noticed that these differences are not as great as in the previous table. This is because there are fewer persons living at the ages above 50 and even if the specific rate remained high there would not be as many deaths. It is for this reason that both the age distribution of deaths and the specific death-rate are important tabulations. The specific rates just given represent practical conditions and take into account the important element of exposure. The difference between the death-rates of males and females at ages 25-29 must not be regarded as having a physiological basis, for at those ages males are more exposed to the dis- ease than females. Except at times of epidemics typhoid fever is not a well- reported disease. It is difficult therefore to obtain reUable specific morbidity rates by sex and ages. Such as have been computed, however, show an age distribution very similar to that of deaths, but with a tendency towards larger per- centages of cases in the earlier years. The fatality of the disease at different ages is not as well- established as it ought to be. Computations by the author, by Newsholme, by A. W. Freeman,^ seem to warrant the following approximate figures: TABLE 93 APPROXIMATE CASE FATALITY IN TYPHOID FEVER Age. Per cent. Age. Per cent. (1) (2) (!)• (2) 15 40 21 10 8 50 25 20 15 60 42 30 18 All ages 14 ' Case Fatality in Typhoid Fever, Public Health Reports, Dec. 8, 1916. SEASONAL DISTRIBUTION OF TYPHOID FEVER 331 ou ■■■ ■^ ~ zo 70 f»»i ,, --., ^y ^ A / ' 60 * y / \ \ / / s \ Lis i\ f ^ l\ / / \ t 50 ' ¥ 5/ V / / \ \ ,4? / \^ \ / r \ >, 40 / ^N / / \ \ ^ -" > s\ r -5 / M p "tS rn N s / ^ .E\/ ' '-0 >v S 17 ^ 80 ^ 20 270 I / s /' \ ^60 ^■' .— ^ ^ \ 18 / li \^ / / \ p50 > /"' \ k, / \ \ \ r' / Is >« / \ \ |40 ^30 rf' y / ^ •^ s / \ \ =, ~" ■A 1— \ 4. -5 ■" P 1 1 IM OF p }& _^ SO 70 \ .' 60 ••, v' 15 .— .-- - .— "N •» N ''/ — s 50 r' ' ^ s ^N ,' ') s / *■ ■^ ~ — \ s •-. -' 1 40 / \ \ y L -- — -5 30 SA N N( IS CO s« Nl lA SO D E C H LE 18 88 1897 1£ 86 -16 95 an 1 _ X h- af cooe OS 0.-I -I 1° ziair(r>;S!>;ozz''i'''a?7S!5d!rl->c3z <3^ ><%^Vrv>- g>»<»^..?^.^ -j^^L^.v,.^ Diseases Nos. 60*76 ^;^■.,..^^y^>^>-r»1'777^.nll■ l-l N08. 187-9 AU other Diseases 1908 ^909 ~ 1910 - 1911 1912 Fig. 54. — Infant Mortality by Months, Classified According to Cause: Boston, Mass. 35§ STUDIES OF DEATHS BY AGE PERIODS Among both male and female infants 37 per cent of the deaths were from malformations and diseases of early infancy; about 27 per cent were from digestive diseases; about 17 per cent were from respiratory diseases. Together the deaths from these causes amounted to four-fifths of all the infant deaths. These percentages are not constant. There is an important seasonal variation; there are also differences according to age and nationality. In 1912, Dr. Wm. H. Davis made an excellent analysis of the infant deaths in Boston for a five-year period. Fig. 54, drawn from figures in his report, shows how the deaths from digestive diseases have fallen during the sum- mer season, but remained almost unchanged during the winter; how the deaths from respiratory diseases are higher in the winter than in the summer; and how the deaths from diseases of early infancy, the general diseases and nervous diseases do not have a marked seasonal dis- tribution. The diagram also shows how the diseases from ill-defined causes have decreased, due, it is said, to better diagnosis. In Boston the diseases were classified by cause and age as follows: INFANT MORTALITY BY CAUSES 359 TABLE 111 CAUSES OF INFANT DEATHS: BOSTON, 1910 Number of deaths. Cause 4 il 1^ 00 -S CO +3 1^ -1 (1) (2) (3) 2 8 1 9 10 32 147 4 213 (4 21 6 2 54 41 3 24 135 2 3 292 (5) 37 17 4 68 153 1 11 99 3 7 400 (6) 43 17 1 80 201 2 3 2 7 12 4 33 405 (7) 58 24 89 112 2 - 2 3 3 8 1 15 317 (8) 52 21 69 108 3 2 2 2 5 1 5 270 (9) I. General disease II. Nervous system III. Circulatory system — IV. Respiratory system . , . V. Digestive system VI. Genito-urinary system VIII. Skin and tissue IX. Bones 1 1 41 305 5 353 213 94 8 370 625 8 10 7 X. Malformations 120 711 XIII. External causes XIV. Ill-defined causes All causes 16 67 ??49 As would be expected from the definition the largest num- bers of deaths from causes incident to early infancy occur among early infants. This is true also of malformations. The intestinal diseases reach their maximum effect between the third and fifth month, the respiratory diseases and the general diseases, which are chiefly communicable, a httle later — say between the sixth and eighth months. In Johnstown important differences were noted between the causes of death among infants of native and foreign mothers. Thus, during the first year of life the following absolute infant mortalities, with subdivisions by cause were found. 360 STUDIES OF DEATHS BY AGE PERIODS TABLE 112 CAUSES OF INFANT DEATHS: JOHNSTOWN Native mothers. Foreign mothers. (1) (2) (3) 104 21 23 14 6 7 33 171 DiarrhcEa and enteritis. . 54 Respiratory diseases 48 Premature births 20 Congenital debility or malformations. . . . Injuries at birth 21 2 Other cause, or not reported 26 In Boston the following figures were given for 1910 for deaths of infants born to native and foreign mothers: TABLE 113 CAUSES OF INFANT DEATHS: BOSTON Eatcs per 1000 births 4 ^1 6a "a . a £ "a tig (1) (2) (3) (4) (5) (6) Congenital debility and malfor- mations 50 34 15 10 2 3 31 37 18 13 .4 3 49 43 . 12 16 1 3 24 22 29 4 2 8 20 Diarrhoea and enteritis 19 Pneumonia and broncho-pneu- monia 16 Diseases of early infancy Tuberculosis Measles, scarlet fever, whooping cough and diphtheria 7 2 4 THE JOHNSTOWN STUDIES 361 The Johnstown studies. — In 1915 the Children's Bureau of the U. S. Department of Labor/ pubhshed an important intensive study of the Infant Mortality of Johnstown^ an industrial city of Pennsylvania. Miss Julia C. Lathrop is the Chief of this bureau. The field work was in charge of Miss Emma Duke. This was essentially a sociological study. Only a few of the simple correlations can here be presented. The report is one which the student may profit- ably read in full. TABLE 114 mPANT MORTALITY AND TYPE OF HOME Housing condition. Infant mortality. (1) (2) Clean, dry 105 127 171 158 162 204 118 198 108 159 ' ' damp Moderately clean, dry " damp Dirty, dry " damn Water supply in house Water closet Yard privy » Infant Mortality Series No. 3. 362 STUDIES OF DEATHS BY AGE PERIODS TABLE 115 INFANT MORTALITY AND SLEEPING ROOMS Infant ■ 'mortality. (1) (2) Number of others sleeping in same room with baby: 2 or less 67 98 123 56 109 3 to 5 Over 5 Baby sleeping in separate bed: Yes No TABLE 116 INFANT MORTALITY AND VENTILATION Ventilation of baby's room. Infant mortality. (1) (2) Good 28 92 169 Fair TABLE 117 INFANT MORTALITY AND ATTENDANT AT BIRTH (1) Physician. Midwife. . Infant mortality. (2) 100 180 THE JOHNSTOWN STUDIES 363 TABLE 118 INFANT MORTALITY AND EDUCATION .OF FOREIGN MOTHERS Infant mortality. (1) (2) Literate 148 214 146 187 Illiterate Do not speak English TABLE 119 INFANT MORTALITY AND AGE OF MOTHER Age of mothers. Infant mortality. (1) (2) Under 20 137 121 143 136 149 20-24 25-29 30-39 The study of feeding was made by months. The following figures show the rate of mortality per 1000 babies ahve at the specified time. 364 STUDIES OF DEATHS BY AGE PERIODS TABLE 120 INFANT MORTALITY AND FEEDING . Specific infant mortality (absolute) Age. Breast feeding only. Mixed feeding. Artificial feed- ing only. 0) (2) (3) (4) Second, month, . . . 72 54 •47 38 26 29 26 18 14 78 92 67 40 32 22 20 16 11 237 217 Third " Fourth " 166 Fifth " 127 Sixth " 92 Seventh " 72 Eighth " 53 Ninth " 25 Tenth " 11 In the early ages the difference between deaths of breast- fed infants and those artificially fed is very great, but the difference becomes less as the baby grows older. TABLE 121 INFANT MORTALITY AND HOUSEHOLD DUTIES Household duty. Infant mortality. (1) (2) Cessation of duties before confinement: None or less than one month One or more months Time of resuming all household duties after con- finement: S days or less ■ 137 113 169 9 to 13 days 165 14 days or more 117 OTHER STUDIES OF THE CHILDREN'S BUREAU 365 TABLE 122 INFANT MORTALITY AND EARNINGS OF FATHER Annual earnings of husband. Infant mortality. Native wives. Foreign wives. (1) C2) (3) Under $521 251 $521 to $624 i46 70 131 76 162 $625 to $779 130 $780 to $899 167 $900 to $1199 152 $1200 or more 78 108 The report also contains statistics relating to reproductive histories of the mothers studied during the investigation. Other studies of the Children's Bureau. — Besides the Johnstown studies, here emphasized because they were first made, the Children's Bureau has made at this writing (1918), intensive studies in Manchester, N. H., Saginaw, Mich., Waterbury, Conn., Brockton and New Bedford, Mass., Ak- ron, Ohio, and Baltimore. A brief account of these most important intensive investigations, based on a first-hand collection of the facts may be found in the Quarterly Publica- tion of the American Statistical Association.' Two tables from this report are of interest: ' Robert M. Woodbury, Infant Mortality Studies of the Children's Bureau, June 1918, pp. 30-53. 366 STUDIES OF DEATHS BY AGE PERIODS TABLE 123 INFANT MORTALITY AND FATHER'S EARNINGS, BALTIMORE Earnings of father per True infant Earnings of father per True infant year. mortality rate. year. mortality rate. (1) (2) (1) (2) No earnings 207.7 $1050-1249 66.6 Under $450 156.7 1250-1449 74.0 S450-S549 118.0 1450-1849 86.3 550- 649 108.8 1850 and more 37.2 650- 849 96.06 Not reported 140.2 850-1049 71.5 All classes 103.5 TABLE 124 INFANT MORTALITY AND ORDER OF BIRTH — MOTHERS OF ALL AGES Number of birth in order. True infant mortality. Number of birth in order. True infant mortality. (•' (2) (1) (2) 1 2 3 4 5 6 115.8 102.7 111.5 127.0 129.3 132.2 7 8 9 10 11 128.2 162.6 142.1 181.1 146.8 Although in general the average infant mortality is less for the second child than for the first or subsequent children, this is a matter which varies somewhat with the age of the mother. For mothers under twenty the mortality is lowest for first children; for mothers aged 30-34 years it is lowest for the third children; and for mothers aged 35-39 it is lowest for fourth children. Perhaps, if nationality were considered, other differences would be noticed. MATERNAL MORTALITY 367 Infant mortality problems. -^ There are many practical problems relating to infant mortality which must be studied with the aid of statistics. The object of the tables here given is to show the complexity of the problem and the futiUty of depending alone upon the current approximate method of stating infant mortahty. Extensive compilations of data for various places and for different years make easy reading and give one a superficial knowledge of the subject, but they do not help us very much in solving real problems. It is the intensive studies which count. What kind of wel- fare work deserves the largest appropriations ? The answer depends upon where the babies are dying, at what age they are dying, under what social conditions, under what remedi- able conditions, and so on. Are the milk stations of our large cities a paying life-saving agency? The answer cannot be told by comparing the conventional infant mortality rates; perhaps the reduction of infant mortality may be among the earliest weeks of Ufe, an age at which artificial feeding is less common. What relation is there between density of popu- lation and infant mortality? The answer cannot be found without splitting up the infant mortality into its constituent parts. The lesson is one which the author wishes to teach in every chapter of this book, namely, that the vital statistician must train himself to analyze his statistics; to be specific; to think first what kind of facts he needs in order to answer a specific question and then go after them, remembering that a small number of well-directed statistics are worth more than vast numbers of general statistics, piled together without regard to internal differences which may make them worthless. Maternal mortality. — Closely associated with infant mortahty we have the problem of maternal mortality. Since the long-ago studies of Dr. Oliver Wendell Holmes, but especially since the rise of bacteriology, there has been 368 STUDIES OF DEATHS BY AGE PERIODS a very great decrease in death-rates from child-bed fever, but even within very recent years we can ^ee an added improvement, which can be attributed to the general at- tention being given to pre-natal care, to laws in regard to mid-wives and similar causes. The following condensed figures for New York city ^ illustrate this decrease. TABLE 125 MATERNAL MORTALITY-RATE, CITY OF NEW YORK Quinquennial period. Rate per 100,000 females (age 15-45). Puerperal sepsis. Other deaths. (1) (2) (3) 1898-1902 1903-1907 1908-1912 1913-1917 25.9 26.1 18.3 15.3 40.5 41.3 35.7 29.8 These figures might more properly have been based on married women within the given ages, or upon births and still-births taken together instead of on all females of child- bearing age, but the chronological differences are so great as to leave no room for doubt as to the main facts. Childhood mortality. — The period of life between the ages of one and five years represents a pecuhar environment which may be described by the words home and play. In this period the physiological influence of the mother on the child becomes less, but her intelligence, ' her social and economic condition, the general environment of the house and the neighborhood become greater. During these four years the specific death-rate of children decreases greatly and the diseases to which they are subject change in character. ' Weekly Bulletin, Dept. of Health, March, 1918. DISEASES OF EARLY CHILDHOOD 369 TABLE 126 SPECIFIC DEATH-RATES OF CHILDREN i U. S. Registration Area, 1910-1915 Rate per 1000 Age. N Male. Female. (1) (2) (3) — 1 year 125.8 101.1 1 + 27.3 25.0 2 + 11.0 10.1 3 + 6.9 6.3 4 + 5.1 4.7 0-5 years 36.0 30.0 5-9 3.3 3.0 10-14 2.3 2.1 1 From Dr. Dublin's paper. The diseases which occur during childhood are especially amenable to preventive measures, a fact which makes their study one of especial importance from the standpoint of life saving. Diseases of early childhood. — Dr. Louis I. Dublin, Statistician of the Metropolitan Life Insurance Company has discussed these diseases in an article on the Mortality of Childhood,! from which the figures for proportionate mortal- ity given in Table 127 are taken. This table gives only those diseases for which the propor- tionate mortality was more than 3 per cent of all deaths. One rather unexpected cause of death looms large in this table — namely, burns. In the second year of Hfe the proportionate mortality was 1.7 per cent, the next year 4.3 per cent, the next 5.9 per cent, the next 5.7 per cent. Dr. ' Quarterly Publications, Am. Statistical Assoc, March, 1918, p. 921. 370 STUDIES OF DEATHS BY AGE PERIODS O H CO lo d -5 o S o ?: ti, o Pi o p$ p< CO • ooeOCOOIr- O 0OU3 §. coi>;eoed« lo COM ? ■ .2 ■ !r . j3 ■ -a 1' 44 u • o : a M a ■ ST £-2 1? : i 1 1 s s i 1 i III flogPHmnn h ;g fe-s OtXJeO cOOO-dH 0(N Si s t^t^r- t^t^lOiti -^co 1 ji T 3 : T) n ^ i ^ e - n M a cd d 1 3 s <; © Q o 8 a a .& g § .3 .t Q«£q dSmSfn & £ a (MtNi-iaiust^eoo OS £ co«i-«ooio-^*HTpTti eo k i .i -& a a o ija g S "a 1 : ^a • S DO (d c a ^ ": w p a ^-' S ■c '?'-a £ : tp o . s •S f^ fl '-H 2 is '1 o —1 oi a *H .a < a u a 1 g e8 -J3 o ro o3 -3 Q .M .r4 £ .ri •_ CO 1 a « Q a 1 MORTALITIES DURING SCHOOL AGE 371 Dublin in the paper referred to gives the specific death-rates as well as the proportionate mortalities. The figures for burns are for the second year 44.1 per 100,000, for the third, 44.8, for the fourth, 39.4, for the fifth, 28.1. The increasing importance of such communicable diseases as diphtheria, whooping cough, measles and the like during this period shows the increasing influence of environment and associa- tion of children with each other. Proportionate mortalities during school age. — During the ages from 5 to 15 when children are ai school we have what is perhaps the maximum opportunity for contact infection. During these ages, therefore, we may expect to see communicable diseases coming to the front in our pro- portionate mortalities. But we also find weaknesses in the human mechanism making themselves felt. Tuberculosis and typhoid fever also begin to loom up as great menaces. TABLE 128 PROPORTIONATE MORTALITY U. S. Registration Area, 1910-15 Ages 5-9. Per ceat. Ages 10-14. Per cent. (1) (2) (3) (4) Diphtheria and croup Scarlet fever 15.8 7,1 5.9 4.4 4.4 3.7 3.5 3.5 3.4 3.4 2.7 2.6 2.5 Tuberculosis of lungs .... Organic diseases of heart. Typhoid fever Appendicitis Diphtheria 10.2 8 6 6 4 Organic diseases'of heart. . . Vehicular accidents 6.3 5 6 Pneumonia Drowning Vehicular accidents Scarlet fever 5 3 Broncho-pneumonia Tuberculosis of lungs Appendicitis 4.4 4.4 3 Tuberculous meningitis .... Burns Acute -articular rheuma- tism 3 Drowning Measles . . ^ . . . 372 STUDIES OP DEATHS BY AGE PERIODS Proportionate mortalities at higher ages. — The following statistics show the proportionate mortalities for age-groups 30-34, 50-54 and 70-74 years. TABLE 129 PROPORTIONATE MORTALITY U. S. Registration -Area, 1914, Males Age 30-34 ^•ei^3. Age 50-54 years. II Age 70-74 years. a) a (1) (2) (3) (4) (5) (6) Tuberculosis 32.0 16.1 6.9 5.4 5.2 4.2 4.1 2.8 2.8 1.9 1.6 Tuberculosis 13.4 U.7 11.0 8.1 8.0 7.7 6.8 3.2 2.9 1.7 1.6 1.4 1.4 1.2 Organic diseases of heart Organic diseases of heart Bright's disease ?1 fi Bright's disease Apoplexy 13 4 Organic diseases of heart 13 8 8 4 Pneumonia 4 H Bright's disease Diseases of arteries . . . Accidents 4 n Suicide Cirrhosis of liver Diabetes S ?. ?, 8 Old age •>, n Broncho-pneumonia. . . Diseases of prostate — 1 9 Acute endocarditis Pleurisy 1.7 1 fl Cirrhosis of liver Diabetes 1 5 1 •i Angina pectoris Influenza 1.4 n 9 Tuberculosis stands at the head of the list until age 70. Organic diseases of the heart increase with age. Accidents diminish. Bright's disease increases. Suicide decreases. Cancer increases, and so on. Of course in a complete study all of these diseases at different ages should be studied by the use of specific rates as well as proportionate mortality. Studies by sex, by season, by nationality, and so on, should also be made. Average age of persons living. — The average age of a community is, of course, the weighted average of the differ- MEDIAN AGE OF PERSONS LIVING 373 ent age-groups. It is the sum of the ages of all the people divided by the total population. In 1880 the average age of the aggregate population of the U. S. registration area was 24.6 years, in 1890 it was 25.6, in 1900, 26.3 years. There has apparently been an increase although the figures do not stand for exactly the same areas. But this result might be due to a les- sening of the birth-rate, to an increase in infant mortal- ity, to an influx of immigrants of middle age or to a reduced death-rate among the aged. That the native birth-rate has been decUning is true, that immigrants of middle age have been entering the country is also true. These would tend to increase the average age. But the infant mortality has been decreasing, not increasing, and the mortaUty in the higher age-groups has rather in- creased than diminished. These factors would tend to decrease the average age. Evidently the problem is so complicated that the average age of the hving cannot be fairly taken as an index of hygienic conditions. Median age of persons living. — Instead of finding the average age of the living the median might be used, but the objections to the average age of the living would apply also to the median, although the magnitude of their in- fluence would be somewhat different. The median age of the population of the United States has greatly increased during the last century as the following figm'es show: 374 STUDIES OF DEATHS BY AGE PERIODS TABLE 130 MEDIAN AGE OF POPULATION: UNITED STATES Year. Median age. 1800 16.0 1810 16.0 1820 16.5 1830 17.2 1840 17.9 1850 19.1 1860 19.7 1870 20.4 1880 21.3 1890 21.9 1900 23.4 1910 24.4 Average age at death. — Nor does the average age at death afford a fair index of the healthfuhiess and physical welfare of a community. The reasons are similar to those just mentioned. A high average age at death may mean simply that the birth-rate is low. There has been, in recent years, a general rise in the average age at death. In Rhode Island, for example, the increase has been as follows: TABLE 131 AVERAGE AGE AT DEATH: RHODE ISLAND Period. Average age at death. Period. Average age at death. (1) (2) (3) (4) 1861-65 1866-70 1871-75 1876-80 29.32 32.42 30.16 31.21 1881-85 1886-90 1891-95 1896-00 33.99 33.42 33.96 34.53 EXERCISES AND QUESTIONS 375 In 1900 the average age at death in the registration states of the U. S. was 36.8 years. For the cities it was 32.4; for the rural districts 44.7 years. In Mass., in 1910, the average age at death was 39.51. In 1913 the average age at death for the U. S. Registration Area was 39.2 years for males, 40.6 years for females, and 39.8 years for the entire population. In a general way, however, the prolongation of life may be regarded as an index of human progress, as Professor W. F. Willcox has pointed out. EXERCISES AND QUESTIONS 1. Compare the infant mortalities for certain assigned large cities and rural districts. 2. Compare the infant mortalities for California cities with those of eastern cities. 3. Compute the seasonal variations of infant mortality for CaE- fornia cities. 4. What is the average infant mortality in New South Wales? Why is it so low? 6. Do the statistics of infant mortality justify the continuance of the milk stations in New York City? 6. In what direction wiU efforts to reduce infant mortality yield the most profitable results? 7. Is poverty, ignorance, race or climate the greatest factor in causing high infant mortaUties? 8. Make a statistical study of some cause of death, to be assigned by the instructor, according to age periods. CHAPTER XII PROBABILITY In the second chapter it was shown that the average, or mean, of a number of figures gave a very inadequate idea of the figiures themselves; that two sets of figures may have the same average yet differ among theniselves in a striking manner. It is often important to find out what these differ- ences, or variations, are. We have seen that one way to do this is to arrange the items in array, that is, in order of magnitude and find the median, the mode, the quartiles and so on, but even this is not enough; it is necessary, if possible, to find some mathematical relation between the. variations. Natural frequency. — It is a curious and important fact that if we measure natural objects, such as the lengths of the leaves on a tree, or the heights of a regiment of men, or the lengths and breadths of nuts, to use illustrations studied by the Eldertons in their Primer of Statistics, we shall find that most of the observations will be very close to the mean of all, that a few will differ from it considerably and that a very small number wiU differ from it very greatly. ' In a thousand observations a certain number are almost sure to differ from the mean by a definite amount, and a certain other number are almost sure to differ from the mean by twice that amount. In fact these relations are so regular as to amount to what may be called a law of nature, a sort of natural frequency. In these variations we shall find some observations larger than the mean and some smaller. Natural frequency can best be understood by an example. 376 NATURAL FREQUENCY 377 In a certain army the results of measurement of the heights of 18,780 soldiers were as follows: TABLE 131 HEIGHTS OF SOLDIERS Height in inches. Number of soldiers. Per cent of soldiers. « (1) (2) (3) 60 + 197 1.05 61 + 317 1.69 62 + 692 3.69 63 + 1,289 6.86 • 64 + 1,961 10.44 65 + 2,613 13.91 66 + 2,974 15.84 67 + 3,017 16.07 68 + 2,287 12.18 69 + 1,599 8.52 70 + 878 4.67 71 + 520 2.77 72 + 262 1.39 73 + 174 0.92 Total 18,780 100.00 It will be seen that the mode, the most commonly observed height, was in height-group 67+, i.e., 5 feet 7 inches and 5 feet 8 inches. The mean was 67.24 inches. If we should at- tempt to stand these 18,780 in array we should have an impossible task. We 3xdght try it, however, and obtain something Uke this : There are 18,780 soldiers in all. The middle one would be niunber 9390, or between this and 9391. By counting up from the left we find that the median is just a Httle below 67 inches. There are, of course, differences in height in each group and with care we could get the median exactly. By taking a weighted average, as described in the second chapter, we could get the mean. But just now we are interested in 378 PROBABILITY the variations. We can plot the number of soldiers by height groups, as in Fig. 55. This will give us a characteristic curve highest in the middle and sloping downwards gently ^UOO J9£ towards either end. This is called a frequency curve. It should be noticed that whereas in the array the height was indicated by the vertical scale it is in this diagram indicated by the horizontal scale. WHAT IS MEAiSTT BY "CHANCE' 379 Coin tossing. — Ten coins were tossed into the air by the students in one of my classes an aggregate of 1250 times, records being kept of the number of heads which came up. The results were as follows: TABLE 132 RESULTS OF COIN TOSSING Number of heads up at once. Number of throws. Number of heads up at once. Number of throws. (1) - (2) (1' (2) 1 2 3 4 5 1 15 62 156 265 288 6 7 8 9 10 266 128 55 13 1 These results when plotted gave a frequency curve which was much hke that obtained for the soldiers. This curve was evidently the result of chance. One cannot tell for any given throw how many heads will come up, yet in the long run we always get some such result as that obtained by the coin tossing students. What is meant by " chance. " — What determines whether a coin thrown into the air will fall with the head up ? Many things, of course, — the way it is held when thrown, the twist with which it starts, the height to which it rises, the manner in which it strikes the floor, the way it rolls, and many other factors. The sum total of these many causes gives what we call "chance." Chance is not the absence of cause, it is the result of a multiplicity of causes. In chance we must judge the result by the combination of these many causes. Often it is the only way we can judge the result. In chance we can never tell exactly any particular result, 380 PROBABILITY but we can form an idea as to the frequency with which any possible result will occur. In the case of the coins we could not tell in advance the result of any particular throw of ten coins but we could safely predict that five heads would be thrown more often than any other number, and that no heads or ten heads would happen least frequently. Is there any way by which the frequency that other numbers of heads would be thrown can be ascer- tained? There is, and it is quite simple. We will start with a single coin. We toss it up. It is an even chance as to whether it comes up a head or a tail. If we should toss the coin a hundred times we would probably have a head in fifty of the throws. In practice it might not come out exactly 50, it might be 48 or 55, but if we tossed the coin an enormously large number of times a head would come up half the time. Let us now take two coins which we will call a and h. If we indicate a head by heavy type then we have the following possible combinations: ab; ab; ab; ab. We thus have the following results: Heads 12 Number of throws 12 1 Total 4 If we have three coins we have the following possible chances : abc; abc, abc, abc; abc, abc, abc; abc. Heads 12 3 Number of throws 13 3 1 Total 8 If we have four coins we have: abed; abed, abed, abed, abed; abed, abed, abed, abed, abed, abed; abed, abed, abed, abed; abed. Heads 12 3 4 Number of throws 14 6 4 1 Total 16 BINOMIAL' THKOREM 381 And so it goes' on until for 10 coins we have: Heads 01 2 3 4 5 6 789 10 Number of throws 1 10 45 120 210 252 210 120 45 10 1 Total 1024 Theoretically, therefore, the coins in 1250 throws should have given us the following numbers: These compare rea- sonably well with those obtained by the students. TABLE 133 THEORETICAL RESULT OF TOSSING 10 COINS 1250 TIMES Number ot heads. Number of throws. Number of heads. Ntimber of throws. (1) (2) (1) (2) 1 6 257 1 12 7 147 2 55 8 55 3 147 9 12 4 257 10 1 5 354 Binomial theorem. — Another interesting fact is that these numbers which we have just obtained as representing what would result from applying the laws of chance to the tossing of two, three and more coins, are the same as are obtained by expanding the sum of two quantities by the binomial theorem, (a + 6)" in which each quantity, a and b is taken as 1, i.e., (1 + 1)". In the problem a head was just as Ukely to come up as a tail. In this expression n is the number of coins. If n = 1, (1 + 1)1 = 1 + 1, n = 2, (1 + 1)2 = 1 + 2 + 1, n = S, (1 + 1)3 = 1 + 3 + 3 + 1, n = 4, (1 + 1)^=1 + 4 + 6+4+1, n = 5, (1 + 1)5 = 1 + 5 + 10 + 10 + 5 + 1. 382 PROBABILITY The binomial theorem, therefore, give^ us a method of finding the shape of any natural frequency curve if we know the number of terms. It should be observed that only the even values of n give an odd number of terms with a middle highest term. Some interesting conclusions may be predicted from this application of the binomial theorem. One of them is that the larger the number of terms the more closely are the items clustered around thp in-dian figure. It follows that the average of a large nunihiT of observations is much more precise than the average oi uuly a few observations. In fact, it can be shown thai i)i< error of a set of observations varies inversely as the square of the number of observations. If we multiply the number of observations by four, we halve the probable error. Chance and natural phenomena. — Does it follow there- fore that the measurements of natural phenomena result from chance ? Certainly, if they follow the binomial law as pointed out. How is it in the case of the heights of soldiers? Here we had 18,780 soldiers. Theoretically, these should have been distributed as shown in Column 3. Actually they were distributed as in Column 2. The differences are very slight. What are the many causes which determine a person's height? It is difficult to say. Possibly inheritance, age, nationality, food supply during the period of growth, early illnesses, habits of sleeping, sitting, standing and many other factors. It would be an interesting subject for discussion. Whatever the causes are they are combined in so many ways that we have no better method of predicting the heights of the soldiers in a regiment than by the application of this law of chance. SKEW CURVES 383 TABLE 134 HEIGHTS OF SOLDIERS Per cent of soldiers. Hdizht in iuclies. XXDJl^lAV aii iii^^JJ*-U» Actual. Theoretical. CD (2) (3) 60 + 1.05 1.00 61 + 1.69 1.71 62 + 3.69 3.68 63 + .6.86 6.75 64 + 10.44 10.51 65 + 13.91 13.99 66 + 15.84 15.84 67 + 16.07 15.31 68 + 12.18 12.60 69 + 8.52 8.84 70 + 4.67 5.31 71 + 2.77 2.67 72 + 1.39 1.18 73 + 0.92 0.61 100.00% 100.00% Skew curves. — In plotting natural phenomena it will be found that not all frequency curves are sjonmetrical. The median is not always the mean; there may be more items on one side of the mean than on the other. The asymmetrical curves are known as skew curves. They are not susceptible of mathematical analysis except by the use of complicated and rather uncertain methods. There are four common types of asymmetrical curves commonly met with in demographic studies. These are shown in Fig. 56. In this diagram A represents the sym- metrical frequency curves, the two sides of which are sym- metrical about the mode. This type of curve has already been discussed. Type B is represented by the age distribu- tion of deaths from measles. In early childhood the curve 384 PROBABILITY rises sharply. Type C is a variant of B. Type D starts off with the mode and steadily diminishes. Age distribu- tion of infant deaths by montlis gives us an example of this curve. Type E, the U-shaped curve, is already familiar to us. It is sub- stantially the curve of spe- cific death-rates by ages. All of these skew curves take many forms. It wiU be remembered that in the case of the law of chance it was assumed that the chance of an event happening and of its not happening were equal. The chance of the coin faUing as a head was the same as that of its falling as a taU, and one or the other was bound to happen. But we can imagine a result de- pending upon many factors, one of which was much more likely to occur than not to occur. This would result in producing a skew curve. There might be many such factors, and these might exist in all sorts of combinations. When statistics naturally plot out as a skew curve it Fig. 56.- TYPE E U-SHAPED - Tjrpes of Frequency Curves. DEVIATION FROM THE MEAN 385 is a sign that they should be investigated to determine, if pos- sible, what the influence is which is producing the skewness. Sometimes it can be found. For example, in a case recently studied the quantity of butter fats in a series of analyses of milk samples was slightly skewed at one end. This was found to be due to the adulteration of about five per cent of the samples with water. Beyond recognizing the skewness of a curve and making some attempt to account for it, the student of vital statistics will do well to let the mathematics of skew curves alone. Karl Pearson and others of -his school have suggested certain methods of mathematical analysis. Frequency shown by summation diagrams. — Another way of expressing "frequency" is by the use of the summa- tion, or cumulative, diagram. In some respects this is more useful than the method of plotting by separate groups. Let us return to our 18,780 soldiers whose heights were measured. If 197 soldiers were between 60" and 61" then 197 were less than 61"; if 317 were between 61" and 62" then 197 + 317, or 514, were less than 62"; and so on. If these results are plotted we shall obtain a characteristic ogee curve. If the distribution is exactly in accordance with the law of natural frequency then the upper and lower parts of the curve will be symmetrical. Instead of using the actual numbers of soldiers beginning with 197 and running up to 18,780, we might have plotted the percentage distribution from 1.05 per cent to 100 per cent. The result would have been the same. Deviation from the mean. — Still another way of study- ing these figures is to find the extent to which the heights of the soldiers differed from the average, or mean, height. The mean height was 67.24". For the sake of simphcity let us call it 67J". ■ We may fairly assume that the height measure- ments were measured accurately and that the average height 386 PROBABILITY of the 197 soldiers in height group 60" - 61" was 60^". Then the average deviation of the height of these 197 soldiers from the mean was 67j — 60J, or 6f ". In the same way the 317 soldiers had an average deviation of 5|; and so on. The average deviation of group 73 — 74" was 73^ — 67j or 6j. Some of these deviations are positive and some are negative, because some of the soldiers are shorter than the mean and some are taller. If we plot these results we obtain the curve shown in Fig. 57. This is the curve of error, so-called. The deviations from the mean are regarded as errors. It is similar to the summation curve of variation. In fact it is the same curve, the only difference being the scale. Mathematicians, physi- cists and engineers look at their data from the standpoint of errors of observation, and therefore their text books which treat of this subject are called "Precision of Measurements," "Theory of Least Squares," and the hke. Natural scientists however speak of "Variation." It is all one. The figures show us that small errors occur very often, large errors occur less frequently, and very large errors rarely occur. In any set of measurements we may assume that errors will exist, and that in natural phenomena there wiU be varia- tions caused by many factors. We are naturally interested to find out the extent of these variations. We want to know the average deviation and the variation most likely to occur. It will not be possible to go into these matters in great detail in this book. Readers who want to know the theory of these matters must study the theory of probability, or "Least Squares." A few methods of dealing with the subject practically will be given because they have an important use even in elementary statistics. In doing so we will consider first a very simple set of figures, and then come back to some more measurements of men, but lest we tire of our 18,780 soldiers we will consider some more recent measurements STANDARD DEVIATION 387 made by Drs. Frankel and Dublin of the Metropolitan Life Insurance Company. Standard deviation. ■'— Let us suppose that we have five figures, or statistics, which represent something, no matter 6 6 o a M j / r go a 1 §2 ■■§ I 6 R y ^ / / • 20 40 60 Per cent of Soldiers 80 100 Fig. 57.- • Percentage Deviation of the Heights of Soldiers from the Mean. what. They are 6, 8, 2, 4, 5. The mean of these figures is 5. The deviations from the mean are respectively 1, 3, —3, — 1, and 0. The average deviation, disregarding signs, is 388 PROBABILITY their sum divided by 5, or 1.6. A more useful quantity is that called the standard deviation. It is obtained by squaring these deviations, finding the average square and taking its square root. If we average the data in tabular form we shall better understand the process. TABLE 135 STATISTICAL DATA Item. Deviation from Mean. Square of Deviation. (1) (2) (3) 6 8 2 4 5 1 3 -3 -1 1 9 9 1 Sum 25 Ave. 5 8' 1.6 20 4 1 Neglecting signs. The average square is 4 and V4 is 2. Hence 2 is the standard deviation. It will be noticed that the standard deviation gives greater weight to the large deviations than a mere averaging of the deviations does. Coefficient of variation. — The ratio between the stand- ard variation and the mean is called the coefficient of varia- tion. In the case just mentioned it is 2 -^ 5, or 0.40. The coefficient of variation is usually expressed decimally. If the variations are very small the coefficient of variation is small. If the variations are large the coefficient of variation is large. In some parts of the country the annual rainfalls do not vary much from year to year. In Massachusetts the coefficient of variation is about 0.17. In other parts of the country there are great fluctuations from year to year. In COMPUTING THE COEFFICIENT OF VARIATION 389 Arizona the coefficient of variation is 0.50. A low coefficient means, in general, that the figures are more dependable; a high coefficient means that they are likely to be untrust- worthy because of their fluctuations. This coefficient is very useful in the study of vital statistics. Computing the coefficient of variation when data are grouped. — This is Hkely to cause trouble to the beginner. It is necessary to use care or mistakes will be made. Sup- pose we have the following items divided into magnitude groups between and 5, the measurements being made to the nearest tenth as shown in columns (1) and (2). TABLE 136 STATISTICAL DATA Magnitude group. Number in group. Average magnitude. Product. Deviation of number in group. Square of deviation. Product. (1) (2) (3) (4) (5) (6) (7) 0-0.9 1-1,9 2-2.9 3-3.9 4r-4.9 6 8 2 4 6 6.45 1.45 2.45 3.45 4.45 2.70 11.60 4.90 13.80 22.25 1.76 0.76 -0.24 -1.24 -2.24 3.10 0.58 0.06 1.54 5.02 18.60 4.64 0.12 6.16 25.10 Total 25 55.25 2.21 54.62 Mean 2 18 . Here we first find the average magnitudes of the numbers in each group, colimm (3). By multiplying these by the number of items in each group and dividing by the number of items we have (4) the weighted average, or the mean of aU the items. This is 2.21. Subtracting the figures in column (3) from 2.21 we have the group, deviations in colimin (5). These are squared (6) and then multiplied by the number of items in each group (7). The sum of the squares divided by 25 gives the average square, i.e., 2.18 and V2.18 is 1.48, the 390 PROBABILITY standard variation. 1.48 -;- 2.21 gives 0.67 the coefficient of variation. Unthinking students sometimes multiply the' figures in column (5) by those in column (2) before squaring. This is wrong. It is the deviations which are squared. The subsequent process is merely to get the weighted average of the squares. Probable error. — Neither the average deviation from the mean nor the standard deviation is the one most likely to occur. It is the median deviation, or the median error, which is most Ukely to occur. It can be shown by calculus that when observations follow the normal law of error, or the normal frequency distribution, i.e., the binomial dis- tribution, the median deviation is about two-thirds of the standard deviation. To be exact, the figure is 0.6745. If we let r stand for this median deviation, this probable error, and if we let x be any individual error, and if n = the number of observations, then, remembering that the sign 2 means "the sum of," we shall see that r = 0.6745 V—- T n This is merely the mathematical way of stating what we have just done. Sx^ means the sum of all the squares of the deviations, means the average square, and y — means the square root of- the average square, i.e., the standard deviation. Where does 0.6745 come from? If we take the curve of error (Fig. 57), and consider the side to the left of the middle ordinate, it will be possible to draw a vertical line somewhere to the left (or the right) of the middle which wiU divide the area included between the curve and the base hne into two equal parts. The height of the ordinate which will do this is 0.6745 that of the middle ordinate. THE PROBABILITY SCALE 391 This probable error is quite useful in statistics. One use is that of throwing out of consideration doubtful observations. Doubtful observations. — Scientists make a distinction between errors and mistakes. Errors are supposed to fall within the hmits of probability; mistakes are supposed to be glaring, erratic observations which really ought to be left out of account, or at least not included when the average is computed. We have all hq,d experiences of this kind. In a daily record of the number of bacteria in a filtered water we may find that where most of the figures are less than 25 per cubic centimeter there is one which exceeds 1000. Shall we include this in the average for the month? If we do we unduly raise the average for the month and bring discredit on the filter. And yet there may be no reason for excluding it. It may have been a fact. And a fact is not to be dis- carded. The theory, of probability gives us a means of teUing whether it should be included in the average or not. If we know the probable error r, as above described, then we shall find that there is an allowable ratio of - which depends upon the number of observations. If we had only three obser- vations then any value of the ratio - which is greater than about 2 should be regarded as outside the probable variations resulting from the law of chance. If n is 10 the limit of - is 3; if n = 30, then the limit of - is 3.5; if n is 100, the hmit is 4; if w is 500, the limit is 5, and so on. These values are merely approximate. The probability scale. — This ratio of -, the ratio of any error to the mean, or most probable error, is useful in another way because on the basis of the binomial distribution we can 392 PROBABILITY compute the frequency with which any value of - is likely to occur. We call this the probability of its occurrence. If X is any error and r is the most probable error then when - = 1 the chances are even that the error will be x. There r are as many chances that the error will be larger than x as that it will be smaller. We may call this a "fifty-fifty" chance, and we may write the probability of its occurrence as i or 0.5. If - is less than 1 the probability that any error r X X will be less than - is less, and if - is greater than 1 the prob- r r ability that any error will be less than - is greater. In fact we shall find that the following relations hold: TABLE 137 PROBABILITY X Probability that any X Probability that any r error will be less than • r r error will be less than - • CD (2) (1) (2) 0.0 0.0000 1.7 0.7485 0.1 0.0538 1.8 0.7753 0.2 0.1073 1.9 0.8000 0.3 0.1603 2.0 0.8227 0.4 0.2127 2.1 0.8433 0.5 0.2641 2.2 0.8622 0.6 0.3143 2.3 0.8792 0.7 0.3632 2.4 0.8945 0,8 0.4105 2.5 0.9082 0.9 0.4562 2.6 0.9205 1.0 0.5000 2.7 0.9314 1.1 0.5419 2.8 0.9410 1.2 0.5872 2.9 0.9495 1.3 0.6194 3.0 0.9570 1.4 0.6550 4.0 0.9930 1.5 0.6883 5.0 0.9993 1.6 0.7195 00 1.000 PROBABILITY PAPER 393 If we compute the values of - which correspond to certain probabiUties we have the following approximate figures: TABLE 138 PROBABILITY Probability. X r Probability. X r (1) (2) (1) (2) 0.01 0.02 0.80 1.90 0.02 0.04 0.90 2.44 0.03 0.06 0.95 2.91 0.05 0.09 0.98 3.45 0.10 0.10 0.99 3.82 0.20 0.38 0.999 4.887 0.30 0.58 0.9999 5.783 0.40 0.77 0.99999 6.592 0.50 1.00 0.999999 7.258 0.60 1.25 0.9999999 7.967 0.70 1.54 Probability paper. — Until recently it has been difficult to use the theory of probability in statistical work, but it is now easy. In 1913, my partner, Dr. Allen Hazen, devised a new kind of plotting paper. The percentage scale was so spaced that any set of figures which follow the natural law of probabihty would plot out not as an ogee curve, but as a straight line. The spacing was based fundamentally on the preceding figures, but it was necessary to take account of the sign of the error, whether positive or negative, and make allowance for this in designing the plotting paper. The 50 per cent, or median line, was placed in the middle of the percentage scale. The other relative distances were as fol- lows. The figures given cover only one side of the 50 per cent line. 394 PROBABILITY TABLE 139 DATA FOR PREPARING PROBABILITY PAPER Line. Relative dis- tance. Line. Relative dis- tance. Line. Relative dis- tance. (1) (2) (1) (3) (1) (21 Per cent. Per cent. Per cent. 50 0.000 17 1.415 0.8 3.573 48 0.074 16 1.474 0.7 3.646 46 0.149 15 1.537 0.6 3.727 44 0.224 14 1.602 0.5 3.821 42 0.300 13 1.670 0.4 3.933 40 0.376 12 1.742 0.3 4.077 38 0.453 11 1.818 0.2 4.267 36 0.531 10 1.906 0.1 4.585 34 0.611 9 1.988 0.09 4.630 32 0.693 8 . 2.083 0.08 4.685 30 0.777 7 2.188 0.07 4.748 28 0.864 6 2.305 0.06 4.817 26 ■ 0.954 5 2.439 0.05 4.900 24 1.047 4 2.596 0.04 5.000 22 1.145 3 2.789 0.03 5.120 20 1.248 2 3.045 0.02 5.290 19 1.302 1 3.450 0.01 5.550 18 1.357 0.9 3.507 As first used the percentage scale was used horizontally, as in Fig. 63. There are some advantages plotting the per- centages as ordinates as in Figs. 58, 59 and 60. In the latter the horizontal scale is the ordinary arithmet- ical scale. The vertical scale may be labeled from to 100 per cent, in either direction, or it may read from to 50 on either side of the median line. ^ It depends upon whether we want to keep the positive and negative errors separate or add them together and consider their magnitude alone. A few examples of the use of this probabihty paper will now be given. For a more complete description of this paper the reader is referred to the author's monograph on the " Element of Chance in Sanitation." ' 1 Jour. Franklin Institute, July, 1916, PROBABILITY PAPER 395 ] - -1 4- " "I"7 ::::::::::::::::::::|: ii^iiiiiiUHMiiiiii ili / - yjjjijiii l\\ilzlzi\ll^l\l\l\zl = \ 'A = ;;;:;;;;:; :::::, :-z::::-z:-zl:\:l:l eeeee;;eee iEEEE ;ee:le e^ ■:::il::-z:l _[. :::i - ■ 1 - - -.(! - -/t - ■ / '.--'.-- zz:-- ' 1 ■■"■ 55 60 65 70 Height in inches. 75 80 Fig. 58. — Distribution of Soldiers According to Height, on Arithmetic-Probability Paper, Plotted 396 PROBABILITY 14 13 22 26 Death Rates Der UQS Fig. 59. — Death-rates of Massachusetts Cities and Towns. Plotted on Arithmetic-Probability Paper. PROBABILITY PAPER 397 r ^ N;:M::;ii:H!;Hi'-:-n;;;;;;;H:;; -■■ —--f%-— -^^ ;:;;:--;;■;:::::-;;;;;;;;;;;;;;; il / 1-/- ■/- T ''^^^'"''""''i'"''''1' Bii^^ :::::::: : : ::::,-^t -: : :: :: ::::::::::::::::::::::::::::::::::: : ; M M! El M MeeH'-eIe :::::::: : ; ::::::::::: !:m MmiiMMiimmHNmiNHHNNHH 'r :::::::::::::::::::::::::::::::::::: .t: ...1 ^ :;:,::::,:;,:,,;,,,,;,,,,,; :::::::: : : :::::::!::: ' " w- \w\\ E E ;eee!e;e; h :::::::: : : :::[::::: :: 90 100 Per cent of Median. 110 Fig. 60. — Percentage Variation of Death-rates of Massachusetts Cities and Towns for Three Different Decades. Plotted on Arithmetic-Probability Paper. 398 PROBABILITY Examples of use of probability paper. — Fig. 58 shows the distribution of soldiers according to height plotted on probability paper. This is based on the observations with which we have already become familiar. It will be noticed that instead of forming the usual ogee curve the points fall on a straight hne. Fig. 59 shows that the death-rates for Massachusetts cities and towns also plot out on this paper as a straight hne. Fig. 60 shows that in 1900-10 the death-rates throughout the state have been more uniform than in 1860-70. This is indicated by the different slope of the lines. For an example of the use of logarithmic probability paper, see Fig. 63. Another use of probability. — Bernouilli's theorem gives us another interesting appUcation of the theory of probabihty. If we let p represent the frequency of an event happening and q the frequency of its not happening, then obviously p -\- q = 1. Unless this fundamental condition holds, the laws of probability do not hold. It is always well to see if there are any other factors than p and q. If we let n represent the number of cases considered, and € the mean error, then Bernouilh says, e = Vnpq. We need not stop here to prove this, but we may see how it can be used. If n is large then e is a fair measure of the deviation from the standard for it is said that in 2 out of 3 cases the deviation will be less than e; in 19 out of 20 cases less than 2 e; and deviations greater than 4 e are very rare. Let us suppose that in a population of 10,000 the general death-rate was 15 per 1000, i.e., 150 deaths in all. Then n = 10,000; p = ,^^; q = Jq^^; then I = \/l0,000 X jj^ X ^ = VmT.TS = 12.15 deaths, THE FREQUENCY CURVE AS A CONCEPTION 399 or 1.2 per 1000. A fluctuation of this amount from year to year would not be outside of the bounds of chance phe- nomena. If the population were 1,000,000 then e would be VI. 4775 or 1.2 deaths in 1,000,000 or 0.012 per thousand. Other criteria than Bernouilli's have been suggested for this computation. The results differ considerably, and none of the methods must be taken as mathematically exact. Let us suppose we are studying an epidemic of typhoid fever in which all the cases, 120, were actually caused by the public water supply. The population was 50,000. There were two milk dealers: A served 40,000 persons; B served 10,000 persons. AVhat would be a chance distribution of cans among these two dealers? If they were distributed uniformly we should expect to find among A's customers 40,000 .ion n« A n> , ■ lO'^OO ., ----,■,-, of 120, or 96; and among B s customers rn nnn ' °^ ^'** Now what is a reasonable variation from these figures? In the case of A, s/ 120 49 880 '^'^^ ^ 50;000 ^ 50^ = 10 approximately. Therefore, if A had any number between 86 and 106 it would be within the bounds of chance. • If he had 116 cases it might be a suspicious circimistance. In the case of B, ■e = \/l0,000 X ^ X g|8g = 2.4 approximately. If, therefore, B had more than 27 cases it would be suspicious. The frequency curve as a conception. — The frequency curve is something far beyond a statistical tool. Prop- erly conceived it stands for a universal principle. Not all the leaves of a tree are alike, not all shells are alike, sol- diers are not all of the same height or weight. We cannot well compare the tallness of pine trees and elm trees with- 400 PROBABILITY out resorting to the frequency curve. One man may say, " The elm tree is the taller; I have seen elms taller than pines." Another says, " That is nothing; pine trees have a greater average height." But the first man is not con- vinced. He goes back to his own observation and insists that he has seen elms taller than pines. To give the true picture both men need to know the frequency of different heights of both elms and pines. Are young women as good scholars as young men? Assuming that we have an adequate definition of what is meant by a good scholar, can we settle the question by saying that we have seen young women who were better scholars than young men, or that the average of scholar- ship is higher among men; must we not know the fre- quency with which we find good scholars and poor scholars among both men and women? It is quite conceivable that among women we have greater extremes of scholar- ship than among men, or vice versa. Are women as well fitted for voting as are men? Suffra- gists point to drunken sots and say, " We are better fitted to vote than they are." When they say this they are com- paring the end of one frequency curve with the middle or the upper end of the other. Such comparisons are utterly meaningless. Sometimes we need to make comparisons on the basis of lower hmits, sometimes on the basis of upper hmits, sometimes we ought to Compare modes, sometimes medians, sometimes averages, sometimes we do not know the facts well enough to make comparisons at all: but through- out all realms of thought an appreciation of the funda- mental importance of the frequency curve will help us to reason soundly and will prevent us from making false comparisons. The frequency curve contains in itself the element of THE FREQUENCY CURVE AS A CONCEPTION 401 beauty. Moons wax and wane; the tide rises and falls; the flowers of spring come, first a few, then many; and they disappear in the same way, a few lingering into summer. It is said that we live in a world of chance. Nothing is more true. We live in a world where many causes are acting with and against each other. We live in a world of frequency curves. Artists and architects recognize this. The ogee curve is the line of beauty. EXERCISES AND QUESTIONS 1. Find data for and plot an example of a typical symmetrical fre- quency curve. (Anthropometrical measurements.) 2. Find data for and plot an asymmetrical frequency curve (specific death-rates for scarlet fever, diphtheria, etc.). 3. Describe the application of BernouiUi's Theorem to the chance distribution of cases among milk customers? [See Am. J. P. H., Apr., 1912, p. 296.] 4. Construct a model to illustrate the general law of probability. [See Rosenau's Preventive Medicine, Chapter on Heredity and Eu- genics.] 6. Repeat the coin tossing experiment described in this chapter. 6. Find the height of 50 males (or females) above eighteen years of age, and compute: a. The average deviation from the mean. b. The standard deviation. c. The coefficient of deviation. d. The probable error. 7. Plot the height records of these persons on "probability paper." 8. Discuss the use of the law of chance in pubUc health studies. (Whipple, Geo. C. The Law of Chance in Sanitation, Jour. Franklin Institute, July, 1916.) 9. Prepare a short statistical abstract of the stature of recruits, U. S. A., 1906-15. [Hoffman, Frederick L.. Army Anthropometry and Medical Rejection. Newark. Prudential Press, 1918.] CHAPTER XIII CORRELATION Correlation is the word by which the statistician describes the correspondences or relations between series, classes or groups of data; in fact, it is largely for the study of these relationships that statistics are collected. Deaths from typhoid fever are arranged by months in order to ascertain if there is a fixed relation between the frequency of such deaths and the season of the year; or they are arranged by the age, occupation or place of residence of the decedants in order to learn of any other correspond- ences which may exist. The heights and weights of men, or women, are compared to see if the variations inheight are related to variations in weight; the length of the arm is compared with some other measurement of the body; the heights of sons are compared with the heights of their fathers. These are all simple correlations. Two sets of measurements only are compared. Often the problem is more comphcated. The infant mortality in cities varies with the season, being highest in the summer; the temperature of the air also varies with the season, being highest in the summer; and the statistician desires to ascertain if there is any definite relation, any correlation, between atmospheric temperature and infant mortality. Here there are three elements to be considered — season, temperature and infant mortality. Also the nimiber of flies ordinarily increases with an increased atmospheric temperature, and the question arises "Is there a fixed re- 402 CAUSAL RELATIONS 403 lation between the increase in the number of flies and the infant mortaUty?" One naturally asks: "Why not eliminate the temperature of the air and study the direct and simple correlation between flies and mortality? That would, indeed, be the best and safest method, but unfortu- nately the data may not exist, or cannot be obtained in comparable form. It is, therefore, necessary to devise some way of studying this problem by indirect correlation, or secondary correlation. Causal relations. — Sometimes statistics are studied merely to determine whether correlation exists between two variables, this result being practically useful. The knowledge that infant mortality increases with the atmospheric tem- perature is in itself of value to the physician and the health officer. More often perhaps the underlying motive in corre- lation studies is that of determining, cause and effect. In the illustration given the question is. Is the increase in atmospheric temperature the cause of the increased mor- tality among infants? Is the increase in the number of flies in the summer the cause of the increased infant mortality? Or, to go back to the examples of simple correlation, Is the increased height of men the cause of their increased weight? Is the tallness of a son the effect of the tallness of his father? Does the establishment of correlation also mean that a causal relation has been estabUshed? To answer this we must consider what is meant by cause. Jevons ' says: "By the cause of an event we mean the circumstances which must have preceded in order that the event should happen. It is not generally possible to say that an event has one single cause and no more. The cause of the loud explosion in a gun is not simply the puUing of the trigger, which is only the last apparent cause or the occasion of the explosion; the qualities of the powder, the proper form of ^ Lessons in Logic, p. 239. 404 CORRELATION the barrel; the existence of some resisting charge; the proper arranging of the percussion cap and powder; the existence of a surrounding atmosphere, are among the circumstances necessary to the loud report of the gun; any of them being absent it would not have occurred." In the above phrase, "the circumstances which must have preceded in order that the event should happen," emphasis must be placed on the word mv^t, otherwise our reasoning is post hoc non propter hoc. [ It is obvious that statistics do not in themselves estabUsh these causal relations. The laws of logic are the primary laws, and the rules of statistics must be subsidiary to them. Westergaard, the celebrated Danish statistician, has recently said (Jour. Am. Stat. Asso., Sept. 1916, p. 259),. "that the task of the statistician is not so much to find the causality himself as to help others to find it. The statistician must be content if he can show that certain groups of numbers have marked^differences, leaving it to physiology, meteorology and other sciences to explain these differences." The statistician can prove nothing by his statistics unless he uses them logically. On the other hand, the statistical arrangements of facts are of the greatest aid in helping to establish causal relations, because by expressing facts by nimibers it is possible to con- centrate extended experiences into quantities which may be ' easily and quickly compared. Correlation and causality. — In studying correlation as a process for determining causality it is necessary to dis- tinguish between the simple correlation which may exist between two variables and the more indirect correlation, or secondary correlation, -which occurs when two series of events, both correlated to a third factor, are compared to each other. The former may be safely used to establish a causal relation; in fact, King says (Elements of Statistics, p. 197), that LAWS OF CAUSATION 405 "correlation means that between two series or groups of data there exists some causal relation." In stating this he evidently had in mind the simple correlation between two variables. And, of course, "causal relation" does not mean "sole cause." Besides correlation we must also estabhsh connection between the two variables. It is not the task of the statistician to do this. It would be more exact to say that a causal relation may be shown by establishing a definite correlation between two series, classes or groups of connected data. It is chiefly in secondary correlations that we err in our logical processes. In mathematics we learned that "two things which are equal to a third are equal to each other," but it is not necessarily true that two series of events which vary as a third are equal to each other, or even are related to each other at all. Infant mortaUty increases with the atmospheric temperature in summer; the softftiess of the asphalt pavements increases with the atmospheric tempera- ture in summer; but we cannot infer that there is any relation between infant mortality and the softness of asphalt pavements. The actual connection between events is not shown by statistics or by the statistical methods except as the data are interpreted according to the laws of logic. Let the reader try to answer questions like these. Why is it not true that there is a causal relation between the soft- ness of pavements and infant mortality? Is it, or is it not, true that there is a causal relation between the presence of flies and infant mortahty? Which shows the higher degree of correlation with infant mortality — the presence of flies or the softness of asphalt ? Laws of causation. — While we are thinking about cor- relation and its relation to causation it will not be out of place to refer to the three methods of induction as stated 406 CORRELATION by John Stuart Mill. The cause of an event may be said to be "the circumstances which must have preceded in order that the event should happen." Mill's first canon is, " If two or more instances of the phenomenon under investigation have only one circum- stance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phe- nomenon." This is the method of agreement. The epi- demiologist follows this principle when he studies case after case of disease looking for some common antecedent circumstance. Here one instance does not establish proof of a cause, and the larger the number of instances the stronger the proof. The second canon is " if an instance in which the phe- nomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in com- mon save one, that one occurring only in the former; the circumstances in which alone the two instances differ is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. This is the method of differ- ence, the method of experiment. This principle also is used in epidemiology. The third canon is called the joint method. " If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances (always or invariably) differ, is the effect, or the cause or an indispensable part of the cause, of the phenomenon." These are sometimes expressed as follows, the large let- ters, A, B, C, etc., representing antecedents, and the small letters, a, b, c, etc., the consequents. METHODS OF CORRELATION 407 Method of Agreement ABC ab c AD E ade AF G af g . A H K ahk Method of Difference ABC ab c B.C b c Joii it Method ABC ab c AD E ade AF G af g AHK ahk P Q pq R S r s T V t V XY X y Methods of correlation. — Correlations may be divided into two classes: — (1) simple, or primary, and (2) secondary. Simple correlations are studied as between two variables, these two variables being compared on the basis of magni- tude, that is they are compared by grouping. Secondary correlations are studied when two variables are compared with each other after first being compared to a third variable — such as time or place. When two variables are so correlated that the numerical values increase and decrease together the correlation is said to be direct. 408 CORRELATION When the correlation is such that the numerical value of one variable increases as that of the other decreases the correlation is said to be inverse. The closeness of correlation is termed the degree of correlation. There are mathematical methods of determining the degree of correlation, according to which perfect correlation is repre- sented by unity and complete absence of correlation by zero. The following are some of the methods used in the study of correlation: Simple correlations (two variables compared directly) : 1. Plotting of original data. 2. Correlation table (grouping by lines and columns), 3. Correlation model (correlation surface). 4. Plotting of group means (Galton). 5. Computation of coefficient of correlation: (a) Galton's method (see Elderton's Primer of Statistics). (6) Karl Pearson's method. 6. Use of mathematical formulae. Secondary correlations (two variables compared on the basis of a third variable) : 1. Comparisons between two plotted lines representing original data, as to: (a) Parallelism. (b) Correspondence of fluctuation in time of oc- currence and in magnitude. (c) Correspondence of cycles. (d) Lag. (e) Inverse relations. 2. Comparison between two plotted lines, each represent- ing variations from the mean. 3. Comparison between two plotted lines, each represent- ing variations from the moving average (or some smoothed line showing trend). GALTON'S COEFFICIENT OF CORRELATION 409 Galton's coefficient of correlation. — Let us suppose that we have the following pairs of observations. Each a has a corresponding b. What is the correlation between a and 6? Offhand one can see that in a general way a and b rise and fall together. But how can we express this relation? TABLE 140 EXAMPLE OF CORRELATION a 5 X 1= y V' ly (1) (2) (3) (4) (5) (6) (7) 7 4 1 1 5 2 -1 1 -2 4 * 2 6 6 1 1 3 1 -3 9 -3 9 9 9 8 3 9 4 16 12 Sum 30 20 20 30 23 Average 6 4 4 6 '4.6 2 2.45 We cannot compare the figures directly. We do not even know that the measurements are the same, a may be expressed in feet, and b may mean years or something else. What have these two sets of figures in common? The deviations from their means may help us. Let us suppose that X represents the deviation of a from its mean, 6, and that y stands for the deviations of b from its mean, 4. Then we can compute the standard deviation of each set of figures, and call these a-^ and ay. These we find to be a/4, or 2, and V6, or 2.45. We must now link together the two sets of observations and we do this by finding the prod- ucts of their deviations, i.e., xy, and the average of xy, i.e., 4.6. This average value of the product of x and y, divided by the product of the standard variations, o-j, and Cy, gives what Galton calls the coefficient of variation. It may be expressed by formula thus: 410 CORRELATION Coefficient of correlation = rKTxCy ' in which n is the num- ber of observations, and Xxy the sum of all the xy's. example, Xxy 23 -^ = 4.6, and the coefficient is In the 4.6 n b ■ 2 X 2.45 = 0.94. This is a close correlation between a and b, because 1 represents perfect correlation and no correlation at all. Pearson's coefficient is not quite the same, but it is enough for practical purpose to remember Galton's. Example of low correlation. — In the monthly bulletin of the Connecticut State Department of Health for Feb., 1918, a radial diagram is given showing that grippe out- breaks in one year are followed by measles the next year, and the statement is made that "the wheel of chance becomes a wheel of certainty." Let us see if these facts will stand the test of correlation. If we place the deaths from grippe in one year side by side with the deaths from measles the following year, we have the following twelve pairs of values for a and b. TABLE 141 a b X x' V V' xy (1) (2) (3) (4) (5) (6) (7) 8 4 15 11 6 8 16 7 12 2 9 25 32 8 26 5 6 22 3 27 12 6 34 -2.25 -6.25 4.75 0.75 -4.25 -2.25 5.75 -3.25 1.75 -8.25 -1.25 14.75 5.06 39.06 22.56 0.56 18.06 5.06 28.06 33.06 3.06 68.06 1.56 217.56 16.92 - 7.08 - 9.08 9.92 - 9.08 -13.08 4.92 -12.08 11.92 - 3.08 - 9.08 18.92 286.29 50.13 82.45 98.41 82.45 171.09 24.21 145.93 142.09 9.49 82.45 357.97 -38.07 +44.25 -43.13 + 7.44 +38.59 +29.43 +28.29 +39.26 +20.86 +25.41 +11.35 +279.07 Sum 123 Average 10.25 181 15.08 441.72 36.81 6.07 1532.96 127.75 11.30 442.75 CORRELATION SHOWN GRAPHICALLY 411 It will be seen that the coefficient of correlation is Sxj/ ^ 442.75 ^ na^cTy 12X6.07X11.30 This is a low correlation. It is less than the coefficient of variation of either grippe or measles. It follows, therefore, that the statement that grippe is followed by measles a year later has little to substantiate it, if all the facts are considered. If we leave out a few exceptional years there does appear to be a general tendency for measles to follow grippe. But what right is there to leave out some of the facts? If they are mistakes they should be left out, otherwise they should be considered in drawing concessions. A few years ago a sanitary chemist tried to show a relation between the color of water and the typhoid fever death-rates in Massachusetts water supplies. Computations of the coefficient of correlation for 54 places where surface water was used gave a figure of 0.16, while for 33 places where ground water was used it was 0.30. In other words, there was very little correlation. In the same cities the correla- tions between the general death-rates and the typhoid fever death-rates were 0.59 and 0.56, respectively. On the other hand, the Eldertons found the coefficient of correlation between the length and breadth of shells to be 0.95; that between the ages of husbands and wives, 0.91. The student will find the use of the coefficient of correlation an admirable weapon for exploding false theories. Correlation shown graphically. — In a general sense any graph with horizontal and vertical scales, in which pairs of observations are represented by a single point is a correlation plot. If the points fall on or near a straight line the correla- tion is high; if the points are so scattered that a straight line cannot be readily drawn to represent them the correlation is low. This needs no further illustration. 412 CORRELAtiON It is possible, however, to determine the coefficient of correlation graphically. In Bowley's Elements of Statistics we find the relation between the marriage-rate and the price of wheat. The first step is to select two suitable scales and plot the data as points. The second step is to find the mean marriage-rate and the mean price of wheat and plot these as 17.0 16.5 1S.0 S16.5 15.0 14.5 14.0 J- rlj 4""" / js^ Ja- 4 i i- / ^ L if" -1 1 i sV t ^ ' t " t h 1 - .-/^ . r J - .'O ,B-MnftTi = IR 17 _^ M •-! 1— " /" T - X J- - I J "H 20 30 40 50 Price of Wheat, In ShllUngs Fig. 61. — Correlation between Marriage-rate and Price, of Wheat. horizontal and vertical Hnes, respectively. The third step is to draw a Hne which will fairly well represent the points. In Fig. 61 this line is marked MN. It must pass through the intersection of the mean hnes, 0. The fourth step is to select any point on MN, as, for example. A, and read from the vertical scale the value of AB. In the example AB is 16.7 — 15.17 = 1.53. This is really the deviation of A THE CORRELATION TABLE 413 from the mean marriage-rate and 1.53 h- 15.17 = 10.15 is the standard variation. In the same way AC is 46.0 — 37.8 = 8.2, the deviation of A from the mean price of wheat, and 8.2 -T- 37.8 = 21.7 is the standard variation. The ratio of 10.15 to 21.7 gives us the coefficient of correlation, 10.15 4- 21.7 = 0.468. By computation Bowley finds this to be 0.47. The graphical method is useful only when the correla- tion is fairly high, because if the correlation is low one cannot tell where to draw the line MN. In drawing this line an effort should be made to place it so that there will be as many points as possible near the line, with the other points as well balanced as possible on either side of the line. This requires experience and a sort of intuitive sense of distances. A recent example of lack of correlation. — The Munic- ipal Tuberculosis Sanitarium of Chicago, in its annual report for 1917, has published an interesting series of diagrams illustrative of the lack of correlation between housing and tuberculosis. Fig. 62 is one of these. The districts are arranged in order of occurrence of tubercu- losis. The one-scale rectangles, "appropriately divided ac- cording to the character of rooms, fail to show any progres- sion coincident with tuberculosis under Chicago conditions. The correlation table. — The correlation table is arranged much Uke a simple plot. There is a horizontal and a vertical arrangement of groups. This tabulation shows to the eye the relation between the two quantities. In Table 142 we see the correlation between the ages of husband and wife is fairly close. Of 669 wives in age-group 40-44, 309 were married to husbands in the same age-group. There is a slight tend- ency for husbands to be slightly older than their wives. The figures are not symmetrically arranged around the mode. The correlation model is used but httle. A description of its construction and use may be found in works on statistical methods. 414 CORRELATION Fig. 62. — Diagram Showing Lack of Correlation between Interior Rooms in Certain Chicago Blocks and Tuberculosis Morbidity. SECONDARY CORRELATION 415 TABLE 142 CORRELATION BETWEEN (1) THE AGE OF WIFE, (2) THE AGE OF HUSBAND, FOR ALL HUSBANDS AND WIVES IN ENGLAND AND WALES WHO WERE RESIDING TO- GETHER ON THE NIGHT OF THE CENSUS, 1901. (CENSUS, 1901, SUMMARY TABLES, P. 182.) TABLE BASED ON 6,317,520 PAIRS; CONDENSED BY OMITTING OOO'S (From Yule's Theory of Statistics, p. 159.) Ages of hus- bands. Ages .of wives. Total. 15- 20- 25- se- 35- 40- 45- 50- 55- 60- 65- 70- 75- 80- 85- (1) (2) (3) (4) es) (6) C7) (8) (9) (10 (11) (12) (13) (14) (15) (16) (17) 15- 20- 25- 30- 35- 40- 45- 50- 55- 60- 65- 70- 75- 80- 85- 2 16 4 1 2 173 185 41 9 3 1 4 240 688 817 793 700 595 483 369 277 175 104 50 18 4 46 402 265 69 17 6 2 1 4 84 411 251 71 20 8 3 1 1 1 10 84 369 219 66 19 8 3 1 1 2 12 80 309 178 57 18 8 3 1 1 1 2 12 66 252 146 46 16 6 2 1 1 2 12 69 195 110 39 11 5 2 1 1 2 10 44 141 81 26 8 3 1 2 10 35 101 53 18 • 5 1 2 6 23 58 31 10 2 1 1 4 13 31 14 4 1 1 2 6 12 5 1 1 1 2 3 1 1 Total 23 414 808 854 781 669 550 437 317 226 134 68 27 8 1 5317 Use of mathematical formulae. — It is often desirable to find the equation of a straight line or curve drawn through a series of points. This is not difficult, but it requires a longer description than can be given here. The student can find good descriptions of the methods used in standard mathematical books. Secondary correlation. — The correlation of two variables is often shown by plotting each against a third quantity, which latter varies in a regular manner. Thus in Fig. 52 we 416 CORRELATION have the number of cases of typhoid fever plotted astordi- nates with months as abscissae, and we have also the atmos- pheric temperature plotted as ordinates with months as abscissae. Here we see that there is a general correspondence between the two curves and we say that there is correlation between the two. One must be very careful in using the graphic method in this way. We may have a diagram in which the correspondence between the two plotted lines is very definite except occasionally, yet these occasional lapses may be enough to upset the correlation. Again two lines may rise and fall together in point of time, and they may even rise and fall apparently the same amounts, yet this may be an incident depending on the scales used. Finally we must not forget that this sort of correlation — where two quantities vary as a third — does not establish causality. In Fig. 53 we have typhoid fever death-rates and popu- lation suppUed with filtered water, both plotted with time as the abscissae; and we notice that as one hne goes up the other goes down, giving a sort of inverse correspond- ence. We are not justified however in caUing this a close correlation. Certainly we are not justified in saying that one is the cause of the other. It may be true, and few will dispute the fact that the filtration of polluted water tends to reduce the typhoid fever death-rate among the consumers of the water, but such a diagram as this does not prove it. As Phelps ^ says, we might plot' a Une showing the increase in the number of telephones which would very much resemble that of the population supplied with filtered water. Pearson does well to call this correla- tion based on comparison with a "common mutual," a " spurious correlation." A good many false conclusions have been based on statistics treated in this way. 1 Am. Jour. Pub. Health, 1917, p. 23. THE LAG 417 The*lag. — When two lines are plotted with the scale of abscissae in common to both variables it often happens that one hne changes in curvature after the other; it lags behind it. Sometimes this lag is very regular, sometimes it is more or less irregular. This lag does not necessarily show lack of correlation. It may, on the other hand, result from cause and effect. It is obvious that a cause must precede in time the effect produced by that cause. It may require a certain interval of time for the cause to make itself felt, and this naturally would produce a lag. For example, let us suppose that it takes ten days after a typhoid infection for the victim to " come down " with the disease; then a plotted line showing by days the number of cases of typhoid fever would lag behind a line showing infection of the water-supply, — if we can imagine such facts to be plotted. Conversely, if we had the two plotted lines we might compute the length of the incubation period of typhoid fever by measuring the lag. If the comparison is between the dates of infection and the dates of deaths from typhoid fever, then, of course, the lag is much longer as it includes not only the period of incubation, but also the run of the disease, and this is not the same for all persons. A device sometimes used is the "set back." If we are comparing two curves, one of which is supposed to represent the cause of the other, we may plot the causal curve on the true dates and we may set back the dates of the resulting curve by an amount equal to the lag. Correlation will then be indicated by the correspondence of the curves. 'This presupposes that the amount of the lag is known. In comparing lagging curves which are apparently correl- ative it is important to distinguish between cause and effect. As we have reiterated, it is not the function of correlation to demonstrate causality. 418 CORRELATION Fig. 52 is an example of the use of the set back. This is a correlation between typhoid fever deaths and atmospheric temperatures, the deaths being set back two months. Coefficient of correlation and the lag. — • It is possible to deal with the lag analytically instead of graphically. We may find that by comparing two series of statistics, date for date, the coefficient of correlation is low; by setting one series back a day and recomputing the coefficient we may find it higher; by setting back two days the coefficient may be higher still; and by using greater set backs the coeffi- cient may increase to a maximum, and beyond that point it may decrease. The set back which'produces the highest correlation may be taken as a measure of the lag. All such matters as these are fully discussed in the text- books of general statistics. Other secondary correlations. — Sometimes the second- ary character of a correlation is not as clearly revealed as in the case of two plotted lines with common abscissae. It has been noticed that poliomyelitis cases seem to follow the river valleys; what is the real correlation here? It does not appear to be a direct correlation. One says that fleas are correlated with the river valleys, and that, secon- darily, the disease is correlated with the fleas; another says that the lines of transportation are along the river valleys and that the real correlation is between poliomyeUtis and the contact of people incident to intercommunication. The whole matter of correlation is almost inseparable from the science of logic. The epidemiologist's use of correlation. — Epidemiology, a branch of medical science, is based fundamentally on the laws of cause and effect. The epidemiologist is continually searching for the cause of outbreaks of disease in order that they may be checked and future outbreaks prevented. In his studies he uses statistics continually and is of necessity THE EPIDEMIOLOGIST'S USE OF CORRELATION 419 mightily interested in correlation. The successful epi- demiologist must have a nose for facts, must be able to analyze these facts skillfully and draw logical conclusions from them. The influence of a particular factor as a cause of disease is often studied by means of statistics. For example, the filtration of a public water-supply may be followed by a reduction of the typhoid fever death-rate among the water takers. This is a sort of correlation, — one change being followed by another. We know, moreover, by inductive reasoning from many such occurrences in the past and also from experimental evidence that this is a correlation which implies causality. In using this method of reasoning, how- ever, it is important to know that the~ change in the water- supply was the only change which occurred. There are scores of instances where this method of reasoning has been used. In Panama the abolition of the mosquito reduced the death-rate from yellow fever. The evidence points to this as a clear-cut case not only of cor- relation, but causality. In Panama also the malaria has been greatly reduced since the anti-mosquito work was be- gun. But here we find that quinine has been used as an additional preventative. In this case therefore we have had two factors changing at about the same time. From ex- perimental evidence there is no doubt in regard to the causal relations- between malaria and the Anopheles mos- quito, but statistically the evidence is not as strong as in the case of yellow fever. In some of the old studies of typhoid fever it was found that the death-rate decreased after the introduction of a sewerage system. This was accompanied by an abolition of house privies. Now it was probably the abolition of the old privies, not the building of the new sewers which produced the result. In other cases a public water-supply 420 CORRELATION was installed at the same time that the sewers were built. A reduction in the typhoid death-rate following these events may have been due to either or to both. The fact should not be overlooked that when epidemics occur there is not infrequently more than a single f&ctor involved. Sometimes an outbreak can be traced to a single initial case, but just as in lighting a fire the match is applied to the paper, the burning paper sets fire to the kindling and the burning kindling sets fire to the coal, so a single case may start infections which may be scattered in various ways. It is important for the epidemiologist to find all of these methods of transmission. Sometimes the epidemiologist is obUged to base his action upon statistics which show correlation without waiting to de- termine whether this correlation also means causation. For example, in the recent pandemic of influenza a certain vac- cine, supposed to have a prophylactic value, was used upon several hundred persons. The question arose, " Shall this vaccine be distributed and generally used? " The data first collected showed a fair degree of correlation between the use of the vaccine and apparent protection against the disease, and on the strength of this finding the vaccine was dis- tributed. Later studies, however, failed to corroborate the correlation at first noticed, and showed that there was no causal relation between the use of the vaccine and failure of persons to take the disease. It was really a' case of correla- tion without causation, — post hoc non propter hoc. And yet the health authorities, compelled to take action one way or the other, were right in basing action on the supposed corre- lation. EXERCISES AND QUESTIONS 421 EXERCISES AND QUESTIONS 1. Is there a correlation between epidemics of poliomyelitis and rain- fall? [See Am. J. P. H., Sept., 1917, p. 813.] 2. Is there a higher correlation between flies and diarrhceal diseases among children than between diarrhcsal diseases and other factors? [See Am. J. P. H., Feb., 1916, p. 143, also Mar., 1914, p. 184.] 3. Is there a correlation between pneumonia and influenza? la there a causal relation? [See Am. J. P. H., Apr., 1916, p. 316.] 4. Is there a correlation between tuberculosis and housing? [See Am. A". J. P. H., Jan. 1913, p. 24.] 6. Look up Dr. Fulton's extravaganza on the subject of statistical logic as applied to the problem of prostitution. [See Am. J. P. H., July, 1913, p. 661.] 6. Study the correlation between plague and fleas. [Am. J. P. H., Aug., 1918, p. 572.] Is there strong presumptive evidence that in- fantile paralysis is spread by fleas? 7. Express Mill's three canons of logic in your own words. 8. Give examples of each in the field of epidemiology. 9. What is meant by quantitative induction? What part do statis- tics play in this? [See Jevon's Lessons in Logic, Chap. XXIX.] CHAPTER XIV LIFE TABLES To the popular mind there is something mysterious and awesome about a Hfe table. The insurance agent, wishing to sell you a policy, asks your age, consults a printed table and tells your " expectation of life " as so many years. What does this mean and how does he arrive at this expectation of life? It does not mean that you will live so many years and then die. It means" that it has been found in the past that most men who have attained your age have lived so many years after reaching that age. It cannot apply to everyone. You may live to be a hundred years, old or you may die to-morrow. The future is uncertain ■ for every individual. But the probability of your future longevity can be deter- mined by making a statistical study of a large group of people who have attained your age, to find out the average number of years which they Uved after reacliing that age. Instead of using the average, i.e., the mean we might find the median number of years hved, or even the mode. All three methods have been suggested, but that based on the mean is the one commonly used. Thus we see that there is nothing mysteri- ous about the "expectation of life"; it has no divine origin. It is merely the application of the ordinary methods of statistics to the experience of mankind in Uving beyond a given age. Probability of living a year. — Although the expectation of life is used by insurance agents to impress the prospective purchaser with the fleeting character of human life, the rates 422 PROBABILITY OP LIVING A YEAR 423 of insurance are not based directly on this expectation, but on the probabiUty of a person of given age living to be one year older. It is this chance of living from year to year, coupled with the growth of money at compound interest which determines what premium the insured at any age must pay. These actuarial methods are too complicated to be entered into here. In the very early days life insurance was virtually a lottery; now it is based on experience. If, as a result of better living conditions, the longevity of the insured is greater than the experience upon which the rates were based, the insurance company is the gainer because the premiums are continued for a longer time and the final pay- ment of the. policy is postponed. If the company is a so- called mutual company, the benefit of increased longevity of the insured is distributed among the policy holders in the form of rebates. But should the longevity of the insured prove to be less than the experience upon which the rates were based the opposite condition would prevail. What is the chance of a person living from year to year? Obviously it is one minus the chance of dying. The chance of dying within one year at any age is nothing else than our old friend the specific death-rate for the given age. Thus if at age 20 the specific death-rate is 7.80 per 1000, the chance of dying within the year is 780_in 100,000, 0.0078 in 1, or 1 chance in 128; at- age 50 the chance is 0.01378, or 1 in 73; at age 70 it is 0.06199 or 1 in 16; at age 80 it is 0.14447, or 1 in 7; at age 90, it is 0.45454, or 1 in 2.2. The chance of hving through the year is 1 less the chance of dying. At age 20 the chance of hving through the year is 99,220 in 100,000, i.e., 0.9920; at age 50 it is 0.98622; at age 70, 0.93801 ; at age 80 it is 0.85553; at 90 it is 0.54546. Or, to put it in another form, — at age 20 the chance of living a year is 99.2 in a hundred; at age 50, 98.6; at age 70, 93.8; at age 80, 85.5; at age 90, 54.5 in a hundred. 424 LIFE TABLES Thus a column showing for each age of life the probability of living, a year can be made by subtracting the yearly specific death-rates from unity, and expressing the results in decimal parts of 1. We might call these specific life-rates, as they are the converse of the specific death-rates. This specific life-rate is never used in ordinary discussion, and there is little reason for using it, as it is probably better to think in terms of specific death-rates. It is the deaths which we are always trying to postpone. A table of specific death-rates and specific life-rates would look hke this. TABLE 143 SPECIFIC DEATH-RATES AND SPECIFIC LIFE-RATES (Abridged from the American Experience Mortality Table.) Age. Population alive at mid-year. Specific death-rate per 100,000 (number dying annually). ■Specific lite-rate per 100,000 (number living through the year). (1) ■ C2) (3) (4) 10 20 30 40 50 60 70 80 90 100,000 100,000 100,000 100,000 100,000 100,000 100,000 100,000 100,000 749 780 843 979 1,378 2,669 6,199 •14,447 45,454 99,251 99,220 99,157 99,021 98,622 97,331 93,801 85,553 One reason why specific death-rates are not used more commonly is because people do not clearly understand them. The base, i.e., 100,000 persons, remains constant for all ages. Actually the number of persons aUve is constantly decreasing as age advances.- One says "you start with 100,000 persons at age 10 and kill off 749 in one year, but the next year you have 100,000 again. I don't understand it." MORTALITY TABLES 425 Now life tables are definitely related to specific death-rates and they take into account this decreasing population. Mortality tables. — In order to make a life table we may first select some large class of people and determine the specific death-rates for each year of age. We start with a certain number of people alive at a certain age. The in- surance companies commonly use age 10 because most insured -persons are older than that, but we might use any other age. We might use age 0, and in making a life table for a general population this would be done. As an illustra- tion, however, let us take the American Experience Mortality Table, which starts at age 10 and which is limited to males. Another reason for taking age 10 is that it is a round number not far from the age at which the specific death-rate is the lowest. For convenience we start with 100,000 as a round number of persons alive at age 10. This number is called the radix of the computation. We might use a million or a thousand, but the former is hardly warranted by the precision of our specific death-rates, while the latter gives too many decimals. In the table, column (1) gives the age, and column (5) the corresponding specific death-rates obtained from the original data. In column (2) we start with 100,000 persons alive at age 10, of these 92,637 livec L to age 20 85,441 ti ( 30 78,106 ti (I 40 69,804 a t 50 57,917 it ■ 60 38,569 tc I 70 14,474 if I 80 847 it I 90 ct 1 96 These figures were obtained as follows ; — 100,000 were alive at the beginning of ag^ 10 and 749 per 100,000 died 426 LIFE TABLES TABLE 144 AMERICAN EXPERIENCE MORTALITY TABLE Age. Num- ber living. Num- ber dying. No. of years expect- ation of life. No. dy- ing of each 100,000 annually. Age. Num- ber living. Num- ber dying. No. of years expectr ation of life. No. dy- ing of each 100,000 annually. (1) (2) (3) (4) (5) (1) (2) (3) (4) (5) 10 100,000 749 48.72 749 53 66,797 1,091 18.79 1,633 11 99,251 746 48.08 752 54 65,706 1,143 18.09 1,740 12 98,505 743 47.45 754 55 64,563 1,199 17.40 1,857 13 97,762 740 46.80 757 56 63,364 1,260 16.72 1,988 14 97,022 737 46.16 760 57 62,104 1,325 16.05 2,133 15 96,285 735 45.50 763 58 60,779 1,394 15.39 2,294 16 95,550 732 44.85 766 69 69,385 1,468 14.74 2,472 17 94,818 729 44.19 769 60 57,917 1,546 14.10 2,669 18 94,089 727 43.53 773 61 56,371 1,628 13.47 2,888 19 93,362 725 42.87 776 62 54,743 1,713 12.86 3,129 20 92,637 723 42.20 780 63 53,030 1,800 12.26 3,394 21 91,914 722 41,53 785 64 51,230 1,889 11.67 3,687 22 91,192 721 40.85 791 65 49,341 1,980 11.10 4,013 23 90,471 720 40.17 796 66 47,361 2,070 10.54 4,371 24 89,751 719 39.49 801 67 45,291 2,158 10.00 4,765 25 89,032 718 38.81 806 68 43,133 2,243 9.47 5,200 26 88,314 718 38.12 813 69 40,890 2,321 8.97 5,676 27 87,596 718 37.43 820 70 38,569 2,391 8.48 6,199 28 86,878 718 36.73 826 71 36,178 2,448 8.00 6,766 29 86,160 719 36.03 834 72 33,730 2,487 7.55 7,373 30 85,441 720 35.33 843 73 31,^3 2,505 7.11 8,018 31 84,721 721 34.63 851 74 28,738 2,501 6.68 8,703 32 84,000 723 33.92 861 75 26,237 2,476 6.27 9,437 33 83,277 726 33.21 872 76 23,761 2,431 5.88 10,231 34 82,551 729 32.50 883 77 21,330 2,369 5.49 11,106 35 81,822 732 31.78 895 78 18,961 2,291 5.11 12,083 36 81,090 737 31.07 909 79 16.670 2,196 4.74 13,173 37 80,353 742 30.35 923 80 14,474 2,091 4.39 14,447 38 79,611 749 29.62 941 81 12,383 1,964 4.06 15,860 39 78,862 756 28.90 959 82 10,419 1,816 3.71 17,430 40 78,106 765 28.18 979 83 8,603 1,648 3.39 19,156 41 77,341 774 27.45 1,001 84 6,955 1,470 3.08 21,136 42 76,567 785 26.72 1,025 85 5,485 1,292 2.77 23,555 43 75,782 797 26.00 1,052 86 4,193 1,114 2.47 26,568 44 74,985 812 25.27 1,083 87 3,079 933 2.18 30,302 45 74,173 828 24.54 1,116 88 2,146 744 1.91 , 34,669 46 73,345 848 23.81 1,156 89 1,402 555 1.66 39,586 47 72,497 870 23.08 1,200 90 847 385 1.42 45,454 48 71,627 896 22.36 1,251 91 462 246 1.19 63,247 49 70,731 927 21.63 1,311 92 216 137 0.98 63,426 50 69,804 962 20.91 1,378 93 79 58 0.80 73,418 51 88,842 1,001 20.20 1,454 94 21 18 0.64 86,714 52 67,841 1,044 19-49 1.639 95 3 3 0.50 100,000 THE "VIE PROBABLE" 427 during the year. Consequently, the number ahve at age 11 was 100,000 - 749 = 99,251. In the next year the specific death-rate was 752 per 100,000. The number dying was, 752 therefore, 99,251 X ^„ -^- „ = 746, and the number aUve at age 12 was 99,251 - 746 = 98,505. And so on. The num- ber dying each year is given in column (3), the number living in column (2). At age 96 all were dead. These are the facts of the case, now how shall we use them? There are three ways, which correspond to the mode, the median and the mean, and they are called respectively the "most probable life-time," the "Vie Probable," and the "Expectation of Life." f The " most probable life-time." — The figures in column 3 form a frequency curve, the mode of which is 2505. There are more deaths at age 73 (i.e., age 73-74) than at any other age. 73 is the fashionable, modish age to die. The chance of dying at that age is greater than at any other age. The difference between a given age and 73 years is called "the most probable hfe-time." At age 10, it is 73 — 10 = 63; at age 20 it is 53; and so on. Above the age 73 the "most probable life-time" becomes a negative quantity, and this is the objection to the use of this computation. It is applicable only to the first part of the frequency curve. The "Vie Probable." — The "Vie Probable" is the number of years which a person (at a stated age) has an even chance of living. It is the difference between a given age and the age at which the number of persons ahve is one-half the number ahve at the given age. The latter is the median age to which the persons who passed the given age hved. At age 10 there are 100,000 persons alive. One-half of this number, i.e., 50,000, are alive at age 64.5±. Hence 64.5 '— 10 = 54.5 is the "vie probable." In this period of time the chance of living or djang is just even. 428 LIFE TABLES At age 20, there are 92,637 persons alive. One-half of this number, i.e., 46,318, were still alive at age 66.5. Hence the "vie probable," for. age 20 is 66.5 — 20 = 46.5 years. The "Expectation of Life." — The "Expectation of life" means the average number of years that persons of a given age will prol^ably survive. It is obtained by finding the average of the lengths of life of all the persons who hved beyond the given age. Thus of the 100,000 ahve at age 10, 3 lived to the age of 95, that is, they lived for (95 — 10 = ) 85 years after the age of 10. 21 Uved to age 94, i.e., 84 years. But these 21 include the 3 who lived to age 95, so there were 18 who hved 84 years. 79 lived 83 years, but these include both the 3 and the 18, so in addition to them (79 — 21 = ) 58 lived 82 years. And so on. The weighted averages of aU of these lives gives what is called the expectation of life. These results are given in colunm (4). In obtaining the figures for column (4) it is most con- venient to begin at the higher ages and work backward. At the beginning of age 95, there were 3 persons alive; at the end there were none alive. Not knowing at what part of the year they died the best assumption is that they died (on an average) at the middle of the year, i.e., they Uved one-half year. Hence at age 95, the average length of the 3 X - hves was — ^-^ = 0.50 year. This is the expectation of life at age 95. At age 94, 21 persons were alive. 3 of these hved 1| years • each; the other 18 died within the year, and may be said to have hved one-half year. Hence we have: 3 X 1.5 = 4.5 18 X 0.5 = 9.0 21 13.5 and 13.5 4-21 =0.64 yr. Hence at age 94 the expectation of life is 0.64 year. COMPARISON OF THE THREE RESULTS. 429 At age 93 we have: 3 X 2.5 = 7.5 18 X 1.5 = 27.0 58 X0.5 = 29.0 79 63.5, and 63.5 X 79 = 0.80 year. In this way we find that at age 10, the average number of years lived by those who passed age 10, was 48.72 years. At age 20 it was 42.20 years; at age 30 it was 35.33 years, etc. Comparisoii of the three results. — The U. S. Life Tables for 1910 give the "complete expectation of life" (computed on the basis of the mean), and from the tables may be ob- tained the "most probable life-time" (based on the mode) and the "vie probable" (based on the median). The follow- ing figures give the results for age zero, that is, they show the expectation of hfe at birth. TABLE 145 COMPARISON OF "EXPECTATION OF LIFE," "VIE PROB- ABLE" AND "MOST PROBABLE LIFE-TIME" Original registration states. (1) White males White females Negro males Negro females White males in cities White males in rural part. . White females in cities. . . .'. White females in rural part Males in Massachusetts . . . . Females in Massachusetts. . Expecta- tion of life. (Mean.) (2) 60.23 53.62 34.05 37.67 47.32 55.06 51.39 57.35 49.33 53.06 ' Vie prob- able."! (Median.) (3) 69.30 63.27 34.85 40.58 55.00 65.33 60.73 67.38 58.82 62.74 Most prob- able 1 life- time. (Mode.) (4) 74.0 73.5 59.5 65.5 68.5 76.5 71.5 76.5 69.5 74.5 1 Approximate. 430 LIFE TABLES Life tables based on living population. — Life tables are usually computed in another way. They are based on the population living at each age as shown by the census returns or by data collected by the insurance companies. Thus we may assume that the figures in column (2) have been ob- tained in this way. If we start with 100,000 persons aUve at age 10 and find that 99,251 were alive at age 11 then the number of deaths during the year must have been 100,000 — 99,251, or 749. Between ages 11 and 12 the deaths were 99,251 - 98,505, or 746; and so on. By this method we compute the deaths, and we may also compute the specific death-rates for each age. This method justifies the use of the term life tables, as the results are based on the living and not on the dying. It is obvious that migrations of population interfere somewhat with this method. It is obvious, also, that concentrations of population on the round numbers present another difficulty. As a matter of practice the ragged data must be smoothed out before a life table can be constructed; otherwise the computed expectations of life would themselves be erratic. These errors of round niunbers creep into the computations of specific death-rates, so that in any case it is necessary to do a certain amount of "smooth- ing" before computing fife tables. One method commonly used is that known as "osculatbry interpolation," which may be found described in such books as Vital Statistics Ex- plained, by Burn. Still another method of computing a Ufe table is to base it wholly on the distribution of deaths, making use of certain mathematical formulas for frequency curves.' Mathematical formula for computing the expectation of life. — There is a mathematical formula for the computa- tion of the expectation of life by the use of which the labor may be shortened. It is usually stated as follows: ' Arne Fisher. Note on the Construction of Mortality Tables by means of Compound Frequency Curves. Proc. Casualty Actuarial and Statistical Society of America, Vol. IV, Pt. 1, No. 9. EARLY HISTORY OF LIFE TABLES 431 ' _ hlx+ ^(a^fl) + kx+2) + kx+3) + ' ' ' _ 1 , ^ e. ^- 2 + ^- /-) '(1+1)+ '(x+2) + ^fa+3) + • • • ''a: o e, = expectation of life, in years, at age x. Ix = number of persons living at age x. hz+i> = number of persons living at age x + 1. kx-t^ = number of persons living at age x + 2, etc. For a more detailed description of these methods the reader is referred to such books as United States Life Tables, 1910, Bureau of the Census, prepared by Prof. James W. Glover and pubUshed in 1916; Life Assurance Primer, by Henry Moir; Vital Statistics, by Newsholme; Mortahty Laws and Statistics, by Robert Henderson. Early history of life tables. — It is not surprising that most of the hfe tables which have been computed have been confined to males of insurable age. Halley, the British astronomer, famous for the comet which bears his name, was the first to use the method. This was in 1692 and related to the town of Breslau. Other famous tables are the North- ampton Table of 1762, the Carlisle Table of 1815 and Dr. Farr's English Table of 1851. In 1843 seventeen American insurance companies com- bined their experiences and published a table known as the Actuaries or Combined Experience Table. It was based on 84,000 policies. The American Experience Table of Mor- tality, now recognized by the insurance companies as the standard for America, was formed by Sheppard Homans in 1868. It is supposed to have been based on the experience of the Mutual Life Insurance Company of New York. In 1869 the H^ Table was pubhshed in England. H^ means Healthy Males. It was based on 180,000 policies. Then there is an 0*^ Table (ordinary life, males) based on over 400,000 lives. This is the Canadian standard. 432 LIFE TABLES Recent life tables. — In 1898 Dr. Samuel W. Abbott published in the annual report of the Massachusetts State Board of Health for that year/ a Hfe table for Massachusetts. This is one of our best American papers on the subject. Dr. Guilfoy, the statistician of the New York City Board of Health, has published the following interesting comparison between the expectations of hfe in 1879-81 and 1909-11. The changes which have taken place during the interval are striking. The figures are as follows: TABLE 146 APPROXIMATE LIFE TABLES FOR THE CITY OF NEW YORK BASED ON MORTALITY RETURNS FOR THE TRIENNIA 1879-1881 AND 1909-1911 Yeare of mor- Expectation of life, 1879 to 1881. Expectation of life, 1909 to 1911. Gain (-f ) or loss C— ) in years of expectancy. nses. Males. Fe- males. Per- sons. Males. Fe- males. Per- sons. Males. Fe- males. Per- sons. CD (2) (3) (4) C6) ■ (6) (7) (8) (9)' CIO) -s 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85+ 39.7 44.9 42.4 38.2 34.4 31.2 28.2 25.3 22.5 19.8 17.2 14.5 12.2 9.9 8.5 7.1 6.2 5.4 42.8 47.7 45.3 41.2 37.3 34.0 31.0 28.1 25.2 22.4 19.4 16.4 13.8 11.2 9.3 7.5 6.5 5.5 41.3 46.3 43.8 39.7 35.8 32.6 29.6 26.7 23.9 21,1 18.3 15.4 13.0 10.5 8.9 7.3 6.4 5.5 50.1 49.4 45.2 40.8 36.6 32.7 28.9 25.4 22.1 18.9 15.9 13.2 10.8 8.8 6.9 5.3 4.1 2.0 53.8 52.9 48.7 44.2 40.0 36.0 32.1 28.4 24.7 21.1 17.7 14.6 11.8 9.4 7.5 5.7 4.5 2.4 51.9 51.1 46.9 42.5 38.3 34.3 30.5 26.9 23.4 20.0 16.8 13.9 11.3 9.1 7.2 5.5 4.3 2.2 +10.4 + 4.5 + 2.8 + 2.6 + 2.2 + 1.5 + 0.7 + 0.1 - 0.4 - 0.9 - 1.3 - 1.3 - 1.4 - 1.1 - 1.6 - 1.8 - 2.1 - 3.4 + 11.0 + 5.2 + 3.4 + 3.0 + 2.7 + 2.0 + 1.1 + 0.3 + 0.5 - 1.1 - 1.7 - 1.8 - 2.0 - 1.8 -■1.8 - 1.8 - 2.0 - 3.1 +10.6 + 4.8 + 3.1 + 2.8 + 2.5 + 1.7 + 0.9 + 0.2 - 0.5 - 1.1 - 1.5 - 1.5 - 1.7 - 1.4 - 1.7 - 1.8 - 2.1 - 3.3 Balan ce +24.8 -15.3 + 9.5 +28.7 -17.6 +11.1 +26.6 -16.6 +10.0 See State Sanitation, Vol. II, p. 300, by G. C. Whipple. A FEW COMPARISONS 433 United States life tables. — In 1916 the Bureau of the Census published a special report entitled United States Life Tables, 1910, prepared under the direction of Prof. James W. Glover of the University of Michigan. This was the first report of its kind in America. The tables are based on the general unselected population, and, therefore, differ from the Ufe tables of the insurance companies. The radix is 100,000 at age 0. The data were obtained from the U. S. Census of 1910. Expectations of life are computed by months up to one year of age, and after that by years up to age 106. Separate tables are given for males, for females and for both sexes combined; there are separate tables also for negroes and whites, and for native and foreign born whites; for cities and for rural districts, — all of these re- lating to the population of the original registration states, namely, the New England states, New York, New Jersey, Indiana, Michigan and the District of Columbia. Separate tables for males and for females are given for the states of Indiana, Massachusetts, Michigan, New Jersey and New York. These tables are well prepared and their results are of much interest. Besides giving the expectations of life computed in the usual way, computations are made on the assumption of a stationary population, that is one where the general ' death-rate is equal to the general birth-rate. These have the advantage of excluding the effect of emigration results and immigration, and from them one can compare the death- rates of different communities for the population above a given age. For these results the reader is referred to the original report. A few comparisons. — It will be interesting to make a few comparisons of the expectations of life at certain ages for different classes of people and at different ages. For greater details the reader should consult Professor Glover's report. 434 LIFE TABLES ^ TABLE 147 EXPECTATIONS OF LIFE, 1910 Age. Original regiatratioa states. (1) Native white males Native white females Foreign-born white males. . . Foreign-born white females . Negro males Negro females White males in cities White males in rural part..'. White females in cities White females in rural part . Males in Indiana Males in Michigan Males in Massachusetts . . . . Males in New Jersey Males in New York 50.58 54.19 (2) 34.05 37.67 47.32 55.06 51.39 57.35 54.70 53.86 49.33 49.08 47.89 (3) 51.93 54.43 50.30 52.24 40.65 42.84 49.13 54.53 52.22 55.54 53.91 54.09 51.14 50.31 49.40 (4) 43,32 45.76 41.75 43.50 33.46 36.14 40.51 45.92 43.51 46.86 45.44 45.57 42.48 41.66 40.79 (5) 35:61 37.98 33.71 35.31 27.33 29.61 32.61 38.10 35.52 39.05 37.76 37.76 34.55 33.86 33.01 40 (6) 28.33 30.33 26.03 27.55 21.57 23.34 25.32 30.20 27.88 31.15 29.99 29.81 26.97 26.57 25.88 (7) 21.20 22.78 19.08 20.09 16.21 17.65 18.59 22.43 20.53 23.27 22.38 22.10 19.79 19.67 19.28 (8) 9.09 9.80 8.40 8.67 8-. 00 9.22 8.14 9.36 8.99 9.76 9.29 9.17 8.58 8.65 8.58 The greater longevity of females as compared with males is ^evident throughout the tables. It is greater for native whites than for foreign born whites, greater for whites than for negroes, greater for rural districts than for cities. The differences between the states depend upon differences in the composition of the population, and upon urban and rural conditions. It is interesting also to compare the specific death-rates for the corresponding ages. The relations between these and the expectations of life are in a general way reciprocal. The specific death-rates are lower in the rural districts than in the cities, especially in the early and the later years; in middle life there is less difference. The differences between whites and negroes are very striking. EXERCISES AND QUESTIONS 435 TABLE 148 ' SPECIFIC DEATH-RATES Age. Registration area. 10 20 30 40 50 70 (1) (2) (3) (4) (5) (6) (7)- (8) Native white males Native white females Foreign-born white males.. . 126.02 104.60 2.37 2.06 2.47 2.09 5.02 5.18 2.59 2.07 2,23 1.80 4.82 4.40 5.10 3.65 11.96 10.74 4.93 4.83 4.10 4.41 7.14 6.13 5.80 5.84 14.96 12.02 7.22 5.39 6.33 5.46 10.02 7.76 10.53 8.55 21.03 17.50 12.10 7.06 8.83 6.65 21.20 11.68 17.92 14.42 31.42 25.52 19.17 10.65 14.44 9.91 57.20 50.24 70.79 Foreign-born white females. 67.87 Ne%ro males 219.35 185.07 133,80 103.26 111.23 84.97 83.98 Negro females 71.27 White males in cities White males in rural part. . . White females in cities White females in rural part . 74.20 52.93 63.60 49.92 EXERCISES AND QUESTIONS 1. Compare the life table for New Haven with that for the U. S. Registration Area. [See Am. J. P. H., Aug., 1918, p. 580.] 2. Compute a Ufe table for some city, to be assigned by the in- structor. 3. Find your own "probability of Kving a year," "vie probable," "most probable life-time," and "expectation of life." CHAPTER XV A COMMENCEMENT CHAPTER This last chapter is to be something hke the day after col- lege commencement. On the day before the student regards his work as finished; his exercises are all completed, _he has passed his examinations, he is to be graduated. But on the day after commencement he finds himself plunging into a world of problems yet unsolved; he sees that most of the tilings he is called upon to do were not in his curriculum; that he must learn to do these things for himself. Little by little he comes to realize that what his stupid old profes- sors had been trying to do was not to tell him all there was to know in the world but to teach him how to think and how to use tools. He had heard much of principles, and laws and formulae and synopses and all that, and had regarded them as the dry parts of his courses — the neces- sary evils. "But little by little he finds that these general principles, these almost self-evident ideas, help him to solve his problems; that his systematic methods of going at a thing help him to do his work more easily and quickly; that by following the dry old laws of logic, his conclusions are somehow better than those of the other fellow who does not take the trouble to see that all the steps in the prob- lem are " necessary and sufficient." In short, he comes to realize that his education has enabled him to do his work easier and better and has given him intellectual confidence. If it doesn't do this for him he has wasted his opportunities in college. 436 MILITARY STATISTICS 437 In the preceding chapters of this book the author has en- deavored to place the emphasis not on the subject matter but on methods of procedure, to outUne the simpler prin- ciples of the statistical method as applied to studies in demography, to warn against the common fallacies which so often creep into discussions of vital statistics, and to urge students and health officers not to be content with such things as general rates but to seek the answers to their'prob- lems by methods of statistical analysis and the use of specific rates and ratios. Let us now take an outlook upon some of the problems of demography as they come piling in upon the health officer from day to day. And if, for convenience' sake, we take them at random, one after the other, without order or system we shall simulate more nearly every-day practice. If we can solve this and that problem or if we can see the steps in the solution we shall know that we have acquired the use of the tools of the statistician, and will have confidence in our own studies. This chapter will also include certain subjects which have not logically found a place in the pre- ceding chapters. Several of these subjects might easily be expanded into chapters of their own. Military statistics. — In general the vital statistics of armies are computed in the same way as those of civil pop- ulations, but instead of using the mid-year estimated population, the mean strength for the year is used as a basis of rates. An army does not increase in numbers as a population grows, slowly by geonietrical progression, but is kept up to a fairly constant strength or is suddenly increased or decreased according to demands made upon it. An army represents a selected population, — males be- tween certain age limits, and above set standards of health and physique. Rates computed for armies are therefore specific rates and they must not be compared with general 438 A COMMENCEMENT CHAPTER rates. The health of the soldiers is carefully looked after by the surgeons, who are obliged to keep records; hence the morbidity records are more complete than in the case of"the civil population. Since 1894, when an international commission for the uni- fication of medical statistics met at Budapest, tables of statistics made up according to certain schedules have been published for most armies. These may be found in the annual reports of the Surgeon General of the U. S. A. In the report for 1916 we find that in the entire U. S. army of 93,262 enlisted men in 1915 the sick admissions " to quar- ters " and " to hospitals " amounted to 745 per 1000. This does not mean 745 different men, for sometimes the same man was admitted more than once. Of these 96 per cent returned to duty, i.e. recovered, 0.65 per cent died, and 3.4 per cent were " otherwise disposed of." The death-rate for the mean strength was 4.6 per 1000. The annual number of days lost through sickness was 9.44 for each soldier, or 12.7 for each " admission." In the pub- lished tables the figures are classified according to the location of the troups, the arms of the service, the season, the larger garrisons, and according to the cause of the sick- ness or death. It should be observed that in the interna- tional tables for the army the international list of diseases, as given on page 257, is not followed. The Surgeon General of the United States uses it, however, in the body of his report. In 1915 in the entire U. S. army (103,842 officers and enhsted men) the following were the rates per 1000 of mean strength: MILITARY STATISTICS 439 TABLE 149 VITAL STATISTICS OF U.S. ARMY: 1915 Death-rates per 1000. From disease. From injury. Total. (1) (2) (3) W Admissions Discharged on certificate of disability 597.0 12.6 2.5 15.1 129.2 1.4 1.9 3.3 726.2 14.0 Died Total losses 4.4 18.4 The percentage of soldiers constantly non-effective was 2.5 per cent. If we look back a few years we find that the health of the army has been improving. TABLE 150 HOSPITAL ADMISSION RATES AND PERCENTAGE OF NON-EFFECTIVES, U.S.A. Year. Admisaion-rate per 1000 Non-efiFectives, per cent. (1) (2) (3) 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1118 1102 1079 964 870 858 806 666 660 726 597 4.8 4.4 4.2 4.1 3.5 3.2 2.9 2.4 2,4 2.5 2.5 440 A COMMENCEMENT CHAPTER Army diseases. — In the consideration of army diseases one must distinguish between peace times and war times; one must also distinguish between the diseases which cause death and those which render the men non-effective. In 1915 the specific death-rates among the American enlisted men in the U. S. A. were, in order of their im- portance, as follows: Per 100,000 Tuberculosis 33 Pneumonia (lobar) 31 Organic heart disease 23 Measles 23 Appendicitis 13 Epidemic cerebro-spinal meningitis 11 The principal causes of discharge were: Per 1000 Mental alienation 3.30 Tuberculosis 1.79 Flat foot 1.25 Venereal disease 0.82 Epilepsy 0.69 Organic heart disease .^ 0.50 The admission and non-effective rates for white enlisted men were: ARMY DISEASES 441 TABLE 151 ADMISSION RATES AND PERCENTAGE OF NON-EFFECTIVES FROM PARTICULAR DISEASES, U. S. A. Admission rate, per 1000 Non-e£fectivea, per cent. (1) (2) (3) Venereal diseases 106 3 4 35 47 9 24 10 35 32 7 6 4 0.47 Tuberculosis 17 Mental alienation 0.09 Bronchitis 06 Tonsilitis 0.07 Appendicitis 06 Malaria 0.05 Mumps 05 Influenza 0.05 Diarrhoea and enteritis 04 Measles 05 Articular rheumatism 04 Hernia 04 In war times we have to consider the venereal diseases, syphilis, gonorrhoea, etc.; the diarrhceal diseases, typhoid fever, cholera, dysentery; the insect-borne diseases, typhus fever, relapsing fever, trench fever, malaria, etc.; scurvy — besides all sorts of diseases associated with wounds. No attempt will be made here to discuss these war diseases, because the Great War will yield statistics better and more complete than any which we now have. Some day it will be in order to make comparisons between the Civil war, the Spanish war and the present Great War. We shall then see what enormous strides have been taken in sanitation, in the use of antitoxins, in providing proper food, in the enforcement of the rules of personal hygiene, in the treatment of the sick and wounded, in the ambulance and hospital service, in the protection of the health of the civil population in war time in factory and home. One 442 A COMMENCEMENT CHAPTER gratifying result of the war seems assured — a world-wide up-lift in public health. We shall hereafter need world- wide vital statistics, that is, we shall need the science of demography. Effect of the Great War on demography. — A thousand and one questions have arisen as a result of the war. What are we to do with the enormous number of non- resident males in the United States? How are we to compute death-rates? Will our usual methods have to be niodified as an emergency measure? What effect has the war had on the marriage-rates, birth-rates and death-rates? A big hole is sure to be made in the male population for the ages of youth and early manhood; fewer young men of twenty in 1920 will mean fewer men of thirty in 1930 and fewer men of forty in 1940. How will this alter the general death-rate? Will the birth-rate rise as a natural reaction to war's destruction or will hard economic conditions keep it low? Can we learn anything from past wars on this matter? Typhoid fever, the past scourge of armies, has been al- most completely conquered. Will the venereal diseases also be conquered? Will the" Great War point out the way to this end? What has been the effect of reduced food rations on health and physique? Will the loss of the most vigorous young men lower the standards of physique by hereditary in- fluences? Will the lessons in hygiene and sanitation be so well learned that their benefits will offset, other baneful influences? We knew approximately the standing of the nations before the ,war as to population, natural rates of growth, migrations, death-rates, and so on — how will these nations stand after the war? Who will be the greatest losers? What will be their most serious losses? STATISTICS OF INDUSTRIAL DISEASE 443 Such questions as these force themselves upon us. Demog- raphy will be the science looked to for the answers. Hospital statistics. — There are many hospitals in the country and they are an increasingly important factor in the control of disease. Some of these hospitals keep good records of their cases and some publish them. Other hos- pitals keep very 'inadequate records and publish nothing.- Uniformity in this matter is most desirable, as a good op- portunity for collecting facts in regard to certain non- reportable diseases and in regard to the fatality of these diseases is being lost. Several plans for unifying hospital statistics have been suggested.' Dr. Charles F. Bolduan/ of the New York City Health Department, suggested the idea of a dis- charge certificate, to be filled out for each case on leaving a hospital, — a certificate comparable to the ordinary death certificate. Anothei: method is to have the annual re- ports (or monthly reports) made 'out on some fixed schedule of statistics and submitted to some central authority.^ Perhaps the U. S. Pubhc Health Service may some day take the lead in the collection of the important data to be secured from hospitals. See also page 471. Statistics of industrial disease. — Statistical studies of industrial diseases are becoming increasingly numerous. It is a most complex and difficult branch of the subject. At the outset we are met with the fundamental difficulty of defining occupations. The extent of this difficulty may be appreciated from the fact that in 1915 the U. S. Bureau of the . Census published an " Index to Occupations" which covered over four hundred pages and included 9000 occupational des- ignations. The report makes 215 main classes, 84 of which are subdivided. This list has been given in Chapter VIII. 1 N. Y. Medical Journal, Mar. 29, 1913. 2 Amer. Jour. Pub. Health, Apr., 1918. 444 A COMMENCEMENT CHAPTER A second difficulty is due to the migration of laborers from place to place, and from one class to another. A third, which grows out of the other two, is the difficulty of getting constant, well-defined classes to serve as the basis of the computation of rates and ratios. A fourth is the oft repeated error of concealed classification. These and other minor difficulties have compelled us to resort to the use of specially gathered statistics, which are often not truly representative of the conditions discussed. For example, the Massachusetts General Hospital re- cently made a study of lead poisoning in its Industrial Chnic. During the first year of this clinic 148 cases of lead poisoning were diagnosed in the hospital as against 147 during the previous five years. This was found by sifting out of the hospital admissions by a trained worker those suspected of being exposed to special industrial hazard. A study of these 148 cases gave an industrial distribution as follows: TABLE 152 Occupation. Number exposed. Number cases. Per cent poisoned. (1) (2) (3) (4) 217 68 56 12 16 11 4 6 8 11 14 10 31 House .... ShiDvard and navv vard 54 169 9 "42" 64 135 30 Rubber workers ... . 7 44 Lead and lead oxide worker "19 " Printers 17 10 Non-industrial Total 148 ECONOMIC CONDITIONS AND HEALTH 445 An attempt to ascertain the rate of attack was made by ascertaining as well as possible the number of persons exposed. These rates are, of course, far too high; 31 per cent of all painters did not get lead poisoning, but only 31 per cent of the exposed persons who were sorted out in this indus- trial clinic. The report does not err in this respect but the reader may get a false impression unless he reads thought- fully. The underlying idea of this clinic is excellent and the work, unfortunately interrupted, was already yielding excellent results. The danger of lead poisoning of men engaged in certain occupations in ship yards was clearly shown. Economic conditions and health. — Poverty and disease mutually influence each other. We cannot expect to solve the problem by attacking either alone. It is most difficult to separate cause from effect. In fact, there is a third major .factor which we may call ignorance — and all three are mutually dependent. Then there are many minor factors. We can correlate these things by statistics, and that is wOrth while because it calls attention to the problems; but the plan of attack must rest upon the fact that the different conditions are mutually related. If we help only a little to raise the economic and hygienic conditions the result is an accelerating social advance; to aid one without the other does not bring about permanent betterment. A glimpse at these mutual relations, as shown by Warren and Sydenstricker,i is instructive. They classified the health of certain garment workers with respect to the annual earnings of the headg of families as follows: 1 Pub. Health Reports, May 26, 1916, p. 1298. 446 A COMMENCEMENT CHAPTER TABLE 153 HEALTH OF GARMENT WORKERS (1) Number of persons Ave. annual earnings Ave. rate of weekly earnings Per cent which actual earnings were of maximum possible earnings Maximum possible earnings for year . . . Ave. number of persons per family Ave. number of children born per family Ave. number of children living per family. Ave. number of children dead per family Infant mortality rate Per cent of male married garment workers who were poorly nourished. Ave. haemoglobin index, Talquist Per cent with haemoglobin index under 80 Per cent of family heads tuberculous. . Annual earninga. S500 (2) 381 $382 $19 38% 5.36 3.78 2.99 0.78 206.9 25.00 85.94 9.94 5.64 S50O-$999 (3) 581 $577 $23 48% $1196 5.38 3.34 2.78 0.56 167.2 15.02 86.99 5.65 5.30 $700 14) 462 $866 $27 61% $1404 4.88 2.75 2.43 0.32 116.5 12.72 87.35 4.42 0.44 Accidents and accident-rates. — Injuries and deaths from accidental causes are attracting much attention nowadays, and rightly so. The death-rate from accidents in the United States is far greater than from typhoid fever. Only a few years ago it was more than 100 per 100,000 of population. Some of the principal causes are railroad accidents, falls, drowning and burns, but there are many accidents associated with different industries. All of these present interesting problems for study and each should be studied by itself. Taking accidents as a general class, we find that the ACCIDENTS AND ACCIDENT-RATES 447 specific death-rates follow closely the death-rates from all causes, decreasing from the first year to a minimum be- tween ages 10-14 and then increasing steadily to the highest ages. Owing to the age distribution of population we find the mode of the accident distribution curve occur- ring somewhere in age group 25-29 years. In the case of railroad accidents among males the mode is found in age-group 25-29 years, that is, the largest number of accidents occurs among males at that period; in the case of falls the mode is in age-group 45^9; in the case of drowning it is at age 20-24. The specific death-rate from railroad accidents is low until the age of twenty, when it rises to above 30 per 100,000 and fluctuates between 30 and 50 for all higher age-groups. The specific death-rate from falls rises steadily from, the tenth year and above 75 years of age exceeds 100 per 100,000. The specific death- rate from drowning on the other hand is highest at about twenty years of age. Except for falls the accident-rates from the major causes are higher for males than for females. If time permitted it would be interesting to follow up this subject of accidents and find the seasonal distribution and classify them in other ways. In studying accidents in industrial establishments we must ask the usual questions, — where, when, what, how, who, and answer them by collecting the necessary statistics. It does not do to follow popular impressions in these mat- ters. Thus it is sometimes said that most accidents occur " at the end of a tired day," yet statistics collected in Massa- chusetts by the Industrial Accident Board showed that it is between 9 and 10 a.m. and 2 and 3 p.m. that accidents are most frequent. Yet this general statement is not enough. We need to know what kinds of accidents are meant. Per- haps some kinds of accidents do occur at the end of the working day. Then there are daily differences to be con- 448 A COMMENCEMENT CHAPTER sidered, and seasonal differences, as well as differences due to the weather. In the case of the English munition fac- tories, which run night and day, the accident mode occurs in the evening. One runs a great risk in generaUzing from composite statistics. There are various ways of expressing accident rates. One is the ratio between annual accidents and number of employees. Another is between annual accidents and the number of full time workers, i.e., 300 days per year. Another is between days lost through accident and full time workers. Differences in the severity of the accidents are also important from an economic point of view. Age distribution of cases of poliomyelitis. — One of the diseases which has recently attracted attention is Anterior PoUomyelitis, commonly known as infantile paralysis. Many attempts have been made to correlate the occur- rences of this disease with factors which might point to the manner of its communic ability. There is an excellent opportunity here for original statistical work based on re- cently accumulated data. As bearing on the theory of contact as a major element in its communicability the age distribution of the cases is important. The disease is essentially one of the early ages. A recent study by the author appears to indicate that the median age is inversely proportional to the density of population. This is like- wise true for measles, whooping cough and similar diseases. It has been noticed that if the cases of poliomyelitis are plotted on logarithmic probability paper they tend to fall on a straight line, except that above the upper decentile there is an irregular divergence from the straight line. From this diagram it is easy to read off the median age or the per cent of cases below any age or between given ages. Fig. 63 shows that in the populous city of New York the median age was 2.5 years, in Boston 3.7 years, AGE DISTRIBUTION OF CASES OF POLIOMYELITIS 449 ,000^ O « ^ o cj tn i~- o w OOICO h> ^9 ta 450 A COMMENCEMENT CHAPTER and in Minnesota 4.6 years. Similar differences were observed in the upper decentiles. These data are not strictly comparable as they were not for the same year and are presented merely to show the advantage of this method of plotting. It is interesting to note that scarlet fever cases plotted by ages on logarithmic probability paper also fall nearly on a straight Une. The Mills-Reincke Phenomenon. — Problems like this offer excellent opportunities to apply the principles of statistics. In 1893-94 Mr. Hiram F. Mills found that at Lawrence, Mass., after the introduction of the sand filter to purify the public water-supply taken from the polluted Merrimac River, there was a material reduction in the general death-rate of the city. Notably typhoid fever was reduced, but this reduction was not sufficient to account for the fall in the general death-rate. , About the same time Dr. J. J. Reincke found the same thing in Hamburg. In 1904 Hazen studied these and other records and stated that " where one death from typhoid fever had been avoided by the use of better water, a certain number of deaths, probably two or three, from other causes have been avoided." In 1910 Sedgwick and MacNutt * published an elaborate study in which Hazen's statement was dignified with the rank of "theorem." The natural inference from such statements is that the purification of a polluted water-supply reduces deaths from causes other than typhoid fever. In Lawrence if one con- siders short periods before and after the introduction of the filter a decrease is observed in several diseases, — as, for example, pneumonia, tuberculosis, cholera infantum and so on. Some have, without sufficient thought, extended the 1 Sedgwick, W. T. and J. Scott MacNutt. On the Mills-Reincke Phenomenon and Hazen's Theorem. Jour. Infectious Diseases, Aug., 1910, pp. 489-564. THE SANITARY INDEX 451 idea back of Hazen's " theorem " to undue limits, and have argued that pure water has the effect of raising the gen- eral health, of lifting the health tone of individuals, and so has a value beyond that of preventing the spread of diseases of the intestinal tract. This is unwarranted and to that extent Dr. Chapin^ has rightly criticized the "theorem." The idea may be correct, but the vital statistics available do not demonstrate it. The correlation between the de- creased typhoid-fever rate and the general death-rate in cities which have introduced water filtration or otherwise bettered their supply is not high. It is more frequently true where the original water-supply has been very badly pol- luted, as was the case at Lawrence. Even at Lawrence it is probable that the pneumonia death-rate was abnormally high just before the filter was built and that the reason for its subsequent decrease had little or nothing to do with water filtration. Yet to condemn the " theorem " al- together is to take too extreme a view. Without doubt infant mortality was reduced by filtration, chiefly through the reduction in diarrhceal diseases. McLaughlin has shown that this has occurred in many places. The trouble with this whole problem has grown out of the use of general rates. If we want to find the effect of filtration we must compare the morbidity and mortality rates for particular diseases before and after filtration, with due regard to changes in population. Somebody who has time ought to restudy this whole matter in the light of recent data. The sanitary index. — Many attempts have been made to devise a " sanitary index," to select and combine certain specific death-rates so as to get for a given place a single figure which, when compared with similar figures for other places, will correlate health and sanitary conditions. We 1 Chapin, Chas. V., "Modes of Infection." 452 A COMMENCEMENT CHAPTER know that the general death-rate will not serve this pur- pose. Even the death-rate adjusted to a standard popu- lation is inadequate. The infant mortality has been claimed as the best index. Dr. Wilmer R. Babt,i the Registrar of the Pennsylvania State Department of Health, has suggested a composite index which illustrates this striving to get an index. It is computed as follows: Sanitary index = Deaths from causes No. 1 to No. 15 plus all infant deaths Population The ratio of all the other deaths to the population is called the residual death-rate. Hence the sum of the two gives the general death-rate. He found that from 1906 to 1915 the general death-rate of the state decHned from 16.0 to 13.8 per 1000 i.e., 13.8 per cent. The " sanitary index," however, declined from 6.5 to 4.5, or 30.8 per cent, while the residual death-rate declined from 9.5 to 9.3 or only 2.1 per cent. This index, it will be observed, takes no account of the changing com- position of the population. Othei's have suggested that the index ought to be based on social . and economic factors as well as vital statistics, and their point seems to be well taken. This only em- phasizes the complexity of the problem. The author be- lieves that it is too early to attempt the estabHshment of a health index, and that better results will be secured by the critical use of specific rates. Current use of vital statistics. — Vital statistics have their historic uses, but their greatest value Ues in their immediate use. It is interesting and ultimately most val- uable to know that a baby has been born at a certain place, on a certain day, of such and such parentage, but it is more > Penn. Monthly Health Bulletin, No. 70, Feb., 1916. CURRENT USE OF VITAL STATISTICS 463 important that the baby shall live and grow up well. No baby should be allowed to come unnoticed .into the world; boards of health or other proper authorities should see to it that every baby born has a good chance to live. In most cases the parents, the physician and the nurse are sufficient caretakers and the public authorities should not be un- necessarily intrusive or over-zealous; on the other hand their advice and aid should be prompt where occasion war- rants, and immediate knowledge of the facts is the only basis of wise action. In reported cases of diseases dangerous to the public health the need for prompt action is even greater. It is by the daily study of such reports that pending epi- demics or local outbreaks of disease may be headed off. Every local health officer should keep on the walls of his office, or on a suitable frame, or in shallow drawers, a series of local maps — one for each important communicable dis- ease. The maps should show the names of the streets. There should be a street index at hand, with the stireet numbers given for each intersection, and with information as to which side of , the street has the odd (or even) numbers. On these maps, with the aid of the index, each case of communicable disease should be marked with a pin imme- diately on receipt of the report. There are many little devices involving the use of pins of different colors for different dates, the removal of pins after recovery, the ad- ditions of pins to indicate death, and so on; the details of which are bound to vary according to local conditions. But the main thing is to study the pins daily. In the case of state departments of health the required maps are of course on a different scale and the cases are arranged by cities and towns instead of streets. Both local and state studies are necessary. In addition to the location maps the health officer needs 454 A COMMENCEMENT CHAPTER to keep up chronological charts for each disease — a separate chart for each. Pins may be used for this work also, or lines may be drawn, black or colored. These charts, together with the maps, answer the questions where and when did the cases occur. For state work another device is convenient, — namely, a summary of cases by cities, towns, or other geographical divisions, and by weeks or months. These should be made up regularly for comparison with past records. All cities have certain numbers of cases of communicable diseases which occur with a fair degree of regularity — and what the health officer needs most to know is whether there is at any time an abnormally large number of cases of any dis- ease. In order to quickly tell this he needs to have at hand certain generalized results of past experience. In New York City Dr. Bolduan has been in the habit of find- ing the average number of cases of typhoid fever, for ex- ample, in each ward and for each week of the year, — but omits from these averages any local outbreak or epidemics. He has called this the " normaUzed average." ' In the author's opinion what is needed here is not the average, with the unusual conditions omitted, but the median. The Massachusetts State Department of Health is using the median under the name of the " endemic index." A better name would be'the endemic median. This can be very easily found for a five- or ten-year period and would serve admirably as a standard of comparison. It would of course need occasional revision. Card systems are generally found most convenient for keeping records of individual reports, and the punched- card system with mechanical devices for sorting and count- ing is the best of all. ' Bolduan, Chas. F., Typhoid Fever in New York City, No. 3 Monograph Series, Aug., 1912. PUBLICATION OF REPORTS 455 Publication of reports. — The author will perhaps be regarded as a heretic on the subject of published reports. He believes, however, that thousands of pages of useless tables of reported cases of disease are printed every year in the United States at enormous expense and that the same amount of money spent in maintaining more complete and inore accurate records in state and local health departments and in studying and using the records from day to day would bring better results. The object of reporting dis^ eases dangerous to the public health is not to pile up records but to prevent the diseases from spreading. State- ments of the occurrences of communicable diseases pub- lished monthly, or even weekly, usually reach their readers too late to be of any practical use, while as historical records such frequent publication is wholly unnecessary. Some pubUcation is desirable, however, but only that which is of real use. Let us consider the case of communicable diseases, for example, as reported to a state department of health. If the number of cases of measles in a city is less than the endemic median, that is, less than the ordinary number of cases, no announcement is necessary; but should the number of cases rise above the endemic median a prompt announcement of that fact in the local paper ' might be of positive benefit as it would sound a warning. If the fire bells were ringing very gently all the time except when a fire occurred and then rang loudly, the public would not heed the warning; and in the same way the constant pub- lication of figures which are of little moment blunts the sense of caution. Arrangements might well be made, how- ever, for the immediate publication of notices of all unusual occurrences of disease in local papers or wherever such notices would do the most good. So far as communicable ' Daily paper preferred, 456 A COMMENCEMENT CHAPTER diseases are concerned the general principle of publication should be' to publish at once or not at all and to publish only the unusual occurrences. The preparation of such notices would by reflex action stimulate the health oflicers themselves, and would assist physicians in making diagnosis of suspected cases. The problem of annual reports is different. Here the object is to establish a record for permanent preservation, useful aUke to health officers, to physicians, and to the in- terested pubUc. The calendar year with its subdivisions is the most convenient unit of time. The vital statistics . of every political subdivision in the country should be published annually, and as soon after the end of the year as possible. Here we find a great amount of unnecessary duphcation. It is a waste of money to have the local Board of Health of Cambridge, Mass., publish certain facts (usually a year or two late), to have the same facts pub- lished by the State Registrar and perhaps by the State De- partment of Health, and finally to have them published again by the U. S. Bureau of the Census, and perhaps by the U. S. Pubhc Health Service. It is worse than waste- ful, because the various tables often fail to agree and all sorts of distressing statistical errors creep in. On the other hand, while the figures for Cambridge may be found in sevetal places, there may be other places where it is diffi- cult to find any statistics at all. Uniformity in this matter is very greatly needed, and this must come through federal control or state cooperation, with uniform minimum schedules to serve as a basis of record. The author believes that no systematic attempt should be made every year to pubhsh specific rates or minute analyses of rates, for the reason that such studies are based necessarily on estimated populations. Such studies are of course very necessary for the study of special problems as PUBLICATION OF REPOKTS 457 they arise, but these results should be pubUshed as special studies and not as a part of a systematic schedule. It would be better to wait for the census years, when the facts of population can be used instead of estimates and to then make a most careful analysis of all vital statistics. Such an analysis made once in five years in Massachusetts would serve every useful purpose, would save much time and expense, would avoid the need of revision and would prevent the publication of figures which contain annoying variations. The principle should be to wait for the facts, and then make a careful analysis based on the facts. Of course, general rates should be published annually, based on estimated populations, but no one need take these very seriously, as in any event they mean httle. If it is thought worth while to publish specific rates for each post censal year, these should be recomputed after the next census has been taken. Various attercipts to establish standards have been made. One of these may be found in the American Journal of Public Health. 1 Another in the annual report of the N. Y. State Department of Health for 1912, another in the Quarterly Publication of the American Statistical Associa- tion ^ and so on. In establishing standards it will be neces- sary to determine what shall be the geographical units, what subdivision of the year, what data and in what' com- binations. The usual facts secured in regard to deaths are (1) place of death, (2) time of death, (3) sex, (4) age, (5) race or color, (6) cause of death, (7) birthplace, (8) birthplace of father, (9) birthplace of mother, (10) marital condition, (11) occupation. The possible number of com- binations of these eleven itenas two at a time is 55, three at a time 165, and four at a time 330. No wonder therefore that there is lack of uniformity in published reports. Any 1 1913, p. 595. 2 1911, p. 510. 458 A COMMENCEMENT CHAPTER standard tables must of necessity be arbitrary. The time has come when uniformity of report is necessary in the in- terest of both economyand efficiency. EXERCISES AND QUESTIONS 1. Distinguish between the environments represented by the follow- ing terms: a. A felt hat and a straw hat factory. 6. A paper box and a wooden box factory. c. An iron and a brass foundry. d. A wholesale and a retail merchant or dealer, e. A farm laborer on his home farm and one working out. /. A clerk in a store and a salesman. ' g. A dressmaker in a factory or shop and one working elsewhere. h. A cook and a servant. i. A paid housekeeper and a servant girl. J. A practical and a trained nurse. 2. To what extent do these terms conceal other important difEer- ences in age or sex or nationality? 3. What data were collected in the industrial clinic of the Massa- chusetts General Hospital? [Monthly Review (Dec, 1917), XJ. S. Bureau of Labor Statistics. Edsall, David J. : The Study of Occupar- tional Diseases in Hospitals.] 4. How would you explain the alleged fact that more cases of in- fectious diseases are reported to the New York City Department of Health on Monday than on any other day, and the fewest on Saturday? 6. How are the medical and vital statistics of the U. S. Navy kept? [See Am. J. P. H., June, 1918, p. 442.] 6. How are the medical and vital statistics of the U. S. army kept? [See Am. J. P. H., Jan., 1918, p. 14.] 7. What facts are needed in the registration of still-births? [See Am. J. P. H., Jan., 1917, p. 46.] 8. Describe the epidemic of poHomyeUtis in New York and New England in 1916. [See Am. J. P. H., Feb., 1917, p. 117.] 9. What proportion of children "take" the common children's diseases at some time? [See Am. J. P. H., Sept., 1916, p. 971.] APPENDIX I REFERENCES To study demography, or even vital statistics, seriously one must have at hand several of the standard textbooks on the statistical method, and certain of the more recent federal, state and municipal reports. One must also have access to files of certain periodicals. The following is a list of some of the more important of these references. It is far from being complete, and is intended merely to pave the way for further searches in the library. A complete list of references to books and articles on the many phases of the subject would be overwhelming. The most recent writings on vital statistics are not necessarily the best for the beginner to study, as some of the soundest and most logical monographs were written many years ago. Of course, the most recent data are the most interesting — but that is another matter. Many references to particular articles will be found scattered through the footnotes of this book and printed in connection with the Exercises and Questions. GENERAL TEXTBOOKS. Newsholmb, Arthtjb. Elements of Vital Statistics. Macmillan Co., 1899. BowLET, Arthur L. Elements of Statistics. New York, Scribners, 1907. BowLEY, Arthtjb L. An Elementary Manual of Statistics. Lon- don, MacDonald and Evans, 1910. Elderton^ W. Palin and Ethei- M. Elderton. Primer of Statis- tics. New York, Macmillan Co, 459 460 APPENDIX I King, Wbllfohd J. The Elements of Statistical Method. New York, Macmillan Co., 1912. Trask, John W. Vital Statistics — a report published by the U. S. PubUc Health Service, Apr. 3, 1914. Yule, G. Udny. Introduction to the Theory of Statistics. London, Griffin & Co., 1912. Whipple, George C. Typhoid Fever. New York, John Wiley & Sons, Inc.,1908. KoREN, John. History of Statistics. New York, Macmillan Co., 1918. PERIODICALS. American Statistical, Association. Quarterly Publications. Vol. I in 1888. American Journal of Public Health. Monthly. The official publication of the Aiherican Public Health Association. Public Health Reports. Weekly. Published by the U. S. Public Health Service. U. S. Bureau of Labor Statistics. Monthly Review. Journal op the Royal Statistical Society. ANNUAL, MONTHLY AND WEEKLY REPORTS. There are scores of annual reports which deal with vital statistics. The following are illustrative: U. S. Bureau of. the Census. Mortality Statistics. Annually since 1900. England and Wales. Annual reports of Registrar-General. (79th report in 1916.) Massachusetts State Registration Reports. Annually since 1842. Massachusetts State Board op Health (now Department of Health). Annually since 1870. State Departments of Health of New York, New Jersey, Penn- sylvania, Ohio, Michigan, Maine, New Hampshire, Connecticut, etc. Annual Reports op Boards of Health of New York City, Boston, Philadelphia, Chicago, Providence, etc. Some boards of health publish monthly reports — New York, Massa- chusetts, Ohio, etc. Some city health departments publish weekly reports — New York, Chicago, etc. APPENDIX I 461 DEMOGRAPHY. Statistique Geneeale db la France. Statistique Internationale du Mouvement de la Population d'aprte les registres d'6tat civil, 1907, 1913. Westergaard, Harold. Die Lehre von der Mortalitat uhd Mor- bilitat, anthropologisch-statistische Untersuchungen. Jena. Gustav Fischer, 1901. Ghaitnt, Capt. John. Natural and Political Observations based upon Bills of Mortality. 1662. (Historical value.) Chadwick, Edwin. Health of Nations. (Historical value.) Fare, William. Vital Statistics — a memorial volume of selec- tions from his reports and writings. Edited by Noel A. Hum- phreys, London. Office of the Sanitary Institute. Meitzen, Dr. August. History Theory and Technique of Statis- tics. Translated by Dr. Roland P. Falkner. Annals of the Am. Acad, of Political and Social Science, 1891. Pearson, Karl. Life, Letters and Labors of Sir Francis Galtoh, Vol. I. Cambridge, England, University Press, 1914. Bailey, Wm. B. Modern Social Conditions. New York, Century Co., 1906. ARITHMETIC. West, Carl S. Introduction to Mathematical Statistics. Colum- bus, R. G. Adams & Co., 1918. Bailey, W. B. and Joseph Cummings. Statistics. Chicago, A. C. McClurg Co., 1917. Westergaard, Harold. Scope and Methods of Statistics. Quar. Pub. Am. Sta. Asso., XV, 1916, pp. 225-291. Secrist, Horace. Introduction to Statistical Methods. New York, MacmiUan Co., 1917. Saxblby, F. M. a Course in Practical Mathematics. London, Longmans, Green & Co., 1908. Thompson, Sylvanus P. Calculus Made Easy. London, Mac- miUan Co., 1917. GRAPHICS. Rbinhardt, Chas. W. Lettering for Draftsmen, Engineers and Students. New York, D. Van Nostrand Co., 1909. Peddle, John B. The Construction of Graphical Charts. New York, McGraw-Hill Co., 1910. 462 APPENDIX I Brinton, Willard C. Graphic Methods for Presenting Facts. New York, Engineering Magazine Co., 1914. Fisher, Irving. The Ratio Chart. Quar. Pub. Am. Sta. Asso., 1917, p. 577. CENSUS — REGISTRATION. WiLBtTR, Cressy L. The Federal Registration Service of the United States: its development, problems and defects. U. S. Bureau of the Census, 1916. Newsholme, Arthur. A National System of Notification and Registration. Jour. Royal. Sta. Soc, Vol. 59, p. 1, 1896. DuRAND, E. Dana. Changes in Census Methods for the Census of 1910. Am. Jour, of Sociology, 1910. U. S. Bureau of the Census. American Census Taking from the First Census of the United States, 1908. U. S. Bureau op the Census. Index to Occupations, alphabetical and classified, 1915. POPULATION. United States Census, 1790-1900. Comprehensive reports, usually in several volumes, published every ten years. U. S. Bureau of the Census. 1910. Population, Vols. I, II and III. U. S. Bureau of the Census. Annual Estimates of Population, are published in a series of bulletins. BuUetia 133, for 1916. U. S. Bureau of the Census. A Century of Population Growth, 1790-1900. Pub. in 1909. Massachusetts State Census. Intermediate between federal censuses since 1845. [Last published report in 1905; report for 1915 in preparation.] Leroy-Bbaulieu, p. The Influence of CivUization on the Move- ment of Population. Jour. Royal Sta. Soc, Vol. 54, 1891. Franklin, Benjamin. Observations concerning the Increase of Mankind. Book, Philadelphia, 1751. Jarvis, E. History of the Progress of Population of the United States. Book, Boston, 1877. . Bailey, W. B. Modern Social Conditions. N. Y., Century Co., 1906. APPENDIX I 4^ GENERAL-RATES. Newsholmb, a. The Declining Birth-rate. New York, Moffat, Yard & Co., 1911. U. S. Bureau of the Census. Birth Statistics. First annual report in 1915. Humphreys, N. A. Value of the Death-rate as a Test of Sanitary Conditions. Jour. Royal Statistical Society, Vol. 37, 1874. Yule, G. M. Oii the Changes in the Marriage and Birth-rates in England and Wales during the past Half Century. Jour. Royal Sta. Soc, Vol. 69, p. 88, 1906. SPECIFIC RATES. Pearson, Karl, Alice Lee and Ethel M. Elderton. On the Correction of Death-rates, 1910. GtiiLFOT, Wm. H. The Death-rate of New York as affected by the Cosmopolitan Character of its Population. Quar. Pub. Am. Sta. Asso., 1907. Andrew, J. Grant. Age Incidence, Sex and Comparg,tive Fre- quency in Disease. London, Bailli^re, Tindall & Cox, 1909. CAUSES OF DEATH. A. P. H. a. Committee Report. The Accuracy of Certified Causes of Death. PubUc Health Reports, Sept. 28, 1917, pp. 1557-1632.' U. S. Bureau op the Census. Manual of the International List of Causes of Death, 1911. U. S. Bureau op the Census. Index of Joint Causes of Death, 1914. U. S. Bureau of the Census. Physicians' Pocket Reference to the International List of Causes of Death, 1918. PROBABILITY. Davenport, Chas. B. Statistical Methods, with Special Reference to Biological Variations. Second edition. New York, John Wiley ' and Sons, Inc., 1904. Fisher, Arne. The Mathematical Theory of Probabilities. New York, Macmillan Co., 1915. Whipple, George C. The Element of Chance in Sanitation. Jour. Franklin Institute, July and Aug., 1916. Weld, LeRot D. Theory of Errors and Least Squares. New York, Macmillan Co., 1916. 464 APPENDIX I Goodwin, A. M. Elements of the PretHsion of Measurements and Graphical Methods. New York, McGraw-Hill Co., 1913. La Place, P. S., Mabquis de. Th^orie analjrtique des probability, 1814. (Historical value.) QuETELET, L. A. S. Lettres sur la th^orie des probabilites, apph- qu6e aux sciences morales et politiques, 1846. (English trans- lation by O. G. Downs, 1849.) Bbownlee, John. The Mathematical Theory of Random Migrar tion and Epidemic Distribution. Proc. Royal Soc. of Edin- burgh, Vol. 31, p. 262, 1910-11. CORRELATION. Jevons, W. Stanley. The Principles of Science. London, Mac- nullan Co., 1907. Pearson, Karl, Alice Lee and Ethel M. Elderton. On the Correlation of Death-rates. Jour. Royal Sta. Soc, Vol. 73, p. 534, 1910. LIFE TABLES. MoiR, Henry. Life Assurance Primer. New York, The Spectator Co., 1912. Henderson, Robert. Mortality Laws and Statistics. New York, John Wiley & Sons, Inc., 1915. Gloveb, Jas. W. United States Life Tables, 1910. U. S. Census, 1916. Burn, Joseph. Vital Statistics Explained. London, Constable and Company, Ltd., 1914. APPENDIX II THE MODEL STATE LAW FOR MORBIBITY REPORTS ADOPTED BY THE ELEVENTH ANNUAL CONFERENCE OF STATE AND TEBBI- TORIAL HEALTH AUTHORITIES WITH THE UNITED STATES PUBLIC HEALTH SERVICE, MINNEAPOLIS, JUNE 16, 1913. A Bill To provide for the notification of the occurrence and prevalence of certain diseaeee. Be it enacted by the Senate and General Assembly of tlie State of ; Section 1. It shall be, and is hereby, made the duty of the State department of health (or commissioner or board of health) to keep cmrently informed of the occurrence, geographic distribution, and prevalence of the preventable diseases throughout the State, and for this purpose there shaU be established in the State department of health a bureau (or division) of sanitary reports which shall, under the direc- tion of the State commissioner of health (State health officer or secre- tary of the State board of health), be in charge of an assistant com- missioner of health who shall receive an annual salary of -. dollars and the necessary expenses incurred in the performance of his duties. The State department of health shall provide such clerical and other assistance as may be necessary for the establishment and maintenance of said bureau. Sec. 2. The following-named diseases and disabilities are hereby made notifiable and the occurrence of cases shall be reported as herein provided: GROUP I. infectious DISEASES Actinomycosis. Dengue. Anthrax. Diphth^ia. Chicken-pox. Dysentery: Cholera. Asiatic (also cholera nos- (a) Amebic. tras when Asiatic cholera is pres- (6) BacUlary. ent or its importation threatened). Favus. Continued fever lasting seven days. German measles. 465 466 APPENDIX II Typhus fever. Whooping cough. Yellow fever. GROTJP I. — INFECTIOUS DIS- EASES — Continued Glanders. Hookworm disease. Leprosy. Malaria. Measles. Meningitis: (a) Epidemic cerebrospinal. (6) Tuberculous. Mumps. Ophthalmia neonatorum (conjunc- tivitis of new born infants). Paragonimiasis (endemic hemoptysis) . Paratyphoid fever. Plague. Pneumonia. PoliomyeHtis (acute infectious). Rabies. Rocky Mountain spotted, or tick, fever. Scarlet fever. Septic sore throat. Smallpox. Tetanus. Trachoma. Trichinosis. Tuberculosis (all forms, the organ or gkoup rv. — diseases of un- part affected in each case to be known origin. specified). Pellagra. Typhoid fever. Cancer. Provided, That the State department of health (or board of health)- may from time to time, in its discretion, declare additional diseases notifiable and subject to the provisions of this act. Sec. 3. Each and every physician practicing in the State of who treats or examines any person suffering from or afflicted with, or suspected to be suffering from or afHicted with, any one of the notifiable diseases shall immediately report such case of notifiable disease in writ- ing to'the local health authority having jurisdiction. Said report shall GROUP II. OCCUPATIONAL DIS- EASES AND INJURIES. Arsenic poisoning. Brass poisoning. Carbon monoxide poisoning. Lead poisoning. Mercury poisoning. Natural gas poisoning. Phosphorous poisoning. Wood alcohol poisoning. Naphtha poisoning. Bisulphide of carbon poisoning. Dinitrobenzine poisoning. Caisson disease (compressed-air illness). Any other disease or disabihty contracted as a result of the nature of the person's employ-. ment. GROUP m. VENEREAL DISEASES Gonococcus infection. Syphilis. Appendix li 467 be forwarded either by mail or by special messenger and shall give the following information: 1. The date when the report is made. 2. The name of the disease or suspected disease. 3. The name, age, sex, color, occupation, address, and school attended or place of employment of patient. 4. Number of adults and children in the household. 5. Source or probable source of infection or the origin or probable origin of the disease. 6. Name and address of the reporting physician. Provided, That if the disease is, or is suspected to be, smallpox the report shall, in addition, show whether the disease is of the mild or virulent type and whether the patient has ever been successively vaccinated, and, if the patient has been successfully vaccinated, the number of times and dates or approximate dates of such vaccination; and if the disease is, or is suspected to be, cholera, diphtheria, plague, scarlet fever, smallpox, or yellow fever, the physician shall, in addition to the written report, give immediate notice of the case to the local health authority in the most expeditious manner available; and if the disease is, or is suspected to be, typhoid fever, scarlet fever, diphtheria or septic sore throat the- report shall also show whether the patient has been, or any member of the household in which the patient resides is, engaged or employed in the handling of milk for sale or preUminary to sale: AtuL provided further, That in the reports of cases of the venereal diseases the name and address of the patient need not be given. Sec. 4. The requirements of the preceding section shall be applicable to physicians attending patients ill with any of the notifiable diseases in hospitals, asylums, or other institutions, public or private: Provided, That the superintendent or other person in charge of any such hospital, asylum, or other institution in which the sick are cared for may, with the written consent of the local health officer (or board of health) having jurisdiction, report in the place of the attending physician or physicians the cases of notifiable diseases and disabilities occurring in or admitted to said hospital, asylum, or other institution in the same manner as that prescribed by physicians. Sec. 5. Whenever a person is known, or is suspected, to be afflicted with a notifiable disease, or whenever the eyes of an infant under two weeks of age become reddened, inflamed, or swoUen, or contain an unnatural discharge, and no physician is in attendance, an immediate report of the existence of the case shall be made to the local health officer 468 APPENDIX It by the midwife, nurae, attendant, or other person in charge of the patient. Sec. 6. Teachers or other persons employed in, or in charge of, pubUc or private schools, including Sunday Schools, shall report immediately to the local health officer each and every Imown or suspected case of a notifiable disease in persons attending or employed in their respective schools. Sec. 7. The written reports of cases of the notifiable disease required by this act of physicians shaU be made upon blanks supplied for the purpose, through the local health authorities, by the State department of health. These blanks shall conform to that adopted and approved by the State and Territorial health authorities in conference with the United States Public Health Service. Sec. 8. Local health officers or boards of health shall withia seven days after the receipt by them of reports of cases of the notifiable diseases forward by mail to the State department of health the original written reports made by physicians, after first having transcribed the information given in the respective reports in a book or other form of record for the permanent files of the local health office. On each report thus forwarded the local health officer shall state whether the case to which the report pertains was visited or otherwise investigated by a representative of the local health office and whether measiu'es were taken to prevent the spread of the disease or the occurrence of addi- tional cases. Sec. 9. Local health officers or boards of health shall, in addition to the provisions of section 8, report to the State department of health in such manner and at such times as the State department of health may require by regulation the number of new cases of each of the notifiable diseases reported to said local health officers or boards of health. Sec. 10. Whenever there occurs within the jurisdiction of a local health officer or board of health an epidemic of a notifiable disease, the local health officer or board of health shall, within 30 days after the epidemic shall have subsided, make a report to the State department of health of the number of cases occurring in the epidemic, the number of cases terminating fatally, the origin of the epidemic, and the means by which the disease was spread; Provided, That whenever the State department of health has taken charge of the control and suppression or undertaken the investigation of the epidemic, the local health authority having jurisdiction need not make the report otherwise required. Sec. 11. No person shall be appointed to the position of local health APPENDIX II 469 ofiBcer in any city, town, or county until after the qualifications of said person have been approved by the State department of health. Sec. 12. In localities in which there are no local health officers or boards of health, and in localities in *hich, although there are health officers or boards of health, adequate provision has not, in the opinion of the State department of health, been made for the proper notification, investigation, and control of notifiable disease, and in localities in which the local health authorities fail to carry out the provisions of this act, the State department of health shall appoint properly qualified sanitary officers to act as local health officers and to prevent the spread of disease in and from such localities and to enforce the provisions of this act: Provided, That salaries and other expenses incurred under the provisions of this section shall be paid by the local authorities. Sec. 13. Any physician or other person or persons who shall fail, neglect or refuse to comply with, or who Shall violate any of the pro- visions of this act shall be guQty of a misdemeanor, and upon conviction thereof shall be sentenced to pay a fine of not less than dollars nor more than dollars or to imprisonment for not less than days nor more than days for each offense: Provided, That in the case of a physician his license to practice medicine within the State may be revoked in accordance with existing statutory provisions. Sec. 14. No license to practice medicine shall be issued to any person until after the applicant shall have ffied with the State licensing board a statement, signed and sworn to before a notary or other officer quali- fied to administer oaths, that said applicant has familiarized himself with the requirements of this act, a copy of which sworn statement shall be forwarded to the State department of health. Sec. 15. Each and every person engaged in the practice of medicine shall display in a prominent place in his or her office a card upon which sections 2, 3, 4, 7, 13, 14, and 15 of this act have been printed with type not smaller than 10-point. A similar card shall be displayed in a prom- inent .place in the office of each and every hospital, asylum, or other public or private institution for the treatment of the sick. These cards shall each be not less than 1 square foot in size and shall be furnished to institutions and licensed physicians without cost by the State de- partment of health. Sec. 16. The sum of dollars is hereby appropriated from any money in the State treasury not otherwise appropriated for carrying out the provisions of this act. Sec. 17. This act shall take effect immediately, and all acts or parts of acts inconsistent with the provisions of this act are hereby repealed. 470 APPENDIX II THE STANDARD MORBIDITY NOTIFICATION BLANK The following model notification blank was alao adopted by the conference of state and territorial health authorities with the United States Public Health Service, June 16, 1913, as the standard notification blank referred to in section 7 of the Model Law as the one to be used in the reporting of cases of the notifiable diseases. This blank is intended to be printed on a post card: [Face of card.] ., 191. (Date.) Disease or suspected disease Patient's name , age , sex , color Patient's address occupation .' School attended or place of employment Number in household: Adults , children Probable source of infection or origin of disease If disease is smallpox, type , number of times successfully vaccinated and approximate dates If typhoid fever, scarlet fever, diphtheria, or septic sore throat, was patient, or is any member of household engaged in the production of handling of milk Address of reporting physician Signature of physician [Reverse of card.] For use of local health department. s s 3 ■i i Health Department, (City) (State) APPENDIX II 471 HOSPITAL DISCHARGE CERTIFICATE Suggested by BoUuan for use in connection with hospital morbidity reports. DISCHARGE CERTIFICATE. Name of hospital Hospital admission No. . Sex Age How admitted — Ambulance or White. Hebrew. own application Colored.. Gentile. or Mongolian. (Tabulation transfer from '■ No.) other hospital. Place of birth . Patient's address Single or married or widowed or divorced or Borough unknown. Date admitted Discharged to — Date discharged. . . , Home. Days in hospital months Other hospital. days Convalescent retreat. (If over a year, omit the days and give only Coroner. years and months.) Occupation — (o) Trade, profession, or particular kind of work. (&) General nature of the industry, business, or establishment in which employed (or employer). Diagnosis and Complications , If operated upon, state nature of operation Condition on discharge: Cured. Improved. Unimproved. Died — Autopsy. No autopsy. Signed House Physician — Surgeon. APPENDIX III THE MODEL STATE LAW FOR THE REGISTRATION OF BIRTHS AND DEATHS A. Bill 1 To provide for the registration of all births and deaths in the State of . Note. — After the bill has been prepared for presentation to the legislature of a State, the title should be carefully revised by competent legal authority. Be it enacted by the legislature of the State of Section 1. That the State board of health shall have charge of the registration of births and deaths; shall prepare the necessary instruc- tions, forms, and blanks for obtaining and preserving such records and shall procure the faithful registration of the same in each primary regis- tration district as constituted in section 3 of this act, and in the central bureau of vital statistics at the capital of the State. The said board shall be charged with the uniform and thorough enforcement of the law throughout the State, and shall from time to time recommend any additional legislation^ that may be necessary for this purpose. Sec. 2. That the secretary of the State board of health shall have general supervision over the central bureau of vital statistics, which is hereby authorized to be established by said board, and which shall be imder the immediate direction of the State registrar of vital statistics, whom the State board of health shall appoint within thirty days after the taking effect of this law, and who shall be a medical practitioner of not less than five years' practice in his profession, and a competent vital statistician. The State registrar of vital statistics shall hold ofiice for four years and \mtil his successor has been appointed and has qualified, unless such office shall sooner become vacant by death, disqualification, 1 Before introducing this biU in any legislature it should be carefully redrafted by a competent lawyer and submitted to the Bureau of the Census for criticism. ' The words "and shall promulgate any additional rules or regular tions" may be inserted in bills prepared for States in which the State board of health has power to make rules and regulations having the effect of law. ^ 472 APPENDIX III 473 operation of law, or other caiises. Any vacancy occurring in such office shall be filled for the unexpired term by the State board of health. At least ten days before the expiration of the term of office of the State registrar of vital statistics, his successor shall be appointed by the State board of health. The State registrar of vital statistics shall receive an annual salary at the rate of dollars from the date of his entering upon the discharge of the duties of his office. The State board of health shall provide for such clerical and other assistants as may be necessary for the purposes of this act, who shall serve during the pleasure of the board, and shall fix the compensation of persons thus employed within the amount appropriated therefor by the legislature. The custodian of the capitol shall /provide for the bureau of vital statistics in the State capitol at — suitable offices, which shall be properly equipped with fireproof vault and filing cases for the permanent and safe preservation of all official records made and returned under this act. Sec. 3. That for the purposes of this act the State shall be divided into registration districts as follows: Each city, each incorporated town, and each- township ' shall constitute a primary registration dis- trict: Provided, That the State board of health may combine two or more primary registration districts when necessary to facilitate registration. Sec. 4. That within ninety days after the taking efiect of this act, or as soon thereafter as possible, the State board of health shall appoint a local registrar of vital statistics for each registration district in the State.^ The term of office of each local registrar so appointed shall be ' Or other primary political unit, as "town," "precinct," "civU district," "hundred," etc. When there are no such units available, the following substitutes for section 3 may be employed: Section 3. That for the purposes of this act the State shall be divided into registration districts £is foUows: Each city and each incorporated town shall con- stitute a primary registration district; and for that portion of each coimty outside of the cities and incorporated towns therein the State board of health shaE defime and designate the boundaries of a sufficient number of rural registration districts, which districts it may change or combine from time to time as may be necessary to insure the convenience and completeness of registration. ^ This method of appointment of local registrars by the State board of health — or perhaps by the State registrar or upon his nomination — with a reasonably long term of service and subject to removal for neglect of duty, is the preferable one for efficient service. Should there be objection, however, to the creation of new offices, the section may be redrafted so that it will provide that township, village, or city clerks, or other suitable officials, shall be the local registrars. 474 APPENDIX III four years, and until his successor has been appointed and has qualified, unless such ofiice shall sooner become vacant by death, disqualification, operation of law, or other causes: Provided, That in cities where health officers or other officials are, in the judgment of the State board of health, conducting effective registration of births and deaths under local ordinances at the time of the taking effect of this act such officials may be appointed as registrars in and for such cities, and shall be subject to the rules and regulations of the State registrar and to all of the provisions of this act. Any vacancy occurring in the office of local registrar of vital statistics shall be filled for the unexpired term by the State board of health. At least ten days before the expiration of the term of office of any such local registrar his successor shall be appointed by the State board of health. Any local registrar who, in the judgment of the State board of health, fails or neglects to discharge efficiently the duties of his office as set forth in this act, or to make prompt and complete returns of births and deaths as required thereby, shall be forthwith removed by the State board of health, and such other penalties may be imposed as are provided under section 22 of this act. Each local registrar shall, immediately upon his acceptance of ap- pointment as such, appoint a deputy, whose duty it shall be to act in his stead in case of his absence or -disability; and such deputy shall in writing accept such appointment and be subject to all rules and regula- tions governing local registrars. And when it appears necessary for the convenience of the people in any niral district the local registrar is hereby authorized, with the approval of the State registrar, to appoint one or more suitable persons to act as subregistrars, who shall be author- ized to receive certificates and to issue burial or removal permits in and for such portions of the district as may be designated; and each sub- registrar shall note on each certificate, over his signature, the date of filing, and shall forward all certificates to the local registrar of the district within ten days, and in all' cases before the third day of the following month: Promded, That each subregistrar shall be subject to the supervision and control of tne State registrar and may be by him removed for neglect or failure to perform his duty in accordance with the provisions of this act or the rules and regulations of the State registrar, and shall be subject to the same penalties for neglect of duty as the local registrar. Sec. 5. That the body of any person whose death occurs in this State, or which shall be found dead therein, shall not be interred, de- posited in a vault or tomb, cremated or otherwise disposed of, or re- APPENDIX III 475 moved from or into any registration district", or be temporarily held pending further dispo^tion more than seventy-two hours after death, unless a permit for burial, removal, or other disposition thereof shall have been properly issued by the local registrar of the registration district in which the death occurred or the body was found.' And no such burial or removal permit shall be issued by any registrar until, wherever practicabfe, a complete and satisfactory certificate of death has been filed with him as hereinafter provided: Provided, That when a dead body is transported from outside the State into a registration district in for burial, the transit or removal permit, issued in accordance with the law and health regulations of the place where the death occurred, shall be accepted by the local registrar of the district into which the body has been, transported for burial or other disposition, as a basis upon which he may issue a local burial permit; he shall note upon the face of the burial permit the fact that it was a body shipped in for interment, and give the actual place of death; and no local registrar shall receive any fee for the issuance of burial or removal permits under this act other than the compensation provided in section 20. Sec. 6. That a stillborn child shall be registered as a birth and also as a death, and separate certificates of both the birth and the death shall be filed with the local registrar, in the usual form and manner, the certificate of birth to contain in place of tjie name of tlie child, the word "stillbirth": Provided, That a certificate of birth and a certificate of death shall not be required for a child that has not advanced to the fifth month of uterogestation. The medical certificate of the cause of death shall be signed by the attending physician, if any, and shall state the cause of death as "stUlbom," with the cause of the stillbirth, if known, whether a premature birth, and, if bom prematurely, the period of uterogestation, in months, if known; and a burial or removal permit ' of the prescribed form shall be required. ' Midwives shall not sign certificates of death for stillborn children; but such cases, and still- births occurring without attendance of either physician or midwife, shall be treated as deaths without medical attendance, as provided for in section 8 of this act. Sec. 7. That the certificate of death shall contain the following items, which are hereby declared necessary for the legal, social, and sanitary purposes subserved by registration records r^ 1 A special proviso may be required for sparsely settled portions of a State. 2 The following items are. those of the United States standard certi- ficate of death, approved by the Bureau of the Census. 476 APPENDIX III (1) Place of death, including State, county, township, village, or city. If in a city, the ward, street, and house number; if in a hospital or other institution, the name of the same to be given instead of the street and house number. If in an industrial camp, the name of the camp to be given. (2) FuU name of decedent. If an unnamed child, the surname preceded by "Unnamed." ' (3) Sex.' (4) Color or race, as white, black, mulatto (or other negro descent), Indian, Chinese, Japanese, or other. (5) Conjugal condition, as single, married, widowed, or divorced. (6) Date of birth, including the year, month, and day. (7) Age, in years, months, and days. If less than one day, the hours or minutes. (8) Occupation. The occupation to be reported of any person, male or female, who had any remunerative employment, with the state- ment of (o) trade, profession or particular kind of work; (6) general natitte of industry, business, or establishment ia which employed (or employer). (9) Birthplace; at least State or foreign country, if known. (10) Name of father. (11) Birthplace of father; at least State or foreign country, if known. (12) Maiden name of mother. (13) Birthplace of mother; atleast State or foreign coimtry, if known. (14) Signature and address of informant. (15) Official signature of registrar, with the date when certificate was filed, and registered number. (16) Date of death, year, month, and day. (17) Certification as to medical attendance on decedent, fact and time of death, time last seen alive, and the cause of death, with con- tributory (secondary) cause of complication, if any, and duration of each, and whether attributed to dangerous or insanitary conditions of employment; signature and address of physician or official making the medical certificate. (18) Length of residence (for inmates of hospitals and other institu- tions; transients or recent residents) at place of death and in the State, together with the place where disease was contracted, if not at place of death, and former or usual residence. (19) Place of burial or removal; date of burial. (20) Signature and address of undertaker "or person acting as such. APPENDIX III 477 The personal and statistical particulars (items Ito 13) shall be authen- ticated by the signature of the informant, who may be any competent person acquainted with the facts. The statement of facts relating to the disposition of the body shall be signed by the undertaker or person acting as such. The medical certificate shall be made and signed by the physician, if any, last in attendance on the deceased, who shall specify the time in attendance, the time he last saw the deceased alive, and the hour of the day at which death occurred. And he shall further state the cause of death, so as to show the course of disease or sequence of causes resulting in the death, giving first the name of the disease causing death (primary cause), and the contributory (secondary) cause, if any, and the duration of each. Indefinite and unsatisfactory terms, denoting only syfnptoms of disesise or conditions resulting from disease, will not be held sufficient for the issuance of a biwial or removal permit; and any certificate con- taining only such terms as defined by the State Registrar shall be returned to the physician or person making the medical certificate for correction and more definite statement. Causes of death which may be the result of either disease or violence shall be carefully defined; and if from violence, the means of injury shall be stated and whether (prob- ably) accidental, suicidal, or homicidal.' And for deaths in hospitals, institutions, or of nonresidents the physician shall supply the informa- tion required under this head (item 18), if he is able to do so, and may state where, in his opinion, the disease was contracted. Sec. 8. That in case of any death occurring without medical attend- ance it shall be the duty of the undertaker to notify the local registrar of such death, and when so notified the registrar shall, prior to the issuance of the permit, inform the local health officer and refer the case to him for immediate investigation and certification: Provided, That when the local health officer is not a physiciaSi, or when there is no such official, and in such cases only, the registrar is authorized to make the certificate and return from the statement of relatives or other persons having adequate knowledge of the facts: Provided further, That if the registrar has reason to believe that the death may have been due to unlawful act or neglect he shall then refer the case to the coroner or other proper officer for his investigation and certification. And the coroner or other proper officer whose duty it is to hold an inquest on the 1 In some States the question whether a death was accidental, suici- dal, or homicidal must be determined by the coroner or medical examiner and the registration law must be framed to harmonize. 478 APPENDIX III body of any deceased person and to make the certificate of death required for a burial permit shall state in his certificate the name of the disease causing death, or if from external causes, (1) the means of death and (2) whether (probably) accidental, suicidal, or homicidal, and shall in any case furnish such information as may be required by the State Registrar in order properly to classify the death. Sec. 9. That the undertaker or person acting as undertaker shall file the certificate of death with the local registrar of the district in which the death occurred and obtain a burial or removal permit prior to any disposition of the body. He shall obtain the required personal and statistical particulars from the person best qualified to supply them, over the signature and address of his informant. He shall then present the certificate to the attending physician, if any, or to the health oflBcer or coroner, as directed by the local registrar, for the medical certificate of the cause of death and other particulars necessary to complete the record, as specified in sections 7 and 8. And he shall then state the facts required relative to the date and place of burial or removal, over his signature and with his address, and present the completed certificate to the local registrar in order to obtain a permit for burial, removal, or other disposition of the body. The undertaker shall deliver the burial permit to the person in charge of the place of burial before interring or otherwise disposing of the body, or shall attach the removal permit to the box containing the corpse, when shipped by any transportation company, said permit to accompany the corpse to its destination, where, if within the State of ■ — , it shall be delivered to the person in charge of the place of burial. [Every person, firm, or corporation selling a casket shall keep a record showing the name of the purchaser, purchaser's post-office address, name of deceased, date of death, and place of death of deceased, which record shall be open to inspection of the State Registrar at all times. On the first day of each month the person, firm, or corporation selling caskets shall report to the State Registrar each sale for the preceding month, on a blank, provided for that purpose: Provided, however, That no person, firm, or corporation selling caskets to dealers or undertakers only shall be required to keep such record, nor shall such report be required from undertakers when they have direct charge of the disposi- tion of a dead body. Every person, firm, or corporation selling a casket at retail, and not having charge of the disposition of the body, shall inclose within the casket a notice furnished by the State Registrar calling attention to the requirements of the law, a blank certificate of death, and the rules APPENDIX III 479 and regulations of the State board of health concerning the burial or other disposition of a dead body.]' Sec. 10. That if the interment or other disposition of the body is to be made within the State, the wording of the burial or removal permit may be limited to a statement by the registrar, and over his signature, that a satisfactory certificate of death having been filed with him, as required by law, permission is granted to inter, remove, or dispose otherwise of the body, stating the name, age, sex, cause of death, and other necessary details upon the form prescribed by the State registrar. Sec. 11. That no person in charge of any premises on which inter- ments are made shall inter or permit the interment or other disposition of any body imless it is accompanied by a burial, removal, or transit permit, as herein provided. And such person shall indorse upon the permit the date of interment, over his signature, and shall return all permits so indorsed to the local registrar of his district within ten days from the date of interment, or within the time fixed by the local board of health. He shall keep, a record of all bodies interred or otherwise disposed of on the premises under his charge, in each case stating the name of each deceased person, place of death, date of burial or disposal, and name and address of the undertaker; which record shall at .all times be open to official inspection: Provided, That the imdertaker, or .person acting as such, when burying a body in a cemetery or burial ground having no person in charge, shall sign the burial or removal permit, giving the date of burial, and shall write across the face of the permit the words "No person in charge," and file the burial or removal permit within ten days with the registrar of the .district in which the cemetery is located. Sec. 12. That the birth of each and every child born in this State shall be registered as hereinafter provided. Sec. 13. That within ten days after the date of each birth there shall be filed with the local registrar of the district in which the birth occurred a certificate of such birth, which certificate shall be upon the form adopted by the State board of health with a view to procuring a fuU and accurate report with respect to each item of information enumerated in section 14 of this act.'' In each case where a physician, midwife, or person acting as midwife was in attendance upon the birth, it shall be the duty of such physician, ' The provisions in brackets may be useful in States in which many fimerals are conducted without regular undertakers. 2 A proviso may be added that shall require the registration, or noti- fication, at a shorter interval than ten days, of births that occur in cities. 480 APPENDIX III midwife, or person acting as midwife to file m accordance herewith the certificate herein contemplated. In each case where there was no physician, midwife, or person acting as midwife in attendance upon the birth, it shall be the duty of the father or mother of the child, the householder or owner of the premises where the birth occurred, or the manager or superintendent of the public or private institution where the birth occurred, each in the order named, within ten days after the date of such birth, to report to the local registrar the fact of such birth. In such case and in case the physician, midwife, or person acting as midwife, in attendance upon the birth is unable, by diligent inquiry, to obtain any item or items of information contemplated in section 14 of this act, it shall then be the duty of the local registrar to secure from the person so reporting, or from any other person having the required knowledge, such information as will enable him to prepare the certificate of birth herein contemplated, and it shall be the duty of the person reporting the birth, or who may be interro- gated in relation thereto, to answer correctly and to the best of his knowledge all questions put to him by the local registrar which may be calculated to eUcit any information needed to make a complete record of the birth as contemplated by said section 14, and it shall be the duty of the informant as to any statement made in accordance herewith to verify such statement by his signatiu'e, when requested so to do by the local registrar. Sec. 14. That the certificate of birth shall contain the following items, which are hereby declared necessary for the legal, social, and sanitary purposes subserved by registration records: ' (1) Place of birth, including State, county, township or town, village, or city. If in a city, the ward, street, and house number; if in a hospi- tal or other institution, the name of the same to be given, instead of the street and house mnnber. (2) FuU name of child. If the child dies without a na,me, before the certificate is filed, enter the words " Died unnamed." If the living child has not yet been named at the date of filing certificate of birth, the space for "Full name of child" is to be left blank, to be filled out subsequently by a supplemental report, as hereinafter provided. (3) Sex of child. (4) Whether a twin, triplet, or other plural birth. A separate certificate shall be required for each child in case of plural births. ' The following items are those of the United States standard certi- ficate of birth, approved by the Biu'eau of the Census. APPENDIX III 481 (5) For plural births, number of each child in order of birth. (6) Whether legitimate or illegitimate.' (7) Date of birth, including the year, month, and day. (8) Full naine of father. (9) Residence of father. (10) Color or race of father. (11) Age of father at last birthday, in years. (12) Birthplace of father; at least State or foreign country, if known. (13) Occupation of father. The occupation to be reported if engaged in any remimerative employment, with the statement of (a) trade, profession, or particular kind of work; (6) general nature of industry, business, or establishment in which employed (or employer). (14) Maiden name of mother. (15) Residence of mother. (16) Color or race of mother. (17) Age of mother at last birthday, in years. (18) Birthplace of mother; at least State or foreign country, if known. (19) Occupation of mother. The occupation to be reported if engaged in any remimerative employment, with the statement of (o) trade, profession, or particular kind of work; (6) general nature of industry, business, or establishment in which employed (or employer). (20) Number of children bom to this mother, including present birth. (21) Number of children of this mother living. (22) The certification of attending physician or midwife as to attend- ance at birth, including statement of year, month, day (as given in item 7), and hour of birth, and whether the child.was born alive or stillborn. This certification shall be signed by the attending physician or midwife, with date of signature and address; if there is not physician or midwife in attendance, then by the father or mother of the child, householder, owner of the premises, or manager or superintendent of public or private institution where the birth occurred, or other competent person, whose duty it shall be to notify the local registrar of such birth, as required by section 13 of this act. (23) Exact date of filing in ofl^ice of local registrar, attested by his official signature, and registered number of birth, as hereinafter pro- vided. Sec. 15. That when any certificate of birth of a living child is pre- sented without the statement of the given name, then the local registrar ' This question may be omitted if desired, or provision may be made so that the identity of parents will not be disclosed. 482 APPENDIX III shall make out and deliver to the parents of the child a special blank for the supplemental report of the given name of the child, which shall be filled out as directed, and returned to the local registrar as soon as the child shall have been named. Sec. 16. That every physician, midwife, and undertaker shall, with- out delay, register his or her name, address, and occupation with the local registrar of the district in which he or she resides, or may hereafter estabUsh a residence; and shall thereupon be supplied by the local registrar with a copy of this act, together with such rules and regulations as may be prepared by the State registrar relative to its enforcement. Within thirty days after the close of each calendar year each local registrar shall make a return to the State registrar of all physicians, midwives, or undertakers who have been registered in his district during the whole or any part of the preceding calendar year: Provided. That no fee or other compensation shall be charged by local registrars to physicians, midwives, or undertakers for registering their names under this section or making returns thereof to the State registrar.' Sec. 17. That all superintendents or managers, or other persons in charge of hospitals, almshouses, lying-in, or other institutions, pubUc or private, to which persons resort for treatment of diseases, confinement, or are committed by process of law, shall make a record of all the per- sonal and statistical particulars relative to the inmates in their institu- tions at the date of approval of this act, which are required in the forms of the certificates provided for by this act, as directed by the State registrar; and thereafter such record shall be, by them, made for all future inmates at the time of their admittance. And in case of persons admitted or committed foptreatment of disease, the physician in charge shall specify for entry in the record, the nature of the disease, and where, in his opinion, it was contracted. The personal particulars and information required by this section shall be obtained from the indi- vidual himself if it is practicable to do so; and when they can not be so obtained, they shall be obtained in as complete a manner as possible from relatives, friends, or other persons acquainted with the facts. Sec. 18. That the State registrar shall prepare, print, and supply to all registrars all blanks and forms used in registering, recording, and preserving the returns, or in otherwise carrying out the purposes of this act; and shall prepare and issue such detailed instructions as may be required to procure the uniform observance of its provisions and the ' This section may be omitted if deemed expedient and the duty of supplying instructions may be assumed by the State ofiBcer. APPENDIX HI 483 maintenance of a perfect system of registration; and no other blanks shall be used than those supplied by the State registrar. He shall care- fully examine the certificates received monthly from the local registrars, and if any such are incomplete or unsatisfactory he shall require such further information to be supplied as may be necessary to make the record complete and satisfactory. And all physicians, midwives, informants, or undertakers, and all other persons having knowledge of the facts, are hereby required to supply, upon a form provided by the State registrar or upon the original certificate, such information as they may possess regardiag any birth or death upon demand of the State registrar, in person, by maU, or through the local registrar; Provided, That no certificate of birth or death, after its acceptance for registration by the local registrar, and no other record made in pursuance of this act, shall be altered or changed in any respect otherwise than by amendments properly dated, signed, and witnessed. The State registrar shall further arrange, bind, and permanently preserve the certificates in a systematic manner, and shall prepare and maintain a comprehensive and continuous card index of all births and deaths registered; said index to be arranged alphabetically, in the case of deaths, by the names of decendents, and in the case of births, by the names of fathers and mothers. He shall inform aU registrars what diseases are to be con- sidered infectious, contagious, or communicable and dangerous to the pubUc ihealth, as decided by the State board of health, in order that when deaths occur from such diseases proper precautions' may be taken to prevent their spread. If any cemetery company or association, or any church or historical society or association, or any other company, society, or association, or any individual, is in possession of any record of births or deaths which may be of value in establishing the genealogy of any resident of this State, such company, society, association, or individual may file such record or a duly authenticated transcript thereof with the State registrar, and it shall be the duty of the State registrar to preserve such record or transcript and to make a record and index thereof in such form as to facilitate the finding of any information contained therein. Such record and index shall be open to inspection by the public, subject to such reasonable conditions as the State registrar may prescribe. If any person desires a transcript of any record filed in accordance here- with, the State registrar shall furnish the same upon application, to- gether with a certificate that it is- a true copy of such record, as filed in his oflSce, and for his services in so furnishing such transcript and certificate he shall be entitled to a fee of (ten cents per folio) (fifty cents 484 APPENDIX III per hour or fraction of an hour necessarily consumed in making such transcript) and to a fee of twenty-five cents for the certificate, which fees shall be paid by the applicant. Sec. 19. That each local registrar shall supply blank forms of certi- ficates to such persons as require them. Each local registrar shall carefully examine each certificate of birth or death when presented for record in order to ascertain whether or not it has been made out in accordance with the provisions of this act and the instructions of the State registrar; and if any certificate of death is incomplete or unsatis- factory, it shall be his duty to call attention to the defects in the return, and to withhold the burial or removal permit imtil such defects are corrected. All certificates, either of birth or of death, shall be written legibly, in durable black ink, and no certificate shall be held to be com- plete and correct that does not supply all of the items of information called for therein, or satisfactorily account for their omission. If the certificate of death is properly executed and complete, he shall then issue a burial or removal permit to the undertaker; provided, that in case the death occurred from some disease which is held by the State board of health to be infectious, contagious, or communicable and dangerous to the public health, no permit for the removal or other dis- position of the body shall be issued by the registrar, except under such conditions as may be prescribed by the State board of health. If a certificate of birth is incomplete, the local registrar shall immediately notify the informant and require him to supply the missing items of information if they can be obtained. He shall number consecutively the certificates of birth and death, in two separate series, beginning with number 1 for the first birth and the first death in each calendar year, and sign his name as registrar in attest of the date of filing in his office. He shall also make a complete and accurate copy of each birth and each death certificate registered by him in a record book suppUed by the State registrar, to be preserved permanently in his office as the local record, in such manner as directed by the State registrar. And he shall, on the tenth day of each month, transmit to the State registrar all original certificates registered by him for the preceding month. And if no births or no deaths occurred in any month, he shall, on the tenth day of the following month, report that fact to the State registrar, on a card provided for such purpose. Sec. 20. That each local registrar shall be paid the sum of twenty-five cents for each birth certificate and each death certificate properly and completely made out and registered with him, and correctly recorded and promptly returned by him to the State registrar, as required by APPENDIX III 485 this act.' And in case no births or no deaths were registered during any month, the tocal registrar shall be entitled to be paid the sum of twenty-five cents for each report to that eifect, but only if such report be made promptly as required by this act. AH amounts payable to a local registrar under the provisions of this section shall be paid by the treasurer of the county in which the registration district is located, upon certification by the State registrar. And the State registrar shall annually pertify to the treasurers of the several counties the number of births and deaths properly registered, with the names of the local registrars and the amounts due each at the rates fixed herein .^ Sec. 21. That the State registrar shall, upon request, supply to any applicant a certified copy of the record of any birth or death registered under provisions of this act, for the making and certification of which he shall be entitled to. a fee of fifty cents, to be paid by the applicant. And any such copy of the record of a birth or death, when properly certified by the State registrar, shall be prima facie evidence in all courts and places of the facts therein stated. For any search of the files and records when no certified copy is made, the State registrar shall be entitled to a fee of fifty cents for each hour or fractional part of an hour of time of search, said fee to be paid by the appHcant. And the State registrar shall keep a true and correct account of all fees by him received under these provisions, and turn the same over to the State treasurer: Provided, That the State registrar shall, upon request of any parent or guardian, supply, without fee, a certificate limited to a state- ment as to th&.date of birth of any child when the same shall be neces- sary for admission to school, or for the purpose of securing employment : And provided further, That the United States Census Bureau may obtain, without expense to the State, transcripts, or certified copies of births and deaths without payment of the fees herein prescribed. Sec. 22. That any person, who for himself or as an officer, agent, or employee of any other person, or of any corporation or partnership (a) shall inter, cremate, or otherwise finally dispose of the dead body of a human being, or permit the same to be done, or shall remove said body from the primary registration district in which the death occurred or ^ A proviso may be inserted at this point relative to fees of city registrars who are already compensated by salary for their services. See laws of Missouri, Ohio, and Pennsylvania. ^ Provision may be made in this section for the payment of sub- registrars and also, if desired, for the payment of physicians and mid- wives. See Kentucky law. 486 APPENDIX m the body was found without the authority of a burial or removal permit issued by the local registrar of the district in which the death occurred or in which the body was found; or (6) shall refuse or fail to furnish correctly any information in his possession, or shall furnish false in- formation affecting any certificate or record, required by this act; or (c) shall willfully alter, otherwise than is provided by section 18 of this act, or shaU falsify any certificate of birth or death, or any record established by this act; or (d) being required by this act to fill out a certificate of birth or death and file the same with the local registrar, or deliver it, upon request, to any person charged with the duty of filling the same, shall fail, neglect, or refuse to perform such duty in the manner required by this act; or (e) being a local registrar, deputy registrar, or subregistrar, shall faU, neglect, or refiise to perform his duty as required by this act and by the instructions and direction of the State registrar thereunder, shall be deemed guilty of a misdemeanor, and upon conviction thereof shall for the first offense be fined not less than five dollars ($5) nor more than fifty dollars (S50), and for each subsequent offense not less than ten dollars ($10) nor more than one hundred doUard (SlOO), or be imprisoned in the county jail not more than sixty days, or be both fined and imprisoned in the discretion of the court.' Sec. 23. That each local registrar is hereby charged with the strict and thorough enforcement of the provisions of this act in his registration district, under the supervision and direction of the State registrar. And he shall make an immediate report to the State registrar of any. violation of this law coming to his knowledge, by observation or upon complaint of any person or otherwise. The State registrar is hereby charged with the thorough and efficient execution of the provisions of this act in every part of the State, and is hereby granted supervisory power over local registrars, deputy local registrars, and subregistrars to the end that aU of its requirements shall be uniformly complied with. The State registrar, either personally or by an accredited representative, shall have authority to investigate cases of irregularity or violation of law, and all registrars shall aid him upon request, in such investigations. When he shall deem it necessary he shall report cases of violation of any of the provisions of this act to the prosecuting attorney of the county, with a statement of the facts ' Provision may be made whereby compliance with this act shall constitute a condition of granting licenses to physicians, midwives, and embalmers. APPENDIX III 487 and circumstances; and when any such case is reported to him by the State registrar the prosecuting attorney shall forthwith initiate and promptly follow up the necessary court proceedings against the person or corporation responsible for the alleged violation of law. And upon request of the State registrar, the attorney general shall assist in the enforcement of the provisions of this act'. Note. — Other sections should be added giving the date on which the act is to go into effect, if not determined by constitutional provisions of the State; providing for the financial support of the law; and repeal- ing prior statutes ineonsistent with the present act. It is desirable that the entire bill should be reviewed by competent legal authority for the purpose of discovering whether it can be made more consistent in any respect with the general form of legislation of the State in which the bill is to be introduced, without material change or injury to the effectiveness of registration. THE STANDARD BIRTH AND DEATH CERTIFICATES The following are facsimile reproductions of the standard birth and death certificates. They have been reduced in size to meet the require- ments of the printed page. The size of the birth certificate is 6| by 7 J inches, and of the death certificate 7\ by 8| inches. Copies can be obtained from the Director of the Census upon request. 488 APPENDIX III UNITED STATES STANDARD CERTIFICATE OF BIRTH § 8| S| w s i§ to "^ •^ « w -•= e « S«§ a .fc » ■a o a a CO 1 O *•& a K Sag is 3^ PLACE OF BIRTH department of commerce and labor BUREAU OP THE CENSUS County of STANDARD CERTIFICATE OF BIRTH Township of.. or < Village of Registered No. . City of (No St.; Ward) {. If child is not yet named, make supplemental report as directed Sex of Child Twin, triplet, or other? Number in order of birth (To be anflwered onl; in eveiit of plural birthsj Legiti- mate? Date of birth , 19.. (MoQth) (Day) (Ybkt) FATHER FULL NAME AGE AT LAST BIRTHDAY. . BIRTHPLACE OCCUPATION Number of children born to this mother, including present birth. . . FULL MAIDEN NAME RESIDENCE AGE AT LAST BIRTHDAY. BIRTHPLACE OCCUPATION Number of children of this mother now living CERTIFICATE OP ATTENDING PHYSICIAN OR MIDWIFE 1 I hereby certify that I attended the birth of this child, who was at M., on the date above stated. (Born alivt or Stillboni) ■ 1 When there was no attending physician ] (Signature) or midmfe, then the father, householder, | etc., should make this return. A stillborn > child is one that neither breathes nor shows I (PhyBjoiM or Midwife) other evidence of life after birth. J Given name added from a supplemental Address ; report , 19 Filed 19 n— 3B5 H Be^etTBT Regietrar APPENDIX III 489 g 4 5 I CO >* — OS -Q.a O S.g ^ s ° IN w S a § « .a 3! SUPPLEMENTAL REPORT OF BIRTH (state) (This return should preferably be made by the person who made the original ) Registered Number i Place of birth i .* No St. (RflgiatratioD diatiiat) I HEREBY CERTIFY that the child described herein has been named: SEX of CHILD 1 Twin.i ] [Number i( triplet, yand2>'3 as DEPABTMENT OF COMMERCE BUTIEATJ OP THE CENSUS STANDARD CERTIFICATE OF DEATH 1 PLACE OF DEATH County State Registered No Township or Village or City No. ...., St., Ward (If death occurred in a hospital or institution, give its NAiaE instead of street and number.) a FULL NAME (a) Residence. No St., Ward (Usual place of abode.) (If nonresident give city or town and State.) Length of residence in city or town How long in U. S., if of for- where death, occvirred. yrs. mos. ds. eign birth? yrs. mos. da. PEItSONAL AND STATISTICAL PAHTICULAH6 * COLOR OR RACE 6 Single, Married, Widowed, or Divorced {Write the word) 6* If married, widowed, or divorced ^HUSBAND of (or) WIFE of ' DATE OP BIRTH (month, day, and year) ^^ 7 AGE Yrs. Mos. Ds. If LESS than 1 day, . . . hrs. or min.? ' OCCUPATION OF DECEASED (a) Trade, profession, or particular kind of work (b) General nature of industry, business, or establishnient in which employed (or employer) . . . . (c) Name of employer ' BIRTHPLACE (city OT town) , (State or country) W NAME OP FATHER 11 BIRTHPLACE OF FATHER (city Or town) (State or country) 12 MAIDEN NAME OP MOTHER " BIRTHPLACE OF MOTHER (city Or town) (State or country) 1* Informant . , (Address) 16 Filed. MEDICAL CERTIFICATE OP DEATH « DATE OF DEATH (mouth, dsy, and year) 19 ' I HEREBY CERTIFY, That I attended deceased from , 19...., to 19,. that Ilast saw h... alive on 19.. and that death occurred, on the date stated above, at m. The CAUSE OF DEATH* was as follows: (duration) , . .yrs mos. . . da. CONTRIBUTORY (SMondKTj) / (duration) . . .yrs. . . mos. . . ds, w Where was disease contracted if not at place of death? Did an operation precede death? Date of Was there an autoxray? What test confirmed diagnosis? (Signed) , l&.D. , 19 (Address) * State the Disease Causing Death, or in deaths from Violent Causes, state (1) Means and Nature of In- jury; and (2) whether Accidental, Suicidal, or Homicidal. (Seoreverse side for additional space.) 19 PLACE OF BURIAL, CREMATION, OR RE- MOVAL 20 UNDERTAKER DATE OF BURIAL TABLE VI.— LOGARITHMS OP NUMBERS. N 0123456789 100 00000 00043 00087 00130 00173 00217 00260 00303 00346 00389 1 0432 0475 0518 0561 0604 0647 0689 0732 077i 0817 2 0860 0903 0945 0988 1080 1072 1115 1157 1199 1242 8 1284 1326 1368 1410 1452 1494 1536 1578 1620 1662 4 1703 1745 1787 1828 1870 1912 1953 199i 2036 2078 S 2119 2160 2202 2243 2284 2325 2366 2407 2449 2490 6 2531 2572 2612 2653 2694 2735 2776 2816 2857 2898 T 2938 2979 3019 8060 3100 3141 3181 3222 3262 3302 8 3342 8383 3423 3463 8503 3543 3583 3623 3663 3703 9 3743 3782 3822 8862 3902 3941 3981 4021 4060 4100 110 04139 04179 04218 04258 04297 04336 04376 04415 04454 04493 1 4532 4571 4610 4650 4689 4727 4766 4805 4844 4883 2 4922 4981 4999 5038 5077 5115 5154 5192 5231 5269 8 5308 5346 5385 5423 5461 5|00 5538 5576 5614 5652 4 5690 5729 5767 5805 5843 5881 5918 5956 5994 6082 6 6070 6108 6145 6183 6221 6258 6296 6333 6371 6408 6 6446 6483 6521 6558 6595 6633 6670 6707 6744 6781 7 6819 6856 6893 6980 6967 7004 7041 7078 7115 7151 8 7188 7225 7262 7298 7335 7372 7408 -7445 7482 7518 9 7555 7591 7628 7664 7700 7737 7773 7809 7846 7882 120 07918 07954 07990 08027 08063 08099 08135 08171 08207 08243 1 8279 8314 8350 8386 8422 8458 8493 8529 8565 8600 2 8636 8672 8707 8743 8778 8814 8849 8884 8920 8955 8 8991 9026 9061 9096 9132 9167 9202 9237 9272 9307 4 9342 9377 9412 9447 9482 9517 9552 9587 9621 9656 5 9691 9726 9760 9795 9880 9864 9899 9934 9968 10003 6 10037 10072 10106 10140 10175 10209 10243 10278 10312 0346 7 0380 0415 0449 0483 0517 0551 0585 0619 0653 0687 8 0721 0755 0789 0823 0857 0890 0924 0958 0992 1025 9 1059 1093 1126 1160 1193 1227 1261 1294 1327 1361 130 11394 11428 11461 11494 11528 11561 11594 11628 11661 11694 1 1727 1760 1793 1826 1860 1893 1926 1959 1992 2024 2 2057 2090 2123 2156 2189 2222 2254 2287 2820 2352 3 2385 2418 2450 2483 2516 2548 2581 2613 2646 2678 4 2710 2743 2775 2808 2840 2872 2905 2937 2969 3001 5 3033 3066 3098 3130 8162 3194 3226 8258 3290 3322 6 3354 8386 8418 3450 3481 8513 8545 3577 3609 8640 7 3672 3704 3735 3767 3799 3830 8862 3893 3925 3956 8 3988 4019 4051 4082 4114 4145 4176 4208 4239 4270 9 4301 4333 4364 4395 4426 4457 4489 4520 4551 4582 140 14613 14644 14675 14706 14737 14768 14799 14829 14860 14891 1 4922 4953 4983 5014 5045 5076 5106 5137 5168 5198 2 5229 5259 5290 5320 5851 5881 5412 5442 5473 5508 8 5534 5564 5594 5625 5655 5685 5715 5746 5776 5806 4 5836 5866 5897 5927 5957 5987 6017 6047 6077 6107 6 6137 6167 6197 6227 6256 6286 6316 6346 6376 6406 6 6485 6465 6495 6524 6554 6584 6613 6643 6673 6702 7 6732 6761 6791 6820 6850 6879 6909 6938 6967 6997 8 7026 7056 7085 7114 7143 7173 7202 7281 7260 7289 9 7319 7348 7877 7406 7435 7464 7493 7522 7551 7580 150 i7flOQ iTfiSH 17667 17696 17725 17754 17782 17811 17840 17869 492 TABLE VI.— LOGARITHMS OF NUMBERS. N 0123466789 150 17609 17638 17667 17696 17725 17754 17782 17811 17840 17869 1 7898 7926 7955 7984 8013 8041 8070 8099 8127 8156 2 8184 8213 8241 8270 8298 8327 8355 8384 8412 8441 3 8469 8498 8526 8554 8583 8611 8639 8667 8696 8724 4 8752 8780 8808 8837 886S 8893 8921 8949 8977 9005 5 9033 9061 9089 9117 9145 9173 9201 9229 9257 9285 6 9312 9340 9368 9396 9424 9451 9479 9507 9535 9562 ■ 7 9590 9618 9645 9673 9700 9728 9756 9783 9811 9838 8 9866 9893 9921 9948 9976 20003 20030 20058 20085 20112 9 20140 20167 20194 20222 20249 0276 0303 0330 0358 0385 160 20412 20439 20466 20493 20520 20548 20575 20602 20629 20656 1 0683 0710 0737 0763 0790 0817 0844 0871 0898 0925 2 0952 0978 1005 1032 1059 1085 1112 1139 1165 1192 3 1219 1245 1272 1299 1325 1352 1378 1405 1431 1458 4 1484 1511 1537 1564 1590 1617 1643 1669 1696 1722 6 1748 1775 1801 1827 1854 1880 1906 1932 1958 1985 6 2011 2037 2063 2089 2115 2141 2167 2194 2220 2246 7 2272 2298 2324 2350 2376 2401 2427 2453 2479 2505 8 2531 2557 2583 2608 2634 2660 2686 2712 2737 2763 9 2789 2814 2840 2866 2891 2917 2943 2968 2994 3019 170 23045 23070 23096 23121 23147 23172 23198 23223 23249 23274 1 3300 3325 3350 3376 3401 3426 3452 3477 3502 3528 2 3553 3578 3603 3629 3654 3679 3704 3729 3754 3779 3 3805 3830 3855 3880 3905 3930 8955 3980 4005 4030 4 4055 4080 4105 4130 4155 4180 4204 4229 4254 4279 S 4304 4329 4353 4378 4403 4428 4452 4477 4502 4527 6 4651 4576 4601 4625 4650 4674 4699 4724 4748 4773 7 4797 4822 4846 4871 4895 4920 4944 4969 4993 5018 8 5042 5066 5091 5115 5139 5164 5188 5212 5237 5261 9 5285 5310 5334 5358 5382 5406 5431 5455 5479 5503 180 25527 25551 25575 25600 25624 25648 25672 25696 25720 25744 1 5768 5792 5816 5840 5864 5888 5912 5935 5959 5983 2 6007 6031 6055 6079 6102 6126 6150 6174 6198 6221 3 6245 6269 6293 6316 6340 6364 6387 6411 6435 6458 4 6482 6505 6529 6553 6576 6600 6623 6647 6670 6694 5 6717 6741 6764 6788 6811 6834 6858 6881 6905 6928 6 6951 6975 6998 7021 7045 7068 7091 7114 7138 7161 7 7184 7207 7231 7254 7277 7300 7323 7346 7370 7393 8 7416 7439 7462 7485 7508 7531 7554 7577 7600 7623 9 7646 7669 7692 7715 7738 7761 7784 7807 7830 7852 190 27875 27898 27921 27944 27967 27989 28012 28035 28058 28081 1 8103 8126 8149 8171 8194 8217 8240 8262 8285 8307 2 8330 8353 8375 8398 8421 8443 8466 8488 8511 8533 3 8556 8578 8601 8623 8646 8668 8691 8713 8735 8758 4 8780 8803 8825 8847 8870 8892 8914 8937 8959 8981 6 9003 9026 9048 9070 9092 9115 9137 9159 9181 9203 6 9226 9248 9270 9292 9814 9336 9358 9380 9403 9425 7 9447 9469 9491 9513 9535 9557 9579 9601 9623 9645 8 9667 9688 9710 9732 9754 9776 9798 9820 9842 9863 9 9885 9907 9929 9951 9973 9994 30016 30038 30060 30081 200 30103 30125 ^MiR smfiH Qnion 5?n9ii .qoM.q .qnsffi'; .qns7fi .30298 I'ABLE VI.— LOGfAlilTHMS OF NUMBEHS. 493 N 0123456789 200 30103 30125 80146 30168 30190 30211 30233 30255 30276 30298 1 0329 0341 0363 0384 0406 0428 0449 0471 0492 0514 2 0635 0557 0578 0600 0621 0643 0664 0686 0707 0728 3 0750 0771 0792 0814 0835 0856 0878 0899 0920 0942 4 0963 0984 1006 1027 1048 1069 1091 1112 1133 1154 5 1175 1197 1218 1239 1260 1281 1302 1323 1345 1366 6 1387 1408 1429 1450 1471 1492 1513 1534 1655 1576 7 1597 1618 1639 1660 1681 1702 1723 1744 1765 1785 8 1806 1827 1848 1869 1890 1911 1931 1962 1973 1994 9 2015 2035 2056 2077 2098 2118 2139 2160 2181 2201 210 32222 32243 32263 82284 32305 32325 82346 82366 82887 32408 1 2428 2449 2469 2490 2610 2531 2562 2672 2593 2613 2 2634 2654 2675 2695 2715 2786 2756 2777 2797 2818 3 2838 2858 2879 2899 2919 2940 2960 2980 3001 3021 4 8041 3062 3082 3102 3122 8143 3163 3188 3203 3224 6 3244 3264 3284 3304 3325 3345 3365 3386 3405 3426 6 8445 8465 8486 3606 8526 3646 3566 3686 3606 3626 7 3646 3666 3686 3706 3726 8746 3766 3786 3806 8826 8 3846 3866 3885 8905 3925 3945 3965 3985 4005 4025 9 4044 4064 4084 4104 4124 4148 4163 4183 4203 4223 220 34242 34262 34282 34301 34321 84841 34861 34380 34400 34420 1 4439 4459 4479 4498 4518 4637 4667 4577 4596 4616 2 4635 4655 4674 4694 4713 4733 4753 4772 4792 4811 3 4830 4850 4869 4889 4908 4928 4947 4967 4986 5005 4 5025 5044 5064 5083 5102 5122 6141 5160 5180 5199 5 5218 5238 5257 6276 5295 5315 5334 5858 5372 5892 6 5411 5480 5449 5468 .5488 6607 5626 5545 5564 558S 7 5603 5622 5641 5660 5679 5698 5717 5736 5755 5774 8 5793 5813 5832 6861 6870 5889 5908 5927 5946 5965 9 5984 6003 6021 6040 6059 6078 6097 6116 6135 6154 230 36173 36192 36211 36229 86248 36267 36286 36305 86324 36342 1 6361 6380 6899 6418 6436 6465 6474 6493 6511 6530 2 ■ 6549 6568 6586 660i 6624 6642 6661 6680 6698 6717 3 6736 6754 6773 6791 6810 6829 6847 6866 6884 6903 4 6922 6940 6969 6977 6996 7014 7033 7051 7070 7088 6 7107 7125 7144 7162 7181 7199 7218 7236 7264 7273 6 7291 7810 7328 7346 7365 7383 7401 7420 7438 7457 7 7475 7493 7511 7530 7548 7666 7585 7603 7621 7639 8 7668 7676 7694 7712 7731 7749 7767 7785 7803 7822 9 7840 7858 7876 7894 7912 7931 7949 7967 798i 8003 210 38021 38039 38057 38075 88093 38112 38130 38148 38166 88184 1 8202 8220 8238 8256 8274 8292 8310 8328 8346 8364 2 8382 8399 8417 8435 8453 8471 8489 8507 8525 8543 3 8561 8578 8596 8614 8632 8650 8668 8686 8703 8721 4 8739 8757 8775 8792 8810 8828 8846 8863 8881 8899 6 8917 8934 8952 8970 8987 9005 9023 9041 9058 9076 6 9094 9111 9129 9146 9164 9182 9199 9217 9235 9252 7 9270 9287 9305 9322 9340 9358 9375 9393 9410 9428 8 9445 9463 9480 9498 9515 9533 9550 9568 9585 9602 9 9620 9637 9655 9672 9690 9707 9724 9742 9759 9777 250 QmnA Qoaii oqoqq oaeAn aosna sQRsi aocQQ 0.9915 39933 89950 494 TABLE VI.— LOUAlilTHMS OF NUMBEKS. N 012 34567 89 250 39794 39811 89829 39846 39863 39881 39898 39915 39933 39950 1 9967 9985 40002 40019 40037 40054 40071 40088 40106 40123 2 40140 40157 0175 0192 0209 0226 0243 0261 0278 0295 3 0312 0329 0346 0364 0381 0398 0415 0432 0449 0466 4 0483 0500 0518 0535 0552 0569 0586 0603 0620 0637 5 0654 0671 0688 0705 0722 0739 0756 0773 0790 0807 6 0824 0841 0858 0875 0892 0909 0926 0943 0960 0976 7 0993 1010 1027 1044 1061 1078 1095 1111 1128 1145 8 1162 1179 1196 1212 1229 1246 1263 1280 1296 1313 9 ■ 1330 1347 1363 1380 1897 1414 1430 1447. 1464 1481 260 41497 41514 41531 41547 41564 41581 41597 41614 41631 41647 1 1684 1681 1697 1714 1731 1747 1764 1780 1797 1814 2 1830 1847 1863 1880 1896 1913 1929 1946 1963 1979 3 1996 2012 2029 2015 2062 2078 2095 2111 2127 2144 4 2160 2177 2193 2210 2226 2243 2259 2275 2292 2308 5 2325 2341 2357 2374 2390 2406 2423 2439 2455 2472 6 2488 2504 2521 2537 2553 2570 2586 2602 2619 2635 7 2651 2667 2684 2700 2716 2782 2749 2765 2781 2797 8 2818 2830 2846 2862 2878 2894 2911 2927 2943 2959 9 2975 2991 300B 3024 3040 3056 3072 3088 3104 3120 270 43138 43152 43169 43185 43201 43217 43233 43249 43265 43281 1 3297 3313 3329 3345 3361 3377 3898 3409 3425 3441 2 3457 3473 3489 3505 3521 8587 3553 8569 3584 3600 3 3616 3632 8648 8664 3680 8696 3712 3727 8743 3759 4 8775 3791 3807 8823 3838 3854 3870 3886 3902 3917 6 3933 3949 3965 3981 3996 4012 4028 4044 4059 4075 6 4091 4107 4122 4138 4154 '4170 4185 4201 4217 4232 7 4248 4264 4279 4295 4311 4826 4342 4358 4373 4389 8 4404 4420 4486 4451 4467 4483 4498 . 4514 4529 4545 9 4560 4576 4592 4607 4623 4638 4654 4669 4685 4700 280 44716 44731 44747 44762 44778 44793 44809 44824 44840 44855 1 4871 4886 4902 4917 4982 4948 4963 4979 4994 5010 2 5025 5040 5056 5071 5086 5102 5117 5133 5148 5163 3 5179 5194 5209 5225 5240 5255 5271 5286 5801 5317 4 5332 5347 5362 5378 5893 5408 5423 5489 5454 5469 6 5484 5500 5515 5530 5545 5561 5576 5591 5606 5621 6 5637 5652 5667 5682 5697 5712 5728 5743 5758 5773 7 5788 5803 5818 5884 5849 5864 5879 5894 5909 6924 8 5939 5954 5969 5984 6000 6015 6030 6045 6060 6075 9 6090 6105 6120 6135 6150 6165 6180 6195 6210 6225 290 46240 46255 46270 46285 46300 46315 46330 46345 46359 46374 1 6389 6404 6419 6434 6449 6464 6479 6494 6509 6528 2 6538 6553 6568 6583 6598 6613 6627 6642 6657 6672 3 6687 6702 6716 6731 6746 6761 6776 6790 6805 6820 4 6835 6850 6864 6879 6894 6909 6923 6988 6953 6967 e 6982 6997 7012 7026 7041 7056 7070 7085 7100 7114 6 7129 7144 7159 7173 7188 7202 7217 7232 7246 7261 7 7276 7290 7805 7319 7884 7349 7863 7378 7392 7407 8 7422 7436 7451 7465 7480 7494 7509 7524 7588 7553 9 7567 7582 7596 7611 7625 7640 7654 7669 7683 7698 300 47712 47727 47741 47756 47770 47784 47799 47813 47828 47842 TABLE VI.— LOGARITHMS OF NUMBERS. 495 • N 0123456 789 300 47712 47727 47741 47756 47770 47784 47799 47813 4;'828 47842 1 7857 7871 7885 7900 7914 7929 794.3 7958 7972 7986 2 8001 8015 8029 8044 8058 8073 8087 8101 8116 8130 3 8144 8159 8173 8187 8202 8216 8230 8244 8259 8273 4 8287 8302 8316 8330 8344 8359 8373 8387 8401 8416 5 8430 8444 8458 8473 8487 8501 8615 8530 8544 8558 6 8572 8586 8601 8615 8629 8643 8657 8671 8686 8700 7 8714 8728 8742 8756 8770 8785 8799 8818 8827 8841 8 8855 8869 8883 8897 8911 8926 8940 8954 8968 8982 9 8996 9010 9024 9038 9052 9066 9080, 9094 9108 9122 SIO 49136 49150 49164 49178 49192 49206 49220 49234 49248 49262 1 9276 9290 9304 9318 9332 9346 9360 9374 9388 9402 2 9415 9429 9443 9457 9471 9485 9499 9513 9527 9541 3 9554 9568 9682 9596 9610 9624 9638 9651 9665 9679 4 9693 9707 9721 9734 9748 9762 9776 9790 9803 9817 6 9831 9845 9859 9872 9886 9900 9914 9927 9941 995i 6 9969 9982 9996 50010 60024 80037 50061 50065 60079 50092 7 50106 50120 60133 0147 0161 0174 0188 0202 0216 0229 8 0243 0266 0270 0284 0297 0311 0325 0338 0352 0366 9 0379 0393 0406 0420 0433 0447 0461 0474 0488 0601 320 60515 60629 60542 50556 60669 60583 60596 50610 50623 50637 1 0651 0664 0678 0691 0705 0718 0732 0745 0759 0772 2 0786 0799 0813 0826 0840 0853 0866 0880 0893 0907 3 0920 0934 0947 0961 0974 0987 1001 1014 1028 1041 4 1055 1068 1081 1095 1108 1121 1135 1148 1162 1175 5 1188 1202 1216 1228 1242 1255 1268 1282 1295 1308 6 1322 1335 1348 1362 1376 1388 1402 1415 1428 1441 7 1465 1468 1481 1495 1608 1521 1634 1548 1561 1574 8 1587 1601 1614 1627 1640 1654 1667 1680 1693 1706 9 1720 1733 1746 1769 1772 1786 1799 1812 1825 1838 330 51851 51865 51878 51891 51904 61917 61930 51943 61967 51970 1 1983 1996 2009 2022 2035 2048 2061 2075 2088 2101 2 2114 2127 2140 2153 2166 2179 2192 2206 2218 2231 3 2244 2257 2270 2284 2297 2310 2323 2336 2349 2362 4 2375 2388 2401 2414 2427 2440 2463 2466 2479 2492 5 2604 2617 2630 2543 2556 2569 2682 2695 2608 2621 6 2634 2647 2660 2673 2686 2699 2711 2724 2737 2750 7 2763 2776 2789 2802 2815 2827 2840 2853 2866 2879 8 2892 2905 2917 2930 2943 2956 2969 2982 2994 3007 9 3020 3033 3046 3068 3071 3084 3097 3110 3122 3135 340 53148 53161 53173 53186 63199 63212 63224 53237 63250 53263 1 3275 3288 3301 3314 3326 3339 3362 3364 3377 3390 2 3403 3416 3428 3441 3453 3466 3479 3491 3504 3617 3 3529 3542 3565 3667 3580 3693 3605 3618 3631 3643 4 3656 3668 3681 3694 3706 3719 3732 3744 3757 3769 6 3782 3794 3807 3820 3832 3845 3857 3870 3882 3896 6 3908 3920 3933 3945 3958 3970 3983 3995 4008 4020 7 4033 4045 4058 4070 4083 4095 4108 4120 4133 4145 8 4158 4170 4183 4195 4208 4220 4233 4245 4268 4270 9 4283 4295 4307 4320 4332 4345 4357 4370 4382 4394 350 fiddfi? fi4419 .54432 54444 54456 54469 54481 54494 64506 54618 496 TABLE VI.— LOGARITHMS OF NUMBERS. , N 0123456789 350 5440V 54419 54432 54444 54456 54469 54481 64494 64506 54518 1 4531 4643 4665 4568 4580 4593 4605 4617 4630 4642 2 4654 4667 4679 4691 4704 4716 4728 4741 4763 4765 3 4777 4790 4802 4814 4827 4839 4851 4864 4876 4888 4 4900 4913 4925 4937 4949 4962 4074 4986 4998 5011 S 5023 5035 5047 5060 5072 5084 .6096 5108 5121 6133 6 5145 6157 5169 5182 5194-5206 6218 5230 5242 525i 7 5267 5279 5291 5303 5316 6328 5340 6352 6364 5376 8 5388 5400 5413 5425 5437 6449 5461 5473 6485 5497 9 6509 5522 5534 6546 5668 6670 5682 6694 6606 6618 360 66630 55642 55664 65666 55678 65691 55703 65715 55727 65739 1 5751 5763 6775 5787 5799 5811 5823 5835 5847 5859 2 5871 5883 5895 5907 5919 6931 6943 6965 6967 5979 3 5991 6003 6015 6027 6038 6050 6062 6074 6086 6098 4 6110 6122 6134 6146 6168 6170 6182 6194 6205 6217 6 6229 6241 6263 626S 6277 6289 6301 6312 6324 6336 6 6348 6360 6372 6384 6396 6407 6419 6431 6443 6465 7 6467 6478 6490 6502 6514 6526 6538 6549 6561 6573 8 6685 6697 6608 6620 6632 6644 6656 6667 6679 6691 9 6703 6714 6726 6738 6750 6761 6773 6785 6797 6808 370 56820 56832 56844 66855 56867 56879 56891 56902 56914 56926 1 6937 6949 6961 6972 6984 6996 7008 7019 7031 7043 2 7054 7066 7078 7089 7101 7113 7124 7136 7148 7169 3 7171 7183 7194 7206 7217 7229 7241 7252 7264 7276 4 7287 7299 7310 7322 7334 7345 7357 7368 7380 7392 6 7403 7415 7426 7438 7449 7461 7473 7484 7496 7507 6 7519 7530 7642 7553 7565 7576 7588 7600 7611 7623 7 7634 7646 7657 7669 7680 7692 7703 7715 7726 7738 8 7749 7761 7772 7784 7795 7807 7818 7830 7841 7852 9 7864 7875 7887 7898 7910 7921 7933 7944 7955 7967 380 57978 57990 58001 68013 58024 68035 58047 58058 58070 58081 1 8092 8104 8115 8127 8138 8149 8161 8172 8184 819i 2 8206 8218 8229 8240 8252 8263 8274 8286 8297 8309 3 8320 8331 8343 8354 8365 8377 8388 8399 8410 8422 4 8433 8444 8456 8467 8478 8490 8501 8512 8524 8535 6 8546 8557 8569 8580 8591 8602 8614 8625 8636 8647 6 8659 8670 8681 8692 8704 871S 8726 8737 8749 8760 7 8771 8782 8794 8805 8816 8827 8838 8850 8861 8872 8 8883 8894 8906 8917 8928 8939 8950 8961 8973 8984 9 . 8995 9006 9017 9028 9040 9051 9062 9073 9084 9095 390 59106 69118 59129 69140 69151 59162 59173 59184 59195 59207 1 9218 9229 9240 9251 9262 9273 9284 9296 9306 9318 2 9329 9340 9361 9362 9373 9384 9395 9406 9417 9428 3 9439 9460 9461 9472 9483 9494 9506 9517 9528 9539 4 9550 9561 9572 9583 9594 9605 9616 9627 9638 9649 5 9660 9671 9682 9693 9704 9715 9726 9737 9748 9759 6 9770 9780 9791 9802 9813 9824 9835 9846 9857 9868 7 9879 9890 9901 9912 9923 9934 994^ 9956 9966 9977 8 9988 9999 60010 60021 60032 60043 60054 60065 60076 60086 9 60097 60108 0119 0130 0141 0152 0163 0173 0184 0195 400 60206 60217 60228 60239 60249 60260 60271 60282 60293 60304 TABLE VI.— LOGARITHMS OF NUMBERS. 497 N 012345678 9 400 60206 60217 60228 60239 60249 60280 60271 60282 60293 60304 . 1 0314 0325 0336 0347 0358 0369 0379 0390 0401 0412 2 0423 0438 0444 6455 0466 0477 0487 0498 0509 0520 3 0531 0541 0552 0563 0574 0584 0595 0606 0617 0627 4 0638 0649 0660 0670 0681 0692 0703 0718 0724 073i S 0746 0756 0767 0778 0788 0799 0810 0821 0831 0842 6 0853 0863 0874 0885 0895 0906 0917 0927 0938 0949 7 0959 0970 0981 0991 1002 1018 1028 1034 104S 1055 8 1066 1077 1087 1098 1109 1119 1130 1140 1151 1162 9 1172 1183 1194 1204 1215 1225 1236 1247. 1257 1268 410 61278 61289 61300 61310 61321 61331 61342 61352 61363 61374 1 1384 1395 1405 1416 1426 1437 1448 1458 1469 1479 2 1490 1500 1511 1521 1532 1542 1553 1563 1574 1584 3 1595 1606 1616 1627 1637 1648 1658 1669 1679 1690 4 1700 1711 1721 1731 1742 1752 1768 1773 1784 1794 S 1805 1815 1826 1836 1847 1857 1868 1878 1888 1899 6 1909 1920 1930 1941 1951 1962 1972 1982 1998 2003 7 2014 2024 2034 2045 2055 2066 2076 2086 2097 2107 8 2118 2128 2138 2149 2159 2170 2180 2190 2201 2211 9 2221 2232 2242 2252 2268 2278 2284 2294 2304 2315 420 62825 62335 62346 62356 62866 62377 62387 62397 62408 62418 1 2428 2439 2449 2459 2469 2480 2490 2500 2511 2521 2 2581 2542 2552 2562 2572 2583 2593 2603 2618 2624 3 2634 2644 2655 2665 2675 2685 2696 2706 2716 2726 4 2737 2747 2757 2767 2778 2788 2798 2808 2818 2820 5 2839 2849 2859 2870 2880 2890 2900 2910 2921 2931 6 2941 2951 2961 2972 2982 2992 3002 3012 3022 3033 7 3043 3058 3063 3073 3083 3094 8104 3114 3124 8134 8 8144 3155 8165 3175 3185 3195 3205 3215 3225 3236 9 3246 8256 8266 8276 3286 3296 3306 3317 3327 8837 430 63847 63357 63367 63377 63387 63397 63407 68417 63428 63438 1 3448 3458 8468 3478 3488 3498 3608 3518 3528 3538 2 3548 3558 3568 3579 3589 8599 3609 3619 8629 3639 3 3649 3659 3669 3679 3689 3699 3709 3719 3729 3739 4 3749 8759 3769 3779 3789 8799 3809 3819 3829 3839 5 3849 3859 3869 3879 3889 3899 3909 3919 3929 3939 6 3949 3959 3969 8979 8988 3998 4008 4018 4028 4038 7 4048 4058 4068 4078 4088 4098 4108 4118 4128 4137 8 4147 4157 4167 4177 4187 4197 4207 4217 4227 4237 9 4246 4256 4266 4276 4286 4296 4306 4316 4326 4335 440 64345 64855 64365 64375 64385 64395 64404 64414 64424 64434 1 4444 4454 4464 4473 4488 4498 4508 4513 4523 4532 2 ■ 4542 4552 4562 4572 4582 4591 4601 4611 4621 4631 3 4640 4650 4660 4670 4680 4689 4699 4709 4719 4729 4 4738 4748 4758 4768 4777 4787 4797 4807 4816 4826 5 4836 4846 4856 4865 4875 4885 4895 4904 4914 4924 6 4933 4943 4953 4963 4972 4982 4902 5002 5011 5021 7 5031 5040 5050 5000 5070 5079 5089 5099 5108 5118 8 5128 5137 5147 5157 5167 5170 5186 5196 5205 5215 9 5225 5234 5244 5254 5263 5273 5283 6292 5302 5312 450 fi.'i.qsn fi.f;.qai fij-i.qil fi.'^.q.'^n anp-RO fi.l.'.fiO R.-invo 65389 65398 65408 498 TABLE VI.— LOGARITHMS OF NUMBERS. . N O 1 2 3 4 5 6 7 8 9] 450 65321 65331 65341 65350 65360 65369 65379 65389 65398 65408 I 1 5418 5427 5437 5447 6456 5466 5475 5485 5495 5504 2 5514 5523 5533 5543 5552 5562 5571 5581 5591 5600 3 5610 5619 5629 5639 5648 5658 5667 5677 5686 5696 4 5706 5715 5725 5734 5744 6753 5763 5772 5782 6792 6 5801 5811 5820 5830 5839 6849 5858 5868 5877 5887 6 5896 5906 5916 5925 5935 5944 5954 5963 5973 5982 7 5992 6001 6011 6020 6030 6039 6049 6058 6068 6077 8 6087 6096 6106 6115 6124 6134 6143 6153 6162 6172 9 6181 .6191 6200 6210 6219 6229 6238 6247 6257 6266 460 66276 66285 66295 66304 66314 66323 66332 66842 66351 66361 1 1 6370 6380 6389 6398 6408 6417 6427 6436 6445 6455 2 6464 6474 6483 6492 6502 6511 6521 6530 6639 6549 3 6558 6567 6577 6586 6596 6605 6614 6624 6633 6642 4 6652 6661 6671 6680 6689 6699 6708 6717 6727 6736 5 6745 6755 6764 6773 6783 6792 6801 6811 6820 6829 6 6839 6848 6857 6867 6876 6885 6894 6904 6913 6922 7 6932 6941 6950 6960 6969 6978 6987 6997 7006 7015 8 7025 7034 7043 7052 7062 7071 7080 7089 7099 7108 9 7117 7127 7136 7145 7154 7l64 7173 7182 7191 7201 470 67210 67219 67228 67237 67247 67256 67265 67274 67284 67293 | 1 7302 7311 7321 7330 7339 7348 7357 7367 7376 7385 2 7394 7403 7413 7422 7431 7440 7449 7459 7468 7477 3 7486 7495 7504 7514 7523 7532 7541 7550 7560 7569 4 7578 7587 7596 7606 7614 7624 7633 7642 7651 7660 5 7669 7679 7688 7697 7706 7715 7724 7733 7742 7752 6 7761 7770 7779 7788 7797 7806 7815 7825 7834 7843 7 7852 7861 7870 7879 7888 7897 7906 7916 7925 7934 8 7943 7952 7961 7970 7979 7988 7997 8006 8015 8024 9 8034 8043 8052 8061 8070 8079 8088 8097 8106 8115 480 68124 68133 68142 68151 68160 68169 68178 68187 68196 68206 1 8215 8224 8233 8242 8251 8260 8269 8278 8287 8296 2 8305 8314 8323 8332 8341 8350 8359 8368 8377 8386 3 8395 8404 8413 8422 8431 8440 8449 8458 8467 8476 4 8485 8494 8502 8511 8520 8529 8538 8547 8556 8565 S 8574 8583 8592 8601 8610 8619 8628 8637 8646 8655 6 8664 8673 8681 8690 8699 8708 8717 8726 8735 8744 7 8753 8762 8771 8780 8789 8797 8806 8815 8824 8833 8 8842 8851 8860 8869 8878 8886 8895 8904 8913 8922 9 8931 8940 8949 8958 8966 8976 8984 8993 9002 9011 490 69020 69028 69037 69046 69055 69064 69073 69082 69090 69099 | 1 9108 9117 9126 9135 9144 9152 9161 9170 9179 9188 2 9197 9205 9214 9223 9232 9241 9249 9258 9267 9276 3 9285 9294 9302 9311 9320 9329 9338 9346 9355 9364 4 9373 9381 9390 9399 9408 9417 9426 9434 9443 9452 5 9461 9469 9478 9487 9496 9504 9513 9522 9531 9539 6 9548 9557 9566 9574 9583 9592 9601 9609 9618 9627 7 9636 9644 9653 9662 9071 9679 9688 9697 9705 .9714 8 9723 9732 9740 9749 9758 9767 9775 9784 9793 9801 9 9810 9819 9827 9836 9845 9854 9862 9871 988a 9888 500 69897 69906 «0014 69923 69932 69940 69949 69958 69966 69975 TABLE VI.— LOGARITHMS OF NUMBERS. 499 N 0123456789 600 69897 69906 69914 69923 69932 69940 69949 69958 69966 69975 1 9984 9992 70001 70010 70018 70027 70036 70044 70053 70062 2 70070 70079 0088 0096 OlOS 0114 0122 0131 0140 0148 3 0157 0165 0174 0183 0191 0200 0209 0217 0226 0234 4 0243 0252 0260 0269 0278 0286 029S 0303 0312 0321 5 0329 0338 0346 0355 0364 0372 0381 0389 0398 0406 6 0415 0424 0432 0441 0449 0458 0467 0475 0484 0492 7 0501 0509 0518 0526 0535 0544 0552 0561 0569 0578 8 0586 0595 0603 0612 0621 0629 0638 0646 0655 0663 9 0672 0680 0689 0697 0706 0714 0723 0731 0740 0749 610 70757 70766 70774 70783 70791 70800 70808 70817 70825 70834 1 0842 0851 0859 0868 0876 0885 0893 0902 0910 0919 2 0927 0935 0944 0952 0961 0969 0978 0986 0995 1003 3 1012 1020 1029 1037 1046 1054 1063 1071 1079 1088 4 1096 1105 1113 1122 1130 1139 1147 1155 1164 1172 5 1181 1189 1198 1206 1214 1223 1231 1240 1248 1257 6 1265 1273 1282 1290 1299 1307 1315 1324 1332 1341 7 1349 1357 1366 1374 1383 1391 1399 1408 1416 1425 8 1433 1441 1450 1458 1466 1475 1483 1492 1500 1508 9 1517 1525 1533 1542 1550 1559 1567 1575 1584 1592 620 71600 71609 71617 71625 71634 71642 71650 71659 71667 71675 1 1684 1692 1700 1709 1717 1725 1734 1742 1750 1759 2 1767 1775 1784 1792 1800 1809 1817 1825 1834 1842 3 1850 1858 1867 1875 1883 1892 1900 1908 1917 1925 4 1933 1941 1950 1958 1966 1975 1983 1991 1999 2008 6 2016 2024 2032 2041 2049 2057 2066 2074 2082 2090 6 2099 2107 2115 2123 2132' 2140 2148 2156 2165 2173 7 2181 2189 2198 2206 2214 2222 2230 2239 2247 2255 8 2263 2272 2280 2288 2296 2304 2313 2321 2329 2337 9 2346 2354 2362 2370 2378 2387 2395 2403 2411 2419 630 72428 72436 72444 72452 72460 72469 72477 72485 72493 72501 1 2509 2518 2526 2534 2542 2550 2558 2567 2575 2583 2 2591 2599 2607 2616 2624 2632 2640 2648 2656 2665 3 2673 2681 2689 2697 2705 2713 2722 2730 2738 2746 4 2754 2762 2770 2779 2787 2795 2803 2811 2819 2827 6 2835 2843 2852 2860 2868 2876 2884 2892 2900 2908 6 2916 2925 2933 2941 2949 2957 2965 2973 2981 2989 7 2997 3006 3014 3022 3030 3038 3046 3054 3062 3070 8 3078 3086 3094 3102 3111 3119 3127 3135 3143 3151 9 3159 3167 3175 3183 3191 3199 3207 3215 3223 3231 640 73239 73247 73255 73263 73272 73280 73288 73296 73304 73312 1 3320 3328 3336 3344 3352 3360 3368 3376 3384 3392 2 3400 3408 3416 3424 3432 3440 3448 3456 3464 3472 3 3480 3488 3496 3504 3512 3520 3528 3536 3544 3552 4 3560 3568 3576 3584 3592 3600 3608 3616 3624 3632 5 3640 3648 3656 3664 3672 3679 3687 3695 3703 3711 6 3719 3727 3735 3743 3751 3759 3767 3775 3783 3791 .7 3799 3807 3815 3823 3830 3838 3846 3854 3862 3870 •8 3878 3886 3894 3902 3910 3918 3926 3933 3941 3949 9 3957 3965 3973 3981 3989 3997 4005 4013 4020 4028 Kun 74nsfi 74044 740.12 74060 74068 74076 74084 74092 74099 74107 500 TABLE VI.— LOGARITHMS OF NUMBERS. N0123456789 650 74036 74044 74052 74060 74068 74076 74084 74092 74099 74107 1 .4115 4123 4131 4139 4147 415S 4162 4170 4178 4186 2 4194 4202 4210 4218 4225 4233 4241 4249 4257 4265 3 4273 4280 4288 4296 4304 4312 4320 4327 4335 4343 4 4351 4359 4367 4374 4382 4390 4398 4406 4414 4421 6 4429 4437 4445 4453 4461 4468 4476 4484 4492 4500 6 4507 4515 4523 4531 4539 4547 4554 4562 4570 4578 7 4586 4593 4601 4609 4617 4624 4632 4640 4648 4656 8 4663 4671 4679 4687 4695 4702 4710 4718 4726 4733 9 4741 4749 4757 4764 4772 4780 4788 4796 4803 4811 560 74819 74827 74834 74842 74850 74858 74865 74873 74881 74889 1 4896 4904 4912 4920 4927 4935 4943 4950 4958 4966 2 4974 4981 4989 4997 5005 5012 5020 5028 5085 5043 3 5051 5059 5066 5074 5082 5089 5097 5105 5113 5120 4 5128 5136 5143 5151 5159 5166 5174 5182 5189 5197 5 5205 5213 5220 5228 5236 5243 5251 5259 5266 6274 6 5282 5289 5297 5305 5312 5320 5328 5335 6343 5351 7 5358 5366 5374 6381 5389 5397 6404 5412 5420 5427 8 5435 5442 5450 5458 5465 5473 5481 5488 5496 5504 9 5511 5519 6626 5534 5542 5549 5557 5565 5572 5580 570 75587 75595 75603 75610 75618 75626 75633 75641 75648 75656 1 5664 5671 5679 5686 5694 5702 5709 5717 5724 5732 2 5740 5747 5755 5762 5770 6778 5785 5793 5800 5808 3 5815 6823 5831 5838 5846 5853 5861 5868 6876 5884 4 5891 6899 5906 5914 5921 6929 5937 5944 5952 6959 6 5967 5974 5982 6989 . 5997 6005 6012 6020 6027 6035 6 6042 6050 6057 6065 6072 6080 6087 6095 6103 6110 7 6118 6125 6133 6140 6148 6165 6163 6170 6178 6185 8 6193 6200 6208 6215 6223 6230 6238 6245 6253 6260 9 6268 6275 6283 6290 6298 6305 6313 6320 6328 6335 580 76343 76350 76358 76365 76373 76380 76388 76395 76403 76410 1 6418 6425 6433 6440 6448 6455 6462 6470 6477 6485 2 6492 6500 6507 6515 6522 6530 6537 6645 6552 6559 3 6567 6574 6582 6589 6597 6604 6612 6619 6626 6634 4 6641 6649 6656 6664 6671 6678 6686 6693 6701 6708 5 6716 6723 6730 6738 6745 6753 6760 6768 6775 6782 6 6790 6797 6805 6812 6819 6827 6834 6842 .6849 6856 7 6864 6871 6879 6886 6893 6901 6908 6916 6923 6930 8 6938 6945 6953 6960 6967 6975 6982 6989 6997 7004 9 7012 7019 7026 7034 7041 7048 7056 7063 7070 7078 690 77085 77093 77100 77107 77115 77122 77129 77137 77144 77151 1 7159 7166 7173 7181 7188 7195 7203 7210 7217 7225 2 7232 7240 7247 7264 7262 7269 7276 7283 7291 7298 3 7305 7313 7320 7327 7335 7342 7349 7357 7364 7371 4 7379 7386 7393 7401 7408 7415 7422 7430 7437 7444 5 7452 ^7459 7466 7474 7481 7488 7495 7503 7510 7517 6 7525 7532 7539 7546 7554 7561 7568 7576 7583 7590 7 7597 7605 7612 7619 7627 7634 7641 7648 7656 7663 8 7670 7677 7685 7692 7699 7706 7714 7721 7728 7785 9 7743 7750 7757 7764 7772 7779 7786^ 7793 7801 7808 600 77816 77822 77830 77837 77844 77851 77859 77866 77873 77880 TABLE VI.-LO(iARITHMS OP NUMBERS. 501 N 0123456789 600 77815 77822 77830 77837 77844 77851 77859 77866 77873 77880 1 7887 7895 7902 7909 7916 7924 7931 7938 7945 7952 2 7960 7967 7974 7981 7988 7996 8003 8010 8017 8025 3 8032 8039 8046 8053 8061 8068 8075 8082 8089 8097 4 8104- 8111 8118 8125 8132 8140 8147 8154 8161 8168 6 8176 8183 8190 8197 8204 8211 8219 8226 8233 8240 6 8247 8254 8262 8269 8276 8283 8290 8297 830i 8312 t 8319 8326 8333 8340 8347 8355 8362 8369 8376 8383 8 8390 8398 8405 8412 8419 8426 8433 8440 8447 845S 9 8462 8469 8476 8483 8490 8497 8504 8512 8619 8526 610 78533 78540 78547 78554 78561 78569 78576 78588 78590 78597 1 8604 8611 8618 8625 8633 8640 8647 8654 8661 8668 2 8675 8682 8689 8606 8704 8711 8718 8725 8732 8739 3 8746 8753 8760 8767 8774 8781 8789 8796 8803 8810 4 8817 8824 8831 8838 8845 8852 8859 8866 8873 8880 6 8888 8895 8902 8909 8916 8923 8930 8937 8944 8951 6 8958 8965 8972 8979 8986 8993 9000 9007 9014 9021 7 9029 9036 9043 9050 9057 9064 9071 9078 9085 9092 8 9099 9106 9113 9120 9127 9134 9141 9148 9155 9162 9 9169 9176 9183 9190 9197 9204 9211 9218 9225 9232 620 79239 79246 79253 79260 79267 79274 79281 79288 79295 79302 1 9309 9316 9323 9330 9337 9344 9351 9358 9365 9372 2 9379 9386 9393 9400 9407 9414 9421 9428 9435 9442 3 9449 9456 9463 9470 9477 9484 9491 9498 9505 9511 4 9518 9525 9532 9539 9546 9553 9560 9567 9574 9581 6 9588 9595 9602 9609 9616 9623 9630 9637 9644 9650 6 9657 9664 9671 9678 9685 9692 9699 9706 9713 9720 7 9727 9734 9741 9748 9754 9761 9768 9775 9782 9789 8 9796 9803 9810 9817 9824 9831 9837 9844 9851 9858 9 9865 9872 9879 9886 9893 9900 9906 9913 9920 9927 630 79934 79941 79948 79955 79962 79969 79975 79982 79989 79996 1 80003 80010 80017 80024 80030 80037 80044 80051 80058 80065 2 0072 0079 0085 0092 0099 0106 0113 0120 0127 0134 3 0140 0147 0154 0161 0168 0175 0182 0188 0195 0202 4 0209 0216 0223 0229 0236 0243 0250 0257 0264 0271 5 0277 0284 0291 0298 0305 0312 0318 0325 0332 0339. 6 0346 0353 0359 0366 0373 0380 0387 0393 0400 0407 7 0414 0421 0428 0434 0441 0448 0455 0462 0468 0475 8 0482 0489 0496 0502 0509 0516 0523 0530 0536 0543 9 0550 0557 0564 0570 0577 0584 0591 0598 0604 0611 610 80618 80625 80632 80638 80645 80652 80659 80665 80672 80679 1 0686 0693 0699 0706 0713 0720 0726 0733 0740 0747 2 0754 0760 0767 0774 0781 0787 0794 0801 0808 0814 3 0821 0828 0835 0841 0848 0855 0862 0868 0875 0882 4 0889 0895 0902 0909 0916 0922 0929 0936 0943 0949 6 0956 0963 0969 0976 0983 0990 0996 1003 1010 1017 S 1023 1030 1037 1043 1050 1057 1064 1070 1077 1084 7 1090 1097 1104 1111 1117 1124 1131 1137 1144 1151 8 1158 1164 1171 1178 1184 1191 1198 1204 1211 1218 9 1224 1231 1238 1245 1251 1258 1265 1271 1278 1285 (iRn fii9Ql 819.QB Bisn? 81311 81318 81325 81331 81338 81345 81351 502 TABLE VI.— LOGARITHMS DP NUIVTREES. N 0123456789 650 81291 81298 8130i 81311 81318 8132S 81331 81338 81345 81351 1 1358 1365 1371 1378 1385 1391 1398 1405 1411 1418 2 1425 1431 1438 1445 1451 1458 1465 1471 1478 1485 3 1491 1498 1505 1511 1518 1525 1531 1538 1544 1551 4 1558 1564 1571 1578 1584 1591 1598 1604 1611 1617 S 1624 1631 1637 1644 1651 1657 1664 1671 1677 1684 6 1690 1697 1704 1710 1717 1723 1730 1737 1743 1750 7 1757 1763 1770 1776 1783 1790 1796 1803 1809 1816 8 1823 1829 1836 1842 1849 1856 1862 1869 1875 1882 9 1889 1895 1902 1908 1915 1921 1928 1935 1941 1948 660 81954 81961 81968 81974 81981 81987 81994 82000 82007 82014 1 2020 2027 2033 2040 2046 2053 2060 2066 2073 2079 2 2086 2092 2099 2105 2112 2119 2125 2132 2138 2145 3 2151 2158 2164 2171 2178 2184 2191 2197 2204 2210 4 2217 2223 2230 2236 2243 2249 2256 2263 2269 2276 6 2282 2289 2295 2302 2308 2315 2321 2328 2334 2341 6 2347 2354 2360 2367 2373 2380 2387 2393 2400 2406 7 2413 2419 2426 2432 2439 2445 2452 2458 2465 2471 8 2478 2484 2491 2497 2504 2510 2517 2523 2530 2536 9 2543 2549 2556 2562 2569 2575 2582 2588 2595 2601 670 82607 82614 82620 82627 82633 82640 82646 82653 82659 82666 1 2672 2679 2685 2692 2698 2705 2711 2718 2724 2730 2 2737 2743 2750 2756 2763 2769 2776 2782 2789 2795 3 2802 2808 2814 2821 2827 2834 2840 2847 2853 2860 4 2866 2872 2879 2885 2892 2898 2905 2911 2918 2924 5 2930 2937 2943 2950 2956 2963 2969 2975 2982 2988 6 2995 3001 3008 3014 3020 3027 3033 3040 3046 3052 7 3059 3065 3072 3078 3085 3091 3097 3104 3110 3117 8 3123 3129 3136 3142 3149 3155 3161 3168 3174 3181 9 3187 3193 3200 3206 3213 3219 3225 3232 3238 3245 680 83251 83257 83264 83270 83276 83283 83289 83296 83302 83308 1 3315 3321 3327 3334 3340 3347 3353 3359 3366 3372 2 3378 3385 3391 3398 3404 3410 3417 3423 3429 3436 3 3442 3448 3455 3461 3467 3474 3480 3487 3493 3499 4 3506 3512 3518 3525 3531 3537 3544 3550 3556 3563 5 3569 3575 3582 3588 3594 3601 3607 3613 3620 3626 6 3632 3639 3645 3651 3658 3664 3670 3677 3683 3689 7 3696 3702 3708 3715 3721 3727 3734 3740 3746 3753 8 3759 3765 3771 3778 3784 3790 3797 3803 3809 3816 9 3822 3828 3835 3841 3847 3853 3860 3866 3872 3879 690 83885 83891 83897 83904 83910 83916 83923 83929 83935 83942 1 3948 3954 3960 3967 3973 3979 3985 3992 3998 4004 2 4011 4017 4023 4029 4036 4042 4048 4055 4061 4067 3 4073 4080 4086 4092 4098 4105 4111 4117 4123 4130 4 4136 4142 4148 4165 4161 4167 4173 4180 4186 4192 5 4198 4205 4211 4217 4223 4230 4236 4242 4248 4255 6 4261 4267 4273 4280 4286 4292 4298 4305 4311 4317 7 4323 4330 4336 4342 4348 4354 4361 4367 4373 4379 8 4386 4392 4398 4404 4410 4417 4423 4429 4435 4442 9 4448 4454 4460 4466 4473 4479 4485 4491 4497 4504 700 84610 84616 84522 84528 84535 84541 84547 84553 84559 84566 TABLE VI.— LOGARITHMS OF NUMBERS. 503 N 0123466789 700 84510 84516 84522 84528 8453S 84541 84547 84553 84559 84566 1 4572 4578 4584 4590 4597 4603 4609 4615 4621 4628 2 4634 4640 4646 4652 4(558 4665 4671 4677 4683 4689 3 4696 4702 4708 4714 4720 4720 4733 4739 4745 4751 4 4757 4763 4770 4776 4782 4788 4794 4800 4807 4813 6 4819 4825 4831 4837 4844 4850 -4856 4862 4868 4874 6 4880 4887 4893 4899 4905 4911 4917 4924 4930 4936 7 4942 4948 4954 4960 4967 4973 4979 4985 4991 4997 8 5003 5009 5016 5022 5028 5034 5040 5046 5052 5058 9 5065 5071 5077 5083 5089 5095 5101 5107 5114 5120 710 85126 85132 85138 85144 85150 85156 85163 85169 85175 85181 1 5187 5193 6199 5205 5211 5217 5224 5230 5236 5242 2 5248 5254 5260 5266 5272 5278 5285 5291 5297 5303 3 5309 5315 5321 5327 5333 5339 5345 5352 5358 5364 4 5370 5370 5382 5388 5394 5400 5406 5412 5418 5425 6 5431 5437 5443 5449 5455 5461 5467 5473 5479 5485 6 5491 5497 5503 5509 5616 5522 5528 5534 5540 5546 7 5652 5558 6504 5570 5676 5682 5688 6594 5600 5606 8 .5612 5618 5625 5631 5637 6643 5649 5655 5661 5667 9 6673 5679 5685 6691 6697 5703 5709 5715 5721 5727 720 85733 85739 85745 86751 85757 85763 86769 85775 85781 85788 1 5794 6800 5806 5812 6818 6824 5830 5836 5842 5848 2 5864 5860 5866 5872 5878 5884 5890 5896 5902 5908 3 5914 5920 5926 5932 5938 5944 5950 5956 6962 6968 4 6974 5980 5986 6992 5998 6004 6010 6016 6022 6028 5 6034 6040 6046 6052 6058 6064 6070 6076 6082 6088 6 6094 6100 6106 6112 6118 6124 6130 6136 6141 6147 7. 6153 6169 6166 6171 6177 6183 6189 6196 6201 6207 8 6213 6219 6225 6231 6237 6243 6249 6265 6261 6267 9 6273 6279 6285 6291 6297 6303 6308 6314 6320 6326 730 86332 86338 86344 86360 86356 86362 86368 86374 86380 86386 1 6392 6398 6404 6410 6415 6421 6427 6433 6439 6445 2 6451 6457 6463 6469 6475 6481 6487 6493 6499 6504 3 6510 6516 6522 6528 6534 6540 6546 6662 6658 6564 4 6570 6576 6581 6587 6693 6599 6605 6611 6617 6623 5 6629 6635 6641 6646 6662 6658 6664 6670 6676 6682 6 6688 6694 6700 6706 6711 6717 6723 6729 6735 6741 7 6747 6753 6759 6764 6770 6776 6782 6788 6^94 6800 8 6806 6812 6817 6823 6829 6835 6841 6847 6853 6859 9 6864 6870 6876 6882 6888 6894 6900 6906 6911 6917 740 86923 86929 86935 86941 86947 86953 86958 86964 86970 86976 1 6982 6988 6994 6999 7005 7011 7017 7023 7029 7035 2 7040 7046 7052 7058 7064 7070 7076 7081 7087 7093 3 7099 7105 7111 7116 7122 7128 7134 7140 7146 7151 4 7157 7163 7169 7175 7181 7186 7192 7198 7204 7210 5 7216 7221 7227 7233 7239 7245 7251 7256 7262 7268 6 7274 7280 7286 7291 7297 7303 7309 7315 7320 7326 7 7332 7338 7344 7349 7355 7361 7367 7373 7379 7384 8 7390 7396 7402 7408 7413 7419 7425 7431 7437 7442 9 7448 7464 7460 7466 7471 7477 7483 7489 7495 7500 760 87606 87512 87518 87523 87529 87535 87541 87547 87552 87558 504 TABLE VI.— LOGARITHMS OF NUMBERS. N 1334:56789 750 87506 87512 87518 87523 87529 87535 87541 87547 87552 87558 1 7564 7570 7576 7581 7587 7593 7599 7604 7610 7616 2 7622 7628 7633 7639 7645 7651 7656 7662 7668 7674 3 7679 7685 7691 7697 7703 7708 7714 7720 7726 7731 4 7737 7743 7749 7754 7760 7766 7772 7777 7783 7789 5 7795 7800 7806 7812 7818 7823 7829 7835 7841 7846 6 7852 7858 7864 7869 7875 7881 7887 7892 7898 7904 7 7910 7915 7921 7927 7933 7938 7944 7950 7955 7961 8 7967 7973 7978 7984 7990 7996 8001 8007 8013 8018 9 8024 8030 8036 8041 8047 8053 8058 8064 8070 8076 760 88081 88087 88093 88098 88104 88110 88116 88121 88127 88133 1 8138 8144 8150 8156 8161 8167 8173 8178 8184 8190 2 8195 8201 8207 8213 8218 8224 8230 8235 8241 8247 3 8252 8258 8264 8270 8275 8281 8287 8292 8298 8304 4 8309 8315 8321 8326 8332 8338 8343 8349 8355 8360 5 8366 8372 8377 8383 .8389 8395 8400 8406 8412 8417 6 8423 8429 8434 8440 8446 8451 8457 8463 8468 8474 7 8480 8485 8491 8497 8502 8508 8513 8519 8525 8530 8 8536 8542 8547 8553 8559 8564 8570 8576 8581 8587 9 8593 8598 8604 8610 8615 8621 8627 8632 8638 8643 7V0 88649 88655 88660 88666 88672 88677 88683 88689 88694 88700 1 8705 8711 8717 8722 8728 8734 8739 8745 8750 8756 2 8762 8767 8773 8779 8784 8790 8795 8801 8807 8812 3 8818 8824 8829 8835 8840 8846 8852 8857 8863 8868 4 8874 8880 8885 8891 8897 8902 8908 8913 8919 8925 5 8930 8936 8941 8947 8953 8958 8964 8969 8975 8981 6 8986 8902 8997 9003 9009 9014 9020 9025 9031 9037 7 9042 9048 9053 9059 9064 9070 9076 9081 9087 9092 8 9098 9104 9109 9115 9120 9126 9131 9137 9143 9148 9 9154 9159 9165 9170 9176 9182 9187 9193 9198 9204 780 89209 89215 89221 89226 89232 89237 89243 89248 89254 89260 1 9265 9271 9276 9282 9287 9293 9298 9304 9310 9315 2 9321 9326 9332 9337 9343 9348 9354 9360 9865 9371 3 9376 9382 9387 9393 9398 9404 9409 9415 9421 9426 4 9432 9437 9443 9448 9454 9459 9465 9470 9476 9481 5 9487 9492 9498 9504 9509 9515 9520 9526 9531 9537 6 9542 9548 9553 9559 9564 9570 9575 9581 9586 9592 7 9597 9603 9609 9614 9620 9625 9631 9636 9642 9647 8 9653 9658 9664 9669 9675 9680 9686 9691 9697 9702 9 9708 9713 9719 9724 9730 9735 9741 9746 9752 9757 790 89763 89768 89774 89779 89785 89790 89796 89801 89807 89812 1 9818 9823 9829 9834 9840 9845 9851 9856 9862 9867 2 9873 9878 9883 9889 9894 9900 9905 9911 9916 9922 3 9927 9933 9938 9944 9949 9955 9960 9966 9971 9977 4 9982 9988 9993 9998 90004 90009 90015 90020 90026 90031 5 90037 90042 90048 90053 0059 0064 0069 0075 0080 0086 6 0091 0097 0102 0108 0113 0119 0124 0129 0135 0140 7 0146 0151 0157 0162 0168 0173 0179 0184 0189 0195 8 0200 0206 0211 0217 0222 0227 0233 0238 0244 0249 9 0255 0260 0266 0271 0276 0282 0287 0293 0298 0304 SOO 90309 90314 90320 90325 90331 90336 90342 90347 90352 90358 TABLE VI.— LOGARITHMS OF NUMBERS. 505 N 0123456789 800 1 2 3 4 5 6 7 8 9 810 1 2 3 4 5 6 7 8 9 820 1 2 3 4 5 6 7 8 9 830 1 2 3 4 5 6 7 8 9 810 1 2 3 4 6 6 7 8 9 8P-" 90309 90314 90320 90325 90331 90336 90342 90347 90352 90358 0363 0369 0374 0380 0385 0390 0396 0401 0407 0412 0417 0423 0428 0434 0439 044S 0450 0455 0461 0466 0472 0477 0482 0488 0493 0499 0504 0609 0515 0520 0526 0531 0536 0542 0547 0553 0558 0563 0569 0574 0580 0585 0590 0596 0601 0607 0612 0617 0623 0628 0634 0639 0644 0650 0655 0660 0666 0671 0677 0682 0687 0693 0698 0703 0709 0714 0720 0725 0730 0736 0741 0747 0752 0757 0763 0768 0773 0779 0784 0789 0795 0800 0806 0811 0816 0822 0827 0832 0838 0843 90849 90854 90859 90865 90870 90875 90881 90886 90891 90897 0902 0907 0913 0918 0924 0929 0934 0940 0945 0950 0956 0961 0966 0972 0977 0982 0988 0993 0998 1004 1009 1014 1020 1025 1030 1036 1041 1046 1052 1057 1062 1068 1073 1078 1084 1089 1094 1100 1105 1110 1116 1121 1126 1132 1137 1142 1148 1153 1158 1164 1169 1174 1180 1185 1190 1196 1201 1206 1212 1217 1222 1228 1233 1238 1243 1249 1254 1259 1265 1270 1275 1281 1286 1291 1297 1302 1307 1312 1318 1323 1328 1334 1339 1344 1350 1355 1360 1365 1371 1376 91381 91387 91392 91397 91403 91408 91413 91418 91424 91429 1434 1440 1445 1450 1455 1461 1466 1471 1477 1482 1487 1492 1498 1503 1508 1514 1519 1524 1529 1535 1540 1545 1551 1556 1561 1566 1572 1577 1582 1587 1593 1598 1603 1609 1614 1619 1624 1630 1635 1640 1645 1651 1656 1661 1666 1672 1677 1682 1687 1693 1698 1703 1709 1714 1719 1724 1730 1735 1740 1745 1751 1756 1761 1766 1772 1777 1782 1787 1793 1798 1803 1808 1814 1819 1824 1829 1834 1840 1845 1850 1855 1861 1866 1871 1876 1882 1887 1892 1897 1903 91908 91913 91918 91924 91929 91934 91939 91944 91950 91955 1960 1965 1971 1976 1981 1986 1991 1997 2002 2007 2012 2018 2023 2028 2033 2038 2044 2049 2054 2059 2065 2070 2075 2080 2085 2091 2096 2101 2106 2111 2117 2122 2127 2132 2137 2143 2148 2153 2158 2163 2169 2174 2179 2184 2189 2195 2200 2205 2210 2215 2221 2226 2231 2236 2241 2247 2252 2257 2262 2267 ' 2273 2278 2283 2288 2293 2298 2304 2309 2314 2319 2324 2330 2335 2340 2345 2350 2355 2361 2366 2371 2376 2381 2887 2392 2397 2402 2407 2412 2418 2423 92428 92433 92438 92443 92449 92454 92459 92464 92469 92474 2480 2485 2490 2495 2500 2505 2511 2516 2521 2526 2531 2536 2542 2547 2552 2557 2562 2567 2572 2578 2583 2588 2593 2598 2603 2609 2614 2619 2624 2629 2634 2639 2645 2650 2655 2660 2665 2670 2675 2681 2686 2691 2696 2701 2706 2711 2716 2722 2727 2732 2737 2742 2747 2752 2758 2763 2768 2773 2778 2783 2788 2793 2799 2804 2809 2814 2819 2824 2829 2834 2840 2845 2850 2855 2860 2865 2870 2875 2881 2886 2891 2896 2901 2906 2911 2916 2921 2927 2932 2937 QoQio Qoo/t? OOQK2 gooK? Q2Q«2 92967 92973 92978 92983 92988 506 TABLE VI.— LOGARITHMS OF NUMBERS. N 0123456789 850 92942 92947 92952 92957 92962 92967 92973 92978 92983 92988 1 2993 2998 3003 3008 3013 3018 3024 3029 3034 3039 2 3044 3049 3054 3059 3064 3069 3075 3080 3085 3090 8 3095 3100 3105 3110 3115 3120 3125 3131 3136 3141 i 3146 3151 3156 3161 3166 3171 3176 3181 3186 3192 6 3197 3202 3207 3212 3217 3222 3227 3232 3237 3242 6 3247 3252 3258 3263 3268 3273 3278 3283 3288 3293 7 3298 3303 3308 3313 3318 3323 3328 3334 3339 3344 8 3349 3354 3359 3364 3369 3374 3379 3884 3389 3394 9 3399 3404 3409 3414 3420 3425 3430 3435 3440 3445 860 93450 93455 93460 93465 93470 93475 93480 93485 93490 93495 1 3500 3505 3510 3515 3520 3526 3531 3536 3541 3546 2 3551 3556 3561 3566 3571 3576 3581 3586 3591 3596 3 3601 3606 3611 3616 3621 3626 3631 3636 3641 3646 4 3651 3656 3661 3666 3671 3676 3682 3687 3692 3697 5 3702 3707 3712 3717 3722 3727 3732 3737 3742 3747 8 3762 3757 3762 3767 3772 3777 3782 3787 3792 3797 7 3802 3807 3812 3817 3822 3827 3832 3837 3842 3847 8 3852 3857 3862 3867 3872 3877 3882 3887 3892 3897 9 3902 3907 3912 3917 3922 3927 3932 3937 3942 3947 870 93952 93967 93962 93967 93972 93977 93982 93987 93992 93997 1 4002 4007 4012 4017 4022 4027 4032 4037 4042 4047 2 4052 4067 4062 4067 4072 4077 4082 4086 4091 4096 3 4101 4106 4111 4116 4121 4126 4131 4136 4141 4146 4 4151 4156 4161 4166 4171 4176 4181 4186 4191 4196 e 4201 4206 4211 .4216 4221 4226 4231 4236 4240 4245 6 4260 4255 4260 4265 4270 4275 4280 4286 4290 4295 7 4300 4305 4310 4315 4320 4325 4330 4335 4340 434S 8 4349 4354 4359 4364 4369 4374 4379 4384 4389 4394 9 4399 4404 4409 4414 4419 4424 4429 4433 4438 4443 880 94448 94453 94458 94463 94468 94473 94478 94483 94488 94493 1 4498 4503 4507 4512 4517 4522 4527 4532 4537 4542 2 4547 4552 4557 4562 4567 4571 4576 4581 4586 4591 3 4596 4601 4606 4611 4616 4621 4626 4630 4635 4640 4 4645 4650 4655 4660 4665 4670 4675 4680 4685 4689 6 4694 4699 4704 4709 4714 4719 4724 4729 4734 4738 6 4743 4748 4753 4758 4763 4768 4773 4778 4783 4787 7 4792 4797 4802 4807 4812 4817 4822 4827 4832 4836 8 4841 4846 4851 4856 4861 4866 4871 4876 4880 4885 9 4890 4895 4900 4905 4910 4915 4919 4924 4929 4934 890 94939 94944 94949 94954 94969 94963 94968 94973 94978 94983 1 4988 4993 4998 5002 5007 5012 5017 5022 5027 5032 2 6036 6041 6046 5061 6056 6061 5066 5071 5076 6080 3 5085 5090 5095 6100 6105 6109 6114 5119 5124 6129 4 5134 5139 5143 5148 5153 5158 5163 6168 6173 6177 6 5182 6187 6192 5197 5202 5207 6211 6216 5221 5226 6 5231 5236 6240 6245 5250 5266 5260 5265 5270 6274 7 .5279 6284 6289 6294 5299 5303 5308 5313 5318 5323 8 6328 6332 5337 6342 5347 5352 5357 6361 5366 6371 9 5376 5381 5386 5390 5395 5400 5405 5410 5415 5419 900 95424 95429 95434 95439 95444 95448 95453 95458 95463 95468 TABLE VI.— LOGABITHMS OF NUMBERS. 507 N 0123456789 900 95424 96429 95434 95439 95444 95448 95453 95458 95463 95468 1 5472 5477 5482 5487 5492 5497 5501 5506 6511 5516 2 5521 5525 5530 5535 5540 5545 6550 5554 5559 5504 3 5569 5574 5578 5583 5588 5593 5598 5602 . 5607 . 5612 4 5617 5622 6626 5631 6636 5641 5646 6660 5655 5660 6 5665 5670 5674 5679 5684 6689 5694 5698 5703 5708 6 6713 5718 5722 5727 5732 5737 6742 6746 5751 6756 7 5761 5766 5770 6775 5780 5785 5789 5794 5799 6804 8 6809 5813 5818 5823 6828 5832 5837 5842 5847 5852 9 5856 6861 6866 6871 5876 6880 6885 5890 689£ 5899 910 95904 95909 96914 95918 95923 95928 95933 95938 95942 95947 1 6962 6967 5961 6966 5971 6976 5980 5985 5990 5995 2 5999 6004 6009 6014 6019 6023 6028 6033 6038 6042 3 6047 6052 6057 6061 6066 6071 6076 6080 6085 6090 4 6095 6099 6104 6109 6114 6118 6123 6128 6133 6137 5 6142 6147 6152 6156 6161 6166 6171 6175 6180 '6185 6 6190 6194 6199 6204 6209 6213 6218 6223 6227 6232 7 6237 6242 6246 6261 6256 6261 6265 6270 6275 6280 8 6284 6289 6294 6298 6303 6308 6313 6317 6322 6327 9 6332 6336 6341 6346 6350 6355 6360 6365 6369 6374 920 96379 96384 96388 96393 96398 96402 96407 96412 96417 96421 1 6426 6431 6435 6440 6445 6450 6454 6469 6464 6468 2 6473 6478 6483 6487 6492 6497 6501 6506 6511 6515 3 6520 6525 6530 6534 6639 6544 6548 6663 6558 6562 4 6667 6572 6577 6581 6586 6591 6595 6600 6605 6609 5 6614 6619 6624 6628 6633 6638 6642 6647 6662 6656 6 6661 6666 6670 6675 6680 6685 6689 6694 6699 6703 7 6708 6713 6717 6722 6727 6731 6736 6741 6745 6750 8 6755 6759 6764 6769 6774 6778 6783 6788 6792 6797 9 6802 6806 6811 6816 6820 6825 6830 6834 6839 6844 930 96848 96853 96858 96862 96867 96872 96876 96881 96886 96890 1 6895 6900 6904 6909 6914 6918 6923 6928 6932 6937 2 6942 6946 6961 6956 6960 6965 6970 6974 6979 6984 3 6988 6993 6997 7002 7007 7011 7016 7021 7025 7030 4 7035 7039 7044 7049 7053 7058 7063 7067 7072 7077 5 7081 7086 7090 7095 7100 7104 7109 7114 7118 7123 6 . 7128 7132 7137 7142 7146 7151 7155 7160 7165 7169 7 7174 7179 7183 7188 7192 7197 7202 7206 7211 7216 8 7220 7225 7230 7234 7239 7243 7248 7253 7257 7262 9 7267 7271 7276 7280 7285 7290 7294 7299 7304 7308 940 97313 97317 97322 97327 97331 97336 97340 97345 97350 97354 1 7369 7364 7368 7373 7377 7382 7387 7391 7396 7400 2 7405 7410 7414 7419 7424 7428 7433 7437 7442 7447 3 7451 7466 7460 7465 7470 7474 7479 7483 7488 7493 4 7497 7502 7506 7511 7516 7520 7625 7629 7534 7539 6 7543 7548 7662 7567 7662 7566 7671 7575 7580 758S 6 7589 7594 7598 7603 7607 7612 7617 7621 7626 7630 7 7635 7640 7644 7649 7653 7658. 7663 7667 7672 7676 8 7681 7685 7690 7695 7699 7704 7708 7713 7717 7722 9 7727 7731 7736 7740 7745 7749 7754 7759 7763 7768 950 97772 97777 97782 97786 97791 97795 97800 97804 97809 97813 508 TABLE VI.— LOGARITHMS OF NUMBERS. X 01234567 89 950 97772 97777 97782 97786 97791 97795 97800 97804 97809 97813 1 7818 7823 7827 7832 7836 7841 7845 7850 785S 7859 2 7864 7868 7873 7877 7882 7886 7891 7896 7900 7905 3 7909 7914 7918 7923 7928 7932 7937 7941 7946 7950 4 7955 7959 7964 7968 7973 7978 7982 7987 7991 7996 5 8000 8005 8009 8014 8019 8023 8028 8032 8037 8041 6 8046 8050 8055 8059 8064 8008 8073 8078 8082 8087 7 8091 8096 8100 8105 8109 8114 8118 8123 8127 8132 8 8137 8141 8146 8150 8155 8169 8164 8168 8173 8177 9 8182 8186 8191 8195 8200 8204 8209 8214 8218 8223 960 98227 98232 98236 98241 98245 98250 98254 98259 98263 98268 1 8272 8277 8281 8286 8290 8295 8299 8304 8308 8313 2 8318 8322 8327 8331 8336 8340 8345 8349 8354 8358 3 8363 8367 8372 8376 8381 8385 8390 8394 8899 8403 4 8408 8412 8417 8421 8426 8430 8435 8439 8444 8448 5 8453 8457 8462 8466 8471 8475 8480 8484 8489 8493 6 8498 8502 8507 8511 8516 8520 8525 8529 8534 8538 7 8543 8547 8552 8556 8561 8565 8570 8574 8579 8583 8 8588 8592 8597 8601 8605 8610 8614 8619 8623 8628 9 8632 8637 8641 8646 8650 865S 8659 8664 8668 8673 970 98677 98682 98686 98691 98695 98700 98704 98709 98713 98717 1 8722 8726 8731 8735 8740 8744 8749 8753 8758 8762 2 8767 8771 8776 8780 8784 8789 8793 8798 8802 8807 3 8811 8816 8820 882i 8829 8834 8838 8843 8847 8851 4 8856 8860 8865 8869 8874 8878 8883 8887 8892 8896 6 8900 8905 8909 8914 8918 8923 8927 8932 8936 8941 6 8945 8949 8954 8958 8963 8967 8972 8976 8981 8985 7 8989 8994 8998 9003 9007 9012 9016 9021 9025 9029 8 9034 9038 9043 9047 9052 9056 9061 9065 9069 9074 9 9078 9083 9087 9092 9096 9100 9105 9109 9114 9118 980 99123 99127 99131 99136 99140 99145 99149 99154 99158 99162 1 9167 9171 9176 9180 9185 9189 9193 9198 9202 9207 2 9211 9216 9220 9224 9229 9233 9238 9242 9247 9251 3 9255 9260 9264 9269 9273 9277 9282 9286 9291 9295 4 9300 9304 9308 9313 9317 9322 9326 9330 9335 9339 5 9344 9348 9352 9357 9361 9366 9370 9374 9379 9383 6 9388 9392 9396 9401 9405 9410 9414 9419 9423 9427 7 9432 9436 9441 9445 9449 9454 9458 9463 9467 9471 8 9476 9480 9484 9489 9493 9498 9502 9506 9511 9515 9 9520 9524 9528 9533 9537 9542 9546 9550 9555 9559 990 99564 99568 99572 99577 99581 99585 99590 99594 99599 99603 1 9607 9612 9616 9621 9625 9629 9634 9638 9642 9647 2 9651 9656 9660 9664 9669 9673 9677 9682 9686 9691 3 9695 9699 9704 9708 9712 9717 9721 9726 9730 9734 4 9739 9743 9747 9752 9756 9760 9765 9769 9774 9778 5 9782 9787 9791 9795 9800 9804 9808 9813 9817 9822 « 9826 9830 9835 9839 9843 9848 9852 9856 9861 9865 7 9870 9874 9878 9883 9887 9891 9896 9900 9904 9909 8 9913 9917 9922 9926 9930 9935 9939 9944 9948 9962 9 9957 9961 9965 9970 9974 9978 9983 9987 9991 9996 1000 00000 00004 00009 00013 00017 00022 00026 00030 00035 00039 INDEX Abbott, Dr. Samuel W., 6, 235, 239, 432. Abscissae, 67. Accident statistics, 446. Accuracy, 26. of state censuses, 145. Adjusted, and gross death-rates, 246-249. death-rates, 240, 245. Adjustment of popxilation, 131. Age, census meaning, 166. composition, effect on death- rate, 231. distribution, 165. distribution of population, in Europe, 182. distribution of population in United States, 182, 184. groups, 170. of mother, infant mortality, 363. plotting, 73. unknown, 171. Ages of man, 221. American Experience Mortality Table, 426. Jom-nal of Public Health, 457. Public Health Association, 6. Analysis of death-rates, 299. Appeal to the eye, 60. Arithmetical increase, 131. Arithmetic probability paper, 395. Army diseases, 440, 441. Array, 39, 41. Averages, 49. Average age at death, 374. age of persons living, 372. Bacterial counts, 26. Batt, Dr. W. R., 452. Ben Day system, 96. BernouilU's Theorem, 398. Bertillon, Louis A., 6. Alphonse, 6. Jacques, 254. Binomial theorem, 381. Biometrics, 2. Birth-rates, 195. Germany and England, 66. relation to death-rates, 195. Birth registration, 109. advantages. 111. incomplete. 111. Births, standard certificate, 488 Blue prints, 96. Bolduan, Dr. Charles F., 443, 4£ Bones, diseases of, 265. Boston, adjusted death-rate, 24j age distribution of infa deaths, 353. causes of infant deaths, 356, 3i 360. infant-mortality, 348. infant mortality by age perio( 356. population density, 152. specific death-rates, 235. 609 510 INDEX Boston, stillbirths, 340. tuberculosis death-rate, 80. Bowley, correlation studies, 412. Bowleys,rulesforenumeration, 106. Brinton, W. C, 59. Brockton, analysis of death-rates, 303. specific death-rates, 305. Brooklyn, typhoid fever, 83. Bum, Vital Statistics Explained, 430. Cambridge, adjusted death-rate, 244, 246. age distribution of population, 172, 175, 176. causes of death, 65 deaths distributed by age, 242. diphtheria, 320. incomplete birth registration, 112. population, 138. population density, 152. population distributed by age, 243. specific death-rates, 233. tuberculosis statistics, 313. Cancer, specific death-rates, 335. statistics, 334. Causal relations, 402. Causality and correlation, 404. Causation, laws of, 405. and correlation, 420. Causes of death, 254. infants, 356, 359, 360. international list, 257. , Census date, 100. U. S., 100. Certificate of birth, standard, 489. of death, standard, 490. Chadwick, Edwin, 6. Chance, 379. element in sanitation, 394. natural phenomena, 382. Chapin, Dr. Charles V., 323, 324, 451. Charts, 93. Chicago, Municipal Tuberculosis Sanitorium, 413. Child mortality, 346. Childhood, early, diseases, 369. mortality, 368. proportionate mortality, 370. Children's Bureau, U. S. Dep't of Labor, 361, 365. Children, specific death-rates, 369. Chronological changes in death- rates, 234. changes in vital rates, 210. Cincinnati, population estimates, 140. Circulatory system, diseases of, 261. Cities, rate of growth, 137. Civil divisions, 103. Classes, 39, 40. Classification, 39. of diseases in 1850, 256. of population, 161. Coefficient of variation, 388, 389. Coin tossing, 379, 381. Collection of data, 17. Color in diagrams, 93. Component part diagrams, 95. Concealed classification, 238. Conception of frequency curve, 399. Connecticut, measles and grippe, 410. Consumption (see Tuberculosis). Corrected death-rates, 189, 239. Correlation, 402. INDEX 511 Correlation, and causality, 404. color of water and typhoid fever, 411. example, 410. Gabon's coefficient, 409. housing and tuberculosis, 413, methods, 407. mosquitoes and malaria, 419. secondary, 415. shown graphically, 411. spurious, 416. table, 413, 415. use by epidemiologists, 418. vaccination and influenza, 420. water filtration and typhoid fever, 416. CredibUity of census, 106. Cross-section paper, 87, 90. Cumulative grouping, 48. plotting, 75. Curves, equation of, 98. Davis, Dr. W. H., 358. Death, average age, 374. certificate, standard, 276, 490. registration, uses of, 115. Deaths, registration of, 113. Death-rates, 186. adjusted to standard popula- tion, 240. analysis of, 299. effect of size of place, 192. limited use, 216. precision, 187. relations to birth-rates, 195. Deceptions, graphical, 61. Demographers, 5. Demography, science, 1. divisions, 2. influence of war, 442. Density of population, 150. Detroit, population of, 138. Deviation from mean, 385. standard, 387. Diagrams, types of, 59, 63. Digestive system, 262. Diphtheria, age susceptibility, 323. fatality, 324. in Cambridge, 320. in Massachusetts, 325. in Providence, 323, 324. urban and rural, 325. Divorce-rates, 200, 216. Double coordinates, 81. Doubtful observations, 391. Dry statistics, 8. Dublin, Dr. Louis I., Ill, 369. Dwellings, number of persons in, 164. Earnings of father, infant mor- tality, 365, 366. Economic conditions and health, 445. Education, infant mortality, 363. Elderton, correlation, 411. Endemic index, 454. median, 454. Enforcement of registration law, 111. England, vital statistics of, 12, 210. Enumeration, 17, 100. Equation of curves, 98, 415. Error of statistics, 19. Error, probable, 390. Errors in age, 167. in published death-rates, 192 in round numbers, 168. Estimates of population, 129, 137, 139. Eugenics, 2. 512 INDEX Expectation of life, 428, 434. formulas for, 430. infants, 355. External causes of death, 266. Fallacy of concealed classification, 238. Families, number of persons in, 164. Farr, Dr. William, 6, 254, 255. Fatality rate, 309. of diphtheria, 324. of typhoid fever, 330. Fecundity, 196. relation to age, 198. Feeding, infant mortality, 36'ii Final death-rate, 191. First-year death-rate, 343. Fisher, Arne, 430. France, vital statistics of, 12, 210. Frequency curve, 378. curve as a conception, 399. natural, 376. Frankel, Dr. Lee K., 122. Galton, Sir Francis, 3, 5, 6. Galton's coefficient of correlation, 409. Garment workers, health of, 446. Genealogy, 2. General death-rates, 186. diseases, 257. vital rates, use of, 204. Generalization, 39, 40. Genito-urinary system, diseases of, 262. Geometric mean, 50. Geometrical increase, 132, 133. Germany, vital rates, 210. Glover, Prof. James W., 433. Gonorrhoea reportable, 120. Graphical deceptions, 61. method of estimating popula- tion, 141. Graphics, statistical, 58. Graunt, Capt. John, 3, 4, 6. Great war, effect on demography, 442. Gross death-rates, 186. Group designations, 45. Group plotting, 71, 74. Grouping, cumulative, 48. percentage, 47. Groups, 39, 40, 43. GuiKoy, Dr., 432. Gummed letters, 94. Halley, Edmund, 4. Hamburg, infant mortality, 341, 343, 344, 353. Harmonic mean, 52. Hazen's theorem, 450. Health officer, use of statistics, 11. Heights of soldiers, 377, 383, 395. Higher ages, proportionate mor- tality, 372. Hoffman, Dr. F. L., 334, 338. Hollerith punching machine, 54. Holt, Dr. Wm. L., 245. Homes and infant mortality, 361. Horizontal scale, 69. Hospital discharge certificate, 471. Hospital statistics, 443. Housing and tuberculosis, 413. Household duties, infant mortal- ity, 364. Hungary, vital rates, 210. Ideal death-rate, 216. Hi-defined diseases, 267. Illegitimate births, 198. INDEX 513 Immigration, 141, 142. Incompleteness of morbidity sta- tistics, 119. Increase, natural rate of, 203. Index, 31. • of concentration, round num- bers, 169. Induction, 14. Industrial accidents, 446. classification, 280. statistics, 443. Inexact numbers, 24, 26. Infancy, diseases of, 265. Infant deaths, age distribution in Boston, 353. causes, Johnstown, 360. Infant mortality, 339. age of mother, 363. age periods, 355. and homes, 361. birth attendance, 362. Boston, 348. education, 363. father's earnings, 365, 366. feeding, 364. foreign cities, 350. household duties, 364. methods of statement, 345. order of birth, 366. problems, 367. reasons for decrease, 349. sleeping rooms, 362. Sweden, 345. U. S. cities, 351. ventilation, 362. Infants, causes of death, Boston, 356. deaths at different ages, 352. Infants, definitions, 339. expectation of life, 355. life tables, 354. Infants, proportionate mortality, 344. specific deathrrates, 341. International classification of dis- eases, 254. list of causes of death, 255, 257. Irregular group plotting, 72. Jarvis, Edward, 6, 108. Jevons, W. Stanley, 10, 403. Johnson, George A., 332. Johnstown, first year mortality, 344. stillbirths, 341. studies, 360, 361. Joint causes of death, 276. Kensington, birth-rates, 199. King, 404. Lag, 417, 418. Laplace, probability studies, 4. Lathrop, Miss Julia C, 361. Lead-poisoning, 444. Least squares, 386. Lettering, 91, 92. Life-rates, 424. Life tables, 422. based on living populations, 430. early history, 431. infants, 354. recent, 431. Living persons, average age, 372. median age, 373. Local death-rates, 190. Logarithmic paper, 87. plotting, 85, 88. Logarithms, 34, 84. table of, 491. Logic, use of, 9. 514 INDEX Lowell, analysis of death-rates, 303. specific death-rates, 305. Malformations, 265. Malthus, 4. Maps, statistical, 96. Marital condition, effect on death- rates, 229. Marriage-rates, 200, 215. Marriage registration, 115. Massachusetts, age distribution, 169. analysis of death-rates, 300. birth-rates, 212. causes of deaths, 310. causes of divorce, 201. death-rates, 1900-10, 212. death-rates by counties, 302. death-rates of cities, 303. death-rates plotted, 396. diphtheria, 325. divorce-rates, 201, 216. errors in death-rates, 194. General Hospital, 444. infant mortality, 347. marriage-rates, 215. monthly death-rates, 214. morbidity registration, 116. population estimates, 140. seasonal mortality, 306. specific death-rates, 236. tuberculosis deaths by years, 317. tuberculosis death-rate, 79. variations in death-rates, 397. venereal diseases, 120. Maternal mortality, 367. Mechanical computers, 53. Mechanics of diagrams, 89. Median, 42. Median age of Uving persons, 373. Medical examiners, 278. MetropoUtan districts, 161. MiUtary statistics, 437. Mill, John Stuart, 406. Mills-Reincke, phenomenon, 450. Mirza, vision of, 224. Misuse of rates, 30. Model state law, births and deaths, 472. state law, morbidity, 465. Monographic method, 14. Monthly death-rates, 214. Morbidity registration, 116. model law, 117. rate, 309. reports, model law, 465. standard blank, 470. Mortahty rate, 308, 425. Moscow, death-rates, 78: Most probable life-time, 427. Moving average, 53. Nationa,l Health Department, 128. statistics, 127. vital statistics, 12. Nationality, effect on death-rate, 230. Natural frequency, 376. Nervous system, diseases of, 260. New Jersey, tuberculosis, 318. New South Wales, 226, 241. NiBW York City, maternal mortal- ity, 367. life tables, 432. resident death-rates, 191. New York, tuberculosis, 320. Newsholme, 199. Nightingale, Florence, 5, 6. Non-reportable diseases, 120. Normalized average, 454. INDEX 515 Nosography, 254. Nosology, 254. not exact science, 297. Notifiable diseases, 118. Notification, 107. Occupation and tuberculosis, 318. Occupation, index, 280. Occupations, list of, 281. Old age, diseases of, 265. One scale diagrams, 64. Optical illusions, 62. Ordinates, 67. Panics, relation to birth-rates, 213. Particular diseases, adjustments of death-rates, 251. Pathometrics, 2. Pearson, Karl, 3, 5, 224, 385. Percentage grouping, 47. of mortality, 308. Peddle's Graphical Charts, 98. Physical examinations, 123. Physicians' pocket reference, 256. Plotting, 66, 70. paper, 90. Poates Engraving Company, 98. Polar coordinates, 81. PoliomyeUtis, age distribution, 48, 448. Population, 129. age distribution, Europe, 182. estimates, 211. race, color, nativity, etc., 161. rate of increase, 136. redistributed by age, 172. types, 178. Powers' statistical machines, 54. Precision, 26. Precision of death-rates, 187. Preliminary death-rate, 191. Prenatal deaths, 340. Primary cause of death, 278. Probability of living a year, 422. Probability paper, 393, 398. ProbabiUty, use of, 398. Probability scale, 391. Probable error, 390. Progressive, character of age dis- tribution, 175. tjfpe of population, 178. Proportionate mortality, 308. childhood, 370. higher ages, 372. U. S., 95. Providence, diphtheria, 323, 324. Puerperal state, diseases of, 263, Quartiles, 42. Quetelet, probability studies, 5. Race and tuberculosis, 319. effect on death-rate, 234. Racial adjustments of death-rates, 249. composition of population, 162. Radial plotting, 82. Rainfall plotting, 68. Rates, 29, 32. Ratios, 27. Ratio cross-section paper, 83. Rectangular coordinates, 66. Redistribution of population, 172, 174. References, 459. Regressive type of population, 178. Registrars, laxity of, 112. Registration, 17, 100, 107, 113. area for deaths, 123. area for births, 127. of morbidity, 116. 516 INDEX Registration of marriages, 115. Registration, model law, 472. Reinhardt's lettering, 91. Reports, publication of, 455. Reports, standards, 457. Representative method, 14. Reproduction of diagrams, 97. Resident, death-rates, 190. Respiratory system, 261. Restricted death-rates, 220. Revised death-rates, 192. estimates of population, 138. Richmond, tuberculosis, 320. Rochester, population estimates, 140. Round numbers, error of, 168. Rural and urban population, 146, 149. Sanitary index, 451. Saxelby's mathematics, 98. Scales, choice of, 77. Schedules of enumeration, 103. School age, mortality of children, 371. Seasonal, deaths from tuberculo- sis, 315. distribution of typhoid fever, 331, 332. mortahty, 306. Secondary correlation, 415, 418. Sedgwick and MacNutt, 450. Senility, 265. Series, 39. Set-backs, 417. Sex distribution, 163. Shattuck, Lemuel, 108. ' Short term death-rates, 194. Sickness, surveys, 122. Skew curves, 383. Skin, diseases of, 264. Sleeping rooms and infant mor- tahty, 362. Slide rule, 35. Smith, Adam, 4. Soldiers, haights of, 377, 383, 395. Specific death-rates, 220, 226, 252. by age and sex, 227. use of, 239. U. S., 435. Specific life-rates, 424. Springfield, population estimate, 143. Spurious correlation, 416. Standard, birth certificate, 109. certificates, 488, 490. certificate of death, 113, 276. Standardized death-rates, 239. Standard, deviation, 387. morbidity blank, 470. miUion, 181. State censuses, 145. States in registration area, 125. State sanitation, 108. Stationary type of population, 178. Statistical, graphics, 58. induction, 14. maps, 96. method, 6, 14. processes, 17. units, 18. Statistics, history of, 3. Stillbirths, 195, 340. Summation diagrams, 75, 385. Sundbarg, 12, 178. Siissmilch, Peter, 4. Sweden, age distribution, 180. increase in population, 203. infant mortality, 345. INDEX 517 Sweden, progressive age distribu- tion, 177. vital statistics of, 12. ' vital rates, 204. Syphilis reportable, 120. Tabulation, 20. Tally sheets, 20. Time plotting, 69. Tuberculosis, age and sex, 311. and housing, 413. and occupation, 318. and race, 319. Boston, 80. death-rate, 79. proportionate mortality, 316. N. Y. and Richmond, 320. seasonal distribution of deaths, 315. Typhoid fever, age distribution, 47, 328. and water filtration, 333. Brooklyn, 83. case fatality, 330. chronological changes, 332. seasonal changes, 331, 332. specific death-rates by ages, 329. statistical study, 327. sjmonyms, 275. Undesirable terms for causes of death, 271. Undertaker, certificate, 114. United States army, vital statis- tics, 438, 439. cancer statistics, 335. causes of death, 311. census, 100. cities, increase in number, 149. United States, cities, list of popu- lations, 154. life tables, 429, 433, 434. population plotted, 88. proportionate mortality, 95. registration area of births, 127. registration area for deaths, 123. tuberculosis statistics, 315. vital statistics of, 12. Units, statistical, 18. Urban and rural population, 146, 149. Variation, coefficient, 388, 389. Variations in death-rate, 192. Venereal diseases, reportable, 120. Ventilation, infant mortality, 362. Vie probable, 427. Vision of Mttza, 224. Vital, bookkeeping, 10. rates, chronological changes, 210. statistics, current use, 452. Wall charts, 93. War, effect on demography, 442. Water filtration and typhoid fever, 333. Wax process, 98. Wedding-rates, 200. Weighted average, 50. Westergaard, 7, 404. Whipple, George C, 108. Whitechapel, birth-rates, 199. Willcox, Walter F., 229, 334. Wright, Carroll D., 6. Zinc process, 97. Subjects Related to this Volume For convenience a list of the Wiley Special Subject Catalogues, envelope size, has been printed. These are arranged in groups — each catalogue having a key symbol. (See Special Subject List Below.) To obtain any of these catalogues, send a postal using the key sym- bols of the Catalogues desired. List of Wiley Special Subject Catalogues I — Agriculture. Animal Husbandry. Dairying. Industrial Canning and Preserving. 2 — Architecture. Building. Masonry. 3 — Business Administration and Management. Law. 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