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Titles included in this collection are listed in the volumes published by the Cornell University Press in the series The Literature of the Agricultural Sciences, 1991-1996, Wallace C. Olsen, series editor. A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN BY J. ARTHUR HARRIS and FRANCIS G. BENEDICT Published by the Carnegie Institution op Washington Washington, 1919 CARNEGIE INSTITUTION OF WASHINGTON Publication No. 279 PBINTED BY J. B. LIPPIKCOTT COMPANY AT THE WASHINGTON SQUABE PRESS PHILADELPHIA, V. B. A. CONTENTS. PAGE Chapter I. Introductory 1 Chapter II. Methods of statistical analysis 9 Chapter III. Individuals and measurements considered 25 1. Measurements considered 25 2. Data analyzed 31 3. Criteria of suitability of materials dealt with 48 4. Recapitulation 69 Chapter IV. On the interrelationship of various physical and physiological measure- ments 71 1. Weight and pulse-rate 72 2. Statiue and pulse-rate 75 3. Pulse-rate and gaseous exchange 78 4. Pulse-rate and total heat-production 80 5. Weight and gaseous exchange 83 6. Stature and gaseous exchange 85 7. Weight and total beat-production 89 8. Stature and total heat-production 95 9. Recapitulation and discussion 105 Chapter V. Changes in metabolism with age 107 1. EUstorical review 107 2. Statistical constants measuring changes in metabolism with age 109 3. Comparison of changes in pulse-rate in relation to age 123 4. Recapitulation and general considerations 125 Chapter VI. A critique of the body-surface law 129 1. Historical 130 2. Physiological evidence on the body-surface law 135 3. Measurement of body-surface area 141 4. Inadequacy of criteria of validity of body-surface law hitherto employed 144 5. Statistical tests of relative value of the Meeh formula and of the Du Bois height-weight chart 151 6. Correlation as a criterion of the vaUdity of the body-surface law 152 7. The prediction-value of body-weight and body-surface 161 8. Further tests of the value of body-weight and body-surface for estimating total heat-production 177 9. Prediction of heat-production from two physical characters 182 10. Prediction of heat-production from two physical characters (stature and body- weight) and age 189 11. Comparison of body-weight and body-surface as bases of prediction in male and female infants 193 12. Recapitulation and discussion 195 Chapter VII. A comparison of basal metabolism of normal men and women 201 1. Historical 201 2. Comparison of metabolism of men and women on the basis of general constants 203 3. Comparison of metabolism of men and women by use of graduation equations. 205 4. Comparison of basal metabolism of male and female new-born infants 219 5. Recapitulation 221 III IV CONTENTS PASE Chafteb VIII. Standard basal metabolism constants for physiologists and clinicians. 223 1. The necessity for and the fundamental nature of standard metabolism constants 223 2. Tables of multiple prediction standard metabolism constants 228 3. Illustrations of practical applicability of standard multiple prediction tables of basal metabolism 230 Illustration A. Tests of normality of series of determinations 230 Illustration B. Metabolism in childhood and youth and in extreme old age. 237 Illustration C. Metabolism of individuals of aberrant physical form 243 Illustration D. Metabolism of athletes 244 Illustration E. Metabolism of vegetarians 245 Illustration F. Metabolism in disease 246 Illustration G. Rationing in periods of emergency 249 4. Recapitulation 249 5. Standard multiple prediction tables of basal metabolism for normal men and women 251 PREFACE. In carrying out the work underlying this volume we have attempted to do more than to treat the available data for the basal metabolism of normal men, women and children by a method which is practically new in its application to human physiology; we have endeavored to make this investigation a prototype of that specialization in methods and cooperation in problems which we believe will be characteristic of the best scientific work of the future. We are convinced that this cooperation of specialists of widely dissimilar training is the only means by which science can attain both the height of refinement of measure- ment and analysis and the breadth of comparison and interpretation which is essential to continued progress. The measiu-ements considered in this volume have been made possible by the painstaking cooperation of a score or more fellow- workers, all of whom are connected or have been associated with the Nutrition Laboratory'. How large their contribution has been will be evident from the names of the observers in the protocols of data and from the references to earlier publications scattered through the follow- ing pages. The exacting clerical and arithmetical work has been carried out at Cold Spring Harbor by the Misses Gavin, Holmes, Lockwood, and Peckham, who deserve the highest praise for the energy and care which they have devoted to this task. We are indebted to Major C. B. Davenport, Director, for permission to have this work carried out at the Station for Experimental Evolution. Finally it is a great pleasure to acknowledge our indebtedness to our associate. Professor W. R. Miles, who went over the first draft of the manuscript with us and offered many helpful suggestions, and to Mr. W. H. Leslie, in charge of the computing division at the Nutrition Laboratory, who has aided in correcting the proofs. Lti taking up this work over two years ago, the authors fully recog- nized that the data must be wholly rearranged and interpreted as the statistical constants might indicate without any regard to opinions heretofore expressed from the Laboratory. Practically all of the con- clusions already drawn at the Nutrition Laboratory have been fully substantiated by the statistical constants, and it is naturally a source of satisfaction that so little of the ground already held has had to be given up as a result of a wholly independent analysis from the outside. This original conviction has been strictly adhered to, and every effort has been made to have the treatment physiologically sound throughout. We have endeavored to carry the analysis of the data to the practicable limits of the biometric formulas, at the same time pre- serving all that is of value in the older and simpler methods of treat- V VI PREFACE ment which are more familiar to physiologists. We shall appreciate the fullest criticism by fellow physiologists, biologists, and statisticians, but criticisms to cany weight must be based on either statistical or physiological foundations and not merely the ex cathedra expression of the personal opinion that the new line of attack is valueless. We are presenting this volume, not as a finished treatment of the subject of basal metabolism, but merely as an introduction to the many problems which await solution by the use of the more refined methods of analysis when more extensive data are available. Nutrition Laboratory of the Carnegie InstitiUion of Washington, Boston, July 10, 1918. Chapter I. INTRODUCTORY. The purposejof this volume is to present the results of a first attempt to analyze the data of basal metabolism in normal men and women by the higher statistical or biometric formulas. ► These methods, associated primarily with the names of Sir Francis Galton and Professor Karl Pearson, are steadily making their way in the most varied fields of biological work. While Pearson and his associates at the Biometric Laboratory and the Galton Laboratory for National Eugenics, University College, London, have touched on vari- ous problems of interest to physiologists in their studies of inheritance and of environmental influence, the methods have, up to the present time, been little employed in the domain of human physiology. Per- haps the most important papers in their bearing upon the problems with which we are here concerned are those by Bell,^ by Whiting,* and by WilUams, Bell and Pearson^ on oral temperature in school children. Valuable as such studies unquestionably are from the standpoint of social and general biological science, statistical constants based on the returns of the public-school medical officer or of the prison surgeon can not be considered adequate for the requirements of modem nutritional physiology, in which measurements of a high degree of accuracy and made under carefully controlled conditions are indispensable. Both the unfamiUarity of the biometric methods to most physiolo- gists and the relative paucity of data on basal metabolism have prob- ably been responsible for the failure of physiologists up to the present time to apply the higher statistical methods in this field. While physi- ologists have been engaged for several decades with the problem of the exact measurement of the metabolism of man and the lower animals, both by the direct determination of the amoimt of heat produced in the calorimeter and by the indirect calculation of heat-production from oxygen consumption and carbon-dioxide excretion, satisfactory data have until recently been exceedingly limited. This state of affairs may be attributed to various causes. First of all, satisfactory apparatus is expensive and technical requirements exacting. The ntmiber of fully equipped laboratories and of adequately trained workers have, therefore, been very limited. Again, there is a personal element in all investigations based on normal human individ- > BeU, Biometrika, 1911, 8, p. 232. ' Whiting, Biometrika, 1915, II, p. 8. > Williams, Bell, and Pearson, Drapers' Company Res. Mem., Stud. Nat. Det., London, 1014, 9 . 1 2 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. uals which is apt to be overlooked by those whose experimentation has been carried out on chickens, guinea pigs, or other animals or plants on the one hand or in the clinic on the other. In the study of normal metabolism the prejudices or suspicions of the subject must be over- come and his convenience considered. This imposes a limitation upon the number of measiu-ements which can be fully realized by those only who have had to meet these difficulties. Finally, the progress of the work has shown the necessity for continuous refinement of method. Thus it is quite impossible to use for present purposes the observations of a few years ago. In the earlier work the necessity for complete muscular repose on the part of the subject under investigation was not fully enough realized. Individuals in the respiration chamber were allowed to move about, telephone, write, or otherwise occupy them- selves. More recent work has indicated that such apparently trivial matters as the difference between the sitting and the reclining position or such shght exertion as that required to raise the hand from the side to the mouth may have a measurable influence on heat-production. Furthermore, it has long been known that the presence of food in the alimentary tract affects heat-production. The stimulatory action of food has, therefore, to be taken into accoimt. Thus the conditions under which the more truly basal metabolism of the individual may be measured have been continually narrowed. Of recent years students of human metabohsm have reached a general understanding concerning the conditions under which the heat- production of an individual should be measured in order to obtain values of the metabohsm constant which shall be comparable from individual to individual, and hence suitable as a standard basis of departure for all studies of the influence of special conditions, whether of sex, age, food, exercise or disease, upon the gaseous exchange. Deter- minations made on the individual during complete muscular repose and at a period 12 hours after the last meal, i.e., inthe post-absorptive condition, g^ve what is commonly known as the basal metabolism. Until very recently the number of measm-ements which fulfil the modem high requirements was necessarily so small that it had not seemed worth while to apply the modem methods of analysis to them. The development of series of measurements sufficiently large to justify the use of the more refined statistical formulas in their analysis has been in part due to a wider reaUzation of the great practical as well as the purely theoretical importance of a detailed and precise knowledge of basal metabolism. The general pubUc, as well as the handful of V nutritional speciaUsts, is being forced these dasrs by conditions of unpre- icedented stress to a realization of the fact that an exact knowledge t of human nutrition is not merely fimdamental in the clinic and useful 'f in home economics, but that it may even he at the basis of national survival. INTBODUCTOEY. 6 The desirability of applying the biometric formulas to the steadily increasing volume of data on basal metabolism in man has more than once suggested itself. Thus, as early as July 1915 Professor August Krogh, of Copenhagen, in his ever stimulating correspondence, urged that the data accumulated by the Nutrition I^aboratory were already so extensive that the modem statistical formulas might profitably be employed in their expression and interpretation. After the manuscript for this volume was practically completed, a paper by Professor Armsby and his collaborators* appeared, giving the correlation between body- weight and daily heat-production and body-surface area and heat- production. Fortunately the niunber of individuals whose basal metabolism has been determined is now fairly large. Dealing as we have in this volume with individuals measured at the Nutrition Laboratory, or by those who have been associated with the Laboratory, we are able to discuss the constants of nearly 250 adtilts and of about 100 infants. In the past these have been treated almost exclusively by the simple method of averages and graphic representation. But a series of metabolism constants, like other biological measurements, show differences among themselves. These differences must be due to either inaccm'acies of measurement, or must represent real physiological differences between the individuals considered. That the latter rather than the former is true seems evident from the fact that technical errors in the noaking of the measm-ements have in all careful work been reduced to a minimum by the frequent use of physical tests of the apparatus, by the measru-e- ment of standard combustions, and by other precautionary measures which have placed the data of gaseous metabolism among the more accurately controlled of the physiological measurements. That the differences between the measiirements of individuals are of the nattu'e of real biological difference rather than of errors of observation is also clear from the fact that such attempts as have been made to obtain a more precise average metabolism constant by reducing the total heat- production to calories per kilogram of body-weight or to calories per square meter of body-siu^ace have effected a material reduction in the amount of variation in the measxu-es of the actually observed metabol- ism of individuals. Notwithstanding this correction for the physical characteristics of the individual due to the reduction of the gross heat- production to calories per kilogram or calories per square meter of body-surface, the variation in the metaboUsm constant is not entirely eliminated. It seems necessary, therefore, in any thoroughgoing inves- tigation of metabolism in man, to take account of the variation from individual to individual, as well as of the general average. Further- more, the fact that some lessening in the differences in the metabolism ' Annsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, p. 1. See also Joum. Agrio. Research, 1918, 13, p. 43. ) A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. constants of a series of individuak is made by reducing them to units of body-weight or body-surface indicates that the total metabolism of 'i the individual is correlated with" his physical characteristics. Thus the desirabiUty of a detailed investigation of the correlation of the various physical and phjrsiological measiu-ements which have been made suggests itself. Such investigations of variation and correlation can be carried out only by means of the biometric formulas. A full justification for the application of the higher statistical methods to the data of basal metabolism is to be found in the fact that these methods have been successfully applied in other fields in which the observational data exhibit comparable irregularity. During the past two decades instances of the demonstration of law and order in processes hitherto apparently chaotic have been rapidly multiplying, while on the other hand, long- maintained biological theories have been shown to be groundless by the mathematical description and analysis of series of measurements. This fact establishes a strong presumption that the same condition will be found to apply in the field of human metabolism. The presumption has seemed to justify at least a preliminary test of the methods. It seems desirable to outline at the start the possibilities of the statistical formulas in their appUcation to the problems of basal metabolism. First of all, these formulas permit a more concise and adequate descriptive statement of the results of experimentation. The statistical method furnishes not merely an average measure of metabolism, but also a measure in a single constant of the deviation of the individual determinations of metabolism from their average value. The average value of the metabolism constant serves many useful piuposes, but it is no more truly a characteristic of the series of measurements which have been made than their differences among themselves. Measures of variabiUty in metabolism are, therefore, quite as necessary for a fuU understanding of the physiologica^problem as are measures of the average values. Such constants have been determined during the course of this work, and expressed in both absolute and relative terms. The measures in absolute terms are particularly useful for some pur- poses, while those in relative terms permit direct comparison of the varialjiUty of metabolism constants with those of other physical and physiological measurements in man. Again, one of the greatest possibilities of the statistical method lies ) in the determination of the degree of association or correlation of differ- , ent physical and physiological or of different physiological characters. For example, we know that in general the total heat-production of a tall individual is greater than that of a short individual, that the heat- production of a heavy individual is greater than that of a Ught individ- ual, and so on. But what is needed for a full and scientific analysis of INTRODUCTOBY. 5 the whole problem is some measure of the intensity of these and many other interrelationships, expressed on such a scale that comparisons between various characters may be easily and directly made. This ejad is readSTy attained by the use of the modem correlation formulas. The analysis may be pushed further. WelSave jusFsaid that tall individuals produce on the average a larger number of calories than short ones, and that hfeavy individuals set free on the average more heat than light ones; but tall individuals are on the average heavier than short ones, and the question naturally arises whether their greater heat-production may not be due exclusively to their greater average weight. This problem can be solved only by correcting the correlation between stature and heat-production for the influence of the correlation of both stature and total heat-production with body-weight,, A quite similar method of analysis may be apphed when it is desired to correct the relationship between two variables, for example between age and heat-production, for the influence of both of two other variables, say statiu-e and body-weight. , Knowing the correlation between two variables (for example, body- i weight and total heat-production) it is possible within certain limits of accuracy to predict the average value of one from the known magni- tude of the other. Thus it is possible to pass at once from measures of interdependence on the imiversal scale of correlation to coefficients showing just how much on the average an associated character increases in units of the actuaJ scale on which it is measured for each unit's change in the first variable. These relationships are of the greatest practical importance, in that they enable us to determine the most, probable metabolism of an unknown subject of ^ven stature, weight, and age, and these predicted values may serve as a control in cases in which it is desired to investigate the influence of particular conditions, e.g. the incidence of a specific disease, on metabolism. ~' Finally, one of the great advantages of the use of the statistical method lies in the system of probable errors which are provided by the biometric constants. Metabolism varies from individual to indi- vidual. If the average value of a series of determinations be employed as a basis of argument concerning some physiological relationship, the worker must fully recognize the fact that a repetition of the measure- ments upon another set of individuals apparently comparable with the first would give averages somewhat different. The probable errors of random sampling, to be discussed in somewhat greater detail in a special section on methods of statistical analysis, do much to establish the limits of trustworthiness of not only the arithmetical means or averages but of . all the other statistical constants. Thus the biometric formulas make possible a far more definite conception of the limits of trustworthiness of metabolism constants than has heretofore been possible. 6 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Turning now from generalities to concrete problems, we may outline very briefly the actual physiological problems upon which we have touched. C First of all it may be stated that this volume contains the raw data for age, body-weight, stature, pulse-rate, and gaseous exchange, with the computed heat-production, in 47 men and 35 women hitherto unpublished. These are laid before the reader, together with the data for 89 male and 68 female adults and the 51 male and 43 female infants already pubUshed from the Nutrition Laboratory. These represent a contribution to the problem of human metabolism of experimentally determined facts which must be taken into account even by those who may be imwilling to accept the results of the statistical analysis to which all the data at our disposal have been subjected. Turning to the results of statistical analysis, properly so called, we note the following: 1. The more important statistical constants of the largest available } series of metabolism measurements have been determined. These '-■ must serve as standards in metabolism work until more extensive data ■ are available. 2. The relationship between physical and physiological measure- ments of the hmnan individual has been discussed in as great detail as possible by means of correlation constants. Specifically, we have ■ considered the relationship between both body-weight and statiu-e, representing physical measurements, and the physiological measure- ments, pulse-rate, gaseous exchange, and total heat-production, and I determination has been made of the effect upon these correlations of '; correction for other factors. 3. The degree of interdependence between various physiological characters has also been considered. Sp ecifical ly, the relationships between pulse-rate and gaseous exchange, and between pulse-rate and total heat-production and heat-production per unit of body-weight and of body-surface have been determined. The illustrations presented in the following pages should amply demonstrate the material advances in our knowledge of physiological processes which may be expected when the degree of interrelationship between various physical characters and physiological activities, or between physiological activities thena^elves, shall be generally measured on a definite quantitative scale. 4. The validity of the so-called body-surface law has been tested by means of criteria hitherto unapplied. This "law" has been discussed as an empirical means of predicting the metabolism of an unknovm subject and as an expression of a true physiological interrelationship. 6. In connection with the investigation of the so-called body- surface law, various methods of predicting the total heat-production of an unknown subject from sex, age, stature, and body-weightTiave INTRODUCTORY, 7 been considered in^detail. Standard tabl^have been prepared from ; whichthemost probable metabolism of a subject, whose normal metab- olism is unknown, may be predicted as a basis of comparison with that measured in a patholi^cal state. Such tables should be of great value in the clinical investigations which should contribute much to the future advancement of medical science. 6. By the use of such tables, the metabolism of subjects of par- ticular characteristics, or subjected to special conditions, has been reconsidered. Specifically, the problems of the typical or at3T)ical character of certain series of metabolism measurements, of the differen- tiation of the sexes with respect to metaboUc activity, of the metabolism of a,thletes as compared with non-athletic individuals, ofvegetarians as compared with non-vegetarians, and of individuals suffering from disease have been investigated. in preparing this report on the results of the application of the biometric formulas to the data of basal metabolism in normal men and women we have utiUzed only the measurements made at the Nutrition Laboratory or by those who have been associated with it. This limita- tion has been made, not because there are not many satisfactory deter- minations which have been made in other laboratories, but because, all things considered, it has seemed most satisfactory to avoid invidious comparisons by the discrimination which would have been necessary had we gone outside the series of determinations for which responsibility rests directly or indirectly upon the Nutrition Laboratory. Finally, a few words concerning the form in which the results of this investigation are presented: It has not seemed desirable to trans- form a research publication into a primer of statistics, or to state results which are necessarily mathematical in a popular and non-mathematical form. We have, however, made every effort to express our results in - a form so clear and direct that they will be fully comprehensible to those without special statistical training. In the case of all the more complicated processes we have given the formulas by which the results were reached. This has been done to enable those who may care to do so to check through our work from the beginning. The reader who is ', interested in end resiilts rather than in methods should pass over these features, just as the general biologist must pass over the details of method and the section on structural formulas in a paper by an organic chemist, realizing that they are essential to the technical development of the subject. The analogy is by no means wide of the mark. The statistical technique is of course complicated, as are the manifold technical refinements necessary in the experimental phases of the measurement of metabolism in man. An adequate presentation of the subject demands a statement of the formulas employed quite as much as a description of the physical and chemical apparatus used in the laboratory phases of the work. With this feature of the following 8 A BIOMETKIC STUDY OF BASAL METABOLISM IN MAN. treatment the non-statistical reader must bear as patiently as possible. There is no royal road to statistical analysis, and the popularization of statistical methods is quite comparable with the problem of the popularization of organic or physical chemistry. The demand for simplification can, so far as those of us who have been working in this field can now see, be attained only at a serious loss of effectiveness. ; To assist the non-statistical reader as much as possible in the under- standing of our results we have added a summary at the end of each ■ chapter in which we have given the results in a form as general and .non-statistical as possible. With these precautions, and with the cooperation of those who may attempt to follow us through these pages, we trust that a highly difficult subject has been presented with- out important loss in the technical detail which is essential to those who may care to piirsue the subject further and in a manner compre- hensible to the general physiologist. Chapter II. METHODS OF STATISTICAL ANALYSIS. Before taking up the actual data with which we have to deal, a brief discussion of the statistical formulas employed will be necessary although it is not possible to give an adequate introduction to the use of the statistical methods. These methods are complicated and many pitfalls aboimd in the field of statistical reasoning. This section may, however, give the reader definitions of terms and a general conception of the method of attack. The first statistical constant to be determined for a series of meas- urements is the arithmetic mean or average value. This is simply the sum of all the observations divided by their number. It is already familiar to the physiologist and need not be discussed further. The second statistical constant with which we shall have to deal in the treatment of these data is a measiire of the deviation of the individual measurements from their average value. Physiologists in common with psychologists and other investigators have sometimes measured the variation in their observations by obtaining and aver- aging the differences between the individual readings and the general average. Thus an average deviation, or an average dispersal, of the individual measurements about the general average for the whole series of individuals dealt with, is obtained. This average deviation is very useful for some purposes, but for more refined work has three disadvantages. (1) Some of the measiu'ements are smaller while others are larger than the general average for the whole series of individuals dealt with. Thus some deviations are positive while others are nega- tive in sign. In obtaining an average value which shall furnish a true measure of scatter both above and below the mean, it is necessary to disregard the signs and thus to do violence to one of the laws of math- ematical iisage. (2) The significance to be attached to a deviation is considered proportional to its actual magnitude. It may be legitimate to regard a large deviation as both absolutely and relatively more important than a small one. (3) The average deviation is poorly suited for use in more complicated statistical work. The larger deviations can be given a proportionately greater weight by squaring all the deviations, summing these squares, and dividing by the number of deviations to obtain the mean-square deviation. The square root of this mean-square deviation is the measure of variation, scatter, or dispersal most used by the statistician. It is called the standard deviation, S. D. or a. There are great practical advantages in the use of the standard deviation, in that it is particularly suited 9 10 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. for the more complicated calculations involved in the determination of measures of interrelationship. The standard deviation may be calculated by actually obtaining the deviations of the individual measurements from the general average, squaring these deviations, dividing by the number of observations, and extracting thesquare root of thequotient. Thus if x represents the value of an individual measurement, x the average of all the N measurements ".^V-Liix-xYVN where a, is to be read "the standard deviation of the measurement x" and Z denotes the smnmation of all the squared deviations. Thus in the case of a series of 16 athletes given in our table of data on p. 40 the total weight is 1181.1 kilograms and the average weight 1181.1/16 = 73.8 kilograms. The sum of all the daily heat-productions is 30,025 calories and the average daily heat-production 1876.6, or in round numbers 1877 calories. The deviation of the individual weights, w, from the average weight, w, and of the individual heat-productions, h, from the average heat-production, h, are given in table 1. Table 1. — Deoiations and tguarea of demotions of hody-weight, w, and heat-production, h, from their respective averages. Subject. w {w—w) (w-wy h ih-h) (h-ly W.A. S C.J. D M. Y. B R.D.8 H. R. W 56.3 56.7 63.6 63.6 73.9 71.2 74.0 66.0 62.4 108.9 82.2 82.1 78.9 79.0 88.6 74.0 -17.5 -17.1 -10.3 -10.3 + 0.1 - 2.6 + 0.2 - 7.8 -11.4 +35.1 + 8.4 + 8.3 + 6.1 + 6.2 +14.7 + 0.2 306.25 292.41 106.09 106.09 0.01 6.76 0.04 60.84 129.96 1232.01 70.66 68.89 26.01 27.04 216.09 0.04 1662 1624 1677 1619 1842 1810 1908 1695 1816 2669 1978 2034 2126 1944 2017 1914 -316 -353 -200 -268 - 36 - 67 + 31 -182 - 61 +682 +101 +157 +249 + 67 +140 + 37 99226 124609 40000 66664 1226 4489 961 33124 3721 466124 10201 24649 62001 4489 19600 1369 P.D.F C.D.R M.A.M W.F.M H. W J. H. R D. H. W E. G M. H. K w. S F.G.R The standard deviations are therefore given by X[iw-wy] = 2649.09, 2[(li-A)»] =961351 2[(te-w)']/iV= 165.5681 = (r„* (r„= 12.867 2;[(/i-fc)*]/iV = 60084.44 =o-a« a^= 245.12 The standard deviation furnishes a measure of variation in terms of the unit in which the variable was measured, i.e., in number of heart-beats, in number of respirations per minute, or in number of calories produced per 24 hours. If comparison between the variability of characteristics measured in different working units is to be made, it is necessary to reduce the two standard deviations to a comparable METHODS OF STATISTICAL ANALYSIS. 11 basis by expressing them as percentages of their respective means. Thus, if X represents heat produced per 24 hours and y represents pulse-rate, it is quite impossible to say from a comparison of a^ and ff„ whether pulse-rate or heat-production is the more variable character. But if the two standard deviations be expressed as percentages of their respective means, p. _ lOOtr, TT _100ov X y it is possible to determine which of the two characters is relatively more variable. Thus in the case of the measurements of body-weight and total heat-production given above, the relative variabilities are : y. _ 100app^,3,g 73.8 1876.6 This relative variation constant is known as the coefficient of varia- tion. It shows in the present case that the body-weight of the athletes is about 4.4 per cent more variable than their daily heat-production. We now turn to the problem of the measurement of interdependence or correlation. Remembering that we are seeking a measure of the degree of inter- relationship of the magnitudes of two variables, it is first necessary to adopt a standard with which individual measures of body-weight, body-surface, metabolism, pulse-rate, or other variables may be com- pared in order to determine their place in their own series. Such a standard is furnished by the average value of the character in the series of individuals available. This arithmetical mean has the advantage for metabolism work that it has been regularly used as a standard value by various workers. The only difference between our use of the mean and that of some other writers on metabolism is that the average value which we employ as a standard is always the average for the particular series of individuals under consideration, not an average for some selected standard series. Thus, in working with athletes, vege- tarians, or all normal men the averages employed as standards are those for athletes, vegetarians, or for all normal men, as the case may be. Let X be the measure of any physical or physiological characteristic of an individual, y the measure of any other physical or physiological characteristic — ^for example, oxygen consumption, carbon-dioxide out- put, or calories of heat-production, in the same individual. Then if we designate by bars the average values of these two characteristics in the series of individuals dealt with, (x—x), (y—y) furnish at once the 12 A BIOMETEIC STUDY OF BASAL METABOLISM IN MAN. measiire of the position of an individual in the whole series of measure- ments. Values with the negative sign indicate a position below the average, values with a positive sign a position above the average of the series as a whole, while the numerical value gives at once the mag- nitude of the deviation. Now remembering that (x— 5) and (y—y) are values with signs, it is clear that if we take the products of these deviations we shall have positive products for all values with like signs and negative products for the values of all deviations with imlike signs. Summing these products with regard to sign for the whole series of individuals under investiga- tion, the net total will be positive if the two measures x and y tend to vary in the same direction, that is, if y tends to be above its mean value in individuals in which x is above its mean value and y tends to lie below its mean value in individuals in which x lies below its mean value. For example, the table for the athletes given above shows the actual amount of the deviation of the weight and the daily heat-production of each individual above or below the mean weight and mean heat- production of the whole group of athletes. The fact that two positive or two negative signs tend to occtu* together shows at a glance that there is some correlation between body-weight and total heat-production. The products of these deviations are given in table 2. Table 2.- -Produett of deviations of hody-weight and daily heat-production from their respective means. Subject. (w—v>) (h-h) (w-w) (h-h) W.A.S -17.5 -315 + 5512.5 C.J.D -17.1 -353 + 6036.3 M.Y.B -10.3 -200 + 2060.0 R.D.S -10.3 -258 + 2657.4 H.R.W + 0.1 - 35 - 3.5 P.D.F - 2.6 - 67 + 174.2 C.D.R + 0.2 + 31 + 6.2 M.A.M - 7.8 -182 + 1419.6 W.F.M -11.4 - 61 + 695.4 H. W +36.1 + 8.4 +682 +101 +23938.2 + 848.4 J. H.R D.H.W + 8.3 +157 + 1303.1 E. G + 5.1 + 5.2 +249 + 67 + 1269.9 + 348.4 M.H.K w. s +14.7 + 0.2 +140 + 37 + 2058.0 + 7.4 F.G.R Sum (S) =fc 0.0 ±0.0 +48331.5 In 15 of the 16 cases the heat-production is larger than the average heat-production when wei^t is larger than the average weight and smaller than the average heat-production when weight is smaller than the average. Smnming the products with regard to sign, we have -f 48335.0-3.5 = -f48331.5, which divided by 16=3020.7188. METHODS OF STATISTICAL ANALYSIS. 13 Thus the sum of the products of the deviations of x and y from their respective means for the whole series of individuals, divided by the number of individuals considered, furnishes a mean product-deviation which is a measure in absolute terms of the closeness of interdependence of the two characters under investigation. To obtain a measure in relative terms (that is in a form to facihtate comparison between unlike characters) some standard of the amoimt of the deviation from the general means in the case of the two characters is essential. The mean product-deviation must be expressed as a fraction of the product of the deviations of the two characters in the whole series of individuals from their respective means — ^that is, of h Here „r,» is to be read "the correlation between statiure and heat for constant body-weight." The technical expression "for constant body- weight" means merely "with the influence of body-weight eliminated." If the correlation between statxu-e and total heat-production were merely the resultant of the correlation between weight and heat- production and weight and stature, „T,h should be sensibly zero. For example, for the 136 men, using the constants as given on pages 59 and 96, we have: r.^ = -F-0.6149 r„. = -1-0.5725 l-r„.« = 0.6722 VT=^= 0.8199 r.» = -1-0.7960 l-r„j^ = 0.3663 y/l^={).mb2 0.6149-0.5725X0.7960 0.1592 "'*'* ~ 0.8199 X0.6052 ~ 0.4962 ~ 1 -»r.A* = 0.8969 Ejr.^ = 0.6745^ 7"^'*' = 0.0519 V N Thus the partial correlation between stature and heat-production for constant body-weight is only about half the magnitude of the uncorrected value. It is clear, therefore, that the greater heat-produc- tion of tall individuals is due largely to their greater weight. The fact that the partial correlation has a material and statistically significant positive value indicates that the observed relationship between stature and metabolism is not merely the resultant of the correlations between stature and weight and between weight and metabolism. 18 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. In certain instances we have found it desirable to determine the relationship between two variables for constant values of two other variables. Thus o„r,A is to be read "the correlation between stature, «, and heat-production, h, for constant age, a, and body-weight, w." The actual formulas used in computing the partial correlation coefficients are given in each instance. The partial-correlation method has been of great service in this study and will, we believe, prove to be a powerful analytical tool in the investigation of physiological relationships in many fields. We now turn to the subject of the probable errors of the statistical constants. Because of the differences which obtain between the individual determinations of a series of metabolism measurements, the statistical constants of such measurements will generally differ to some extent from series to series. For example, the average heat-production per square meter of body-surface per 24 hours of 72 men selected by Gephart and DuBois from a Nutrition Laboratory publication is 926.65 calories, whereas the average heat-production of 64 other men examined by the Nutrition Laboratory is 924.14 calories. Thus the two series differ in heat-production per square meter of body-surface by 2.51 calories. The standard deviations of heat-production per square meter of the two series are 62.59 and 71.92 calories, or show a difference of 9.33 calories. When another series of measurements is available it will probably give averages and variabiUties which differ slightly from either of these. That this shoidd be so is simply a matter of common experience. The statistician as such can do nothing whatever to eliminate the individuality of the subjects to which these differences are primarily due or to minimize the slight experimental errors of measuremente upon which they to some extent depend. He can, however, furnish criteria of the trustworthiness of statistical constants based on series of observations of known variability and mmiber. These criteria are the so-called probable errors, or more precisely probable errors of random sampling. Such probable errors are entirely statistical in nattire and have nothing whatever to do with the possible errors of measurement. They assimie the technical or biological correctness of the observations and measure merely the degree of trustworthiness of statistical con- stants based on series of observations. In the calculation of the probable error two factors must obviously be taken into account. The first is the variability, the second is the number of the measiu'ements dealt with. If a character, either physical or physiological, is extremely variable it is obvious that an average based upon a given number of determinations will be less trustworthy than one based upon a character which is very slightly variable. For example, the addition of one very heavy individual to a series will METHODS OF STATISTICAL ANALYSIS. 19 make an enormously greater difference in the average weight of the series than it will in the average pulse-rate, for body-weight is a far more variable character than pulse-rate. The trustworthiness of a constant based on a series of measxu'ements is inversely proportional to the variability of the individual measurements. On the other hand it is reasonable to assimie that the precision of a statistical constant increases as the nimiber of observations upon which it is based becomes larger. Thus the average metabohsm of 100 individuals is admittedly more desirable as a basis for physiological generalization than an aver- age based on 10 individuals; yet the trustworthiness of the constants is not directly proportional to the number of observations upon which they are based, but stands in the ratio of the square roots of these numbers. Thus the probable error of an average based on 10,000 individuals would not be 100/ 10000 = 1/100 of that based on 100 individuals, but only VlOO/VlOOOO = 1/10. The practical conse- quence of this relationship is that while precision increases with the number of the observations, the increase in precision is not directly proportional to the labor involved in the making of the measurements. After a degree of precision which meets the practical requirements is attained, further work may be regarded as lying beyond the limit of diminishing retmns. Of coiu-se the need of greater refinement may at any tii^e arise and demand the accumulation of a mmiber of data wWch for earlier work would have been considered superfluous. Details concerning the calculation of the probable errors — a term having an historical significance and not as appropriate as might be foimd — ^which can be obtained from text books on statistical methods, need not detain us here. A few words are in order concerning the inter- pretation of the probable error, the value appended with a plus and minus sign to the various statistical constants. It is in reality a measure of the variability of that constant which would be found if it could be determined an infinitely large number of times upon random samples of the same number of measurements and drawn from the same population as that upon which the constant is based. It is a measure of this variability of the statistical constant about its mean so chosen that half of the values would lie inside and half of them outside the limits of the probable error. Thus if the mean value of a character in an infinitely large population were 86 and the probable error for samples of 100 were ^5, 86^5 would indicate that if a large series of samples of 100 individuals each were drawn at random from this population half of these would show averages ranging from 81 to 91 while the remaining 50 per cent would lie below 81 and above 91. The distribution of these means based on random samples of 100 individuals each would be an orderly one. Thus in the comparison of two means it is possible for the statistician to estimate the chances for (or against) their being based on identical material. Or, conversely. 20 A BIOMETEIC STUDY OF BASAL METABOLISM IN MAN. it is possible to estimate from the observed differences in the constants the chances of the materials being differentiated. This is, of course, the practical application of the principle. The physiologist desires to know, for example, whether an observed difference between two con- stants, one based on athletic and the other on non-athletic individuals, indicates a real biological or physiological difference attributable to ath- letic training, or whether it is merely of the order to be expected as the result of random drawing of groups of subjects of the number dealt with. For example, the daily heat-production of 16 athletes is found from table 16 to be 1876.56 ±41.33 calories. That of the first supple- mentary series of 28 men is 1605.18*28.19 calories. The difference between these two constants is 271.38 ±50.03 calories. The difference is 5.42 times as large as its probable error and the odds against its being due to errors of random sampling are large.* Thus we may conclude that athletes are different from ordinary individuals in their gaseous metabolism. Again we note that in a series of 72 men selected by Gephart and Du Bois from the Nutrition Laboratory publications the average heat- production is 1623.46*14.11, whereas in another series of 64 indi- viduals it is 1641.05 ±19.48. The difference is 17.59 ±24.05. Thus the difference is less than its probable error and can not be considered statistically significant. In short the two groups of men may be con- sidered to show the same average metabolism. The practical use of the probable error is almost invariably in the carrying out of comparisons. The investigator desires to know whether a particular statistical constant differs either from some preconceived or theoretical standard or from some other constant. For example, the physiologist may wish to know whether the mean metabolism of women differs significantly from that of men. In the case of correlation an apparently, but not essentially, different problem presents itself. One often desires to know whether there be any relationship at all between two variables. He then inquires whether an empirically found value of the correlation coefficient has a "significant" value. This is necessary because of the fact that if correlations were based upon small series of individuals drawn at random from an infinitely large series in which the correlations were zero, a numerical value would in many instances be obtained. This is true for the same reason that a small number of determinations of basal metabolism on a group of febrile patients would show an average value differing from that ob- tained on a small group of normal subjects, whether there be any real influence of fever on metabolism or not. In such cases we wish to know whether the correlation differs * Throughout this volume we have taken differences of 2.5 or 3 times as large as their probable errors to be significant, always remembering that the interpretation of probable errors is difficult when the number of observations is small. METHODS OF STATISTICAL ANALYSIS. 21 significantly from zero, which would be found if an infinitely large series of observations were available. For example, in table 18 we show that the correlation between stature and pulse-rate in 121 men is +0.0916 *0.0608, while for 90 women it is -0.0669 ±0.0708. These constants differ from zero by 1.51 and 0.94 times their probable errors and consequently would not be considered to prove the existence of a real positive correlation between statiu-e and pulse-rate in the case of men as a class or of a real negative correlation in the case of women as a class. In short, the probable error indicates that the series of deter- minations available is too small to justify any generalization concerning the niraierical magnitude of the correlation between stature and mini- mum or basal pulse-rate other than that it is exceedingly small if it exists at all. A comparison of the coefficients obtained in the sub- samples shown in table 18 justifies this view, for in the several series available for adult males the coefficients are sometimes positive and sometimes negative in sign. If we turn from the relationship between stature and pulse-rate to that between statiire and total heat-production given in table 32, Chapter IV, we note that the correlation for the total males is +0.6149 ±0.0360, while for the total females it is +0.2318 ±0.0629, The first of these two constants is 17.1 while the second is 3.7 times as large as its probable error. Thus there can be no question whatever concerning the statistical significance of the deviation of these correlation coeffici- ents from the zero which would be the average value if there were no correlation between stature and total heat-production. We may con- clude, therefore, that as far as the relationship between stature and total heat-production is concerned the series of determinations available furnish a fair basis for generahzation concerning the numerical rela- tionship between stature and total heat-production in men and women at large. This discussion of the probable error has been of the most general nature, but it may be sufficient to dispel the confusion which seems to exist in the minds of some between technical errors of measiirement and the probable errors of random sampling of statistical constants, and to enable the reader imaccustomed to statistical reasoning to follow argu- ments based on probable errors in the following pages. Finally a few words concerning the actual routine of calculation are in order. The formulas for the determination of r used in explaining this coefficient above are not the most useful for practical work. In the calculation of the standard deviation it is quite unnecessary to ob- tain the actual deviation in each case. If the deviations are not wanted for other purposes the standard deviation is easily obtained from'' , = V^ix')/N - [S(x)/iV]* = V2(x^)/iV-x« ' Harris. Am. Nat., 1910, 44, p. 693. 22 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. where S(x) and S(x*) denote the sums of the individual measurements and their squares. Furthermore we may write . _S(xj/)/iV- -xy ff,o-„ where S(x2/) denotes the smn of the product of the two measures under consideration, the bars denote their means, and the sigmas their standard deviations. This method is particularly suited for physiological work. The worker has merely to sum the products of the two measures under consideration for all the individuals dealt with, divide by the number of individuals, subtract the product of the means of the two variables from this mean product, and divide the remainder by the product of the two sigmas. The standard deviations are easily obtained by sum- noing the squares of the actual measurements, dividing by the number of individuals, subtracting the square of the mean of the character, and determining the square root of the remainder. Table 3. — Calculalion of moments of body-weight and daily hecU-prodvction. Subjects. Body- weight in kilos. Body- weight squared. Total beat- pro- duction. Heat- production squared. Product, weight times total beat. W.A.S C.J.D M.Y.B R.D.S H.R.W P.D.F C.D.R M. A. M 56.3 66.7 63.5 63.6 73.9 71.2 74.0 66.0 62.4 108.9 82.2 82.1 78.9 79.0 88.5 74.0 3169.69 3214.89 4032.25 4032.25 5461.21 6069.44 6476.00 4356.00 3893.76 11869.21 6756.84 6740.41 6226.21 6241.00 7832.25 5476.00 1562 1524 1677 1619 1842 1810 1908 1696 1816 2569 1978 2034 2126 1944 2017 1914 2439844 2322576 2812329 2621161 3392964 3276100 3640464 2873025 3297856 6648481 3912484 4137156 4519876 3779136 4068289 3663396 87940.6 86410.8 106489.6 102806.6 136123.8 128872.0 141192.0 111870.0 113318.4 278675.1 162691.6 166991.4 167741.4 153576.0 178604.5 141636.0 W. F. M H W J. H. R D.H.W E. G M.H.K w. S F.G.R Sum (X) 1181.1 89836.41 30025 57305137 2264739.6 This method gives constants with the maximum degree of exact- ness. It has the special advantage for physiological work that, after the fundamental summations have been made for a first series of experi- ments, subsequent determinations may be added and the correlation on the basis of a larger N determined merely by the addition of the summations of first and second powers and products for the new series. Or, if one suspects that a single aberrant individual, or group of indi- viduals, has too much weight in determining a given coefficient, the METHODS OF STATISTICAL ANALYSIS. 23 first and second powers and the products for the specific individual, or the sum of these values for the group of individuals, may be subtracted from the original value of 2 (a;), ^{x^), 2;(y), l^{y^) and S(x2/) and the means, standard deviations, and correlation be redetermined on the basis of the reduced N. This has been the method followed in the calculations of the present study. We have used the original measurements as published in the fimdamental tables, pp. 38-47, without modification or grouping. This has necessitated rather heavy arithmetical work, since the squares and products have been very large. The course has, however, the merit of introducing no error not already inherent in the data. As an illustration of method we again take the constants for body- weight and daily heat-production in our smallest series, the 16 athletes. The values required are given in table 3. These give S(w) =1181.1 2(u>') =89836.41 N = 16 2(w)/N = w= 73.8188 (r„ = Vi:{w^)/N-w* = 12.8670 X{h) =30025 2(A0 =57305137 ^ = 1876.5625 c^ =245.1209 2(uj;i) =2264739.6 2(w;;i)/iV = 141646.225 and finally ^ 141546.225 - (73.8188 X 1876.5625) ^^ g.-- '""* 12.8670X245.1209 l-r« =0.0828 ^, = 0.0140 That in presenting our results we have retained more figures than are really significant for physiological work is quite as clear to ourselves as to anyone who may desire to lop off the constants. But we have borne continually in mind the fact that these constants may in many instances be required for further calculation. It has seemed desirable, therefore, to retain a number of places sufficiently large to enable those who care to do so to check particular phases of our work without going back to the raw data. Chapter III. INDIVIDUALS AND MEASUREMENTS CONSIDERED. In the first of the three sections into which this chapter is divided we list up and briefly discuss the measurements (both physical and physiological) considered in these pages. In the second section we catalogue the series of individuals with the results of the measurements which have been made upon them. These are the data upon which our constants are based. In the third section we apply certain criteria adapted to determining the smtability for the pmposes of the present study of the individuals upon whom measiu*ements have been made. I. MEASUREMENTS CONSIDERED. The following are the measurements which have been considered. The symbol in parenthesis is the one used to designate the measurement in the statistical formulas. A brief explanation of the method employed in making the determination is given later. Stature (s), or height, in centimeters. Body-weight (to), in kilograms. Body-surface, or area, in square meters, as estimated by Lissauer formula (ol). Body-surf a«e, in square meters, as estimated by Meeh formula (ajr). Body-surface, in square meters, as estimated by Du Bois height-weight chart (ai>). Pulse-rate (p), in beats per minute. Carbon-dioxide output (c). Total in cubic centimeters per minute. Oxygen consumption (o). Total in cubic centimeters per minute. Carbon-dioxide production, in cubic centimeters per minute, per kilogram of body- weight (Ck). Oxygen consumption, in cubic centimeters per minute, per kilogram of body-weight Body-temperatuie ((}. Heat-production (A). Total heat-production (indirect calorimetry) per 24 hours in calories. Heat-production per 24 hours per kilogmm of body-weight (hi,). He^t-production per 24 hours per square meter of body-surface according to Lissauer formula (Ax). Heat-production per 24 hours per square meter of body-surface estimated by Meeh formula (Ajr). Heat-production per 24 hours per square meter of body-surface estimated by Du Bois height-weight chart [ho). The following are the details which seem essential to an understand- ing of the measTirements utilized. StcUure. — Statiu-e, without shoes, was measured in adults by means of a graduated vertical rod with an adjustable horizontal bar which was lowered to the top of the head. 25 26 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. In infants the length must be taken as comparable with the stature of the adult. In discussing the data for infants we shall, therefore, refer to the relationship between stature and other characters rather than to that between length and other characteristics. This is done to maintain uniformity in the statistical symbols. In measuring iriants the vertical rod was of course replaced by a fixed and a movable vertical on a horizontal scale. Body-weight. — Body-weight, in kilograms, was always taken with- out clothing. While weight of clothing may be a negligible factor in life-insurance examinations, or even in anthropometric investigations, it can not be disregarded in careful physiological work. Experience at the Nutrition Laboratory has shown that weight of clothing will amount to about 4.0 kilograms for men and 2.5 kilograms for women. Body-surface. — In conformity with the custom of physiologists, heat-production has for certain purposes been expressed in calories per square meter of body-surface per 24 hours. The measvu-ement of body-surface presents very great difficulties. If the superficial area of our subjects had been measured directly a series of determinations one-tenth as large as that here considered could probably not have been secured. The whole question of body- surface in relation to heat-production will be discussed in detail in Chapter VI. For the moment it is necessary to note merely that for infants siirface was estimated by the Lissauer' formula where a = area in square centimeters and w-weight in kilograms. When the original Nutrition Laboratory series was published * the Meeh formula ' a = 12.S12-^w* for adults was generally accepted. The results of later studies have also been expressed by this formula and in addition estimated by the Du Bois height-weight chart,* which is based on the linear body-surface formula of D. and E. F. Du Bois.* This covers sufficiently the physical measurements. The body temperature of our own subjects has not been consid- ered. In discussing the literature we have, sometimes, referred to temperature, designated in our formulas by t. In such cases the reader must consult the paper cited for details as to measurement. The physiological determinations can best be explained by a single general description of the apparatus and method of experimentation. > Liaaauer, Jahib. f. Kinderheilk, 1902, N. F., 58, p. 392. ' Benedict, Enunes, Roth, and Smith. Joum. Biol. Cbem., 1914, 18, p. 139. • Meeh, Zeitschr. f. Biol., 1879,, 15, p. 425. * Du Boia and Du Bois, Arch. Intern. Med., 1916, 17, p. 863. ' Du Bois and Du Boia, Arch. Intern. Med., 1916, IS, p. 868. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 27 Before proceeding to technical details a few words on the general principles involved may be useful to the reader who approaches this subject for the first time. The calorie is the unit of measurement of energy transformation. Theoretically the measiu-ement of heat-production by the calorimeter is the only correct method of measuring the amount of the katabolism. Practically the technical difficulties of the actual measurement of the quantity of heat produced by a living organism are so great that for many purposes direct may be replaced by indirect calorimetry — that is, by the calculation of heat-production from the amount of the respira- tory exchange and the ratio of the volume of carbon dioxide exhaled to the volume of oxygen absorbed. The application of this method depends upon the fact that the heat set free in the combustion of a given substance may be determined with precision in the laboratory. Thus to make possible the calculation of the total heat-production from the measurements of the two gases in the respiration chamber, or when possible from measures of the two gases and of nitrogen excretion, it is necessary to ascertain only the calorific values of unit volimaes of oxygen and carbon dioxide for the combustion of the substances which are oxidized in the human body. The consideration of the COs/02 ratio, or the respiratory quotient as it is commonly designated, as well as the actual volumes of the two gases, is necessary because of the fact that the calorific value of either of these gases is determined by the nature of the substances oxidized. Thus a liter of COj derived from the combustion of carbohydrates (starch) corresponds to 5.043 calories,® a liter of CO2 derived from fat corresponds to 6.680 calories, and a liter of CO2 derived from protein has an equivalent of 5.690 calories. The calorific equivalents for a liter of oxygen are 5.043 calories for carbohydrates, 4.755 calories for fat, and 4.600 calories for protein. Thus the ratio of the carbon dioxide set free to the oxygen used in the combustion of carbohydrates, fats, and protein is, within limits, constant and specific. For the combustion of all carbohydrates, the COj/Oj ratio must be unity. Since the composition of the several fats and proteins varies, the COj/Oj ratio must also vary slightly. There are other difficulties to be considered in the indirect deter- mination of heat-production. The synthesis of fats from carbohydrates greatly disturbs the CO2/O2 ratio. The use of indirect calorimetry for work in man has, however, been fully justified by the experimentation of Atwater and his associates ^ and shown to be applicable to short periods by Gephart and Du Bois.* • Benedict and Tompkina, Boston Med. and Surg. Joum., 1916, 174, p. 858; average values obtained from table 1. 'Atwater and Benedict, U. S. Dept. Agr., Office Ezpt. Sta., 1899, Bui. 69; 1902, Bui. 109; 1903, Bui. 136. Benedict and Milner, U. S. Dept. Agr., Office Ezpt. Sta., 1907, Bui. 175. ■ Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 850 and p. 854. 28 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. At the present time it is generally admitted by students of metab- olism that for the short observation periods, which are essential for the measurement of the individual in a state of complete muscular repose and in the post-absorptive condition, the errors of computation of heat-production by the indirect method are actually less than those of direct measurement in the calorimeter.® We have expressed total heat-production in calories per 24 hours. This has seemed to us the most desirable unit for a universal standard. In employing this unit of time there has been no attempt to obscure the fact that the actual measm-ements covered shorter periods. In practically all cases, however, the 24-hour constant is based upon a number of periods. Since in indirect calorimetry the thing actually measured is the gaseous exchange, we have worked out and discussed the chief statis- tical constants for the measures of gas volume as well as for the total heat-production indirectly derived from them. Anyone who may be inclined to discredit the results as expressed in calories computed by the formulas of indirect calorimetry may see our chief conclusions established by the constants based on the directly measured gaseous exchange. In passing, it is worth while to note that the high degree of con- sistency in our oxygen and carbon-dioxide measurements affords strong evidence for the trustworthiness of our constants. The coefficients of correlations between oxygen consumption and carbon-dioxide excretion in the adults ^° are given in table 4. Table 4. — Correhiion hetvxen two measruTea o} gaseous exchange. Series. N Correlation between COt and 0., y„ E. Men, Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary scries Original and first supplementary series . . Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 88 71 28 116 19 64 135 66 36 101 0.9799 0.8962 0.9488 0.9350 0.9507 0.9432 0.8738 0.9333 0.9335 0.0069 ±0.0169 0.0072 ±0.0101 0.0123 0.0069 0.0366 0.0109 0.0076 0.8794*0.0188 0.9662*0.0076 0.8917*0.0137 142.0 53.0 131.8 92.6 77.3 136.7 23.9 85.6 124.5 46.8 127.1 65.1 ' A review of the problem of direct and indirect calorimetry is given by Krogh, The Respira- tory Exchange of Animals and Man. Longmans, Green and Co., London, 1916, p. 9. " Because of the technique in the measurement of oxygen consumption and carbon-dioxida production necessarily adopted in the case of infants, we have not been able to include the correlations for these series. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 29 All of the constants are of a very high order indeed. In the original published series r= 0.949 =±=0.007, while in the Gephart and Du Bois selection r =0.935 =*=0.010. The first two series of men (N = 116) gives r = 0.943 =t 0.007, while the whole series {N = 135) gives r = 0.934 ± 0.008. The first and second series of women differ a httle more in the correla- tions. In the first r =0.879 ±0.019, whereas in the second the result is r = 0.966 =±=0.008, a difference of 0.087*0.021. The high correlations justify great confidence in the technical phases of the work. Had there been large errors in the measurement of either oxygen consumption or carbon-dioxide production, correla- tions of the order here tabled could hardly have been secured. The basal metabolism of all our subjects was measured by well- known methods. A few determinations were made by the Tissot method" with all of the niceties of manipulation that have been worked out by Dr. T. M. Carpenter, of the Nutrition Laboratory staff. *^ The larger number of measurements in the original Nutrition Laboratory series were made with a universal respiration apparatus devised at the Nutrition I^ab- oratory and designated as the unit apparatus. The earUer and more modem forms of this apparatus^^ differ somewhat in the provision made for expansion in the closed air-circuit. Certain of the results obtained with the bed calorimeter'^ are quite comparable with those due to the use of the imiversal respiration apparatus and are included in the original Nutrition Laboratory series. Finally, a number were made with the clinical respiration apparatus at the New England Deaconess Hospital, under the skillful technique of Miss M. A. Corson, of the Laboratory staff." An elaborate series of comparisons, in which all of these various methods have been critically tested, shows that the basal metabolism determined by any one is comparable with that determined by any other.'® The heat-productions determined directly in the bed calorimeter are omitted, and are replaced by those indirectly computed from the gaseous exchange and the respiratory quotient. Thus all the values of total heat-production are due to indirect calorimetry and are exactly comparable among themselves. All of the apparatus employed at the Nutrition Laboratory was made and tested there. That used at Battle Creek was built on the ground, but was subsequently tested and approved by Roth and one " Tissot, Joum. de physiol. et de pathol. g6n., 1904, 6, p. 688. " Carpenter, Carnegie Inst. Waah. Pub. No. 216, 1915, p. 61. " For the original description see Benedict, Am. Joum. Physiol., 1909, 24, p. 345. The more modem form is described in Deutsch. Archiv. f. klin. Med., 1912, 107, p. 156. " Benedict and Carpenter, Carnegie Inst. Wash. Pub. No. 123, 1910, p. 45. " The description of this apparatus is given in detail by Benedict and Tompkins, Boston Med. and Surg. Joum., 1916, 174, pp. 857, 898, 939. '• Carpenter, Carnegie Inst. Wash. Pub. No. 216, 1915. 30 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. of US. All of the operators acquired their technique personally in the Nutrition Laboratory. The data are, therefore, due not merely to uniform method and apparatus but to comparable manipulation throughout. The routine involved the appearance of the subjects at the Labora- tory at about 8 a. m., in the post-absorptive conchtion, i.e., about 12 hours after taking their last food. They then lay down upon a couch or bed and remained perfectly quiet, usually half an hour prior to the first period. Absence of muscular activity during the experimental periods was assured by the bed being provided with a graphic registering device which indicated the slightest alteration in the change of position of the center of gravity of the body, or by the attachment of a chest or thigh pneumograph which registered shght muscular movement. Experiments were usually made in several periods of 15 minutes, with interims of 15 to 20 minutes. To secure the most representative value possible, experiments were usually made two, and frequently many more, days with the same subject. The pulse was nearly always taken, and usually the oral tempera- ture. Subjects with febrile temperature were rejected. In selecting the periods of observation to be used, those in which there was an absence of muscular activity were chosen. This wae assured by having the individual under observation lie on a bed, one side of which rested on a knife edge while the other was supported by a spiral spring. A change in the level of the bed altered the tension of a pneimiograph connected with a tambour and kymograph. The smallest motion of any kind, even a movement so slight as to be imperceptible to the observant trained nurse, disturbed the linearity of the kymograph record. Thus periods of perfect muscular repose could be selected on the basis of an instrumental record alone, without the possibility of the personal equation of the observer plajdng any part. In the respiration calorimeter, in which each experiment lasted at least 1^ hours, such complete muscular repose could not be obtained as in the shorter periods with the universal respiration apparatus. But here the subjects fully understood the necessity for quiet, and while the Iqrmograph records naturally show somewhat greater irregularity in the long than in the selected short periods, the subjects were remark- ably quiet and the irregularities in the tracings are so slight as to indi- cate negligible muscular activity. The computation of heat-production is usually based upon the oxygen consumption, making allowances for the slight changes in the calorific equivalent of oxygen with varying respiratory quotients. The calorific value of oxygen is much more nearly constant, irrespective of the character of the katabolism, than is that of carbon dioxide, and hence ua practically all of the cases we have used the oxygen consiraip- tion. In a few instances where the oxygen determinations were faulty, INDIVIDUALS AND MEASUREMENTS CONSIDERED. 31 we have used the carbon-dioxide production. When either the oxygen or the carbon-dioxide determination was missing, we have assumed, when no better evidence is available, a common respiratory quotient of 0.85. In certain cases w^e have used quotients determined on the day antecedent to or the day subsequent to the period on which a constant is based. Usually the quotient of 0.85 is used. As in these short experiments it was frequently difficult to secure accurate collection of urine, we have not attempted to compute the calories from protein nor the non-protein respiratory quotient, but have taken the calorific equivalent of oxygen as used by Zuntz and Schumburg," making no special correction for the influence of the protein metabolism upon the respiratory quotient and the calorific equivalent of carbon dioxide and oxygen. In short experiments, par- ticularly with uncertainty as to the nitrogen excretion in the urine, this procedure is recommended by Loewy*® as giving results practically within 1 per cent of the true value. 2. DATA ANALYZED. The data analyzed in this volume were gathered in the course of the various investigations which have been carried out at the Nutrition Laboratory, or by those collaborating with this Laboratory, during the past several years. Two series have been published. The data are given in full in this publication and are therefore available to anyone who cares to go over the analytical phases of the present treatment. The materials are the following : A. A series of 51 male and 43 female infants investigated by Benedict and Talbot.^' This series was chosen rather than the first series published by Benedict and Talbot^ because, in the opinion of these workers, the second series represents a far more homogeneous series of materials. This will be designated as the infant series. B. A series of measurements on 89 men and 68 women made at various times at the Nutrition Laboratory and elsewhere by cooperating investigators, and published^' as a basis for a comparison of basal metabolism in men and women, athletic and non-athletic indi- viduals, vegetarians and non-vegetarians, and so forth. This will be designated as the anginal adult series to distinguish it from two sup- plementary series of measurements of adults hitherto unpublished. C. Determinations of basal metabolism in 28 men and 1 woman carried out subsequently to the series described immediately above. These data will be designated as the First Supplementary Series. (The woman has been included with the second supplementary series.) D. The Second Supplementary Series. This comprises 19 men and 34 women. " Zuntz and Schumburg, Physiologie des Marsches, Berlin, 1901, p. 361. " Loewy, Oppenheimer's Handbuch der Biocbemie, Jena, 1911, 4, (1), p. 281. » Benedict and Talbot, Carnegie Inst. Wash. Pub. No. 233, 1915. » Benedict and Talbot, Carnegie Inst. Wash. Pub. No. 201, 1914. " Benedict, Emines, Roth, and Smith, Journ. Biol. Chem., 1914, 18, p. 139. 32 A BIOMETBIC STUDY OF BASAL METABOLISM IN MAN. These four series are the sources of the constants published in this volume. From the figures given in the protocols in which these data are brought together (pages 38 to 47) the reader who desires to do BO may verify the calculation of any of our constants. The exact statement of the several measurements of each individual subject will not have its primary value in the possibility of the verification of the arithmetic of the present work, but in enabling the physiologist to criticize freely our fundamental observations or groupings of observations. These series form units of data upon which constants have been based. It may seem to the reader that physiologically more satisfac- tory results might be secured by sorting the entire number of individ- uals in these several series into more homogeneous groups as determined by some special structural or physiological character, for example, according to age, statiire, body-weight, body-surface, or pulse-rate. For the sake of argument, at least, this must be admitted. Such divisions will be made in the latter part of this volume. With regard to the question of division of materials the following considerations must be borne in mind. In segregating the data for purposes of analysis, two factors must be taken into accoimt. The more finely the materials are sub-divided the more uniform will the groups of observations be, provided, of course, that the divisions are logically made. On the other hand, the smaller the groups are made the larger will be the probable errors of random sampling attaching to the final constants, for these probable errors are inversely proportional to the square roots of the numbers of observations upon which they are based. The method of dividing the materials has been determined by both physiological considerations and by the practical exigencies of the work. When the apphcation of biometric formulas to the problem of basal metabolism in man was taken up, the only series of data available were the original series of adults and the infant series. These were classified according to sex in both series. The women of the original adult series have not been further sub- divided for purposes of general calculation. The men, however, are both more numerous than the women and apparently more hetero- geneous in physiological characteristics. A number are athletes and a number are vegetarians. After the work which has been done on the metabolism of athletes^* it would seem unjustifiable to merely lump together athletes, non- athletes, vegetarians and non-vegetarians and all other individuals of the same sex without determining what results are to be secured when they are treated independently. We have, therefore, segregated a '^ Benedict and Smith, Journ. Biol. Chem., 1015, 20, p. 243. See also page 244 of tliis volume. INDIVIDUALS AND MEASUKEMENTS CONSIDERED. 33 group of 16 athletes and computed all the constants upon which we have based our arguments for the individuals of this group alone. The smalhiess of the number of individuals available necessarily results in relatively high probable errors. The same course was also followed for the male vegetarians, but the number of these was so small that many purely statistical diflBculties arose, and since the metabolism of vegetarians has not been shown to differ significantly from that of men at large, ^^ we have omitted the discussion of this group. After the segregation of these two groups, the athletes and the vegetarians, there remain 62 other individuals, which have been used as the basis of another series of correlations. These are designated as the "men of the original series other than athletes and vegetarians," or for convenience merely as the "other men." The constants are also computed for the whole series of 89 men of the original series. When the first supplementary series became available it was treated as a whole in the case of men and also combined with the total men of the first series. The same course was followed when, before the completion of the long routine involved in the calculations, the second supplementary series fortunately came to hand. To avoid all possible objections which might arise from the fact that the individuals included were selected and the groups limited by one or the other of the authors of this report, we have felt it desirable to work out the constants on the basis of materials grouped for purposes quite different from the present ones by some other investigator. Most fortunately this has been done by such experienced workers as Gephart and Du Bois** who have combined their own 7 metabolism determinations for men with 72 of the 89 published by Benedict, Emmes, Both, and Smith, for the purpose of obtaining an average metabolism constant. From the 89 men of our original adult series, Gephart and Du Bois have seen fit to discard 17. While we shall discuss the validity of their reasons for this coiuse, we are heartily glad to have at our dis- posal, for comparison with the groupings of subjects arranged or limited by ourselves, those which have been approved by others whose training and personal experience in the clinic justifies them in passing judgment upon such matters. The elimination has been made by Gephart and Du Bois in the following manner : "All those over 50 years of age were arbitrarily excluded and also those under 20 years of age." " BcDedict and Roth, Joum. Biol. Chem., 1915, 20, p. 231. See also page 245 of this volume. " Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 858. 34 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. By this ruling the following individuals,^^ 10 in all, were withdrawn from the series: (87) F. P. (73) L. D. A. (81) V. G. (77) W. W. C. (22) E. J. W. (67) F. M. M. (31) H. F. (3) M. H. K. (79) C. H. H. (7) H. W. "In order to rule out those who were distinctly over or under weight, the subjects were all plotted in a curve, the height forming the abscissae and the weight the ordinates. All but 9 of the subjects could be grouped between two lines not very far apart. Of the 9, W. S., 0. F. M., Prof. C, H. F., F. E. M., and F. A. R. were evidently much heavier in proportion to their height. " Two of the 9, R. A. 0.=* and B. N. C, were evidently very light in pro- portion to their height. E. P. C. came just outside the line, but so close that he has not been excluded from the averages." This gives "a fairly homogeneous total" of 79 individuals "where average metabolism was 34.7 calories per square meter per hour, or exactly the same as that of the original 89 before the addition of 7 and the exclusion of 17." Note that (31) H. F. is excluded on the basis of both age and ratio of weight to height. Thus the individuals omitted from the Nutrition Laboratory series are 17 in number as follows: (2) W. S. (75) R. A. C. (or R. I. C.7) (73) L. D. A. (28) O. F. M. (25) B. N. C. (77) W. W. C. (30) Prof. C. (87) F. P. (67) F. M. M. (31) H. F. (81) V. G. (3) M. H. K. (17) F. E. M. (22) E. J. W. (7) H. W. (36) F. A. R. (79) C. H. H. This series we have designated as the Gephart and DuBois selection. Thus Gephart and Du Bois have settled for us the question of the specific men of the original 89 studied at the Nutrition Laboratory to be included in the determination of a set of statistical constants; but difficulties arose when the first and second supplementary series of men became available for analysis and we attempted to apply the same criteria to them in order to obtain a larger number of subjects chosen according to approved clinical standards. The elimination of individuals on the basis of age presented no obstacle. Of course the distinction between a man of 20 and another of 19 is a purely arbitrary one, but such arbitrary distinctions have to be made, and in selecting according to standards established by others one merely has to follow the rules which have been laid down. For the elimination of subjects on the basis of height and weight the case is quite different. Here too the division is necessarily an arbi- trary one, but Gephart and Du Bois have given no definite criteria by " The numbers in parentheses and the initials refer to the fundamental table of data on pages 38 to 47. ^ Evidently a misprint for R. I. C. of Benedict, Emmes, Roth, and Smith. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 35 which the individuals who are to be discarded may be distinguished from those who are to be retained in the series. They have said merely that "all but 9 of the subjects could be grouped between two lines not very far apart," Had not the authors designated by initials the men to be excluded in this specific series of determinations it would have been impossible for another writer to decide, without actual statistical criteria, which should be thrown out. It is, therefore, quite out of the question to divide any other series in a comparable manner without determining (o) what shall be the slope of the lines which cut off the outlying mem- bers of a series on the basis of height and weight, and (&) what the amount of separation of these lines shall be, i.e., what body-weights may be allowed in any group of individuals of the same height, or vice versa. The selection of a criterion by which individuals are to be discarded from a series ^^ is so important a matter (if those in presmnably good health are to be discarded from control series on the basis of physical configuration at all) that it seems worth while to go into the matter in some detail. The individuals to be segregated are distributed in a scatter diagram or a "correlation surface," according to the measure of heights and weights. From this siu-face it is desired to cut off certain areas, representing individuals of aberrant ratios of weight to height. Any line of division should take into account the general averages for both Etatiure and body-weight. We shall, therefore, select as a standard a line which will pass through the intersection of these two means. This establishes one position of the line. The slope must be ascertained. This is determined by the correlation between the two variables. Thus the equation required is given by e A. — Fundamental data for male infants. Obser- Body- surface Heat-production per vations. Body- weight in Height 24 hours No. Age. in in Pulse- Calories Calories Days. Peri- ods. kilo- grams. centi- meters. square meters, Lissauer. rate. Total calories. per kilo- per square 3 gram. meter. 2i days 2 2 3.63 52 0.243 97 166 46 685 5 7hrs. 1 1 3.82 52.5 0.252 112 137 36 544 6 3Jdays 2 3 4.32 52 0.273 116 191 44 697 8 2 days 2 3 3.48 51 0.236 117 160 45 673 10 2 days 2 3 3.45 52 0.235 116 162 48 694 15 4 days 3 3 3.64 50 0.243 122 162 44 665 18 7 days 1 2 2.84 50.5 0.207 105 108 38 519 19 IJ days 2 3 3.50 53 0.237 114 155 44 653 25 4 days 2 3 3.32 51.5 0.229 123 158 47 686 27 4 days 2 2 3.58 52 0.240 111 169 48 703 30 2 days 3 4 3.33 51 0.230 114 144 43 623 31 4 days 1 2 3.56 53.5 0.239 117 158 45 662 32 2|days 2 3 3.42 47.5 0.234 116 140 41 604 33 5 days 2 2 3.73 52 0.248 129 153 41 617 36 21hrs. 1 1 3.33 53 0.230 129 154 46 670 46 5hrs. 1 2 3.83 51.5 0.252 126 152 40 603 47 5hrs. 1 2 3.51 52 0.237 107 143 41 601 51 2 days 2 2 3.73 52.5 0.248 96 154 42 623 53 2 days 1 2 2.87 47.5 0.209 126 143 50 684 54 IJ days 1 2 3.31 50 0.229 106 129 39 563 55 16hrs. 1 2 3.45 50 0.235 124 151 44 641 56 4 days 3 4 3.19 51.5 0.224 121 150 47 669 57 22hr8. 2 3 3.75 54 0.249 105 153 40 611 60 4i days 1 2 3.60 52 0.241 117 149 42 617 61 2Jhis. 1 2 3.26 49.5 0.226 121 123 38 542 62 3 days 3 3 3.30 49.5 0.228 116 134 41 588 66 14hrs. 1 2 3.19 51 0.224 103 122 38 543 67 3 days 2 3 4.74 54 0.291 122 193 41 669 68 4 days 2 3 2.12 46 0.170 113 103 48 604 69 19hrs. 2 3 3.44 50 0.235 110 142 42 609 70 2 days 2 2 3.56 51 0.239 109 153 43 640 71 3 days 2 2 3.96 53.5 0.258 106 172 44 667 72 2J days 2 3.29 50.5 0.228 110 157 48 687 73 7hrs. 2 3.63 50 0.243 106 164 45 673 74 2 days 2 3.63 52 0.243 94 156 43 640 75 11 days 2 2.65 47.5 0.198 100 132 SO 664 76 13 hrs. 2 3.16 50 0.222 101 137 44 618 78 12hrs. 2 2.48 47 0.189 101 109 44 577 80 3 hrs. 1 3.47 51.5 0.236 109 128 37 642 82 3 hrs. 1 2.74 49 0.202 101 95 35 470 83 3 hrs. 2 3.73 52 0.248 131 148 40 597 85 9 hrs. 1 3.52 52 0.238 109 144 41 605 87 3} hrs. 2 3.94 51 0.257 118 146 37 567 89 8 hrs. 1 3.24 49.5 0.226 107 124 38 549 90 2i days 3 3.00 50 0.214 86 138 46 641 93 4 hrs. 3 3.53 50.5 0.238 127 136 39 573 94 3i hrs. 1 3.20 50 0.224 117 136 43 607 99 2ihrs. 1 3.58 51.5 0.240 103 122 34 508 100 eihrs. 1 4.65 54 0.287 130 186 40 648 101 5} hrs. 1 3.88 51.5 0.254 109 126 32 496 104 3 hrs. 1 3.32 51 0.229 107 105 32 459 INDIVIDUALS AND MEASUREMENTS CONSIDERED. 39 Table B. — Fundamental data for female infants. Obser- Body- Heat-production per vations. 24 hours. Body- Height surface No. Age. weight in in Pulse- Calories Calories Days. Peri- ods. in kilo- grams. centi- meters. square meters, Lissauer. rate. Total calories. per kilo- gram. per square meter. 2 6i days 2 2 3.80 53 0.251 99 152 40 606 4 2 days 2 3 3.28 46.5 0.227 105 139 43 612 9 2 days 1 2 4.04 51 0.262 109 178 44 677 12 5 days 2 2 4.17 52.5 0.267 112 171 41 639 13 2 days 3 4 3.25 50 0.226 113 138 43 612 16 2i days 4 4 4.03 53 0.261 113 175 44 670 17 15 hrs. 1 2 3.66 52.5 0.244 118 174 48 713 20 3^ days 1 2 3.54 52 0.239 110 153 43 638 21 2 days 1 2 2.92 50 0.211 121 136 47 645 22 2J days 1 2 2.72 49 0.201 114 128 47 635 26 5 days 2 3 3.46 50 0.235 113 151 44 645 29 2^ days 3 4 3.37 50 0.232 112 150 45 652 34 2 days 1 2 2.90 50.5 0.210 115 134 47 638 35 4 days 3 4 4.33 54 0.274 109 175 41 640 37 13 hrs. 1 2 2.49 46.5 0.189 119 99 40 522 38 IJ days 1 2 3.90 51.5 0.255 127 156 40 610 39 9 hrs. 1 1 2.95 50 0.212 105 113 38 533 40 4J days 2 3 2.78 49.5 0.204 111 134 48 655 42 3 days 2 4 3.95 54 0.258 113 176 45 684 43 2 days 1 1 3.62 50 0.242 119 165 46 682 44 2 hrs. 1 2 3.57 51 0.240 103 136 38 567 45 1 day 2 3 2.56 46.5 0.193 110 107 43 558 48 6 days 1 2 4.52 54.5 0.282 132 188 42 667 49 4 days 1 2 2.75 47.5 0.203 114 130 47 638 50 Iday 1 1 2.75 48.5 0.203 89? 142 52 700 52 2i days 3 4 3.54 50 0.239 114 138 39 579 58 Iday 2 4 3.01 49 0.215 111 139 46 647 59 IJdays 2 2 3.60 52 0.241 112 150 42 621 63 3 days 1 2 2.37 47.5 0.183 125 109 46 596 64 7 hrs. 1 2 3.37 48 0.232 98 128 38 552 65 2 days 2 3 2.63 49 0.197 116 127 48 644 79 4 hrs. 1 2 4.14 52.5 0.266 116 153 37 575 81 4 hrs. 1 1 3.29 50 0.228 114 167 51 732 84 2^ hrs. 1 2 4.11 54 0.264 109 133 32 604 86 6 hrs. 1 1 3.32 51 0.229 103 120 36 524 88 9 hrs. 1 2 2.62 47.5 0.196 96 122 47 623 91 13 hrs. 1 1 3.33 49.5 0.230 113 140 42 609 92 4 hrs. 1 1 3.78 51 0.250 112 157 42 628 95 5ihrs. 1 1 2.84 46.5 0.207 123 100 35 483 96 3} hrs. 1 1 3.23 51.5 0.225 99 113 35 502 97 4ihr8. 1 2 2.82 48 0.206 113 112 40 542 98 5 hrs. 1 3 2.86 47.5 0.208 102 98 35 471 103 2ihi8. 1 1 3.29 49 0.228 125 130 40 570 40 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. o IS Is 1 ■;jBqo ;qai9A -^mSiaq 'm'-bs J8d "saTioi^o t*MOOr-tOeo05«DOOOU300000t»OOt»0>U5000:SlOO(ON>0 03O03O^03OO03Oad03030303O030DQ00)00t-0B00O0303 •qaawj '•ni bs jad eaucpQ NCOCDOCOO>i-ltC>eOO>00000;DOOeOlOt»0>-ICOCONMe»5TOtD ooooooodoooo030oooooowcoooooaor^t^oooot>>cooot*oooot« ■oicn jad sauoiBO o5ootDooo--<"5'-it^oo-*03WTiio»t^t-:e«)»oNaiNi^Mooo>"s sauoiBO jB^ox a500J-H005inoo«DOioooototo>o"3tt>Tia3oioa>'4oi^piooococoTisit-u5toeOJ»-iN'^ NNC^lCONNCONNWNNNNNNNNClNW'-liHiHOJNCil •0-3 m appcoip-noqjvQ C4 •-4 CO c^ lo CO N U3 r> ■ o o> co '4< p co m t- oo e* t> >o ■* Til .* O •* ■* N Cn •H 00 c4 CO Til CO b- ?4 00 o 13 o t« o ■ co co oo ^h to o to >a to U3 U3 to t-> r« to to US to uj to o to u3 r« iQ to ■ t^ uj ui - 1 d n Body-surface in square meters. •^jBqs iqaiam-iqaiaq s 1 d a n a ^ a < ■■Binni -joj qaajii jCg -Kia^aoipaao m ^^qSpH S§88SSS5§SgggK|S||S|g|gSS|gS| -SIUBiSO] nim!)q3;3M-yCpog o>ooas>-iMoiTj>ou3t>eoot«oc4C40coe4tO'<ONC00S^CSWC0^*-tOI^*-t00»0tN,N0J00^H,-IC«l00» Sc3»-HSN(NXiN(NC^INe»NNej^^^'HWWWfc<: E. 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B.L. ... o -HC,:cT.«-^r^oocso^2c,3:22J:22§e5S5?5SS^S5 INDIVIDUALS AND MEASUREMENTS CONSIDERED. 41 s 1 s 1 s.i 1.1 1 1 s 1 1 s 1 s s 1 iB £ 1 s 1 1 1 s s § 1 |.|s 1 1.|| 1 1 » l-i miostoooo«)t-o5i^cOT)ior~0300oa50>c<5N>oeot^u5m«ou30'*MCQtoo>-<>ooo-Hoo>-!^t-j eoo30>aicooos03050t^ -Hot"eot»aiosNNttimtD>noaico;DooCT>o>m.-iioco"5co;^ooi2«o tSt>.0050-*COtDOO^O(N(NOQOiOT((rte<3t^OJCOTlOlOC>><-IS!2riOONOaON»-l t^t»t^«ooooooooot~oor-ooi^oot-t^ojoooot-t~(»oot--oot~t>-oot»oo05ooooooi~csooooa>o>t>. eor»o>t»eor^>ONO»05t~m'<*i05tDtDcoo»-*i^-*ooo5«OTiooot»tDNMMO>'*tDooi-iN-»ioo-*o>e<5'*-Hcop;u3.ieo o>^S(io>HrHCeoao«ooa>^o>t^t^ot>a>>-oa>Soo>o C4C4f-4i-.tC4C4C4C^ClC4^Hi-ii-lC4i-li-4C4f-HC4^H«-ti-Hi-H*H*-t*Hi-li-H*-4*-(C4C4C4i-(i-HC4i-4t-tC4C4v-l >oo«oSco>oSto>o>a>ou3'4<oScO(OioSiQ;o>ou3r~r~;o>oiaocou3cc>ou30 ■<«-!i-H'-»i-i>-;>-;'-;oooooo»oso»050JOsos050i**ffioo>*roooooooooS5oo NNNe«Ncie4e4eiNNN«Nc4NNNN»H»Hi-;-H^.-!iH.- 05t-ooo50io5CTi050>»ooooooo>aaoa>oi ' UJ '.A^ U_f U,^ l_^ -^r ^^ .^V ■qa8p\[ 'ui •bs jad 8auoi«3 00 CO o b* CO o WW ^' ^- >.-« 00 r^ 00 00 00 00 a> TiirHt^a>QcooDcoc^co>Hcoa>oooocQa>oocoeoc40i ^*NOQ-^o>oiNMe<50>eSffi' ooooa>a>Sc»r~aiaiooaoooa3aoo>t^t^t^oor^oooO( •ojiJi jad Bauo|BQ ooe<3'ncopast^wo>i-;aO'^'HO>-ii-'5t>.Tiot>^t^030odc^*cocdoiocou3cood -saiioiBa jB^ox cocoio>o3cocDin'jn'-wooo> M ^ V o "3 a 'a°3 ni naaXxQ 'joeo c6c4e^coc<3coc<}mcoconeococoeQeococoeocicJc6eo CO -♦^ 00 63 fl -a -a ni naajCxQ CO N eo M o CO Oi *^ CO N N -H « N N cOTi«ooeeopieor~oo5^eoo5>neoeo'*h-"50>>o rt^eoeo-HOcocoOi-i'HeoocTi»OS0»«^t».S>Olt-t~0»tOt»00lO>0^NO — "-co •ajBj-aspij iNi-icDNN^>-H.-iwo!^.-ir»u5r-.oe>ooeoo50»c»eoio 0> u 3 2." ■gad n ■?j'Bq3 ^qSiaAV-^qaiaq siog nci ./Ca -joj qaap^ iCg rteot^'^t->ncopot>.ooNcoi^'OT(coeot- r-r-:cocqocot.;cococo!0>n>oco>nco>o>oiniQ'cnoo TjiTfi'^coeoNNNriQoooot^cO'ONoqgtO'^asrt^coMOiO) 0000000D0000000q000qt~;t-;t>;Wt-;t-;t^C0COC0>n>Oe^f-4'-O5l>-^^O5'<1*NWCOa3CDNiOQr(cD^U500 t^t«cocor«cooor«r^t^coir3cot^^r*cDc0coeoiooocDb«oooot^ 'Siai^aan^naa ai )q3ia£[ ■BnrajSo[ni ai :)q3iaM-i(pog pooooe-<'Hoot^eoi-coN'<^t>^t^t^t>^c6cococ6u3<4<<4o6coca> ioio>':>n>o>o>a>ou30>0'n>0'Ou3'0>Q>o^Ti<^o>t»t~t>t^co i.2 O 53 "U •-HrHeMe<-iTtit»>noo>-ieoa»eO'»ioeocONcoNe* C^ OSrH C4^CO CI a Q UJrH-llHOON'S'MCOClMOieOI Tli 1-H t-t • ■ CO N rt eo ■<«" 00 ^t*'^^^o^^'H^•lr5coc^^^u^o>■.J< NCOC»Ni-lNOJCO.-lNi-ie-cNNeOCa)d)So> INDIVIDUALS AND MEASUREMENTS CONSIDERED. 43 ^as as 3 sill ssllsllllslJ J J . .Ic36 a9000>ooo030>a>a9t^cx)aioooooooooooocooosooo>aooooocoa>a><-iooa>oooo03aoa3ooasoo ooj>oot^3Ja>oot»oor-i~oot^ooooi>oooooooor-t-oot>.t>.osooooooooooooot^t-oeoooot~oot>. i-lO«>OOeO.-lOOtCO*ONe«u;-HOt>.i-ieCtOOU5lOt~.-Ht^U3lOMlOOOMt-.t~-*r-lMN'* Sislsi5igi|Pii5i§252||S|S|e33ii|g||||||| e<5e<5eocoeoTi;cQ«MeoeO'*eoe<3coweoeom-*eo-*MeoeC'i'eoeoe<5ro l§§i§i§ii2iiissiiiiiSsli§isilii§asiiSs§li g2i§§IS2§S$|S|S^SSB^§SSSS§g2§|^S§g§§i||S| Sg5gSSJ5S3SS£;gg§£;8§gSgSSE;S :::: :Z ■■■■■• -^ ■ :S^S S8§§§3oSS5SS5SE^§f2gigg5SSSS2§§SgSfc§Si2E:?|KKSg!§g 2.08 2.06 2.04 2.03 ?S^^S§§8SSSSoS§E:g?sS?3^^2§8§S8Sg§§SSfSK2gg ggSgi2SKfgK|SgSS5gSgSS^S?SgSSSg§g§f:g§§SSSSg lONN^^>o<»^^■*e<5T^ooNcp•*05■^os>qp^^e^o^'HC)Ol^-;c^^^coeo5D(C>T)l^^»ot»Ttla5^ooP^05■*^o-HoocOl-leooe<5e<^■c^oo^-•^^l CO "-1 N -^ .1 N -H gi§S?SS?SS?§:§SSS§?52Sg?3?3SS!2gg5SSSg3SSSSg?SSgSSJ5S A.J.O.... Dr.R.F... J. H. G.... Dr. F. W. P A. F J. L.S W. H. D... Dr. E. J. . . T. J. L. . . . A. J. G.... H.W. F... K. H. B. .. E. D. B. . . A.S J. V. M... W. K E. S. M. . . T. A Dr. A. H. R T. N. R. . . T. CD... Prof. W. M. W. H. B... F. W. R... R. R. D. . . Dr. C. G. W P.. H L. M. S. . . I.B.S.... W. A. W... C. J. J. . . . R. B •d Sfe§§SSS|S§§|§§2n22322522§SgggS|gg§§S§g§S§ | 44 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 1 o Qosaoi^asasassasE Emmes. Emmes. Roth. s. u r s 'jajara ajBnbs jad saiioiBQ t;SINOOlOONOC>b-COT)lOeO-S"«tt>Ot- oooox(X>ooooaoaot~t>xoo>r-o>ooooo300 ■Binmioj qaajij 'jai^am aavnbs jad sauoi'BQ in00NejI^CONt-OSNOJ«(OC»5t»'>JI00COO> ■uibj3oipi -"^d sauoiBQ 05><5i-ii--»P)i-lONCOC>»COOOOO->l<-*Ni-i-H Gaseous ex- change per kilogram per minute. ■3-a m uaaXxQ t>;Qqiopci eieicieic6e6t<3t6neie6mmeimmne6c6 i •00 m appcoip-uoqjBg i Gaseous ex- change per minute. •O'O m naSiCxQ «D-*00C<3OCJt»NN00e000l^e0C0t~«0NC3 •pincQcoNpoocioooeoor^NOONO •0-0 m apreoip-noqjcQ c» n o -^ oe»> toiotototoustoototot^t^totoooiototor^ Body-surface in square meters. ■jjBqo ^qSiaM -?q3iaq BTog nQ ^Cg ^tDN-HO0l»rt'*tON'Hpu5-HCO0OtOr»N pppoot^^t^t^t^tor^t^ptotoptoptqto ci 5 '«inauoj qaa}\[ Xg iOTi<'4)ppo;a;po;ppoqGqooooaooq(>b H •Riajampuao m tqaiajj m'^»Ht»o-Hto-H»HoooOTio»>OTi 09 1.1 1^ «C0tCt»tOiOt-.tOl»tDtD'0 1 I 5jdWWdi»dbM!h4«ijSSa ^.l.iE.g.2.8.i.g.a.8.i^ja.g.|Sg d -HNCO'^custtt^oomo-HNrO'Ttiiotot^oom K 1 INDIVIDUALS AND MEASUREMENTS CONSIDERED. 45 i J i i i SBjEEEESB^oESBESEE^BBBBEgaaBBoQ&SBSS 0-*mTOtt)CD^-*w0500(N05«aSeoK.^^(N(NSMtDot--roloK-NM(NOOiO«D oooooooooooioooot^i^oooooooocnwooosooooooooooooorot-ooooot^osooooo ^H ^ 1-t ■*01rtt~rJl00OMO'>!(ltDC0Me>JOC* ioou5oa>MOtoaieviiot-..-iTHiou3eooo-HinrtOco-«»< T(<-o(Ncoe^Ne>eococOTtieoc>»->!)*<— ico.-HMOcoTfie-r~050tOOOt»05CD03.-IOOOO 2lSi2S&SSS22222S§S2:S2S3l22SS22SS2§S feRR§SS!2gS?SSSS§§8ffggKf:SS{:S8SgSf2SSSfSSgSS§ SgSSSSSSSgSSSSgSogSgSSS^SSSSSgS^SSS^:^^ SSS3g?g??2?SfffcgS{2S;KSSKSSgg§§§?S5o!SfeS!§SS!gSSS 2S222§2SSS§222222l§2222^2i§il2222222 feE;Sgg!gSSSSS?ggggggS3SSggggg?5§SS^^^^^ ■«»««o«oiooo«Di-oor^»o«wooo>ntDtt>ece>NN 2Si32gS53^gS§S?3S£;S2Sg2?5c32S2SS!?32?5S^S!S;?58 »J . . PO • . • • . . SwiJW-a5--;dQ!Sc=;i-ihjfaij SSg3SSSSSiS§gS5?S5SS^£;?§§S5?SS5:^S?!5!^5gSggSS 46 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. i i H ■ . .sss . .Is s ll^ocS 1 = a o ! 'jajam arenbs jad saiioj^o ^-oooooooot-t»t^aOQOooi^wt»u5mt-(N.oo •niBiaoipi Jad sauopa 05»osc<5mioo»T(ir-t-*r-'^rtOt^t-M«oo •6 .S ■sauofBo ib;ox ■a-o m na3jCxo 1 •O'o ut appcoip-noqj«Q U ^ ill K d c •a a at aaaSxQ 1 •a-a m aprxoip-uoqjBQ o •a;Bj-tfb[iij O 00 00 t~ » "O « to t- 00 O CD t^ O O . • . . S <« s . •C S E PQ •^jBqa ^q3iaM -^q3raq siog rq iCg i-*ocooco^^^^co»o^^O'©ooosoo'*NC^ 1 d ■Binauoj qaap^ Xg ooocoepiOf-*oooiOTjHooco^H"#eooco^ ffltOU3U5i6lOlO>OTtlTjiTj. > 00 i -HNN — -< — >nN'-r3i-i05t^'i^.(5mNropp OOt000005'*0-*K5iOOOlOroNOO'-iOO!000'*i-lO«-*lOt-.»-iQO'*OSOOS05C>505 ■*ioo-*'>»'Os^oa=co05ioooo5->)it^rteomo»--i coNcoeo«coe6eocoeomc<5«'TfJNMc<5eo ,-it.T)(T)it»oosioin»ONr~ira«»T)it-inNioosoot^(^oor»Tiiffloo CO'*i-tNroi-l.-lt~050Mt~tO-9fflOOOSO> SS|||g|Sfe||gS§2SSSgS|g§||S|SS S§§§SSS§§iiiS2S2S2SSg|g§3§SSi • ^o^» • • t^ 00 so -to -o • -tot^uj .(o»j '^owosictot^ioo g?S!§g§E;E;S3S^§^S?S;gSS?2SSf:SSggS!5^ 2!B2H^a^6^s2s^!^ilg^^iSi!!S!2 SSSggS|§Sg5gggS5||||gSgSgSSSS sSilisssssliiSISiS^Ssiiillsll -Hl-lrtTHNN»Ne«<-lNi-('-li-li-lN.-IMe<>i>i>QoaoQoooQOooouoooOooc&0)0)oo>a^(&o>Oi030000 48 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. The name of the observer in the final column of tables C and D fixes the laboratory at which the determinations were made. The places for the several observers are: Carpenter, Nutrition Laboratory. Means, Nutrition Laboratory. Cathcart, Nutrition Laboratory. Riche, Nutrition Laboratory. Miss Corson and Miss Johnson, New Eng- Roth, Battle Creek Sanitarium. land Deaconess Hospital, Boston. Smith, Sjrracuse University. Eminea, Nutrition Laboratory. Miss Tompkins, Nutrition Laboratory. Higgjns, Nutrition Laboratory. 3. CRITERIA OF SUITABILITY OF MATERIALS DEALT WITH. In this volume we have limited ourselves to the discussion of the metabolism of normal infants and of normal men and women. It is important that the conception of normal as used in its present connection be made perfectly clear at the outset. First of all, it means individuals in presumably good health. Second, it is important to remember that, as we have used the term, the normal man is not an individual of any preconceived dimension, but a group of infants, men, or women representing the typical condi- tion in the population. The population at large has a certain mean, variability, and corre- lation of the measured parts of the human beings of which it is made up. We may, therefore, properly inquire whether the subjects studied at the Nutrition Laboratory agree reasonably well in correlation as well as in mean and variability with men and women as they have been studied by anthropologists. If they do agree in the physical characters for which a basis of comparison may be seciu'ed, within the limits of the probable errors of the determinations, we may feel confident that we are dealing with "representative," "typical," or "normal" men and women. If they differ too widely from the population at large, our data can not be considered altogether free from criticism. In the following paragraphs we shall test the suitability of our material for the solution of problems concerning the physiology of a species, man, by ascertaining whether the sample of subjects dealt with is really representative of man in general in mean, variability, and correlation. In presenting oiu" constants we are, of course, fully aware that these problems have been so extensively investigated by anthro- pologists and actuaries that no material contribution to the anthropo- logical problems can be made on the basis of the number of individuals examined in this paper — a number which, while large from the physio- logical standpoint, is relatively small as compared with the more satisfactory anthropological series. In the field of metabolism this coiirse seems to have a particular justification. Practically the chief purpose of studies of the basal metabolism of normal subjects is to obtain a basis of comparison on which, in connection with studies in the experimental laboratory or INDIVIDUALS AND MEASUREMENTS CONSIDERED. 49 medical ward, conclusions may be drawn concerning the influence of special conditions, diets, or diseases upon metabolism. If results of the kind are to be of general value they must be universally valid and universally applicable. To be generally valid and broadly applicable the fundamental series should be based on individuals t3T)ical, not merely in average but in variability and correlation, of the population as a whole, rather than composed of individuals conforming to some personal preconception of "normal." First of all we may present the actual statistical constants of the series of data which we have analyzed, and compare them with others based on larger numbers of individuals. Otherwise our own constants will not be discussed in great detail here, but form the basis of most of the calculations in the following chapters. Table 5. — Physical constants of male and female new-born infants. Series. •V Average. Standard deviation. Coefficient of variation. Male. Weight 51 51 51 51 51 43 43 43 43 43 94 94 94 94 94 3.459 ±0.0430 112.39 ±0.9524 144.55 ±1.974 0.2350±0.0020 50.971 ±0.1665 3.336 ±0.0564 111.77 ±0.8705 140.37 ±2.389 0.2294 ±0.0026 50.163 ±0.2265 3.403 ±0.0350 112.11 ±0.6525 142.64 ±1.537 0.2325 ±0.0016 50.601 ±0.1408 0.4554 ±0.0304 10.08 ±0.6734 20.90 ±1.396 0.0209 ±0.0014 1.763 ±0.1178 0.5483 ±0.0399 8.46 ±0.6155 23.22 ±1.689 0.0250±0.0018 2.202 ±0.1601 0.5036 ±0.0247 9.38 ±0.4614 22.09 ±1.087 0.0230 ±0.0011 2.025 ±0.0996 13.17 ±0.89 8.97 ±0.60 14.46±0.99 8.88 ±0.59 3.46±0.23 16.44±1.23 7.57 ±0.55 16.54±1.24 10.89 ±0.80 4.39 ±0.32 14.80±0.74 8.37 ±0.41 15.49 ±0.78 9.88 ±0.49 4.00 ±0.20 Pulse-rate Total heat Surface. . . . Female. Weight Total heat Length Both Sexes. Weight Total heat Length Consider first the problem of the variation and correlation in stature and weight in the series of subjects dealt with. In doing this we shall lay emphasis upon variability as well as upon average dimensions. This is done because in selecting a series of meas- urements to be considered typical of the population at large it is quite as important that they represent the diversity of the population as that they show the proper average values. The physical constants for our male and female infants are giyen in table 5. For body-weight we have the following series of infants for compari- son with our own. Quetelet's classic series,''* as reduced by Pearson,^* gives the follow- ^Quetelet, Anthropom^trie, 1871, p. 355. » Pearson, The Chances of Death, 1897, 1, p. 307. S.D. C. V. 0.482^0.029 14.66*0.90 0.538*0.034 17.62*1.16 50 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. ing means, standard deviations, S. D., and coeflScients of variation, C. V., for new-bom male (iV =63) and female (iV =56) Belgian babies : Mean. Male infants 3.289*0.041 Female infants 3.053 * 0.048 Reducing the data of the Anthropometric Committee's Report to the British Association,^" we find for 451 boy infants and 466 girl infants : Mean. S. D. C. Y. Male infants 3.230*0.016 0.508*0.011 15.73*0.36 Female infants 3.151*0.015 0.480*0.011 15.22*0.35 From Stuttgart babies, 500 of each sex, Pearson deduced from Elsasser's measurements : Mean. S. D. C. V. Male infants 3.233*0.013 0.439*0.009 13.57*0.29 Female infants 3.151 *0.013 0.418*0.009 13.28*0.29 For the 1000 male and 1000 female new-bom infants measured in the Lambeth Lying-in Hospital (London) Pearson ^* found: Mean. S. D. C. V. Male infants 3.312*0.011 0.519*0.008 15.664*0.242 Female infants 3.208*0.010 0.456*0.007 14.228*0.219 Dr. Rood Taylor ^^ has kindly allowed us to use his series of measurements of new-bom infants, deposited at the Wistar Institute. These are very heterogeneous racially. We find for his 120 boys and 122 gu-ls: Mean, Male infants 3.496*0.026 Female infants 3.368*0.026 A comparison of our constants with those due to anthropologists is made in table 6. Here the signs of the differences show whether the constants for our babies are larger (+) or smaller (— ) than those deduced by others. Our infants show a slightly, but only slightly, greater average body- weight than either of the European series available for comparison. In 5 of the 8 comparisons the difference is less than 0.2 kilogram. In general the differences may be regarded as statistically significant in comparison with their probable errors. Our infants are slightly but not significantly lighter than Dr. Rood Taylor's series. In variability, as measured in the absolute terms of the standard deviation and in the relative terms of the coefficient of variation, our series show an excellent agreement with those which have been pub- lished. In 7 of the 10 comparisons our standard deviations are slightly greater, while in 3 of the 10 comparisons they are slightly less than " British Association Report, 1883, p. 286. " Pearson, Proc. Roy. Soc. Lond., 1809, 66, p. 25. " Taylor, Am. Joum. Physiol., 1918, 45, p. 669. S.D. C.V. 0.419*. 018 11.99*0.53 0.423*. 018 12.57*0.55 INDIVIDUALS AND MEASUREMENTS CONSIDERED. 51 those due to other observers. The differences can be looked upon as statistically trustworthy in only 2 or 3 of the comparisons. Quite comparable results, as far as the smallness of the differences are con- cerned, are found for the coefficients of variation. In 5 of the 10 cases our series are relatively less variable and in 5 cases relatively more variable than those with which they are compared. The differences are statistically insignificant except in 3 or 4 cases. Thus our babies are sUghtly heavier than those measured by others except Taylor, but agree excellently in variabihty, both absolute and relative. Table 6. — Comparison of weight of Nutrition Laboratory babies with other series. Series. Average. Diff. ^diff. Standard deviation. Diff. ^dijf. Coefficient of variation. Diff ^diff. British association: +0.229*0.046 +0.185*0.058 +0.147*0.044 +0.128*0.067 +0.170*0.059 +0.283*0.073 +0.226*0.045 +0.185*0.057 -0.037*0.050 -0.032*0.062 4.98 3.19 3.34 1.91 2.88 3.88 5.02 3.25 0.74 0.52 -0.053*0.032 +0.068*0.041 -0.064*0.031 +0.092*0.041 -0.027*0.041 +0.010*0.052 +0.016*0.031 +0.130*0.041 +0.036*0.035 +0.125*0.044 1.66 1.65 2.06 2.24 0.66 0.19 0.52 3.17 1.03 2.84 -2.56*0.96 +1.22*1.28 -2.49*0.92 +2.22*1.25 -1.49*1.26 -1.18*1.36 -0.40±0.94 +3.16*1.26 +1.18*1.03 +3.87*1.35 2.67 0.95 2.71 1.78 1.18 0.87 0.43 2.51 1.15 2.87 Girls Lambeth hospital: Girls Belgian babies: Boys Girls Stuttgart babies: Boys Girls Dr. Taylor's series: Boys Girls For comparison with our results for length we may reduce the British Association data used for body-weight above. The constants for the 451 boy and 466 girl babies are : Mean. S. D. C. V. Male infants 49.58*0.11 3.48*0.08 7.02*0.16 Female infants 49.07*0.10 3.25*0.07 6.62*0.15 We may also compare Pearson's constants for full-term male and female infants (1000 each) from the Lambeth Lying-in Hospital.^ His results are : Mean. S. D. C. Y. Male infants 52.08*0.07 3.38*0.05 6.50*0.10 Female infants 61.11*0.06 2.99*0.05 5.85*0.09 Dr. Rood Taylor's infants give the following values for total length : Mean. S. D. C. V. Male infants 51.18*0.13 2.04*0.09 3.98*0.17 Female infants 50.07*0.12 2.03±0.09 4.08*0.18 Comparison with our own series is made in table 7. The average length of our babies is slightly greater than the British Association series but slightly less than the Lambeth Hospital series. "Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 25. 52 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Our boys are slightly shorter and our girls a little longer than Dr. Taylor's series, but the differences cannot be asserted to be significant. All our variabiUties, both absolute and relative, as shown by the differences between standard deviations and coefficients of variation in table 7, are less than the British series, indicating that our measurements were made upon a group of infants somewhat more uniform. Our male infants are slightly less variable and our female infants somewhat more variable than Dr. Taylor's series. Table 7. — Comparison of length of Nutrition Laboratory babies with other series. Series. Average. Diff. E, diff. standard deviation. Diff. ^diff. Coefficient of variation. Diff. E. diff. British association: Boys Giris Lambeth hospital : Boys Giris Dr. Taylor's series: Boys Girls +1.39=i +1.09^ 0.20 0.25 -1.11*0.18 -0.95 ±0.24 -0.21±0.21 +0.10=t0.26 6.95 4.36 6.17 3.96 1.00 0.37 -1.72±0.14 -1.05*0.17 -1.62=i -0.79=i 0.13 0.17 -0.27±0.15 +0.17±0.18 12.29 6.18 12.46 4.65 1.83 0.93 -3.56 ±0.28 -2.23 ±0.36 -3.04±0.25 -1.46 ±0.34 -0.52±0.29 +0.33 ±0.37 12.71 6.19 12.16 4.29 1.79 0.89 The correlations between stature (length) and weight in our infants are as follows : For males N=51, r,„= 0.770 ±0.038 For females Ar=43, r,„ =0.864 ±0.026 For both sexes Ar=94, r,„ = 0.821 ± 0.023 For comparison with those we have the constants based on 1000 male and 1000 female full-term new-bom infants from the Lambeth Lying-in Hospital by Pearson '*. The results are : For males i\r=1000, r„„ = 0.644 ±0.012 For females i\r=1000, r™ = 0.622 ± 0.013 Reducing the Anthropometric Committee's ^* data, which as noted by Pearson are somewhat heterogeneous in origin, we find: For males iV=451, r™ = 0.665 ±0.018 For females iV=466, r™, = 0.539 ± 0.022 The correlations between length and weight in Dr. Rood Taylor's series are : For males r™=0.668±0.034 For females r™= 0.749 ±0.027 For both males and females our correlations are higher than those foimd by others. The differences are : Pearton'a aeriet. Britiah Aaaociation. Taylor*» iert'ei. For males, +0.126±0.04O +0.105±0.042 +0.102±0.051 For females, +0.242 ±0.029 +0.325±0.034 +0.115±0.037 ** Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 25. ** British Association Report (Southport), 1883, p. 286. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 53 In most cases the differences axe apparently statistically significant in comparison with their probable errors. Thus our series of infants, both male and female, are certainly more highly correlated in their weight and length than the series studied by others. Simamarizing the results of this brief and superficial comparison, it appears that while our series differ in correlation, they may never- theless be considered to show a very satisfactory general agreement in both mean, and variability with babies studied by others. Con- sidering the possible influence of race, age, and social status, the agreement seems rather remarkable. We assert, therefore, that we are dealing with the constants of "normal" male and female infants, not merely because they are appar- ently normal from the comparative standpoint of the obstetrician, but because they give statistical constants in fair agreement with those for babies studied by others. We now turn to the constants for adults. Since these are funda- mental to the determination of many of the relationships in subsequent sections, we shall give them for each of the various subseries. The constants for stature appear in table 8, those for body-weight in table 11. Table 8. — Statislical constants for stature in adults of Nutrition Laboratory series. Series. N Average. Standard deviation. Coefficient of variation. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 177.44=1 171.82=1 172.45=1 172.75=1 174.61=1 172.97=1 172.95=1 173.20=1 172.96= 1.57 0.58 0.56 0.56 1.04 0.50 ^0.75 ^0.09 =0.44 161. 87 ±0.43 162.14=t0.57 161.96='=0.34 9.33 =t 1.11 6.79 =fc 0.41 7.80=1=0.39 6.98 =t 0.39 8. 17 =t 0.74 7.94=1=0.35 4.83=fc0.53 8.21=1=0.49 7.59=1=0.31 5.29=1=0.31 4.99=1=0.40 5.19=fc0.24 5.26±0.63 3.95=1=0.24 4.53 ±0.23 4.04=1=0.23 4.68=1=0.42 4.59=1=0.20 2.79=1=0.31 4.74 =fc 0.28 4.39 =»= 0.18 3.27=1=0.19 3.08=1=0.25 3.20=1=0.15 If the criterion of the suitability of our series of individuals were mean statiu:e only, we should be embarrassed by the wealth of available materials for comparison. Stature is one of the more conspicuous and more generally interesting characteristics of races or of the populations of different geographic divisions. The number of average statures available is therefore very large. But our comparison involves not merely the average value, but the distribution of the statures around the average. Hence we must base our comparisons on series which have full data for the determination of variability as well as of type. 54 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. For comparison, we have the constants for the stature of 1,000 students 18 to 25 years of age, measured in the Harvard gjmonasium and published by Castle,'® and for 25,878 American recruits calculated by Pearson.'" Turning to the English, we have Schuster's'* values for Oxford students aged 18 to 23 or more years, Pearson's'® and Macdonell's*° constants for Cambridge undergraduates and for Mac- donell's*' Scottish students. Turning to data other than that for students, Pearson*^ has given a series of constants drawn from his family records and Pearson and Lee*' have supplied those for first and second generations of British famihes. Table 9. — StatisHcal constants for stature in men and women in general. Series. American : Harvard students Army recruits English: Oxford students Cambridge students, Pearson . . . Cambridge students, MacDonell Pearson's second generation Pearson's family records Pearson's parental generation . . . New South Wales criminals Scottish students MacDonell's convicts Goring's convicts Swedes Hessians French Bavarians, Pearl Bavarians, Pearson Men. Mean. Standard devia- tion. 175.34 170.94 176.50 174.91 174.88 174.37 172.81 171.91 169.87 171.70 166.46 166.29 169.79 167.36 166.80 166.55 165.93 6.58 6.56 6.61 6.41 6.46 6.88 7.04 6.86 6.58 5.94 6.45 6.76 6.81 7.19 6.47 6.39 6.68 Coeffi- cient of varia- tion. 3.76 3.84 3.74 3.66 3.70 3.95 4.07 3.99 3.87 3.46 3.88 4.06 4.01 4.30 3.88 3.84 4.02 Women. Mean. standard devia- tion. 162.26 162.23 159.90 158.70 158.09 158.71 156.18 156.10 154.71 163.85 6.00 6.63 6.44 6.07 6.15 Coeffi- cient of varia- tion. 3.70 4.09 4.03 3.83 3.89 6.72 4.23 6.90 4.40 6.79 4.36 6.21 4.02 6.55 4.26 While it is now known that, in England at least, certain classes of criminals are differentiated from the general population, it is interesting to compare the constants for 3000 non-habitual male criminals** meas- ured at Scotland Yard and analyzed by Macdonell,** the constants for 3000 men studied by Goring** in his masterly treatment of the British " Castle, Heredity and Eugenics, Cambridge, 1916, p. 61. " Pearson, The Chances of Death, 1897, 1, p. 276. » Schuster, Biometrika, 1911, 8, p. 49. " Pearson, Pioe. Roy. Soc. Lond., 1899, 66, p. 26. «> Macdonell, Biometrika, 1901, 1, p. 191. " Macdonell, Proc. Anat. and Anthrop. Soc. Univ. Aberdeen (Jide E. Pearson, Biometrika, 1911, 8, p. 49). *' Pearson, The Chances of Death, 1897, 1, p. 294. " Pearson and Lee, Biometrika, 1901, 2, p. 370. ** The majority of the prisoners were English and Welsh, many were Irish, and only a few Scotch. None were foreigners. All were over 21 years of age. «> MacdoneU,Biometrika, 1901, 1, p. 191. « Goring, The English Convict., Lond., 1913, pp. 178-179. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 55 criminal, and for a large series of New South Wales criminals for which we are indebted to Powys.*^ For races other than Anglo-American we have Pearson's** Bavarian and French men and women and Pearl's" constants for Swedes, Hes- sians and Bavarians. The means, standard deviations and coefficients of variation of these various series are assembled in table 9. Comparison of the constants for stature of our total men and total women with these various series is facilitated by the differences in table 10. These are taken so that a positive sign indicates higher mean or variability in the Nutrition Laboratory series. Table 10. — Comparison of iUUislical constants for stature in Nutrition Laboratory series tdth the values for men and women in general. Series. I American : Harvard students Army recruits English : Oxford students Cambridge students, Pearson . . . Cambridge students, MacDonell Pearson's second generation Pearson's family records Pearson's parental generation New South Wales criminals Scottish students MacDonell's convicts Goring'a convicts Swedes Hessians French Bavarians, Pearl Bavarians, Pearson Men. Women. Mean. Standard devia- Coeffi- cient of Mean. Standard devia- Coeffi- cient of varia- tion. tion. tion. tion. -2.38 + 1.01 +0.03 +2.02 + 1.03 +0.55 -3.54 +0.98 +0.65 -1.95 + 1.18 +0.73 -0.30 -0.81 -0.50 -1.92 + 1.13 +0.69 -1.41 +0.71 +0.44 -0.27 -1.44 -0.89 -1-0.15 +0.55 +0.32 +2.06 -1.25 -0.83 -1-1.05 +0.73 +0.40 +3.26 -0.88 -0.63 +3.09 + 1.01 +0.52 +3.87 -0.96 -0.69 +1.26 +1.65 +0.93 +6.50 + 1.14 +0.51 +6.67 +0.83 +0.33 +3.17 +0.78 +0.38 +3.25 -1.53 -1.03 +5.60 +0.40 +0.09 +5.78 -1.71 -1.20 +6.16 +1.12 +0.51 +5.86 -1.60 -1.15 +6.41 +1.20 +0.56 +7.25 -1.02 -0.82 +7.03 +0.91 +0.37 -1.89 -1.36 -1.06 As far as average stature is concerned, our series show a superiority practically throughout. Only the Oxford, Cambridge, and Harvard men, Cambridge women, Pearson's filial generation measurements for both men and women, and Pearson's Bavarian women are taller than the subjects included in our normal series. Now comparison of average statures involves very great difficulties. In none of these series is there a correction for the slight premaximum increase or the postmaximum decrease occurring in the age period ordinarily designated as adult life. This is probably a matter of negli- " Powys, Biometrika, 1901, 1, p. 44. <* Pearaon, The Chances of Death, 1897, 1, p. 295. " Peari, Biometrika. 1905, 4, p. 13. 56 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. gible importance. A far greater difficulty is inherent in the factor of racial differentiation. One has only to glance at such tables as those of Martin*" or the discussion and maps of Ripley®^ to realize how great the racial, geographical, and social factors are in determining the average stature of a group of individuals. The fact that our normal men and women are taller than those with which we have compared them may be due to one or more of three factors. a. A differentiation of the American population from the Exiropean with respect to stature. 6. An indirect selection of the taller men and women from the gen- eral American population due to the individuals volimteering for these metaboUsm observations being a superior class.*'' c. Unconscious selection of taller individuals for metabolism meas- iu"ements by those who have had to choose among the subjects who presented themselves. Some CAadence on the first of these questions is afforded by abstract- ing from Martin's Anthropologie the average statures, as far as given in the comparative table (p. 213-217). Men. WoTficn, French ....164.1 157.0 Bavarians ...165.6 Swedes .... 170.9 American whites . . . . ....171.9 Enelish ....172.8 159.9 Even if we increase the stature of the French and Bavarian men by 1 cm. to correct for the age at which measurements were made for military purposes, we note that the American white population stands next to that of the noiddle classes of Great Britian in stature. Fortimately we may take from Baxter's*' report the average stat- ures of immigrants of various nationalities. As abstracted by the Anthropometric Committee of the British Association** they are as follows: Centi- Centi* Centt- meUrt. melerM. meters. Norwegians 171.9 English 169.2 French 168.3 Canadians, chiefly Hungarians 169.2 Poles 168.2 French 170.3 Germans 169.1 Italians 167.7 Swedes 170.0 Swiss 168.7 Spaniards 166.8 Danes 169.4 Russians 168.7 Portuguese 166.3 Dutch 169.3 " Martin, Lehrbuch der Anthropologie, 1914. See especially pp. 204-237. •' Ripley, The Races of Europe, 1900. See especially pp. 78-102. '' How great the influence of social differentiation may be is well shown by a comparison of the regression slopes for fraudulent criminals and for criminals at large, in Goring's English Convict- It is also clear from the Swiss data for stature by occupation given on page 90 of Ripley's Races of Europe. ' Baxter, Statistics, Medical and Anthropological, 1875. H British Association Report (Southport), 1883, pp. 269-271. See also W. H. Holmes, Am. Journ. Pbya. Anthrop., 1918, 1, p. 84. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 57 Thus racial differentiation between European and American popu- lation is ample to account for the observed differences in our mean statures. Our men are intermediate between the general population and a highly selected group like Harvard University students.** In regard to variability, our men are more variable and our women are less variable throughout than those studied by others for purely anthropometric pmposes. Since the average stature for Americans seems to be higher than that of most of the European groups with which they are compared, the absolute variability would be expected to be greater in Americans; but the relationships noted hold whether variability be measured in centimeters by the standard deviation or in percentages of the total stature by the coefficient of variation. Table 11. — Statistical constants for body weight in adults. Series. N Average. Standard deviation. Coefficient of variation. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series. . . Second supplementary series Other than Gephart and Du Bois selection All men o{ three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 73.82*2.17 63.03*0.77 64.33*0.77 63.33*0.67 62.69*1.34 63.94*0.67 65.06*1.13 64.96*1.02 64.10*0.60 54.49*0.88 60.36*1.35 56.48*0.76 12.87=1 9.02=1 10.73=1 8.37 =i 10.48=1 10.69^ 7.30=" 12.04^ 10.30 =i 1.53 0.55 0.54 0.47 0.94 0.47 0.80 0.72 0.42 17.43 =i 14.32^ 16.68=1 13.22=1 16.72=1 16.73=1 11.22=1 18.54 =i 16.06=1 2.14 0.88 0.87 0.76 1.55 0.76 1.24 :1.14 0.67 10.78*0.62 11.84*0.95 11.49*0.54 19.78*1.19 19.61*1.64 20.35*1.00 Now, admitting freely that many of these differences are statis- tically significant, we nevertheless feel that one can hardly examine these constants collected by various writers in anthropometric investi- gations, with no physiological purpose whatever in view, in comparison with our own without being impressed by the general suitability of our materials as a basis for generalizations applicable to large popula- tions. Our averages seem to be roughly representative of the American population. Our men are somewhat more variable than we would Hke, but our women are distinctly less variable than women in general. It is clear, therefore, that our series of individuals is characterized not merely by an average stature comparable with that of men in general, but that it exhibits (at least in the males) a variability of stature which is (roughly speaking) tjrpical of the population at large. This "lack of uniformity" or "lack of homogeneity" in the series of '^ The average stature of 327 Amherst College students (of average age 21.5 years) is 172.9 cm. Anthropometric Committee's Report Brit. Ass. Kept. (Southport), 1883, p. 260. 58 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. men and women dealt with is one of its chief merits. If laboratory studies of basal metaboUsm are to have a broad application in medical and social science they should be made upon series representa- tive of the population at large. It is only under these conditions that generalizations of wide usefulness can be safely made. Our constants for body-weight, taken vnthout clothing, in the various series are given in table 11. For comparison with our own series of body-weights we are fortu- nate in having the table of weight taken vnthout clothing of 1,000 Harvard men aged 18 to 25 years published by Professor Castle, °^ that for Oxford undergraduates, weighed with clothing but without boots, given by Schuster,*' the values for 1,000 Cambridge men and 160 Cambridge women given by Pearson,*^ and Pearson's *® reduction of Francis Galton's series of body-weights, taken with ordinary indoor clothing, for British men (iSr = 520) and women (N = 276). Goring has given a most valuable series from British prisons,®" measured in shirt and trousers only. For Germans (Bavarians) Pearson ®^ has determined constants for the 535 men and 340 women measured by Bischoff, The results, uncorrected for weight of clothing, are as follows: ilean. S. D. C. V. Castle's Harvard men 65.66 7.84 11.94 Schuster's Oxford men 68.91 7.45 10.80 Pearson's Cambridge men 69.30 7.51 1083 Pearson's Cambridge women 56.97 6.36 11.17 Galton's British men 64.86 4.54 10.37 Galton's British women 55.34 4.60 13.37 Goring's convicts 64.45 7.80 12.09 Pearson's Bavarian men 50.17 10.?8 20.67 Pearson's Bavarian women 41.92 10.51 25.07 Unfortimately the number of series of body-weight measurements available for comparison is small. Furthermore body-weight is a much more variable character than stature. One must, therefore, expect greater actual differences between series of observations made at different times and places. How large the differences may be is shown by the great discrepancy between the British and the Bavarians. Our data show constants of roughly the same order of magnitude as those available for comparison. In turning to the problem of the closeness of correlation in the stature and weight of the subjects examined as a criterion of their "normality" as compared with men at large, it will be important to " Castle, Heredity and Eugenics, Cambridge, 1916, p. 61. " Schuster, Biometrika, 1911, 8, p. 49. ■• Pearson, Proc. Roy. Soc. Lend., 1899, 66, p. 26. ** Pearson, The Chances of Death, 1 : 305, 1897. Constants slightly erroneous. «> Goring, The English Convict, 1913, pp. 178-179. >i Pearson, The Chances of Death, 1: 305, 1897. We can offer no explanation for the great variation in the German series. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 59 remember that in selecting our series for comparison we must choose those of adult age in order to eliminate the influence of growth. Some of the best studies on the correlation between stature and weight — ^for example, those of Boas ^^ and of Boas and Wissler ®^ on Toronto and Worcester children, as well as the more recent investigation of Elder- ton " on the stature and weight of Glasgow school children, carried somewhat farther by Isserlis,®' are therefore not available for our present purposes. The correlations between stature and weight in our adults are given in table 12. Table 12. — Corrdalion between weight and stature and partial correlation between weight and stature for constant age in the several series. Series. N Correlation Partial correla- tion oTwt ^ r Difference Men. Original seriea: Athletes 16 62 89 72 28 117 19 64 136 68 35 103 0.6943*0.0873 0.4010=«=0.0719 0.5320 ±0.0613 0.6654 ±0.0443 0.7461*0.0565 0.5712*0.0420 0.6031*0.0984 0.5149*0.0620 0.5725*0.0389 0.2191*0.0779 0.5386*0.0809 0.3267*0.0594 7.95 6.68 10.37 15.02 13.21 13.60 6.13 8.31 14.72 2.81 6.66 5.48 0.6361*0.1004 0.3999*0.0720 0.5376*0.0508 0.6773*0.0431 0.7468*0.0564 0.5783*0.0415 0.6960*0.0998 0.5362*0.0601 0.5772*0.0386 0.2205*0.0778 0.4969*0.0859 0.2995*0.0605 6.34 6.55 10.58 15.71 13.24 13.93 6.97 8.92 14.96 2.83 6.78 4.95 +0.0582 +0.0011 -0.0056 -0.0119 -0.0007 -0.0071 +0.0071 -0.0213 -0.0047 -0.0014 +0.0417 +0.0262 Others Whole seriea Gephart and Du Bois selection First supplementary Original and first sup- plementary series Other than Gephart and Du Bois selection All men of three series. . Wonun. Supplementary series. . . Both series The partial correlations in which the influence of age is eliminated have been computed from the formula a' ««« ^ ' io« ' aw' Oi Vl-r "Vi- and placed beside the others for comparison. It is to be noted that correction for the influence of age has modified the values of the constants very little indeed. They have sometimes been slightly raised and sometimes sUghtly lowered by correction for this factor. Age differences in the series can not, therefore, account for any of the observed differences in correlation. « Boas, Kept. U. S. Comm. Educ, 1896-97, p. 1541. " Boas and Wissler, Rept. U. S. Comm. Educ, 1904, p. 26. X Elderton, Biometrika, 1914, 10, p. 288. u Isserlis, Biometrika, 1916, 11, p. 50. 60 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. The results in table 12 seem very reasonable and consistent with one exception. The original published series of women seems abnorm- ally low in comparison with the second series and with men. The relationships for the original series and the supplementary series are shown in diagrams 2 and 3. The straight lines in these diagrams represent the equations: For origmal series w= — 17.83+0.45* For supplementary series w= —146.68+ 1.28 s Clearly the rate of increase in weight per centimeter of length is much greater in the supplementary series. STATURE IN CENTIMETERS DiAOBAM 2. — ^Relationship between stature and weight in original series of women. See text for discussion of four aberrant individuals in upper part of field. In the original series one notes four individuals towards the upper part of the field who are very heavy in relation to their stature. These are Miss O, A., Dr. M. D., Miss H. H., and Miss H. D. If these be removed the variabiUty in body-weight is greatly reduced, i.e., from 10.78 to 6.87. The correlation is raised from r =0.219 to r = 0.340, but this constant is still considerably lower than that in the supple- mentary series. Apparently the observations are fairly well grouped around the straight lines and we must simply admit that, in gathering small samples of data, two groups were secured which differed sensibly in the degree of correlation of their bodily characters. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 61 The relationship between statiire and body-weight in the total male (iV = 136) and the total female (iV = 103) series may now be represented in a different way. The straight-line equation connecting weight and stature in the total series are : For men w= -70.303+0.777s For women w= -60.332-i-0.721s These are represented on the same scale for the two sexes on dia- gram 4. The "mean body-weight" has been calculated for each grade of statiu-e. With less than 150 individuals available for each sex the "averages" sometimes represent a single individual merely and are extremely irregular. The straight line serves fairly well to smooth them. STATURE IN CENTIMETERS Diagram 3. — Relationship between stature and body weight in supplementaiy^series of women. See diagram 2 and text. The diagram brings out clearly a point noted above, namely the unfortunate narrowness in the range of variation of statiu-e in our series of women. For comparison we have several series of data. First of all may be mentioned Castle's®® 1000 Harvard men — gjTnnasium records with- out clothing — ^which give: r =0.704 ±0.015 Pearson,®^ working with measiu-ements of 1000 male and 160 female Cambridge students, found : For men r=0.486±0.0I6 For women r =0.721 ±0.026 " Castle, Heredity and Eugenics, Cambridge, 1916, p. 61. " PeatBon, Proc. Roy. Sec. Lond., 1899, 66, p. 26. 62 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. For Oxford men, E. Schuster"* found the following correlations between height and weight, the latter unfortunately taken with the clothing except the boots: Age 18, AT =129, Age 19, N^SaO, Age 20, AT =209, Age 21, AT =137, Age 22, AT = 95, r= 0.50 ±0.04 r =0.63 ='=0.02 r= 0.68=*= 0.03 r=0.76*0.02 r=0.72*0.03 General average. . . 0.66 For stature and body-weight in 2502 British convicts, weighed in trousers and shirt only, Goring'® finds: r„, =0.555 ±0.009 Again for height and weight in 500 male criminals examined by Goring, the correlations deduced by Whiting^" are : For stature and weight r»>=0.580=t0.020 For Btature and weight with age constant. . . .iirw= 0.583 ±0.020 /■>» /S3 iss IS3 iss 113 ne ia3 m is3 m STATURE IN CENTIMETERS DiAoaAM 4. — ^Variation in mean body-weight of men and women with Btature. Our correlations for men are, roughly speaking, of the same order of magnitude as those which have been published by others. Unfortu- nately, only Pearson's small series of women, but slightly larger than our own, is available for comparison. The agreement here is not good. Only further work on the relationship between stature and body-weight in women will answer the question of the degree of correlation to be expected between these two physical characters. u SchuBter, Biometrika, 1911, 8, p. 51. •• Goring, The Eneliah Convict, Load., 1913, p. 389. TO Whiting, Biometrika, 1915, 11, p. 8. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 63 The materials for adults may be tested for normality, in the general sense in which we have used the term here, in two other ways. Age and stature, in adult life, should not be sensibly correlated except as a result of post-maximum shrinkage. Our data cover a portion of the age of pre-maximum increase and of post-maximum decrease as well as the age of maximum stature. Our correlations are given in table 13. Some of the constants are positive while some are negative. In only the athletes are the coefficients as much as 2.5 times as large as their probable errors. When N is small the ordinary stand- ards of trustworthiness can no longer be maintained. Taking the results as a whole, we have no reason to conclude that in the age range covered by our data there is any great change in stature with age. Table 13. — Correlation between age and stature and age and weight and partial correlation between age and weight for constant stature. Series. Men. Original series: Athletes Others Whole series Gephait and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series Other than Gephart and Du Bois selection All men of three series Wotnen. Original series Supplementary series Both series N 16 62 89 72 28 117 19 64 136 68 35 103 Correlation between age and stature -0.4346±0.1368 +0.0687 ±0.0853 -0.1651 ±0.0696 +0.0283 ±0.0794 +0.0641±0.1269 -0.1230± 0.0614 -0.1594±0.1608 -0.1972*0.0810 -0.1154±0.0571 +0.0921 ±0.0811 +0.2395 ±0.1076 +0.1462±0.0650 Er 3.18 0.81 2.37 0.36 0.51 2.00 1.06 2.43 2.02 1.14 2.23 2.25 Correlation between age and weight -0.3763 ±0.1447 +0.3037±0.0778 -0.0106±0.0716 -0.1476±0.0778 +0.1565±0.1243 +0.0209±0.0623 -0.1185±0.1526 +0.0515 ±0.0841 +0.0067±0.0578 -0.0050±0.0818 +0.4422±0.0917 +0.2867 ±0.0610 2.60 3.90 0.15 1.90 1.26 0.34 0.78 0.61 0.12 0.06 4.82 4.70 Partial correlation -0.1160±0.1664 +0.3022 ±0.0778 +0.0926 ±0.0709 -0.2230±0.0765 +0.1636± 0.1241 +0.1120±0.0616 -0.0284±0.1646 +0.1820±0.0816 +0.0893±0.0674 -0.0259±0.0817 +0.3828 ±0.0973 +0.2557±0.0621 ^ T 0.69 3.88 1.30 2.9S 1.32 1.82 0.18 2.23 1.66 0.32 3.93 4.12 For comparison with our own constants we have those for 500 criminals examined by Goring. The correlations deduced by Whiting^^ are: For age and stature r„= +0.023±0.030 For age and stature with weight constant ».r„= —0.070 ±0.030 General observation suggests that individuals tend to gain in weight with increasing age," even after the normal period of growth has passed. In support of such general observation may be cited the " Whiting, Biometrika, 1915, II, p. 8. ^' It seems quite possible that the correlation between weight and heat-production may be somewhat disturbed by the correlation of weight with age. It is, therefore, necessary to investigate such relationships as this in detail. 64 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. constants obtained by Whiting ^^ for age and weight in 500 criminals examined by Goring. The correlations deduced are: For age and weight r»„= +0.136±0.030 For age and weight with stature constant ,r««,= +0.151 ±0.030 These constants indicate a slight increase in weight with increasing age. Our own materials show the correlations given in table 13. Since the problem of any actual gain in weight after the completion of growth involves a consideration of the stature of the individuals, the correla- tions for age and weight have been corrected for the influence of stature by the use of the formula _ _ 'aw ™" ' la *gtD a* aw / — - -- — — Vl-r„»Vl-r„« Among the men only the correlation for the 62 "other men" of the original series can be looked upon as statistically significant. The partial correlations between age and weight for constant stat- ure are positive in all the larger series of men, excepting only the Gephart and Du Bois selection,^^ and indicate a slight tendency for increase in body-weight with age in men. The women of the first series show practically no correlation be- tween age and body-weight. Correction for the possible influence of stature does not materially alter the relationship. The supplementary series, however, shows material and statistically significant positive correlation, indicating decided increase of weight with age. The corre- lation is not so large, but nevertheless apparently statistically signifi- cant, for the total available women. The values of the gross correla- tions are but slightly reduced when correction is made for the influence of stature by the use of the partial correlation formula. The constants for the second series of women and for the entire series of women seem to suggest that women have a greater tendency than men to increase in weight with age. The apparent contradiction between the results of the first and of the supplementary series is perhaps due to differences in age. The indiAdduals of the second series are on the average about 13 years older than those of the first. Thus the average age in the first series is 26.7 years, whereas that of the second series is 39.9 years, and that of all the women is 31.1 years. The first series shows a standard deviation of only 9.9 years around the average age of 26.7 years, whereas the second series shows a standard deviation of 16.0 years around the average age of 39.9 years, and the whole series shows a variation of 13.8 years around the average of 31.1 years. " Whiting, Biometiika, 1915, 11, p. 8. " The negative correlation and the negative partial correlation for constant stature found in the Gephart and Du Boia selection are perhaps due to the arbitrary removal of individuals which do not conform to a preconceived standard. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 65 Higher correlation between age and weight in a group of women averaging 40 years in age than in a group averaging 27 years of age is in accord with the rather general belief that after the climacteric women tend to gain in weight. The variation constants for body-surface measured by the Du Bois height-weight chart appear in table 14. Table 14. — Statistical constants for hody-suTface in aduUs as estimated by Du Bois height-height chart Series. N Average. Standard deviation. Coefficient of variation. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection .... First supplementary series Original and first supplementary series Second supplementary series Other than Gephart and Du Bois selec- tion All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 1.904 ±0.0326 1.742 ±0.01 13 1.760±0.0114 1.753 ±0.0108 1.759 ±0.0228 1.760±0.0102 1.775*0.0168 1.773 ±0.0149 1.762 ±0.0091 1.566 ±0.01 13 1.637 ±0.0180 1.590 ±0.0099 0.1933±0.0230 0.1315±0.0080 0.1593*0.0081 0.1360 ±0.0076 0.1785±0.0161 0.1631 ±0.0072 0.1089±0.0119 0.1765±0.0105 0.1567 ±0.0064 0.1378±0.0080 0.1577±0.0127 0.1485 ±0.0070 10.15±1.22 7.55 ±0.46 9.05 ±0.46 7.76 ±0.44 10. 15 ±0.92 9.26±0.41 6.14±0.67 9.96±0.60 8.89 ±0.37 8.80 ±0.51 9.63 ±0.78 9.34 ±0.44 For this character we have no comparable data from other sources. The constants are, therefore, of primary importance in their relation to the further calculation necessary for the discussion of subsequent sections. The average body-surface is about 1.8 square meters in men and about 1.6 square meters in women. The variabiUty of the super- ficial area of the body is about 9 per cent of this amount in both sexes. The coefficients of variation occupy an intermediate position between those for stature and those for body-weight, as shown in the final columns of tables 8 and 11, in every series. The constants for pulse-rate are set forth in table 15. The only comparable data of which we are aware are those of Korosy and Goring for conscripts and convicted men. For pulse-rate in 500 convicts examined by Goring the constants determined by Whiting " and the difference from our own for men are: Mean. S.D. C.V. 2 Our whole aeries. 61.26±0.41 6.73 ±0.29 10.99*0.48 3 Whiting't whole teriea. 74.22*0.25 11.06*0.17 14.89*0.24 4 Difference between tandS. 12.96*0.48 4.33*0.34 3.90*0.54 S Whitino't weak'^minded. 77.62±0.58 11.85±0.41 15.27*0.54 6 Difference between t and B. 16.36*0.71 5.12±0.50 4.28*0.72 These values are far larger than ours, in mean, absolute variability, and relative variability. This is clearly due to the facts (a) that they Whiting, Biometrika, 1915, 11, pp. 1-37. 66 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. are made upon a series of individuals from which physically and men- tally abnormal men were not excluded, and (b) that the rates were taken with the convict sitting in his cell, writing, reading, or doing nothing about 15 minutes ajter early dinner instead of 12 hours after the last meal and in a state of complete muscular repose. Table 15. — SUiiistical constants for pulse-rate in adults. Series. N Average. Standard deviation. Coefficient of variation. Men. Original aeries: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series . . . . Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both 16 62 88 71 28 116 50 121 68 22 90 62.00^1.01 60.81 ='=0.54 60.92 ±0.47 61.27=1=0.61 62.54 ±0.87 61.31 ±0.41 61.26±0.68 61.26±0.41 69.12 ±0.67 67.27±1.18 68.67 ±0.59 6.98±0.71 6.29 ±0.38 6.48 ±0.33 6.43 ±0.36 6.81 ±0.61 6.60±0.29 7.14±0.48 6.73 ±0.29 8.18±0.47 8.20±0.83 8.26±0.41 9.64±1.16 10.34±0.63 10.64±0.66 10.49 ±0.60 10.89±0.99 10.77 ±0.48 11.6S±0.80 10.99 ±0.48 11.83±0.69 12.19±1.26 12.01 ±0.61 Korosy's data for conscripts^' are physiologically more nearly com- parable with our own. They were taken on a group from which all individuals not having a perfectly healthy heart had been excluded. The coimtings were made in the early morning soon after the men were wakened and while they were still in a position of rest. The constants deduced by Bell'^ are compared with our own as follows : K6r6av*» aeriet. Our aeriea. Differanee. Mean 64.21 ±2.71 61.26±0.41 2.95*2.74 S. D 8.49 ±0.36 6.73 ±0.29 1.76 ±0.46 C. V 13.22 ±0.40 10.99 ±0.48 2.23 ±0.62 These results are in much closer agreement with our own than the determinations on convicts; but means, absolute variabilities, and relative variabilities are larger than in our series. Since pulse-rate is a physiological measure well known to be affected by other physiological factors, we take these facts to indicate that our records for pulse-rate — and in consequence those for metabolism as well, for both were measured simultaneously — ^have been determined vmder conditions which introduced the minimum external influence. Turning to a more detailed examination of our own constants, we note that the women have a more rapid and more variable pulse than the men. The averages are: '• Korosy, Deutsch. Archiv. f. klin. Med., 1910, p. 267. " Bell, Biometrika, 1911, 8, p. 232. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 67 Pot original Nutrition Lahoratory tmcf . For 89 men 60.92±0.47 For 68 women 69.12=^0.67 For all men Ar = 121 For all women N= 90 +8.20*0.82 For all available data. 61.26*0.41 68.67*0.59 +7.41*0.72 In both comparisons the women show from 7 to 8 beats per minute more than the men, and these differences are about 10 times as large as the probable errors of their determination. The sexual differentiation thus indicated has been noted by other writers. Thus Leonard Hill/* in an article on "The mechanism of the circulation of the blood" says : "The pulse frequency is greater in women than in men, but this difference almost disappears if men and women of equal stature are compared." Langendorff, in his article on the circulation of the blood," states that the pulse of adult men resting in bed is about 60, while standing it is 70 to 75 per minute, and that in women it is somewhat higher. Professor Robert Tigerstedt*° states that in all ages, from 2 years on, the pulse-rate of the woman is higher than that of the man. The smaller size of the woman plays a r61e, but even if individuals of the same stature are compared the difference is persistent though smaller. We now turn to the constants for total heat-production. Table 16. — Statistical constants Jot total heat-production per 24 hours in adults. Series. N Average. standard deviation. Coefficient of variation. Men. Original series : Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 1876.56*41.33 1607.97*12.20 1638.36*14.64 1623.46*14.11 1605.18*28.19 1630.42*13.05 1639.84*26.77 1641.05= 1631.74= ^9.48 = 11.84 1354.69*12.25 1338.51*18.78 1349.19*10.31 245.13*29.23 142.38* 8.62 204.82*10.36 177.55* 9.98 221.14*19.93 209.32* 9.23 172.99*18.93 231.04*13.77 204.66* 8.37 149.74* 8.66 164.72*13.28 155.18* 7.29 13.06*1.68 8.85*0.54 12.50*0.64 10.94*0.62 13.78*1.27 12.84*0.58 10.65*1.17 14.08*0.86 12.54*0.52 11.05*0.65 12.31*1.01 11.50*0.55 The means, standard deviations and coefficients of variation for total heat-production in calories per 24 hours are given in table 16. The entries in this table, representing as they do the constants for the most extensive series of data available on basal metabolism in men and women, have a great deal of interest. The first column shows " Hill, Schafer's Tezl^Book of Physiology, London and New York, 1900, 2, p. 101. " LangendoifF, Zuntz and Loewy's Lehrbuch der Physiologie des Menschen, Leipzig, 1913, 2, Aufl., p. 373. ■° Tigerstedt, Lehrbuch der Physiologie des Menschen, Leipzig, 1913, 7, Aufl., 1, p. 282. 68 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. that the average basal metaboUsm of normal men is measured by a daily heat-production of about 1600 to 1650 calories. All the series, even those in which the number of individuals is very small, are reason- ably consistent except for the athletes, which show an unusually high metabolism. Women show an average daily heat-production, when in complete muscular repose and in the post-absorptive state, of about 300 calories per day less than men. The average daily basal heat-production of new-bom infants is, as shown in table 5, about 140 to 145 calories. This is about 10 per cent of that of adult women. In examining these values one must, however, remember that they are uncorrected for the influence of stature, body-weight, or age, all of which have important r61es as proximate factors in the determination of the basal daily heat-production of the individual. The second colimm shows the great variability in basal heat- production from individual to individual. The variabilities range from 142 to 245 calories for men and from 150 to 165 calories for women. For the larger series 140 to 230 calories for men and 150 to 160 calories for women maybe taken as the variabiUties expressed in round numbers. It is evident that with such large variations in the daily basal metabol- ism of the normal individual the prediction of the heat-production of an individtual subject wiU always have a high probable error — ^that is, a limited trustworthiness. In infants the standard deviations are about 21 to 23 calories per day (table 5). In speaking of standard deviations of 140 to 230 calories for adults and of 21 to 23 calories for infants as large, one must not forget that these are for organisms giving daily average heat-productions of 1300 to 1650 calories for the adult and of 140 to 145 calories per day for the infantile state. If the standard deviations be expressed as percentages of the average daily heat-production we have the constants in the third column of table 5 for the infants and table 16 for the adidts. To gain a definite idea of the relative variabiUty of basal metabolism as compared with other more familiar physical magnitudes and physio- logical activities, it seems worth while to examine these constants in some detail. First of all we note that the values range from 8.85 to 14.08 per cent for men and from 11.05 to 12.31 for the women, with constants for the whole series of data for the two sexes of 12.54*0.52 for the men and 11.50 =*=0.55 for women. These values can not, with due regard to their probable errors, be asserted to differ significantly. In the infants the coefficients of variation are somewhat higher, being 14.46 for the boy babies, 16.54 for the girl babies, and 15.49 for infants irrespective of sex. The difference between the two sexes is 2.08=*= 1.59, which is statistically insignificant and hence can not be regarded as indicative of a real physiological difference in variability of heat production between the sexes. INDIVIDUALS AND MEASUREMENTS CONSIDERED. 69 Comparing with other characters dealt with in this volume, we note that the metabolism of a group of individuals is from 2 to 3 times as variable as their stature, (table 8), but is not in any instance as vari- able as their body-weight (table 11). The relative variability of total heat-production is also, roughly speaking, from 20 to 25 per cent greater than body-surface area as measured by the Meeh formula (table 50). This point is of particular interest because of the fact that if heat-production were proportional to body-surface area, as maintained by many, the variability of these two measures should be the same. To a full consideration of this matter we shall retimi in Chapter VI. These values are by no means as large as those which have been found for the variation of weight of internal organs in man. For example. Greenwood's*^ series shows coefficients of variation for the weight of the spleen of 38.2 and 50.6 per cent in normal and hospital populations. The same author finds a coefficient of variation of from 22.2 to 32.4 for the weight of the heart in hospital series and 17.7 in normal series. For the weight of the kidneys the coefficients are 21.1 to 24.6 for hospital and 16.8 for normal subjects. For the weight* of the liver the constant is 20.8 to 21.1 for hospital series and 14.8 for healthy series. Comparison of the relative variability of total heat-production with that of another physiological measiirement, pulse-rate, shows that the two are roughly of the same order of magnitude. In the whole series of men total heat-production shows a variation of 12.54 ±0.52 as compared with 10.99*0.48 for pulse-rate, a difference of -1-1.55 ±0.71. In the whole series of women the comparable values are 11.50 =*=0.55 for heat-production and 12.01*0.61 for pulse-rate, a difference of —0.51 ±0.82. Thus the two differences for total series are opposite in sign, and neither can be looked upon as statistically significant in comparison with its probable error. Unfortunately pulse-rate is not available for all the individuals but this can hardly affect the correctness of the conclusion. These comparisons with characters the variability of which is more famihar to the general biologist and physiologist, will perhaps indicate the relative magnitude of variation in total heat-production. The individual constants will be extensively used in the analysis of the various problems in the following chapters. 4. RECAPITULATION. This chapter has had a threefold purpose. A. To describe the measurements dealt with and to give the symbols by which they are designated in the subsequent discussion. B. To give protocols of the actual measurements analyzed in subsequent sections. These comprise 51 male and 43 female infants " Greenwood, Biometrika, 1904, 3, p. 45; Greenwood and Brown, loc cit., 1913, 9, p. 481. 70 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. and 136 men and 103 women. Of the adult records, those for 47 men and 35 women are published here for the first time. C. To test the normality of our series of data, upon which physio- logical generaUzations are to be based. In considering this problem we have emphasized a conception of normaUty which differs somewhat from that heretofore maintained by other students of metabolism. 1. Realizing that practically the greatest importance of a knowl- edge of the basal metabolism of the normal individual is for the calcu- lation of the 24 hoiu-s' requirement of the healthy individual and for the establishment of control values to be used as a basis for conclusions concerning the influence of special conditions or the incidence of specific diseases on metabolism, we have made it a condition of inclusion in our series that the individual be in presumably good health. 2. Since the populations which must be considered in rationing problems are made up of physically varied individuals, it is essential that any generaUzation which shall be applicable to these populations be grounded on series of individuals showing like range of physical dimensions. Since iadividuals in the hospital ward do not conform to any individual physiologists conception of "the normal man," but represent the entire range of physical dimensions and proportions, the non-pathological controls which are to be used as a basis of comparison shoidd showa comparable rangeof physical dimensions and proportions. 3. Since some of the theoretical physiological problems to be con- sidered have to do with the relationship between variations in physical characteristics and physiological activities, it is essential that the sub- jects investigated show average dimensions and variability and correlation of dimensions typical of men and women as a class. Thus, when we speak of a series of normal individuals we do not mean a group of men similar to the figures in the Laocoon or a group of women conforming to the Venus of Milo, but those who are in pre- simaably good health and otherwise are typical of men or women of the same race as the anthropologist knows them. With such a concep- tion of normality it is impossible to discard individuals merely because they are too heavy in proportion to their stature or too tall in propor- tion to their weight. On the other hand, it is of course quite as unallowable to form standard series containing disproportionate numbers of very fat or very lean individuals, as it is to discard both of these extremes and include only those of average proportions. The "normality" of such series must be judged by comparison of their statistical constants with those of men and women at large. Such criteria have been applied to the data discussed in this volume. This conception of normality must, we believe, be generally ac- cepted if investigations of himoan metabolism are to yield the results of the greatest theoretical interest and practical importance. Chapter IV. ON THE INTERRELATIONSHIP OF VARIOUS PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. Our knowledge, in quantitative terms, of the degree of interrela- tionship of the various physical characteristics of man is now very extensive indeed. Relatively Uttle is known of the closeness of inter- dependence of physical magnitudes and physiological activities in series of individuals; yet it seems clear that this subject should receive careful quantitative treatment. Again, it seems to us self- evident that the determination of true quantitative measures of the degree of interdependence of the various physiological activities should make possible material advances in our knowledge of these functions. This position will be justified whatever the outcome of actual investigations. If it be shown that various physiological measurements are correlated with physical characteristics, such relationships must form part and parcel of our system of knowledge concerning human morphology and physiology. If, on the other hand, it be found that between certain of the physical and phjrsiological measurements there is no sensible relationship, it wlU be clear that the physical character- istics need not be considered in the selection of individuals which may be regarded as comparable for use in studies of such physio- logical activities as have been shown to be uncorrected with physical characteristics. Again, if various physiological activities be shown to be correlated, a knowledge of the intimacy of the interdependence of a great variety of physiological functions will contribute materially to ova compre- hension of the himian body as a coordinated whole. Since our general experience of comparative and ex|)erimental physiology is such as to render it rather difficult to conceive of an entire lack of interdependence between the great majority of the phjrsiological activities of the organ- ism, those which show minimum intensities of relationships will be of particular interest. In this chapter we shall discuss the correlation between the two physical characteristics available, stature and body-weight and various physiological measurements pertinent to metabolism investigations. Another physical characteristic is body-surface area, but since this is to receive special attention in a subsequent chapter, it will be left out of account here. We shall, first of all, deal with the relationship between stature and weight on one hand and pulse-rate on the other. We shall then con- 71 72 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. sider measures of the degree of interdependence of pulse-rate and gaseous exchange and total heat-production. With these data at our disposal, we shall proceed to a consideration of the relationship between physical characters and metabolism. Since the physical characteristics, stature and weight, have been shown to be correlated, it is sometimes necessary in discussing the relationship between either of these and physiological characters to anticipate results to be given in detail later. 1. WEIGHT AND PULSE-RATE. In the series of normal infants we find the correlation between weight and pulse-rate, r„p, and the test of significance furnished by the ratio of the constant to its probable error, rjEr : For males N=h\, r„>. =0.3114 ±0.0853, r/£r=3.65 For females iV=43, r»/=0.1570 ±0.1003, rjEr = 1.56 Difference 0.1544*0.1317 For both Ar=94, r„/=0.2289 ±0.0659, r|Er=^A^ The coefficient for females is only about 1.5 times as large as its probable error, and so can not be considered to prove that there is any correlation whatever between pulse-rate and body-weight. The value for boys is numerically larger than that for girls, but in comparison with its probable error the difference between the constants for the two sexes is not statistically significant. The constant for the male babies and that for male and female babies suggest a real interdependence between weight and pulse-rate, but the number of individuals is, statistically speaking, so small that caution must be used in asserting that in male infants as a class there is any relationship between pulse-rate and body-weight. Even if one be inclined to accept these correlations as indicating a real physiological relationship between body-weight and pulse-rate, he must remember that it can not be asserted, without further analysis, that there is a direct biological nexus between body-weight as such and pulse-rate. Body-weight is correlated with stature, and it is quite possible that the observed correlation between body-weight and pulse-rate is in part at least the resultant of correlations between stature (length) and body-weight and between stature (length) and pulse-rate. Furthermore, one must remember that all these variables may change with age, and that in any detailed investigation covering the whole period of life such age changes must be fully taken into account. Consider first of all the correction to the correlation between weight and pulse-rate to be made for stature. The partial correlation PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 73 between weight and pulse-rate for constant stature is required. Thus Vl-r„.Vl-r.p= gives the desired constants. In the infants the results are: For males ,ra,^=0.3073 *0.0855 For females ,r«,j.=0.1442*0.1007 For both ,r„;,=0.2167 ±0.0663 Correction for stature has slightly but not materially reduced the corre- lation between body-weight and pulse-rate. The partial correlations for the males and for the males and females are about 3.6 times as large as their probable errors and may be statistically significant. The correlations between body-weight, lo, and pulse-rate, p, for the several adult series and the partial correlations between body-weight and pulse-rate for constant stature appear in table 17. Table 17. — Correlation helween weight and pulse-rate and partial correlation between weight and pidse-rate with stature constant and loith age constant. Series. Correlation between weight and pulse-rate ''tcp Partial correla- tion between weight and •"■uip pulse-rats t^wp -0.3548*0.1474 -0.0881*0.0860 -0.0402*0.0719 -0.0611*0.0797 +0.0957*0.1263 2.41 1.04 0.56 0.77 0.76 -0.0303*0.0626 0.48 +0.0198*0.0954 -0.0207*0.0613 0.21 0.34 -0.2835*0.0752 -0.1077*0.1421 -0.2398*0.0670 3.77 0.76 3.58 Partial correla- tion between weight and pulse-rate E a'wp Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 88 71 28 116 SO 121 68 22 90 +0.1579 =i -0.1634=1 +0.0055 =i -0.1458=i +0.0786i 0.1644 0.0834 0.0719 0.0783 0.1267 +0.0162*0.0626 +0.1884 = +0.0365 = 0.0920 0.0612 -0.2942*0.0747 -0.0872*0.1427 -0.2483*0.0667 0.96 1.96 0.08 1.86 0.62 0.26 2.05 0.60 3.94 0.61 3.72 +0.0673*0.1679 -0.1904*0.0826 +0.0055*0.0719 -0.1608*0.0780 +0.0894*0.0126 +0.0200*0.0626 +0.2121*0.0949 +0.0430*0.0612 -0.2971*0.0746 -0.1423*0.1409 -0.2359*0.0671 0.40 2.31 0.08 2.06 7.10 0.32 2.23 0.70 3.98 1.01 3.52 The constants are both low and irregular, sometimes negative and sometimes positive in sign. They indicate practically no relationship between body-weight and pulse-rate in men, but suggest a slight nega- tive relationship in women, i.e., that slower pulse is associated with greater body-weight. With regard to their probable errors the corre- lations are practically without exception statistically insignificant in magnitude. Only the original series of women and (through its influ- ence) the total series of women show a correlation over 3 times as large as its probable error. 74 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. If the influence of stature upon the correlation between body-weight and pulse-rate be eliminated by determining the partial correlation between body-weight and pulse-rate for constant stature, the results are practically unchanged. The partial correlations, like the correla- ■30 7S 100 105 no BODY WEIGHT IN KILOGRAMS Diagram 5. — ^Distribution of individual men with respect to body-weight and pulse-rate. Note the lack of relationship as shown by wide scatter of individual measurements and slight slope of the line. Compare diagrams 6 and 7. BODY WEIGHT IN KILOGRAMS DiAORAU 6. — ^Relationship between body-weight and pulse-rate in women. Compare diagrams 5 and 7. tions, are low and irregular in magnitude. Only the original and the total series of women may be considered possibly significant in compari- son with their probable errors. Correcting for the possible influence of age by evaluating Vl-r ' Vl-» PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 75 we find the values given in comparison with the gross correlations in the final column of table 17. Correction for age has not materially changed the values. The most interesting point about these results is the persistently negative values for the women. We shall note that women seem to differ from men in several correlations to be considered later. The distribution of the individual observations for the grand total male (iV = 121) and grand total female (iV = 90) series is shown in the two scatter diagrams 5 and 6. The straight lines are given by the equations: Men, p =59.7782 +0.0232 w; Women, p =78.5659-0.1775 w The slightness of the slope of the lines and the wide scatter of the dots about the theoretical mean values show clearly the insignificance of the relationship between body-weight and pulse-rate in our series. 2. STATURE AND PULSE-RATE. In the series of infants the correlation between stature (length) and pulse-rate is: For males AT = 51 t,„ = 0.1529 ±0.0922 r/Er= 1.66 For females A'^=43 r,p=0.0981 *0.1019 r/£r = 0.96 Difference 0.0548=t=0.1374 For both iV=94 r^ =0.1294*0.0684 r/Er= 1.89 The value for the males is higher, but in comparison with its prob- able error certainly not significantly higher, than that for the females. Neither of the constants taken alone can be considered to differ sig- nificantly from zero. That all three are positive in sign suggests that there Jmay be some slight positive relationship between stature and pulse-rate in infants. But pulse-rate is more closely correlated in infants with body- weight. Thus comparing the correlations of stature and weight we have the following values : For ataivra For vtight and Difference in and pulfc-rojtf. pulae-rate, correlation. Males 0.1529*0.0922 0.3114*0.0853 0.1585*0.1256 Females 0.0981*0.1019 0.1570*0.1003 0.0589*0.1430 Difference 0.0548*0.1374 0.1544*0.1317 For both 0.1294*0.0684 0.2289*0.0659 0.0995*0.0950 For both males and females the correlation between weight and pulse-rate is higher (but in comparison with its probable error not significantly higher) than that between length and pulse-rate. Since stature and weight are closely correlated, i.e., in infants For males r^=0.7703 *0.0384 For females r^ =0.8642*0.0260 For both r =0.8209*0.0227 76 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. it is necessary to ascertain the influence of the correlation between weight and pulse-rate upon that between stature and pulse-rate. Determining the correlation between statiu-e and pulse-rate for constant weight by the partial correlation formula Vl-r.„»Vl-r„p« we have : rx> vTsp vXsf rjr> In males 0.1529=1=0.0922 -0.1436 ±0.0925 -0.2965=1=0.1306 In females 0.0981 =1=0.1019 -0.0756 =t0.1023 -0.1737=1=0.1444 In both sexes 0.1294 =»= 0.0684 -0.1053 =t0.0688 -0.2347 =t0.0973 Thus correction for weight has reversed the sign of the correlation between stature and pulse-rate in infants. The partial correlations are negative in sign, but neither can be considered statistically signifi- cant in comparison with its probable error. We now turn to the data for adults. These appear in the first colunm of constants of table 18. Table 18. — Correlaiion between stature and puUe-rate and partial correlation between stature and pulse-rate with weight constant and with age constant. Seriee. N Correlation be- tween stature and pulse-rate Er Partial correla- tion between stature and pulse-rate Partial correla- tion between stature and pulse-rate O'tj, Men. Original series: Athletes Others Whole series Gepfaart and Ihi Bois selection First supplementary series Original and first supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 88 71 28 116 50 121 68 22 90 -|-0.6376=fc0.1199 -0.2108=1=0.0818 -1-0.0728*0.0715 -0.1498±0.0783 -f-0.0200±0.1274 -1-0.0710=*=0.0623 +0.3339*0.0848 -1-0.0916=1=0.0608 -0.0844 =t0.0812 -0.0014=1=0.1438 -0.0669=1=0.0708 4.48 2.58 1.02 1.91 0.16 1.14 3.94 1.61 1.04 0.01 0.94 -f0.6021=*=0.1075 -0.1607=1=0.0834 -1-0.0829*0.0714 -0.0703*0.0796 -0.0583*0.1270 -1-0.0754*0.0623 -1-0.2814*0.0878 -1-0.0865*0.0609 -0.0214*0.0817 +0.0635*0.1432 +0.0107*0.0071 5.60 1.93 1.16 0.88 0.46 1.21 3.21 1.42 0.26 0.44 1.51 +0.4883*0.1284 -0.2157*0.0817 +0.0486=1=0.0717 -0.1502*0.0782 +0.0240*0.1274 +0.0550*0.0624 +0.3102*0.0862 +0.0772*0.0612 -0.0738*0.0813 -0.0455*0.1436 -0.0542*0.0709 3.80 2.64 0.68 1.92 0.19 0.88 3.60 1.27 0.91 0.32 0.76 The values are partly negative and partly positive in sign. They vary widely in magnitude. For the athletes the constant is positive and of medium magnitude, but the 62 other men give a negative corre- lation of the order r = —0.2. As a result, the correlation for the whole series is, in comparison with its probable error, sensibly zero. The same is true for the first supplementary series of men and for the whole series of men (121 in number) for which records of both stature and pulse-rate are available. For all three of these larger series the corre- PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 77 lation is, however, positive in sign, indicatiDg that taller individuals have a more rapid pulse. If, however, one turns to the Gephart and Du Bois selection of male subjects he finds a negative correlation of the order r = —0.15, thus indicating that the taller men have a less rapid pulse. This is also the relationship suggested by the constants for the women, who give a consistently negative but statistically insignificant correlation. Inspection of the means obtained without grouping the values for stature — as given in diagram 7 for the total available men (N = 121) and for the total available women (N = 90) — shows (a) how widely scattered the average pulse-rates for any given stature are, and (6) « r ; < .-v '. I ^-■' 1 /ei /ss 173 in 183 in m iss STATURE IN CENTIMETERS Diagram 7. — Variation of mean basal pulEe-rate with stature in men and women. Note extreme irregularity of means and different slopes of the straight lines in the two sexes. Compare diagrams 5 and 6 for body-weight and pulse-rate. how slight is the change in average pulse-rate associated with differ- ences in stature. The straight lines in the diagrams are due to the equations : For men N=12l p=47.7179+0.0783 f Forwomen iV= 90 p=86.0430-0.1073* If the relationship between stature and pulse-rate be corrected for the correlation of weight with stature, we find the partial correlations between stature and pulse for constant weight, like the uncorrected correlations, are low in magnitude and irregular with regard to sign. The exception is the athletes, but these are too few in number to justify attaching much significance to the probable errors of the constants. The partial correlations between stature and pulse-rate for constant age are given by a' an 'an ' o Vl-r « a/1- -r * 'op The results obtained by applying this formula appear in the final column of table 18. 78 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Correction for age has not materially changed the values of the constants. Summarizing the results of these various calculations we note that in male and female infants and in our male adults taken as a class there is a suggestion of positive correlation between statiu-e and pulse-rate, i.e., of an increase of pulse-rate with stature. In the adults this is, however, largely due to the athletes and the vegetarians in the original series. The Gephart and Du Bois selection of males and the female series suggest a negative relationship between stature and pulse-rate. Thus the results for infants and adults, if either are really biologically significant, indicate a different relationship at the two ages. As far as the available data justify conclusions concerning the problem, they seem to indicate that there is only a very slight, if any, interdependence between stature and minimum or basal pulse-rate in man. 3. PULSE-RATE AND GASEOUS EXCHANGE. Since it is well known that pulse-rate and gaseous exchange are closely related in the individual, it seems desirable to determine whether in a series of individuals at complete muscular repose and in the post-absorptive state a correlation between pulse-rate and gaseous exchange and between pulse-rate and total heat-production will be foimd to exist. Table 19. — Correlation between pulse-rate and gaseous exchange. Series. TV Correlation be- tween pulae-rate and carbon-dioxide N Correlation be- tween pulse-rate and oxygen Difference Men. Original series: Athletes Others Whole aeries Gephart and Du Bois selection First supplementary series Original and first supplementary series. . . . Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 15 62 87 70 28 115 50 120 -|-0.2981±0. -(-0.0306*0, +0.1416±0. -t-0.0691±0. -|-0.1387±0. -|-0.1482±0. -(-0.2384*0. -t-0.1539±0. ,1587 ,0856 ,0709 ,0802 1250 0615 0900 0601 66 -0.0734*0.0826 22 -(-0.4811*0.1105 88; -(-0.0497*0.0717 16 62 88 71 28 116 50 121 68 22 90 -fO.2963 -t-0.0718 -(-0.2045 -(-0.1197 -(-0.2085 -f-0.1976 -fO.2788 -(-0.2012 0.1538 0.0852 ±0.0689 0.0787 0.1219 * 0.0602 0.0880 0.0588 - 0.0018 =i -(-0.0412=1 -f 0.0629=1 -(-0.0506=' -(-0.0698=1 -(-0.0494 =J -f 0.0404 =i -f 0.0473=1 0.2210 0.1208 0.0989 0.1125 0.1746 0.0861 0.1259 0.0841 -(-0.0318*0.0817 -(-0.3656*0.1246 -(-0.1331*0.0698 -(-0.1052*0.1162 -0.1155*0.1665 -f0.0834*0.0100 Table 19 gives the correlations between pulse-rate and oxygen con- sumption and pulse-rate and carbon-dioxide production, and the differ- ences in these correlations, for the various series with which we have worked. The results are reasonably consistent in indicating a low but significant positive correlation between pulse-rate and oxygen con- sumption and pulse-rate and carbon-dioxide excretion, larger gaseous exchange being associated with more rapid pulse-rate. PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 79 In the original series of women we find a slight negative correlation between pulse-rate and gaseous exchange, the women with the slower pulse showing the higher carbon-dioxide excretion. For oxygen eon- sumption the correlation is sensibly zero. The second series shows a substantial positive correlation. The sUght negative relationship between pulse-rate and carbon-dioxide excretion in the original series of women naturally pulls down the positive correlation in the supple- mentary series, so that a resultant low positive correlation is obtained in the total series of women. The correlation between pulse-rate and oxygen consumption is more intimate than that between pulse-rate and carbon-dioxide excretion. If we determine the partial correlation between pulse-rate and gaseous exchange for constant body-weight by the formulas vT Vi- Vl-r„p»Vl-r we find the results set forth in table 20. Table 20. — Comparison of partial correlalions between pulse-rate and gaseous exchange for constant body-weight with gross correlations between pulse-rate and gaseoiis exchange. Series. N Partial correla- tion between pulse-rate and carbon-dioxide Differ- v>' pe E T N Ul'^pc = 0.1020 b 0.0512 1 0.0360 0.1918=1=0.0788 0.3182*0.1025 0.2331*0.0628 11.80 6.13 13.41 11.69 10.64 16.08 6.73 12.25 17.06 2.43 3.10 3.71 +0.0121 =t 0.0974 +0.0457*0.1011 +0.0050*0.0644 +0.0276*0.0743 -0.0207*0.0901 +0.0125=1 +0.1738=" 0.0652 0.1639 +0.0262*0.0743 +0.0258*0.0523 -0.0498*0.1110 +0.0245*0.1460 -0.0244*0.0887 0.12 0.46 0.08 0.37 0.23 0.23 1.06 0.34 0.49 0.46 0.17 0.28 Table 27. — Equations showing variation of gaseous exchange with stature. Series. A^ Regression of CDs on stature. N Regression of Oi on stature. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series . Second supplementary series Other than Gephart andDuBois selection All men of three series Women. Original series Supplementary series Both series 15 62 88 71 28 116 19 64 136 66 35 101 =-219.66+2, =+ 31.69+0. =-160.61+2 =-136.80+1, =-177.44+2, =-155.98+2, =-113.11+1. =-164.04+2. =-162.74+2, 665 935 ,075 915 105 035 815 085 015 C =+ 13.78+0.895 C =- 4.10+1.025 C =+ 7.60+0.945 16 62 89 72 28 117 19 64 136 68 35 103 =-242.66+2.875 =+ 2.33+1.335 =-153.32+2.255 =-140.18+2.165 =-258.58+2.805 =-170.27+2.345 =-293.91+3.065 =-206.60+2.555 =-177.27+2.385 =+ 69.99+0.775 =- 62.07+1.665 =+ 29.93+1.015 women oxygen consumption increases from about 0.75 to 1.50 c.c. for each centimeter of stature, whereas in men the values are 2 to 3 c.c. for each centimeter of stature. Comparable but somewhat lower values are found for CO2 excretion. Diagram 10 shows the mean oxygen consumption of men and PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 87 women of different statures. Comparable values for carbon-dioxide elimination are represented in diagram 11. The straight lines are given by the equations for total men and women in table 27. Because of the relatively small numbers of individuals for statistical work, the medium value of the correlation between stature and gaseous exchange, and the wide variation in stature and gas volume, the means show great irregularity. The straight line probably represents the four sets of averages as well as any other single cTirve of a higher order. At least it does not seem worth while at the present time to try any other equation \mtil further materials are available. 3S0 • 3*0 320 300 ^ ^^ ISO •' V, ■260 ..-A^ 6^""^ ?to /'• ;' ' no ."'. •••■ V- 200 ■ISO ^^ v' .'' ■i 1*3 /J7 iss 160 iSt IM 172 176 180 m m in ISS STATURE IN CENTIMETERS DiAGRAU 10. — Mean oxygen consumption by men and women of various statures. In this and the preceding sections we have shown that oxygen consimiption and carbon-dioxide excretion are correlated with both body-weight and stature and have discussed the degree of the relation- ship. We now have to inquire whether the correlations between physi- cal characters and gaseous exchange differ consistently in the case of the two gases. It might at first appear that these two values should be identical, but that the correlations between the physical characters and gaseous exchange would not necessarily be identical for the two gases is shown by the fact that the correlation between the two meas- ures of gaseous exchange, while necessarily very high indeed, is not perfect. This point is brought out by the discussion of the correlation between oxygen consumption and carbon-dioxide production in Chapter III. 88 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Turning to the question of the relative magnitude of the correlation between physical measurements and oxygen consumption and physical measurements and carbon-dioxide excretion, we may refer to the differ- ences between the correlations for weight and the two gases as given in table 24 and for stature and the two gases as set forth in table 26. The correlation for weight and gaseous exchange shows that, with an insignificant exception in the case of the total women, the relation- ship between body-weight and the amoimt of oxygen consumed is higher than that between body-weight and the quantity of carbon- dioxide eliminated. The same is true, with three exceptions only, in the lower correlations between stature and gaseous exchange. IS2 IS6 leo IS4 les m ne wo m* ie» isz STATURE (N CENTIMETERS Diagram 11. — Mean carbon-dioxide production by men and women of various statures. The differences in correlations between body-weight and stature and the two gases are of a low order of magnitude, and because of the small number of individuals available can not be considered statistically significant for the individual series; but taking the data as a whole, there can be scarcely a doubt that the correlations between physical characters and oxygen consumption are significantly higher than those for physical characters and carbon-dioxide excretion. In view of the fact that the total volume of oxygen consumed is not excreted as carbon dioxide, one might perhaps have expected the lower correlation between physical characters and gaseous exchange to be found for the gas which, considered alone, gives the minimum measure of the katabolic transformations occurring in the body. The same relationship has been shown to hold in the correlation between the volume of the two gases and pulse-rate discussed on page 78. PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 89 The second point of interest pertains to the problem of the relative magnitude of the correlations for weight and gaseous exchange and stature and gaseous exchange. The differences between the correlations for stature and oxygen consumption and carbon-dioxide excretion, and body-weight and oxy- gen consumption and carbon-dioxide excretion are shown in table 28. With one single and numerically insignificant exception in the case of oxygen, the correlation between weight and gaseous exchange is higher than that between stature and gaseous exchange. A number of the differences are large enough in comparison with their probable errors to be looked upon as statistically significant. Table 28. — Comparison of correlations between weight and gaseous exchange and stature and gaseous exchange. Series. Difference DifF. ^WO ^BO ^diff. N +0.1797±0.0674 2.67 15 +0.1968±0.0872 2.26 62 +0.1944±0.0S20 3.74 88 +0.1854*0.0597 3.11 71 +0.1747*0.0723 2 42 2S +0.1989*0.0437 4.55 116 -0.0061*0.1449 0.04 19 +0.1815*0.0418 4.34 135 +0.5590*0.0865 6.46 66 +0.1401*0.1364 1.03 35 +0.3619*0.0761 4.76 101 Difference Diff. diff. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection. . . First supplementary series Orig'al and first supplementary series Second supplementary series All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 136 68 35 103 +0.1677=1 +0.1911i +0.1723=1 +0.1971 =i +0.0887=1 +0.1 747 =i +0.0940=1 +0.1693=1 ^0.0747 0.0929 0.0542 0.0632 0.0762 0.0465 0.1729 0.0453 +0.4916*0.0871 +0.1314*0.0140 +0.3691*0.0748 2.24 2.06 3.18 3.12 1.16 3.76 0.54 3.74 5.64 9.39 4.93 Body-mass is, therefore, a more important factor in determining (in the statistical but not necessarily in the causal sense) gaseous exchange than is stature. 7. WEIGHT AND TOTAL HEAT-PRODUCTION. That large individuals should produce absolutely more calories than small ones would seem a natural a priori assumption. Our prob- lem at this moment is to determine how intimate is the relationship between body-mass and heat-production. Examining, first of all, the residts for the series of infants we find: Formales N=5l r»* =0.7520*0.0411 r/.Er-=18.30 For females iV =43 r„A=0.8081 *0.0357 r/Er=22.64: Difference 0.0561 ±0.0544 Disregarding sex and treating boy and girl babies together, we have r„A = 0.7833 ±0.0269 r/Er = 29.12 90 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. These results are larger than those for stature (length) and total heat, which are 0.1329=1=0.0712 smaller for males, 0.0655=^0.0583 smaller for females, and 0.0985 =«= 0.0457 smaller for male and female babies considered together. The change in actual heat-production in calories per 24 hours for a variation of a kilogram in body-weight is shown by the regression equations, which are : For males fc=25.16+34.52u> For females h =26.18+34.23 u> The results are in remarkably close agreement. In both male and female babies a difference of 100 grams in weight between two subjects would mean a probable difference of 3.4 calories in their daily heat-production. The results are represented graphically in diagram ■190 r -p ■ISO ky'^^^ i K O B a. no 110 no /-., < u I J 1 m m 120 ^^-^_ ^ •■— MALE INFANTS •-- •- FEMALE INFANTS 219 2e* IS3 i3i X69 4M 4J» 4H BODY WEIGHT DiAGBAM 12. — Mean total daily heat-production by male and female infanta of various body-weights. 12. The Unes for the boy and girl babies he very close together indeed. While the observed means show considerable irregularity, this is appar- ently attributable to the (statistically) small number of observations available, and a straight Une seems to serve quite as well as a curve of a higher order to smooth the results. Turn now to the available data for the adults. The correlations between body-weight and heat and the partial correlations between body-weight and heat-production for constant stature are set forth in table 29. Considering first the actual correlations between body-weight and total heat-production, it is clear that the relationships are very high. For men they are of the order r = 0.80 in the larger series, although the PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 91 smaller subdivisions show fluctuations from r=0.58 for the 19 men of the second supplementary series to r = 0.96 for the 16 athletes of the original series. For women the results are somewhat lower. For the original series the correlation is r=0.76, a value in good accord with that for men, but the constant for the supplementary series is only r=0.45, a con- stant lower than the minimum relationship found in the several group- ings of men. The low value in this supplementary series has the effect of reducing the measure of interdependence based on the original female series when the two are combined, with the resultant correlation of r =0.61 for the 103 women. Table 29. — Comparison of amekUion between weight and toted heat-'production and partial correlation between weight and total heat-prodtiction with stature constant. Series. N Correlation between weight and heat- production ''wh ''vih '^wh Partial corre- lation between weight and heat- production s^wk fwh Difference Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Oiiginal and first supplementary series. . . Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 0.9577 ±0.0139 0.6251 ±0.0522 0.8012±0.0256 0.7879 ±0.0301 0.8664±0.0318 0.8176 ±0.0207 0.5758±0.1034 0.8022 ±0.0301 0.7960± 0.0212 0.7575 ±0.0349 0.4536±0.0906 0.6092±0.0418 68.90 11.98 31.30 26.18 27.25 39.49 5.67 26.66 37.66 21.71 5.01 14.57 0.9259 ±0.0240 0.5481 ±0.0599 0.7105± 0.0354 0.6526 ±0.0456 0.7196±0.0614 0.7192±0.0301 0.3609±0.1346 0.7177 ±0.0409 0.6867 ±0.0306 0.7472 ±0.0361 0.3556± 0.0996 0.5803±0.0441 38.58 9.15 20.07 14.31 11.72 23.89 2.68 17.55 22.44 20.70 3.57 13.16 -0.0318 -0.0770 -0.0907 -0.1353 -0.1468 -0.0983 -0.2149 -0.0845 -0.1093 -0.0103 -0.0980 -0.0289 The nature of the relationship between body-weight and total heat- production is clearly brought out by diagram 13, which gives the aver- age heat-productions for each weight grade for both men and women (total series) and the theoretical heat-productions due to the straight- line equations, For total men iV-136 For total women iV=103 fe= 617.493 +15.824 u; A =884.5276+ 8.227 w Thus heat-production increases 15.8 calories for each kilogram of body-weight in the men and 8.2 calories for each kilogram of body- weight in the women. The averages for the women are very irregular and apparently not well represented by a straight-line equation. The agreement of the empirical and the theoretical means in the case of the men is excellent for the groups containing a considerable number of subjects, i.e., for those from 45 to 77 kilograms in weight. 92 A BIOMETEIC STUDY OF BASAL METABOLISM IN MAN. We now turn to the partial correlations between weight and heat for constant stature. When we say we determine the correlation between body-weight and total heat-production for constant stature we mean that we determine from the whole material at our disposal, by the use of appropriate formulas, the correlation which would be foimd (within the limits of the probable errors of random sampling) if it were possible to sort our materials into groups of individuals of approximately like stature without so reducing the number of individ- uals in the groups as to render imtrustworthy the correlation between weight and total heat-production. The physical relationships involved in such determinations should be borne clearly in miad. If we determine the correlation between weight and total heat-production in individuals of constant height it is clear that the heavier individuals must be the "heavier set," plumper or fatter individuals. ■2S00 f ■2300 > ■ZIOO ^ ^ ■1900 ..^^^"^^^ 4 ■ 1700 ^ <^ ■1500 ^ -<^ =^ j!0^r:y^ ■1300 y"^ ^ r^ ^^"--^ ■1100 ■' yy •' J7 *7 57 (1 77 87 57 BODv WEIGHT IN Kilograms DiAGBAM 13. — Mean total daily heat-productions of adults, varying in body-weight. Obtaining the partial correlations for weight and total heat per 24 hours for constant stature by »' ttA "~ Vl-r„.« Vl- r.K^ we find the following values for infants: For males 0.7520*0.0411 0.5493*0.0660 For females 0.8081 *0.0357 0.4937*0.0778 For both 0.7833 *0.0269 0.5313 *0.0499 Correction for stature has very considerably reduced the correlation between body-weight and total heat-production. In the case of boy babies there is a reduction of 0.2027 or about 27 per cent, in the case PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 93 of the girl babies a reduction of 0.3144 or about 39 per cent, while if sex be disregarded the reduction is 0.2520 or about 32 per cent. The results indicate, however, that the correlation is primarily due to body- mass rather than to body-length. The partial correlations for men and women are laid beside the gross correlations in table 29. We note that without exception the correction for stature has reduced the correlation between weight and total heat-production. The amount of reduction is not, however, large. For the various series it is as follows: Percentagt Men: Reduction. Original series, i^=89 11.3 Gephart and Du Bois selection, N=72 17.2 First supplementary series, N=2& 16.9 Original and first supplementary series, N = 117 12.0 Total men, iy? = 136 13.7 Women: Original series, N=68 1.4 Supplementary series, iV = 35 21.6 Total women, JV = 103 4.7 The results which are based upon moderately large series of men are fairly regular. The smaller groups, of course, give much more variable percentages. The two series of women differ very greatly. The whole series of women seems to show a much smaller reduction in the correlation between weight and heat as a result of the correction for stature than do the total men. When more data are available, the detailed investigation of this point will be well worth while. We now tiu-n to the corrections for age in the adults. The results due to the formula 'tph 'ah'avj o' toA Vl-r„.«vT / oV ^ -^ ' ow 1 are laid beside the gross correlations in table 30. The results in this table are very striking. The partial correlations are, with the insig- nificant exception of the small series of athletes, larger than the original correlations imcorrected for age. Thus age heterogeneity has a meas- urable disturbing influence on the relationship between body-weight and total heat-production. When this influence is removed the close- ness of correlation is increased. Correcting for the influence of both age and stature, we have the partial correlations between weight and heat-production given by the formula i»r^ji V(l -ra.^-r.J-raJ+2r„,r„„r,J) V{1 -r„* -r.^' -r„fc^-l-2r„r„jr.i) 94 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. These can be best understood if they are laid beside (1) the gross correlations between weight and heat, r^s, beside (2) the correlations for weight and heat for constant stature and (3) the correlations be- tween weight and heat for constant age. This is done in table 31. Table 30. — Comparison of correlations between weight and heat-proditction and between weight and heat-proditction for constant age. Series. N Correlation between weight and heat- production Partial correla- tion between weight and heat-production a''wh Difference Men. Original series: Athletea Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series . . Second supplementary series Other than Gephart and Du Bois selection All men of three series Women Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 0.9577 ±0.0139 0.6251^0.0522 0.8012*0.0256 0.7879*0.0301 0.8664*0.0318 0.8175*0.0207 0.5758*0.1034 0.8022*0.0301 0.7960*0.0212 0.7575*0.0349 0.4536*0.0906 0.6092*0.0418 0.9544=1 0.7032=" 0.8524=" 0.7983=1 0.8955 =i 0.8624=1 0.6009 =i 0.8583 =J 0.8384=1 0.0150 0.0433 0.0196 0.0288 0.0252 0.0160 0.0989 0.0222 0.0172 0.7776*0.0323 0.6040*0.0724 0.7117*0.0328 -0.0033 -1-0.0781 +0.0512 -1-0.0104 +0.0291 +0.0449 +0.0251 +0.0561 +0.0424 +0.0201 +0.1504 +0.1025 We note that in all cases correction for age and stature has decreased the values of the correlations between weight and heat-production in men but increased the constants measuring the relationship in women. Thus correction for two of the disturbing factors in the relationship between weight and heat-production has tended to bring the results obtained for the two sexes into closer agreement. For the total series the differences between the gross and the partial correlations are : Gross Partial wh. aa wh. Men 0.7960 *0.0212 0.7510 *0.0252 Women 0.6092 ±0.0418 0.6866 *0.0351 Difference 0.1868 *0.0469 0.0644 *0.0432 Thus the difference between men and women is 3 times as large before correction for the influence of stature and age has been made as it is after the influence of these two variables has been eliminated. The difference between the gross correlations in the two sexes is prob- ably significant in comparison with its probable error. The difference between the correlations corrected for the influence of age and stature is probably not statistically significant. Comparing the partial correlations for both age and stature constant with those for stature only and age only constant, we note that the PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 95 differences between them are not large. The addition of the correction for age to that for stature has not greatly influenced the measure of the degree of interdependence between weight and heat. Table 31. — Comparison of gross correlation between weight and total heat-production and partial correlations between weight and heat-production for constant stature, constant age, and constant stature and age. Gross corre- lation for weight and heat- production Correlation Correlation Correlation corrected for corrected for corrected for Series. N the influence the influence both stature of stature of age and age ^v,h i'vh a^wh at^wh Men. Original series: Gephart and Du Bois selection . 72 0.7879*0.0301 0.6526*0.0456 0.7983*0.0288 0.6386*0.0471 Other than Gephart and Du Bois selection 64 136 0.8022=1:0.0301 0.7060*0 0212 0.7177*0.0409 0.6867*0.0306 0.8683*0.0222 0.8384*0.0172 0.7942*0.0311 0.7510*0.0252 All men of three series Women. Original series 68 7675*0 0349 7472*0 0361 7776*0 0323 7674*0.0336 Supplementary series 35 0.4536*0.0906 0.3556*0.0996 0.6040*0.0724 0.6197*0.0832 103 0.6092*0.0418 0.5803*0.0441 0.7117*0.0328 0.6866*0.0351 8. STATURE AND TOTAL HEAT- PRODUCTION. In infants the correlation between stature (length) and total heat produced is fairly high. The results are : For males iV = 51 r.A = 0.6191 ±0.0582 r/£r = 11.22 Forfemales iV=43 m =0.7426*0.0461 r/£r-16.11 Difference 0.1235*0.0719 Both constants are imquestionably significant. That for females is somewhat higher than that for males. In comparison with its probable error the difference can not, however, be considered signifi- cant. Disregarding sex the correlation for the 94 babies is : r.i =0.6848 ±0.0369 r/E, = 18.66 Expressing these results in terms of actual change in total heat- production with differences in stature we have the following equations For males A = -229.58 -t-7.34t For females A = -252.55-J-7.83« which are represented graphically in diagram 14. The excellent agreement of the results for the two sexes is shown by the close parallelism of the two fines. While the observed means are very irregular because of the limited number of individuals, these straight fines serve fairly well to represent them, and until further data are available it is not worth while to try equations other than the linear. 96 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. For the various adult series the correlations between stature and total heat appear in table 32. The constants for adults are positive throughout, indicating greater total heat-production by taller individuals. •— •= MALE INFANTS •— •- FEMALE INFANTS STATURE IN CENTIMETERS DiAOBAH 14. — Mean total daily heat-production of infants classified according to stature. In the men the correlations are of the order r = 0.60. Because of the smallness of the groups of individuals — and possibly also for biological reasons — ^the constants for the subseries fluctuate between Table 32. — Compariaon of correlation between aUUure and total heat-production mth the eorreUOion between weight and total heat-prodtiction. Series. N Correlation between stature and heat- production Correlation between weight and heat- production 'IT* Difference Diff. Ediff. Men. Original series : Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series . . . . Second supplementary series Other than Gephart and Du Bois selection, All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 36 103 0.7861=^0.0644 0.4261=^0.0701 0.6098=^0.0449 0.5966 ='=0.0512 0.7071 =*=0.0637 0.6218=^=0.0382 0.5589=^=0.1064 0.6290±0.0510 0.6149=^0.0360 0.1913=^0.0788 0.3139=^=0.1028 0.2318=^=0.0629 0.9577=1 0.6251=1 0.8012=1 0.7879=" 0.8664=1 0.8175=" 0.5758=" 0.8022=" 0.7960=" 0.0139 0.0522 0.0256 0.0301 0.0318 0.0207 0.1034 0.0301 0.0212 -1-0.1716=1 -1-0.1990=1 -1-0.1914=1 -1-0.1913=1 -1-0.1593 =J -1-0.1957=" -1-0.0169=" -1-0.1732=1 -1-0.1811=" 0.0659 0.0874 0.0517 0.0594 0.0712 0.0434 0.1077 0.0592 0.0418 0.7575=^0.0349 0.4536=fc0.0906 0.6092^0.0418 -1-0.5662=^0.0862 -1-0.1397*0.1370 -l-0.3774=t0.0765 2.60 2.28 3.70 3.22 2.24 4.51 0.16 2.93 4.33 6.57 1.02 4.99 r=0.43 for the 62 non-athletic and non-vegetarian individuals of the original series, and r=0.79 for the 16 athletes. For the larger series, the values are in very good agreement indeed, considering them in comparison with their probable errors. PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. " 97 The women show correlations which differ remarkably from those found in the men. The original series is characterized by a correlation of only r=0.19, the supplementary series by a correlation of only r =0.31, and the total series by a correlation of r =0.23. Comparing the total available materials for adult men and women, we find the following correlations and their difference: For 136 men r,;;- 0.6149=^0.0360 For 103 women r,j^ =0.2318*0.0629 Difference 0.3831 *0.0725 The difference is over 5 times as large as its probable error and certainly suggests a significant difference in the correlation between STATURE IN CENTIMETERS Diagram 15. — Distribution of total daily heat-productions of men of various statures. stature and total heat-production in men and women. Against the conclusion that this is a real sexual differentiation, may be possibly urged the fact (demonstrated immediately above) that in the infants the correlations are of about the same magnitude, the constant for girl babies being, as a matter of fact, slightly greater than that for boy babies. 98 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. The results for the relationship between stature and total heat in the two sexes may be conveniently compared in diagram 15 for men and 16 for women. The straight-line equations are: For men ft = -1237.637+16.589* For women ft= 226.S8S+ 6.931 1 Thus heat-production increases about 16.6 calories per day in men and 6.9 calories per day in women for each variation of 1 cm. in stature. The constant term fixes the position of these lines when represented graphically. The averages represented in diagram 17 show that the heat-productions for men are regularly higher than those for women of the same stature. There is a strong suggestion of non-linearity in the case of the averages for men, but the numbers of individuals in the classes, especially the very tall and the very short indiAdduals, is so small that detailed mathematical analysis seems unprofitable at present. g teas D -ises ■ses 170 ISO STATURE IN CENTIMETERS Diagram 16. — Distribution of total daily heat-productions of women of various statures. We have now to consider the problem of the relative magnitude of the correlations for body-weight and total heat-production and stature and total heat-production. Total heat is correlated with weight some- what more closely than with stature in both males and females. The differences for infants are: StatUTt and total heat. Males 0.6191 ±0.0582 Females 0.7426*0.0461 Difference 0.1235*0.0719 Both sexes 0.6848*0.0369 Weight and total heat. 0.7520*0.0411 0.8081*0.0357 0.0561*0.0544 0.7833*0.0269 Difference in correlation, 0.1329*0.0712 0.0655*0.0583 0.0985*0.0457 On the basis of the present data for infants the differences in the correlations can not be considered statistically significant. The more extensive data for adults also consistently show higher correlations between weight and total heat than between stature and PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 99 total heat. The actual differences and their probable errors appear in table 32. The correlations are consistent throughout in indicating a more intimate relation between body-weight and total heat-production than between stature and total heat-production. Notwithstanding the (statistically) few individuals considered, a number of the differences may be looked upon as individually significant in comparison with their probable errors. m 233! Zi3S 2ISS ■ ■20SS ■ISM ^^ ■less ■iTir less ISSS ■i4es fx^ > A 5 ■I39S ^ V ^ < V ^ \ r-^' ^ V'' ^ .'' » . 4 i*e IS2 le ISO le* res m f7€ 180 164. m ISZ 196 STATURE IN CENTIMETERS Diagram 17. — Mean daily heat-production of normal men and women of various statures. The differences in correlation vary considerably from series to series, ranging from 0.017=^0.108 in the 19 men of the second sup- plementary series to 0.566 ±0.086 in the original women. We note, however, that the probable error is so high in the case of the second supplementary series of men that it can not really be asserted to differ significantly from the other groups of men. The larger groups of men show a difference of the order r^h—T,h = 0.19. In the women the differ- ences are much larger because of the very low correlations between stature and total heat-production. In the preceding section we considered the influence of age on the correlation between body-weight and total heat-production. It now 100 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. seems desirable to eliminate the possible influence of age upon tlie correlations between stature and total heat-production by using the partial correlation formula o»'m = '"•A— ^Kira* Vl-r„« Vl-r„»' With such low correlations as those which have been demonstrated between age and stature in Chapter III, the correction due to the correlation between age and stature will be small. Table 33. — Corrdation between stature and total heat-production and partial correlation hetween stature and total heai-prodiKtion tmth age constant. Series. N CoTielation between stature and heat ••.A Partial correlation be- tween statute and heat a^ih a^th Differ- ence Men. Origiiial series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Oiisinal and first supplementary series. . . . Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 0.7861=1 0.4261=1 0.6098=1 0.5966^ 0.7071 =i 0.6218=1 0.5590 =d 0.6290=1 0.6149=1 0.0644 0.0701 0.0449 0.0512 0.0637 0.0383 0.1064 0.0510 0.0360 0.1913=fc0.0788 0.3139=1=0.1028 0.2318=^0.0629 12.21 6.08 13.58 11.65 11.10 16.24 5.25 12.33 17.08 2.43 3.05 3.69 0.7324=1=0.0782 0.4397 =»= 0.0691 0.5977=*= 0.0460 0.6542 =fc 0.0455 0.7175=fc0.0618 0.6175 =t 0.0386 0.6608 =t0.1061 0.6093=1=0.0530 0.6129=^0.0361 0.2196 =t 0.0778 0.3737 =t0.0981 0.2700 ="=0.0616 9.37 6.36 12.99 14.38 11.61 16.00 5.29 11.49 16.98 2.82 3.81 4.38 -0.0537 -f-0.0136 -0.0121 -1-0.0576 -i-0.0104 -0.0043 -(-0.0018 -0.0197 -0.0020 -f0.0283 -1-0.0598 -1-0.0382 The results are laid beside the gross correlations in table 33. In the larger series of data the differences between the gross correlations and the partial correlations are in no case as large as their probable errors. The disturbing influence of age upon the correlation between stature and total heat-production is, therefore, insignificant. Since stature and body-weight are known to be correlated charac- ters (see Chapter III), it is clear that the correlation between stature and total heat-production might be merely the resultant of the corre- lation between weight and heat-production and weight and stature. The fact that the correlation between stature and total heat-production is consistently lower than that between weight and total heat-produc- tion would, superficially considered, seem to support this view. To test the question critically we must have recourse to the partial correlation coefficient between stature and heat-production for constant body-weight. Inserting the values of the correlation coefficients for stature and heat, weight and heat, and stature and weight in the PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 101 partial correlation formula for stature and total heat for constant weight, 'ah """' ic«' iiifc a1',K = Vl-r »Vl- we find for the infants : »•„*' For males 0.6191 ±0.0582 For females 0.7426^0.0461 0.0949^0.0936 0.1492^0.1006 If sex be disregarded, we have : Trt =0.6848 ±0.0369 „r.» =0.1178 *0.0686 In comparison with their probable errors the partial correlations are sensibly 0. All three are, however, positive in sign. Correction for body-weight has almost but apparently not entirely wiped out the relationship between stature and total heat-production. For adults the results of the gross correlations and the partial cor- relations have been presented in table 34. Table 34. — Correlation between ilatwre and total heat-prodiietion and partial correlation between stature and total keat~produetion with weight constant. Series. N Correlation between stature and total heat-produatioD Uh ^r. ,K Partial corre- lation between stature and total heat-production ui'th v>r,h u'tk Differ- ence Men. Original series: Athletes Others Whole series Gephart and Du Bois selection. . . First supplementary series Original and first supplementary series Second supplementary series All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 136 68 35 103 0.7861 <^0.0644 0.4261*0.0701 0.6098*0.0449 0.5966*0.0512 0.7071*0.0637 0.6218*0.0382 0.5589*0.1064 0.6149*0.0360 0.1913*0.0788 0.3139*0.1028 0.2318*0.0629 12.21 6.08 13.58 11.65 11.10 16.28 5.25 17.08 2.43 3.05 3.69 0.5851 0.2453 0.3623 0.1573 0.1827 0.3275 0.3246 0.3207 0.1109 * 0.0805 0.0621 0.0775 * 0.1232 0.0557 0.1384 *0.0619 0.0397*0.0817 0.0927*0.1130 0.0445*0.0663 5.28 3.05 5.83 2.03 1.48 5.88 2.3S 6.18 0.49 0.82 0.67 -0.2010 -0.1808 -0.2476 -0.4393 -0.5244 -0.2943 -0.2343 -0.2942 -0.1516 -0.2212 -0.1873 It is clear that in every series the correlation between stature and total heat-production is reduced when correction is made for body weight. The partial correlation between stature and heat for constant weight is not on the average zero. Instead, we have fairly substantial positive values throughout. Some of the constants taken individually may very reasonably be considered significant in comparison with their probable errors. The actual magnitude is of the order „r,A = 0.30 in the larger series of men, although the first supplementary series gives only „r,A=0.18 and the Gephart and Du Bois selection gives jr^^O.16. The women seem to differ from the men and to agree with the infants 102 A BIOMETEIC STUDY OF BASAL METABOLISM IN MAN. in indicating that correction for weight has practically, but not entirely, eliminated the correlation between stature and heat-production. As a result of the analysis in this and the preceding section, we have shown that the correlation between weight and total heat-production is appreciably lowered when the factor of stature is eliminated by the use of the partial correlation coeflScient and that the correlation be- tween stature and metabolism is considerably reduced when the factor of body-weight is eliminated in a similar manner; but in neither case does the correlation disappear. Thus there is a relationship between weight and metaboUsm which is independent of stature, also a relation- ship between stature and metabohsm which is independent of weight. These partial, residual, or net correlations, however one cares to desig- nate them, are of a positive character. In other words, if a group of individuals of identical weight be examined the taller individuals will be found to have the higher metabolism. If a group of individuals of the same stature be examined, the heavier individuals will be found to have the greater metabohsm. It is evident that our partial correlations have a direct bearing on the problem of the metabolism of fat and lean individuals, a subject which has received considerable discussion in the literature of basal metabolism. If individuals of the same body-weight be classified according to stature, the taller individuals will necessarily be thinner than the shorter ones. The partial correlations show that in a given weight class the taller individuals have the greater gaseous exchange. In a group of individuals of identical weight, slendemess or spareness of build can result only from reduction in weight of bone, muscle, or fat. Reduction in fat mass seems the most probable source of an increase of stature without alteration in weight. We conclude, therefore, that the leaner individuals are those showing the higher metabolism. The partial or residual correlation is not in this case large. In turning to the data which show that within a group of individuals of the same stature the heavier individuals show the higher heat- production, the reader may beUeve he sees a contradiction to the con- clusion that the leaner individuals are those showing the higher metabolism. But such does not, on closer analysis, seem to be the case. In a group of individuals of the same stature, differences in body-weight may be due to fat, which in the main is inert in its direct contribution to metabolism, or they may be due to differences in the mass of mus- cular and other active tissues. Thus there is no incompatibility what- ever in the statements that within a group of individuals of the same weight the taller have the greater metabolism, whereas in a group of the same statxire the thicker individuals show the greater metabolism. The recent investigation of Armsby and Fries,' in which they demonstrated a disproportionately high heat-production in a fat as ' AmiBby and Fries, Journ. Agr. Res., 1918, 11, p. 451. PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 103 compared with a lean period in a steer does not seem to invalidate the conclusion that human individuals who are relatively tall for their weight have a higher metabolism than shorter ones. In the case of the fattening experiment reported by Armsby and Fries the experi- mentally induced changes in the nutritional level of the animal were brought about with relatively great rapidity. Concomitant with the fattening there was an increase of 36 per cent in the basal katabolism, just as in the case of a man undergoing a 31-day fast at the Nutrition Laboratory there was a 28 per cent decrease in the basal katabolism.* Without further evidence one would not be warranted in assuming that like differences would necessarily be found between different individuals of relatively permanent lean and fat physical constitution. More recent investigations have shown that the basal metabolism of the human subject is profoundly affected by sudden modifications of the nutritional level, particularly those which are accompanied by rapid reduction in body-weight. If the food-intake be reduced below the maintenance level it is plain that with constant basal reqiiirements there must be draft upon previously stored body-reserves. Experiments with human subjects along this line demand a high degree of personal integrity and veracity on the part of the subjects. Such requirements were fulfilled by two squads of 12 men each from the International Y. M. C. A. College at Springfield, Massachusetts.^ The first squad was kept for a period of 4 months upon a much re- stricted diet with an energy content of approximately one-half to two- thirds of the caloric requirements prior to the test. During the first few weeks there was a pronounced decrease in body-weight. After the body-weight had fallen on the average 12 per cent, an increase in the diet was made to prevent fiu-ther loss in weight. Measurements of the groups as a whole in the large respiration chamber at the Nutrition Laboratory in which the 12 men slept every alternate Saturday night gave the basal metabolism during deep sleep. The normal demand of the men prior to the reduction in diet ranged from 3200 to 3600 net calories. After a decrease of 12 per cent in weight only 1950 calories were required to maintain this weight. The heat output as measured by indirect calorimetry and on the basis of calories per kilogram of body-weight and calories per square meter of body-surface was essentially 18 per cent lower than at the beginning of the study. Throughout the period of loss in weight and for some time following there was a marked loss of nitrogen. In round numbers these men lost approximately 150 grams of nitrogen. The nitrogen output per day at the maintenance diet of 1950 net calories * Benedict, CarneKie Inst. Wash. Pub. No. 203, 1915. Also Am. J. Physiol., 1916, 41, p. 292. 'Benedict; Proc. Amer. Phil. Soc, 1918, 57, p. 479. Also Benedict and Roth, Proe. Nat. Acad. Sci., 1918, 4, p. 149. Also Benedict, Roth, Miles, and Smith, Carnegie Inst. Wash. Pub. 280. (In press). 104 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. was about 10.5 as compared with 14 grams in a control group with unrestricted diet. This lowering of the metabolism accompanying the assumption of a thinner buUd is apparently opposed to the conclusions drawn above, according to which thinner individuals show a higher metabolism. Apparently, however, we have here, as in the fattening experiments of Armsby and Fries and in the prolonged fast of 31 days, to do with the special factor of rapid experimentally induced changes in the nutritional level of the organism, and not with the relatively permanent differences between fat and lean individuals. Determining the partial correlation between stature and total heat- production in calories per day for constant body-weight and constant age by the formula io'"»A = *'.)i(l —TqJ) —ra,rai,—r^,r„},-\-ra^ (Xa, r^i, +rah r„,) 'V^(l-»-a„''-r„.'-r„.'+2r„„r„OV'(l-r„„*-r„fc*-r,A»-|-2r„„r„fcr„0 and comparing the results with the gross correlations, r,^ and the corre- lation corrected for weight, .r^, and for age, o*",*, we have the results in table 35. Tabix 35. — Compariton of gross eorreloHon between sUiture and toUd heat-production and partial correlatUms between itatture and heat-production for constant weight, for constant age, and for constant age and weight. Series. N Gross correla- tion between stature and heat- production Correlation corrected for influence of weight Correlation corrected for influence of age Correlation corrected for both age and weight Men. Original series: Gephart and Du Bois selection Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 72 64 136 68 35 103 0.6966 ±0.0512 0.6290=^0.0510 0.6149*0.0360 0.1913*0.0788 0.3139=fc 0.1028 0.2318±0.0629 0.1673*0.0775 0.4220*0.0693 0.3207*0.0519 0.6542*0.0455 0.6093*0.05300 0.6129*0.0361 0.2561*0.0743 3442*0.0743 0.2899*0.0530 0.0397 * 0.0817 0.2196* 0.0778 0.0784 * 0.0813 [737*0.0981 0.1064*0.1127 0.0445*0.0663to.2700*0.06160.0850*0.0660 r- The correlations for stature and heat-production are positive throughout, even after correction has been made for both age and weight. This fully substantiates the conclusion drawn above concern- ing the existence of an independent physiological relationship between stature and heat-production. The partial correlations for both age and weight constant are in some cases higher and in some cases lower than those in which weight only is corrected for. This shows the relatively small influence of age on the correlation between statxire and heat- production. This influence is small, not because there is no relationship PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 105 between age and metabolism, but because in adults there is little rela- tionship between age and stature. 9. RECAPITULATION AND DISCUSSION. 1. Our series of data show practically no relationship between basal \ or minimum pulse-rate and body-weight in adults. In new-bom infants there may be a slight positive correlation, more rapid pulse being asso- ciated with greater body-weight, but further investigation is necessary before final conclusions can be drawn. 2. As far as our data show, there is practically no relationship between statiu'e and p.ulse-JateJn man.* 3. There is a low but significant positive correlation between \ minimum pulse-rate and gaseous exchange in men, larger gaseous ej^hange being associated. with _more rapid pulse-rate. The series of women available show as yet inexpUcable inconsistencies in these relationships. The correlation between pulse-rate and oxygen con- sumption is more inornate than that between pulse-rate and carbon- dioxide excretion. Physiologists have long been familiar with the correlation between pulse-rate and metaboUsm in the same individual, that is with the intra-individual correlation between the rate of the heart-beat and the amount of thei katabolism. Here, however, we are dealing with the problem of the relationship between the TniniTwiiTn pulse-rates of a series of individuals and their basal metabolism con- stants — ^that is, with inter-individual correlation. 4. The inter-individual correlations between pulse-rate and gross heat-production are positive throughout, but low and variable in mag- nitude. When correction for body-size is made by expressing heat production in calories per kilogram of body-weight or in calories per square meter of body-surface, the magnitude of the correlations is materially raised. This indicates that the relationship is one of real physiological significance. The most intimate correlations are obtained when correction for body-size is made by expressing heat-production in calories per square meter of body-surface. This result has an obvious bearing on the so-called body-surface law, to be discussed in ChapterVI. 5. There is j, high positive correlation between body-weight and gaseous exchange. The correlations are of the order r=0.75 for men and r=0.60 for women.' Expressed in actual gaseous exchange, this degree of correlation means that in men oxygen consumption increases about 2.27 and carbon-dioxide excretion increases about 1.89 c.c. per minute for an increase of 1 kilogram of body-weight. For women the values are about 1J.7 c.c. O2 and 1.02 c.c. CO2 per kilogram of weight. These are the values for the grand total series. Those for the several sub-series differ considerably among themselves. * Conclusions 1 and 2 must be understood to be limited to our own data for minimum or basal pulse-rates. They may not be strictly valid for subjects under other conditions. This question may be treated by one of us later. 106 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 6. There is a substantial correlation between stature and gaseous exchange. The correlations for men are of the order r=0.60, while f orwomen they are of the order r = 0.30. In terms of actual gas volume these coefficients show that oxygen consumption increases about 1 c.c. for each increase of 1 cm. in stature in the women, whereas in the men the increase is between 2 and 3 c.c. Comparable, but somewhat lower values are found for carbon-dioxide excretion. 7. The correlations between both stature and body-weight on the one hand and oxygen consumption on the other are higher than those between these two physical characters and carbon-dioxide excretion. Since the total voliune of oxygen consumed is not excreted as carbon dioxide this result should have been expected. 8. Comparison of the correlations between body-weight and gase- ous exchange and those between stature and gaseous exchange shows that the correlation between weight and gaseous exchange is higher than that between stature and gaseous exchange. Thus body-mass is a mo re im portant factor than is stature in determining (in the statistical but not necessarily in the causal sense) gaseous exchange. 9. The correlations between body-weight and total heat-production ajehigh. Thus coefficients of the order r = 0.75 to r =0.80 have been found for male and female new-bom infants, of the order r=0.80 in men and r =0.60 in women. In terms of actual heat productions these correlations, taken in connection with the means and standard devia- tions, show that in the new-bom infants a difference of 100 grams in body-weight implies a difference of about 3.4 calories in daily heat- ptcduction. In the adults a difference of one kilogram in body-weight is followed by an average difference of 8.2 calories in heat-production in women and 15.8 calories in men. 10. There is a si^dficant positive correlation between stature (body-length) and total Eeat-production in both new-bom infants and a(Mts^^ The correlations are consistently lower than those for weight and total heat-production. 11. Since tall individuals are on the average heavy individuals, and since heavy individuals are on the average tall individuals, it has been necessary to inquire to what extent the correlation between total heat- production and stature is merely the statistical resultant of the correla- tions between weight and heat and stature and weight, and to inquire to what extent the correlation between weight and heat-production is merely the resultant of the correlation between stature and heat- production and between weight and stature. In proceeding in this way we have been treating the data in a purely objective manner, basing our treatment on no physiological theory concerning the relative importance of stature or weight in determining basal metabolism. Our results show that both stature and body-weight have independent sig- nificance in detenniniiig the basal metabolism of the normal individual. Chapter V. CHANGES IN METABOLISM WITH AGE. The significance of a knowledge of the relationship of metabolism to age is twofold. First, the change of normal basal metabolism with age is in and for itself a problem of prime physiological importance. Second, metabolism determinations in the hospital ward have little value as a basis for medical theory or practice except as the constants are interpreted in comparison with those for normal controls. It is important, therefore, that in selecting controls for comparison with pathological cases the influence of the age factor in both health and disease should be fully known. Our treatment in this place differs from that accorded the problem by earlier writers in that we have actually determined statistical con- stants measuring the rate of change in metabolism with age during the period of adult, or practically adult, life. Ultimately it will be necessary to undertake an examination of the change of physical and physiological characters other than direct or indirect heat measurements as a first step towards a closer coordi- nation of investigation in human metabolism and the results of general biological research. Such coordination should be to the advantage of both the special field of human nutrition and the broader field of general biological theory. In this place we shall merely present, and statistically discuss, the available data for human basal metabohsm in relation to age. A com- parative examination of age changes in other physical and physiological characters must be reserved for the future. 1. HISTORICAL REVIEW. It was of course inevitable that the problem of the dependence of metabolism on age should be considered in a general comparative way as soon as determinations of the basal metabolism of infants, youths, and adults began to be made. While the observations of Andral and Gavarret ^ can not be taken as basal, we have determined the correlation between age and C0» production per hour in the men 17 to 102 years of age and in the women * Andral and Gavanet, Ann. de chim. et phys., 1843, 8, 3 air., p. 129. 107 108 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 19 to 82 years of age, using the constants as tabled by Sond^n and Tigerstedt.2 We find : For men J\r=29 r^ = -0.629*0.076 For women JV = 17 v = -0.058*0.163 Both coeflBcients are negative, suggesting a decrease in gaseous ex- change with age; that for men is large. Most imfortunately stat\u-es and weights of these individuals are not given. It is not possible, therefore, to correct for these factors which are later shown to have a large disturbing influence on the meas- ure of the relationship between age and metabolism. In view of this fact, and that the constants for the individual subjects may show a considerable variation due to their not being truly basal, and further that the nimiber of individuals is small, better agreement with the results presented for our own series of subjects could perhaps not have been expected. The classic work of Sond^n and Tigerstedt themselves,' while dis- cussing in a most exhaustive way many of the fundamental questions of metabolism, is based on observations made before the precautions necessary for basal determinations were tmderstood. Magnus-Levy and Talk,* in 1899, concluded that the basal metab- olism is low in infancy, high in childhood, and low after the onset of old age. They considered it essentially constant during the period of adult life. We have determined the correlations between age and calories per 24 hours, computed from the data of Magnus-Levy and Falk. We find : Correlation '•o* In men, N = 10 -0.238*0.201 In men and old men, JV •'IS -0.481 *0.134 In women, N = U -0.576*0.120 In women and old women, iV = 17 —0.569 *0.111 Thus in both the men and women studied by Magnus-Levy and Falk heat-production is shown to decrease with age. We may, of course, further investigate the relationship between age and heat-production in the series of Magnus-Levy and Falk by determining the partial correlation between age and heat-production for constant body-weight. The results are as follows: Partial Correlation vj'tth For men -0.147*0.209 For men and old men -0.712*0.086 For women -0.210*0.172 For women and old women -0.727*0.077 ' Sond^n and Tigerstedt, Skaad. Arch. f. Fhyaiol., 1895, 6, pp. 55-56. ' Sond^n and Tigerstedt, loc. eil. * Magnus-Levy and Falk, Arch. f. Anat. u. Fhya., Physiol. Abt., 1899, Suppl. p. 361. CHANGES IN METABOLISM WITH AGE. 109 Again the probable errors are high because of the small numbers of individuals studied. But one can hardly examine the results as a whole without reaching the conviction that Magnus-Levy and Falk were in error in concluding that metabolism remains essentially constant dur- ing adult life. Metabolism decreases throughout adult life, and this decrease is shown by the statistical analysis of their own data to be as evident after correction for the influence of body-size has been made as before. Carbon-dioxide production in boys of 10 to 18 years of age has been investigated by Olin," although not under strictly basal conditions. One of the objects of the investigations which have been under way on himian basal metabolism at the Nutrition Laboratory for a number of years has been the determination of the changes which take place in metabolism throughout the entire period of life. It was the intention to base this investigation upon a number of subjects siiffi- ciently large to eliminate the influence of individual variations at dif- ferent ages, and thus to obtain a smoothed curve of basal metabolism of both male and female individuals throughout the entire period of life. Before this program was complete Du Bois • combined the extensive data already published from the Nutrition Laboratory with fragmentary data from other sources and attempted to draw a curve of human basal metabolism for the entire period of life. In our opinion the time is not yet ripe for an imdertaking of such magnitude. While data are still being accumulated for this purpose, and while the results based on 136 men and 103 women are subject to revision as more extensive materials for the earlier and later periods of life are obtained, it seems desirable to analyze in a preliminary way the age changes in the subjects considered in this volume. Certain difficulties in the way of combining different series of measurements to secure a picture of the metabolic activity of the human subjects from birth to death will be indicated in Chapter VIII (p. 243). 2. STATISTICAL CONSTANTS MEASURING CHANGES IN METABOLISM WITH AGE. The range of ages of the individuals in each class, and the statistical constants of age in years, in the several groups of subjects appear in table 36. The constants showing the correlation between age and total heat- production in calories per 24 hours are given in table 37. Without exception the values of Vah are negative in sign, thus indicating that in ' Olin, Finaka ULk.-eallsk. handl., HelBuigfoTB, 1915, 57, p. 1434. At the time of going to press the GermaD report of this research, announced for appearance in the Skandi- naviscbes Archiv fiir Pbysiologie, is not available and hence analysis of the data is unfortunately now impossible. < Du Bois, Am. Joum. Med. Sci., 1918, 102, p. 781. Also Med. Bull. Cornell Univ., 1917, 6, pt. 2, p. 33. 110 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. groups of individuals of the age-range here under consideration total heat-production decreases with increasing age. Nine of the 12 values are over 3 times as large as their probable errors. They are, however, extremely irregular in magnitude, ranging from —0.092 ±0.126 in the first supplementary series of men (iV=28) Table 36. — Statistical constants of age in adults. Series. ;. Age range. 16 19-29 62 16-63 89 16-63 72 20-43 28 19-45 117 16-63 19 18-62 64 16-63 136 16-63 68 15-74 35 18-73 103 15-74 Average. Standard deviation. Coefficient of variation. Men. Original series: Athletes Others Whole series Gephart and Du Boia selection First supplementary series Original and first supplementary series Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 22.06=1 26.08 =i 26.15=i 25.74=1 25.64=1 26.03^ 32.11 = 28.16= 26.88= 0.45 ^0.64 ^0.56 0.44 =0.71 =0.46 =2.09 =0.94 = 0.51 26.66 ±0.81 39.86±1.82 31.15=>=0.92 2.66 ±0.32 7.51*0.45 7.86=1=0.40 5.57=fc0.31 5.56=1=0.50 7.38 =t 0.33 13.53 =t 1.48 11.20 =*=0.67 8.77 =fc 0.36 9.88 ="=0.57 15.97*1.29 13.79=4=0.65 12.04 =b 1.46 28.78=»=1.88 30.07 =fc 1.97 21.63 =fc 1.27 21.67*2.04 28.30='= 1.35 42.15=1=5.37 39.77=^2.72 32.63=1=1.47 37.04 =t2.42 40.07=1=3.71 44.27=1=2.46 Table 37. — Correlation between age and total heat-production and partial correlation between age and heat-production for constant stature and for constant body-weight. Series. N Gross correlation between age and beat- production fah '■ah ^ah Correlation corrected for influence of weight w^ah uj'"oA Correlation corrected for influence of stature t'^'ah .^o* J^ah Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series Other than Gephart and Du Bois selec- tion All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 -0.4664=^0.1319 -0.1292=1=0.0842 -0.3529*0.0626 -0.3716*0.0686 -0.0917=t 0.1264 -0.2954*0.0569 -0.5007*0.1159 -0.3003*0.0767 -0.3062*0.0524 -0.2322*0.0774 -0.1796*0.1103 -0.2034*0.0637 3.54 1.53 5.64 5.42 0.73 5.19 4.32 3.92 5.84 3.00 1.63 3.19 -0.3977*0.1420 -0.4290*0.0699 -0.5766*0.0478 -0.4192*0.0655 -0.4609=1=0.1004 -0.5428*0.0440 -0.5328*0.1108 -0.5728*0.0566 -0.5147*0.0425 -0.3499*0.0718 -0.4755*0.0882 -0.4976*0.0500 2.80 6.14 12.04 6.40 4.59 12.34 4.81 10.12 12.11 4.87 5.39 9.95 -0.2240*0.1602 -0.1756*0.0830 -0.3227*0.0641 -0.4842*0.0609 -0.1942*0.1227 -0.2817*0.0574 -0.5029*0.1156 -0.2313*0.0798 -0.3003*0.0526 -0.2566*0.0764 -0.2764*0.1053 -0.2465*0.0624 1.40 2.12 5.03 7.95 1.58 4.91 4.35 2.90 5.71 3.35 2.62 3.95 to —0.601 ±0.116 in the second supplementary series (iV = 19). While the probable errors of these constants are relatively very high because of the small numbers of individuals available, this need not be taken as the final explanation of the highly irregular values. Both stature and body-wei^t vary greatly in human individuals, and, as pointed out on page 63, this variation in the adult is largely independent of CHANGES IN METABOLISM WITH AGE. Ill age. But while age and body-weight and age and stature are very little correlated in adult life, stature and weight, especially the latter, are closely correlated with metabolism. Thus irregularities of stature or body-weight would tend to dilute the correlation between age and total heat-production. The reader who has followed the lines of reasoning employed in preceding sections of this voliune will at once suggest that there are two ways in which the influence of these disturbing factors can be eliminated. First, we may determine the partial correlation coefficients between age and total heat-production for constant stature and for constant body-weight. Second, we may make the corrections for the influence of body-weight or of both body-weight and stature by ex- pressing metabolism in terms of calories per kilogram or calories per square meter of surface and subsequently correlate these heat-produc- tions per standard unit with age. We have carried out the analysis by both methods. Table 38. — Correlation between age and heat-produclion per kilogram 0/ body-weight and comparieon leiih correlation between age and total heat-produclion. Series. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementaiy series Original and first supplementaiy series. . . . Second supplementary series Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 64 136 68 35 103 Correlation between age and total heat-production 'ok -0.4664*0.1319 -0.1292*0.0842 -0.3529 ±0.0626 -0.3716*0.0686 -0.0917*0.1264 -0.2954*0.0569 -0.5007*0.1159 -0.3003*0.0767 -0.3062*0.0524 -0.2322*0.0774 -0.1796*0.1103 -0.2034*0.0637 ''ah ""oA 3.54 1.53 5.64 5.42 0.73 5.19 4.32 3.92 6.84 3.00 1.63 3.19 Correlation between age and heat-production per kilogram Tahk 4-0.0439 -0.4633 -0.4208 -0.2626 -0.4629 -0.4276 -0.3885 -0.4791 -0.4078 0.1683 0.0673 0.0588 0.0740 0.1002 0.0510 * 0.1314 0.0650 0.0482 -0.1510*0.0799 -0.6533*0.0653 -0.4931*0.0503 •"o** rahi. 0.26 6.88 7.16 3.55 4.62 8.38 2.96 7.37 8.46 1.89 10.00 9.80 rahi^ -rah -1-0.5103 -0.3341 -0.0679 -f0.1090 -0.3712 -0.1321 -f0.1122 -0.1788 -0.1016 -1-0.0812 -0.4737 -0.2897 The partial correlations between age and heat for constant body- weight, US' ah ^/i-rj Vl-r„ and the partial correlations between age and heat for constant stature, r.H are laid beside the gross correlations in table 37. The correlation between age and heat-production per kilogram of body-weight is com- 112 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. pared with the gross correlation in table 38. The same comparison for heat-production per unit of body-surface is made in table 39. The partial correlations for age and total heat-production for con- stant stature in table 37 show about the same irregularities as the gross correlations. The constants are sometimes lower and sometimes higher than the original coeflBcients. This failure of correction for stature to make a large difference in the correlations between age and heat-production is to be expected because of the relative laxness of the correlation between stature and heat-production, as demonstrated on page 96. Table ZQ.^-CorrehUion between age and heat-proditctUm per square meter of body-ewface and com,pariaon uiith correlation between age and total heat-production. Series. N Surface estimated, Meeh formula. Surface estimated, Du Bois height-weight chart. Difference Difference •"o^if '■"''Af Taho rahj^ ^rahif ^Tahj) Men. Origiiial series: Athletes 16 62 89 72 28 117 19 64 136 68 35 103 -0.4637*0.1339 -0.4817*0.0658 -0.6622*0.0489 -0.4124*0.0660 -0.4402*0.1028 -0.6401*0.0442 -0.4966*0.1166 -0.6778*0.0562 -0.5111*0.0427 -0.2746*0.0766 -0.6255*0.0694 -0.5437*0.0468 3.39 7.32 11.50 6.25 4.28 12.22 4.26 10.28 11.97 3.63 9.01 11.62 -0.4203*0.1388 -0.4243*0.0702 -0.5253*0.0518 -0.4672*0.0621 -0.3498*0.1119 -0.4819*0.0479 -0.5203*0.1128 -0.4986*0.0634 -0.4698*0.0451 -0.3647*0.0715 -0.6637*0.0779 -0.6238*0.0482 3.03 6.04 10.14 7.62 3.13 10.06 4.61 7.86 10.42 4.96 7.24 10.87 +0.0127*0.1879 -0.3526*0.1068 -0.2093*0.0794 -0.0408*0.0949 -0.3486*0.1628 -0.2447*0.0721 +0.0041*0.1643 -0.2775*0.0949 -0.2049*0.0678 -0.0423*0.1082 -0.4459*0.1304 -0.3403*0.0787 +0.0461*0.1916 -0.2951*0.1095 -0.1724*0.0812 -0.0956*0.0922 -0.2581*0.1688 -0.1865*0.0742 -0.0196*0.1619 -0.1983*0.0996 -0.1636*0.0693 -0.1225*0.1054 -0.3843*0.1349 -0.3204*0.0800 Others Whole series Gephart and Du Bois selection First supplementary series Original and first sup- plementary series Second supplementary Other than Gephart and Du Bois selection All men of three series . . Women. Oriianal series Supplementary series . . . The case is quite different with the partial correlations for age and metabolism for constant weight. With one single exception, in which the difference is small, the constants for the relationship between age and heat corrected for the influence of body-weight are numerically larger than the uncorrected values. A careful study of these values shows how greatly correction for body-weight has smoothed the series of constants for the relationship between age and metabolism. They range from —0.350 to —0.576 when the two sexes are considered to- gether, but when the probable errors are taken into account the con- stants can hardly be asserted to differ significantly among themselves. The larger series indicate the medium correlation of —0.5 between age and heat-production for constant weight. CHANGES IN METABOLISM WITH AGE. 113 Turning now to the correlations between age and heat-production per unit of body-weight and body-surface, we may compare the corre- lations between age and total heat-production with those between age and relative heat-production, i. e., heat-production per kilogram of weight or per square meter of body-surface, in tables 38 and 39. From table 38, in which the correlations between age and total heat-production are compared with those between age and heat per kilogram of body-weight, we note that in all cases except the athletes^ heat per kilogram of weight is negatively correlated with age — ^that is relative heat-production as well as total heat-production decreases with age. In the larger series of men, with the exception of the Gephart and Du Bois selection and the second supplementary series, the correlation between age and relative heat-production is numerically larger than that between age and gross heat-production. This is also true in the supplementary series and in the grand total series of women. Thus variations in the size of the individuals as measiu'ed by weight tend to disturb to some extent the correlations between age and heat- production. TiuTiing now to the correction for differences in size resulting from the expression of heat-production in calories per square meter of body- surface we have the results set forth in table 39. Without exception the 24 correlations are negative in sign. With three exceptions only^ the correlations between age and heat-production per square meter of body- surface are of a more strongly negative order than the correlations between age and total heat-production. In determining the relationship between age and total heat- production, correction for the influence of both body-weight and statiu'e may be made by the use of the partial correlation formula for two variables constant 'aAV-*- '3W ) 'aoTah ' wo' ujA"!"' »w\' «o' «jfc"1~' M' wo/ aurah * Comparing the values of ^.r^.^ with the gross correlations, r^h, and the partial correlations for stature and weight, ,rah and „r^, we have the results in table 40. Correction for both stature and weight has not given constants very different from those in which the correlation is corrected for weight only. Correction for both stature and weight has rendered the correla- tions between age and heat-production in the two sexes much more ' There are only 16 athletes. The age range is only 19-29 years, and the correlation is small in actual magnitude and only about one-fourth of its probable error. 'All of these exceptions are trivial in magnitude and only a fraction of their probable errors. 114 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. alike. Thus the differences between the correlations and partial correlations for the two sexes are : Corrtlation. Partial carrttalien. •"oA twfah Men -0.3062 ±0.0524 -0.4995 ±0.0434 Women -0.2034 ±0.0637 -0.5016 ±0.0497 0.1028±0.0825 0.0021 ±0.0660 The fact that correction for stature and body-weight has made the constants sensibly identical gives us great confidence in the reality of the physiological law connecting age change and metabolism. Table 40.— Comparison of gross correlation between age and heat-prodiuMon and partial correlation between age and heat-prodticlion for constant stature, constant weight, and constant stature and weight. Series. JV Gross correla- tion between age and heat-production ^ah Correlation corrected for influence of stature t'ah Correlation corrected for influence of weight w^ah Correlation corrected for influence of stature and weight gw^ah Men. Origioal series: Gephart and Du Bois selection. . Other than Gephart and Du Bois selection All men of three series Women. Original series Supplementary series Both series 72 64 136 6S 35 103 -0.3716±0.0686 -0.3003±0.0767 -0.3062±0.0524 -0.2322±0.0774 -0.1796±0.1103 -0.2034±0.0637 -0.4842±0.0609 -0.2313±0.0798 -0.3003 ±0.0526 -0.2656 ±0.0764 -0.2764±0.1053 -0.2465 ±0.0624 -0.4192 ±0.0666 0.5728±0.0666 -0.5147±0.0425 -0.3499±0.0718 -0.4755±0.0882 -O.4976±0.0S0O -0.4585 ±0.0628 -0.5285±0.0608 -0.4995 ±0.0434 -0.3556±0.0714 -0.4778±0.0880 -0.5016±0.0497 Having considered the intensity of the interrelationship of age and total heat-production as measured on a universal standard scale, we may now consider the actual amount of change in metabolism which takes place with increase in age. This can best be done by expressing the relationship in the form of regression equations. In these predic- tion equations a=age in years, /i = total heat per 24 hours, ht, = heat- production per 24 hours in calories per kilogram, and ho = heat-produc- tion per 24 hours in calories per square meter of body-surface by the Du Bois height-weight chart. Inserting the proper values in the linear equations given on page 14 of Chapter II, we have the following values : Men, original series, athletes, iV =16 A>°2825.88-43.03a Aj -25.071 -1-0.025 a Men, original series, others, AT =62 A = 1671.89 -2.45 a Men, original series, whole series, N • ft = 1878.72 -9.19 a Men, original series, Gephart and Du Bois selection, N=72 A -1928.41 -11.85 a Men, first supplementary series, AT =28 A-1688.79-3.65a A4-30.219-0.169o A;^ -29.241 -0.134 a A^- 28.322 -0.098 a Aj -30.111 -0.167 o Ai,=1119.61-6.17o Ac =1019.08 -3.63 a Ac = 1045.07 -4.38 o Afl= 1061.81 -6.25 a Ai,= 1013.81 -4.04 a CHANGES IN METABOLISM WITH AGE. 115 Men, origiiial and first supplementary series, JV=117 A = 1848.47 -8.38 a A^ =29.366—0.139 a Men, second supplementary series, 7^ = 19 A = 1845.34 -6.40 a Aj=27.588-0.070a Men, other than Gephart and Du Bois selection, N—6i A = 1815.48 -6.20 a A;t=28.862-0.116a Men, of three series, N = 136 A = 1823.80 -7.15 a Women, original series, N=68 A = 1448.54 -3.52 a Women, supplementary series, iV =35 A = 1412.33- 1.85 o A4=28.590-0.147a Women, both series, N=103 A = 1420.47 -2.29 a Aj =28.308 -0.124 a A* =28.703 -0.112 a A4= 26.580 -0.046 a Ab = 1037.51 -4.29 a Ac = 1016.38 -2.89 a Aj, = 1014.29-3.200 Az) = 1022.17 -3.60 a Ad = 927.58 -2.33 o Ad =948.70-3.220 Ai,=942.25-2.96o These equations fail to give the comparative view of the relationship between age and total heat and age and heat per unit of body-size that is afforded by the correlation coefficients. They give information of a very different and very essential sort concerning the relationship between age and heat-production. DiAOBAM 18. — ^Daily heat-production of women classified according to age. The variable term of the equations for the regression of total heat on age shows that in the larger series of men the daily heat-production of an individual decreases by an average amount of 2.45 to 11 .85 calories per 24 hours for each year of life. Naturally 7.15 calories, based on the whole series, must be taken as the most probable value. With the women the decrease in heat-production per 24 hours is 1.85 calories in the 35 supplementary women, 3.52 calories in the 68 women in the original series, and 2.29 calories in the whole (103) series. Naturally the latter value must be taken as the standard until further data are available. Diagrams 18 and 19 show the distribution of the individual meas- urements with reference to the straight-line equations. 116 A BIOMETEIC STUDY OF BASAL METABOLISM IN MAN. The regressions of heat per kilogram on age show that there is an average yearly decrease of from 0.098 to 0.169 calorie per kilogram per 24 hours in heat-production in the larger series of men and from 0.046 to 0.124 calorie per 24 hoiors in the larger series of women. Absolute values are of course much larger in the case of body- surface because the number of square meters of area is much smaller than thenumber of kilograms of weight. The constants show an DiAGKAu 19. — ^Daily heat-production of men claaaified according to age. annual decrease of from 3.20 to 5.25 calories per square meter per 24 hours in the larger series of men and from 2.33 to 2.96 calories per square meter per 24 hours in the larger series of women. In the foregoing discussion the influence of the factor of body-size has been to some extent minimized by expressing the decrease in heat-production in calories per kilogram of body-weight and in calories per square meter of body-surface as estimated by the Du Bois height- weigbt chart. It is quite possible to correct for the influence of both stature and weight in a different way. We have akeady used the partial correla- CHANGES IN METABOLISM WITH AGE. 117 tion coeflBcients between age and heat-production for constant stature, ,roA, and between age and heat-production for constant body-weight, „roft, and finally the partial correlation between age and heat-production for both stature and weight constant, i.e., „roj. These express the interrelationships between age and heat produc- tion, correction being made for statiu'e, for weight, and for stature and weight, on a relative scale. To obtain the actual smoothed change in metaboUsm per year with correction for the influence of stature and weight we have merely to determine the partial regressions, p, i.e., <^aA, wPtth, tuPah, The needful regression slopes in calories per 24 hours are given by : urah vifah "7^ vih°a grah ^ t'oh ' thPa where the partial correlations are already known (table 40) and the partial standard deviations are given by : = <7a Vl -r„»« Vl -„r., » = .rA Vl -r.* = vT^ ,^ n 2i 27 n n 42 47 a ST S2 *^ DiAOBAif 22. — ^Mean daily heat-production per square meter of body-surface of men and women classified according to age. ship between age and heat-production is more intimate if correction be made for the irregularities of body-size. Result (2) will be tested by statistical methods below. Results (3) and (5) are expressions of the sexual differentiation in adults which will be reserved for treatment in detail in Chapter VII. CHANGES IN METABOLISM WITH AGE. 121 We shall now turn to a more detailed consideration of (4). To^test more critically the linearity of the regression of total heat-production on age we may have recourse to the calculation of the correlation ratio* and the application of Blakeman's test for Unearity of regression. To secure correlation ratios which shall be of value we must group with regard to age. Table 42 shows the age grouping adopted, the number of individuals, and the mean heat-productions in the total men and women. For age and total heat-production as deduced from this table^the correlation coefficient, Tah, and correlation ratio, viah, are: Correlalion Corr^ation eoeffieimt, r. roiio, i). Men -0.3017 ±0.0526 0.3575 ±0.0504 Women -0.1946^0.0639 0.3458±0.05S5 The correlation coefficients for the two sexes differ so greatly that one would be inclined at first to suspect arithmetical error, but the value for the women ungrouped with respect to age as recorded on page 111 is essentially identical with this constant, i.e., — 0.2034 ± 0.0637 as compared with -0.1946*0.0639. The correlation ratios are in much closer agreement than the corre- lation coefficients. With regard to their probable errors the correlation ratios do not differ. The difference between the correlations for men and women is 0.1071 * 0.0827, a value which, while large in comparison with the constants upon which it is based, by no means represents a certainly trustworthy difference. Applying Blakeman's criterion where Xi is the value of 0.6744898/\/jv from Miss Gibson's tables,'" we find: For men C/^f-1-72 For women C/^f "2.33 Applying the same methods to the problem of the interrelationship between age and total heat-production per kilogram of body weight we have forr„^^and>7,j^: CartHalion Carrtlatian coefficient, r. ratio, i}. For men -0.3840 ±0.0493 0.4414 -oCOieS For women -0.4962 ±0.0501 0.5695 ±0.0449 The correlation coefficients and the correlation ratios are numer- ically higher in both sexes. The correlations are but slightly more * Blakeman, Biometrika, 1906, 4, p. 332. " Gibson, Biometrika, 1906, 4, p. 385. Also in Peanon'a Tables for Statisticians and bio- metricians, Cambridge, 1914. 122 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. consistent than those for age and gross heat-produ'ction. The differ- ence between the two sexes is only 0.1122 ±0.0703, and is therefore insignificant in comparison with its probable error. The difference between the two correlation ratios is 0.1281 ±0.0647, or approximately twice its probable error and of questionable biological significance. Applying Blakeman's criterion we find : For men C/^f =l-96 For women J/F^ =2.23 On the basis of the usual criterion, regression can not be asserted to be non-linear in either sex. Turning now to the measures of heat-production corrected for body-size by reduction to calories per square meter of body-surface by the Du Bois height-weight chart, we have for rai, and »?„* : Correlation Correlatum eoeSicient, r, ratio, i). For men -0.4584 ±0.0457 0.5008 ±0.0433 For women -0.5149=1=0.0489 0.5824±0.0439 Difference 0.0565 =^0.0669 0.0816 ±0.0617 Again the differences between the constants for men and women can not be considered to differ significantly. Blakeman's criterion gives For men C/^{=l-80 For women C/^{=2.16 The results can not be considered to show that regression is non- linear. The calculation of the correlation ratios and the interpretation of the results of Blakeman's test on a series of only 136 and 103 indi- viduals presents some difficulties. We have not apphed the corrections to the correlation ratio suggested by Pearson and "Student," never- theless we feel justified in concluding from the results of Blakeman's test and from the graphical test of the linearity of regression that throughout the age range involved the change in metabolism with age can be satisfactorily represented by a straight line. When larger series of data are available the use of regression coefficients of a higher order may be justffied. A discussion of the practical appUcation of correction for age is reserved for Chapters VII and VIII. Before leaving the subject of the change of metabolism with age, it seems desirable to compare the heat-production per square meter of body surface by the Du Bois height-weight chart given by our equations for total men (N = 136) and for total women (N = 103) with the "normal standards" for various ages calculated by Aub and Du Bois " from their age curve and that given by Lusk.'^ "Aub and Du Bou, Arch Intern. Med., 1917, 19, p. 831. Also Cornell, Univ. Med. Bull., 1918, 7, No. 3, 19th paper, p. 9. "Lusk, Science of Nutrition, Piiiladelphia, 3 ed., 1917, p. 129. CHANGES IN METABOLISM WITH AGE 123 The results in terms of calories per square meter per 24 hours appear in table 43. Without exception the values of daily heat-production as given by Aub and Du Bois are higher, and sometimes very materially higher, than those indicated by our equations showing the regression of heat- production per square meter of body-surface by the height-weight ch^t on age. 3. COMPARISON OF CHANGES IN PULSE-RATE IN RELATION TO AGE. We now turn to a comparison of the changes in another physiological character. It seems desirable in this connection to consider the pos- sible relationship between age and pulse-rate. Table i3.— Comparison of Auh and Du Bois standard normal with daily metabolism given by regression equation. Age in years. Men. Women. Aub and Du Bois normal stand- ard. Metab- olism as given by equa- tion. Differ- ence. Aub and Du Bois normal stand- ard. Metab- olism as given by equa- tion. Differ- ence. 14-16 (IS) 16-18 (17) 18-20 (19) 21-30 (25.5) 31-40 (35.5) 41-50 (45.5) 51-60 (55.5) 61-70 (65.5) 71-80(75.5) 1104 1032 984 948 948 924 900 876 852 968 961 954 930 894 858 822 786 750 -fl.36 + 71 -1- 30 + 18 -f- 54 + 66 + 78 + 90 4-102 1032 960 912 888 876 864 840 816 792 898 892 886 867 837 808 778 748 719 -H34 -1- 68 + 26 + 21 + 39 + 56 4- 62 -f- 68 -1- 73 Our data for adults give the correlations between age and pulse-rate shown in table 44. The partial correlations, given by • ''op Vl-r„.2 Vl-r Vl -r„„» Vl- r ^ are laid beside the gross values. All the correlations are numerically low. Taken individually no one of the series would be regarded as certainly significant in compari- son with its probable error by any careful statistician. Considering the series as a whole and noting that 9 out of the 11 constants are negative in sign, we consider that there is a reasonable probability that pulse-rate decreases with age. This probability is increased when correction is made for the possible influence of weight and height. The partial correlations, „rop, ,rap, are the same in sign as the original correlations. Since correction for the two most conspicuous physical characters of the individual have left the relationship between age and pulse-rate 124 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. practically unchanged, there can be little doubt that there is a slight but definite relationship between these two variables in the range of age covered by our data for adults. Pulse-rate decreases slightly with advancing years. This decrease is not directly due to any change in stature or weight. As far as we are aware the only correlations available from the literature are those provided by Whiting." Table 44. — Correlation between age and pulse-rate and partial correlation between age and pulse-rate for constant stature and constant body-weight. Series. N Correlation between age and pulse-rate E. Partial correla- tion between age and pulse-rate «,'•, op Partial correla- tion between age and pulse-rate Men. Origiiuil aeries: Athletes Others Whole series Gephart and Du Bois selection. . . . First supplementary series Original and first supplementary series Other than Gephart and Du Bois se- lection All men of three series Women. Original series Supplementary series Both series 16 62 88 71 28 116 60 121 - 0.2597 =J +0.0581 =i -0.1405=1 -0.0963=1 -0.0609=1 -0.1252=1 -0.1947=1 -0.1483=1 i= 0.1573 1 0.0583 1=0.0705 i= 0.0793 i=0.1270 ^0.0616 1=0.0918 i= 0.0600 -0.1260=1=0.0805 -1-0.1084 =fc0.1421 -0.0855±0.0706 1.65 0.68 1.99 1.21 0.48 2.03 2.12 2.47 1.65 0.76 1.21 0.2189=" -1-0.1146=1 -0.1405=1 -0.1180=1 -0.0743=1 - 0.1257 :i -0.2177 =i - 0.1500 =i 0.1605 0.0845 0.0705 0.0789 0.1268 0.0616 0.0909 0.0599 -0.1323 =4=0.0804 -1-0.1666=1=0.1403 -O.O313=t0.O710 1.36 1.36 1.99 1.60 0.69 2.04 2.39 2.60 1.65 1.12 0.44 -0.0343 =t0.1684 -1-0.0744 =4=0.0852 -0.1297 =t0.0707 -0.0969=4=0.0793 -0.0623±0.1270 -0.1170='=0.0618 -0.1461=1=0.0934 -0.1400=1=0.0601 -0.1338=fc 0.0803 -1-0.1177=1=0.1418 -0.0760=1=0.0707 0.20 0.87 1.83 1.22 0.49 1.89 1.56 2.33 1.67 0.83 1.07 For age and pulse-rate in 500 criminals examined by Goring the correlations deduced by Whiting are: For age and pulse rap •= -1-0.121 =i=0.022 For age and pulse with temperature constant tTap = +0.174 =»= 0.022 For age and ptilse with respiration constant r^ap = +0.117 ±0.022 For age and pulse with stature constant ,rap = +0.124 =4=0.022 For age and pulse with weight constant u,rap = +0.107 ±0.022 For age and pulse with both weight and stature constant u»'°ai> = +0.097=1=0.022 These values, both the gross correlation between age and pulse-rate and the correlation corrected for various other physical and physio- logical characters, are low but consistently positive throughout. Thus they indicate that pulse-rate increases with age instead of decreasing as in our series. This contradictory result may possibly be due to the essentially different conditions under which the rates were measured. Our determinations were made with the subject lying down and at complete muscular repose in the post-absorptive state; they, therefore, probably represent the minimum or basal pulse-rate for individuals in their state of nutrition. Goring's countings were made with the patient sitting in his cell after early dinner, either idle, reading, or writing. The " Whiting, Biometrika, 1915, 11, pp. 8-19. CHANGES IN METABOLISM WITH AGE. 125 average pulse-rate found by Whiting for these data was 74.22, which is 12.96 beats or 21.2 per cent higher than our average for men. Pos- sibly pulse-rate in older individuals is more susceptible to increase due to physiological or physical activity than it is in younger. If so, this difference in the conditions under which the rates were measured, may be sufficient to account for the differences in the correlations. 4. RECAPITULATION AND GENERAL CONSIDERATIONS. In this chapter we have considered the relationship between age and basal metabolism in adxilt men and women. The significance of such an investigation is twofold. From the theoretical side the mor- phological and physiolopcal changes which accompany the aging of the individual constitutes one of those groups of fundamental problems which has always attracted the interest of biologists and of the medical profession. Any contribution of actual fact is a valuable addition to the vast Uterature. From the practical standpoint, a knowledge of the quantitative relations between age and basal metabolism is essen- tial for the establishment of standard controls to be used in applied calorimetry. The results of the present study show that throughout the whole } range oFwhat we commonly^ designate as adult life the heat-production , of_the individual decreases. Thecorrelation between age and heat- production is therefore negative in sign^ lower daily heat-production being associated with greater age. The gross correlations are of the . order —0.31 for men and —0.20 for women. Daily heat-production has been shown in the foregoing chapter to be correlated with both stature and body-weight. Since in adult life these vary for the most part independently of age, it is evident that if the correlation between age and metabolism be due to definite and progressive physiological changes in the tissues of the organism with increasing age, the measure of the'correlation between age and metab- olism will be lowered by the disturbing influence of these factors. Coirecting for the influence of statiure makes relatively little differ- ence in the intensity of the correlation between age and metabolism. Correction for the influence of body-size by expressing heat-production in calories per kilogram of body-weight raises the numerical value of the correlation coefficient for age and heat-production froni — 0.31 to —0.41 in the total series of men and from —0.20 to —0.49 in the total series of women. If correction be made for body-size by expressing heat-production in calories per square meter of body-surface as esti- mated by the Du Bois height-weight chart, the correlation is increased (in the negative direction) from —0.31 to —0.47 for the men and from -0.20 to -0.52 for the women. Comparable results are obtained by correcting the correlations between age and heat-production for the influence of physical dimen- 126 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. sions by the use of partial correlation formulas. If the partial correla- tion between age and metabolism for constant stature and body-weight be compared with the gross or uncorrected correlations, it will be foimd that the numerical values of the interdependence of the two variabl*ffl has been raised from —0.31 to —0.50 for the men and from —0.20 to —0.50 for the women. These statistical results indicate in the clearest way the existence of fundamental changes in the tissues and their physiological activities with age. This evidence inheres not merely in the fact that the intens- ity of the interrelationship is increased when correction is made for the disturbing influence of body mass in both of the sexes, but that when these corrections are made the results for the two sexes are rendered very nearly identical. Expressingihe relationships between age and metabolism in terms ' of the actual decrease in daily heat-production per year, we note that this amoimts to about 7.15 calories in men and 2.29 calories in .women. Of com^e men and women differ greatly both in stature and weight and in daily heat-production. The decrease in heat-production per kilogram of body-weight is more nearly identical in the two sexes, i.e., j 0^12 calorie in men and 0.124 calorie in women. The decrease in \ calories per square meter of body-surface area, as estimated by the Thi Bois height-weight chart, is 3.60 calories per 24 hours per year in men and 2.96 calories per 24 ho\u^ per year in women. The problem of the regression of heat-production (either gross heat-production or heat per kilogram of body-weight or per square meter of body-siutface) on age is one of both great theoretical interest and practical importance. It is of great physiological interest to deter- mine the rate at which metabolism decreases with advancing years, to ascertain whether this changes at some period of life, and (if so) how these rates of change or periods of change correspond with other physio- logical periods. Certainly this phase of the problem of growth, age, and death should take rank with the others which have been investi- gated. The quantitative statement of the laws governing the change in metabolism with age is the first logical step in the analysis of this problem. From the practical standpoint, determination of these laws is essential for the calculation of standard control values to be used as a basis of comparison in physiological and pathological research. Tests of the rate of change throughout the age-range of adult life indicate that it is essentially uniform, so that, as far as the data at present are adequate to show, it can be expressed as well by the slope of a straight line as by a curve of a higher order. The data for the lower and higher age-groups are still inadequate, and the exact limits of appUcability of a straight line for the expression of changes in metabolism with age must remain a problem for future consideration. CHANGES IN METABOLISM WITH AGE. 127 Practically the linear nature of the change of metabolism with age is of great importance in connection' with the establishment of standard control series to be used in applied calorimetry — ^a subject to be fully discussed in Chapter VIII. For the purposes of throwing some light on the general problem of senescence, we have brought together for comparison such quantita- tive data as are available on the changes of another physiological character with age. Pulse-rate in our own data shows a sUght decrease with increasing age. The amount of change is so small that its nature has not been investigated. Referring to the problem of senescence, rejuvenescence, and death in man and other higher animals, Child ^* says : "As regards the relation between senescence, death, and rejuvenescence, the higher animals and man differ from the lower organisms in the limitation of the capacity for regression and rejuvenescence under the usual conditions. Senescence is therefore more continuous than in the lower fortns^^ and results in death, which is the final stage of progressive development. These character- istics of man and the higher animals are connected with the evolutionary increase in the physiological stability of the protoplasmic substratum and the higher degree of individuation which results from it." Now, without passing any judgment on the validity of Child's extension to the higher vertebrates of his remarkable experimental results with planarians and other lower forms, we may point out that our own quantitative results fully substantiate his conclusion concern- ing the greater continuity of senescence in the higher forms. In man, changes in metabolism after physical maturity are not merely contin- uous, they are uniform in amount, so that they can be reasonably well represented by the slope of a straight line. " Child, Senescence and Rejuvenescence, Chicago, 1915, p. 309, " Italics ours. CHAPTER VI. A CRITIQUE OF THE BODY-SURFACE LAW. The simple relation between the voliime and the surface-area of comparable solids has always appealed to biologists. Absorption, secretion, or excretion, whether of water, of aqueous solutions, or of gases, are surface phenomena. GiUs, lungs, glands, or other organs which are highly specialized for these functions in the higher organisms are primarily characterized by great surface exposure. Thus the well- being of the organism as a whole in many ways depends upon the ratio of the surface-area to the mass of many of its tissues. Again, except when great changes in the proportion of parts are concomitant with increase in size, it is evident that growth must decrease the ratio of external surface-area to body-mass. Inphylogeny the same relationship obtains as in ontogeny. In organisms of gen- erally similar physical conformity, the larger species must expose a relatively smaller siirface. It is therefore natural that one should find the two-thirds power relationship considered in various general writings on body-size. A whale in the Arctic exposes relatively far less siurface to the surrounding water than a flsong-fish in the tropics. An auk in the Arctic exposes relatively far less surface for the loss of heat than a humming-bird in the tropics. Biologists have not failed to grasp the possible significance of such facts for geographical distribution. Turning to an entirely different phase of the general discussion, we may refer to the investigations of Dreyer, Ray, and Walker,* in which they considered blood-volume, area of the cross-section of the trachea, and area of the cross-section of the aorta in various animals and birds in relation to this principle. Surface rather than volume has been suggested as an important factor in muscular work. In the problem of the physiology of excretion it has been stated that the volume of urine is not proportional to the weight of the kidney but to the internal surface. Snell and Wamecke have attempted to arrange vertebrates in series according to relative brain-weight, brain-surface, and intelligence. Perhaps the most ex- treme application of the principle in biological theory is that in Miihl- mann's theory of old age, which depends upon the change in the relation of siu^ace and volume with increasing size.^ ' Dreyer and Ray, Phil. Trans., 1909-1910, 201, ser. B, p. 133. Dreyer, Ray, and Walker, Proc. Roy. Soc, 1912-1913, 86, ser. B, pp. 39 and 56. ' See bibUography and eztensiTe discussions of Mtkhlmann's writings by Minot, The Problem of Age, Growth, and Death, 1908, and by Child, Senescence and Rejuvenescence, 1916. 129 130 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Given an inert body at a temperature higher than its medium, the rate of loss of heat will be determined to a large degree by the nature and extent of its surface-area and the difference in temperature of the body and its medium. For three-quarters of a century, or more, various physiologists have urged that the heat-production in different individuals and species of animals is proportional to their surface-area. Our purpose in this chapter is threefold: (a) To outline briefly the history of the so-called body-surface law. (6) To discuss certain phys- iological evidences bearing upon the question of its vaUdity. (c) Finally, to test it by the application of biometric formulas to the series of data available for this investigation. I. HISTORICAL. While discussions of the so-called "body-surface law" generally begin with the work of Rubner,^ and while it is frequently referred to as "Rubner's Law" the conception of surface and volume relation- ships in the balance between thermolysis and thermogenesis seems to have been quite prevalent at least among French writers, at a much earUer date. Thus Robiquet and Thillaye, in reporting on a memoir submitted to the Academy of Medicine of Paris * by Sarrus and Ra- meaux, refer to the arguments of the authors as based upon "une prop- osition de g^om^trie incontestable, une loi physique g6n^ralement admise et quelques faits physiologiques plus ou moins bien con- states." These they state as follows: "Voici done les bases sur lesquelles s'appuie le travail dont il s'agit. " 1° Entre deux polySdres semblables, les volumes sont comme les cubes, et les surfaces comme les carr^s des cdt^s homologues. "2° Toute chose ^tant 4gale d'ailleurs, des corps de mSme nature perdent k chaque instant des quantit^s de chaleur qui sont proportionnelles k T^tendue de leur surface libre. "3° Dans les animaux de mSme esp^ce, consid^r^s k l'6tat normal et places dans des conditions identiques, les quantit^s de chaleur d^velopp^e dans un temps donn4 sont proportionnelles aux quantit^s d'oxyg^ne absorb^ par I'acte de la respiration, ou bien encore sont proportionnelles au volume d'air inspire pendant la mime dur^e; en admettant toutefois que I'air introduit dans les poumons k chaque inspiration abandonne toujours la m£me proportion de son oxygdne. "Si actuellement nous admettons que la temperature des animaux est constante, c'est reconnattre que chez eux il y a une parfaite ^galit^ entre la chaleur qu'ils produisent et celle qu'ils ^mettent. Or, comme la d^perdition est proportionnelle k I'^tendue des surfaces libres et que celles-ci sont comme le carr^ des cdt^s homologues, il faut n^cessairement que les quantit^s d'oxyg^ne absorbs, ou, ce qui est I'^quivalent, que la chaleur produite d'une part et perdue de I'autre soit conune le carr6 des dimensions correspondantes des animaux que Ton compare, condition indispensable et qui peut £tre remplie de plusieurs maniferes." * Rubner, Zeitschr. f. Biol., 1883, 19, p. 635. * Robiquet and Thillaye, Bull. Acad. roy. de mid., Paris, 1839, 3, p. 1094. A CRITIQUE OF THE BODY-SURFACE LAW. 131 The memoir by Rameaux and Sarrus was never published in full by the Acad4mie de Midedne, but abstracts had appeared earUer in Comptes Rendus ^ and through a letter to Quetelet in the Bulletins de V Academic Roy ale de Bruxelles,^ and the final memoir was read by Rameaux before the Belgian Academy in 1857 and pubUshed in 1858/ In none of these publications is the proposition that heat-production is proportional to body-sm^ace emphasized as a new conception. In his volume of 1889 Richet,^ in referring to one of his tables, calls attention to "la demonstration physiologique de ce fait bien connu que la production de calorique est fonction de la surface et non du poids." Ten years after the appearance of Rameaiix's preliminary papers Bergmann ® attempted to explain the relatively higher food demands of small as compared with those of larger animals of the same species by the generalization that the heat-production of a body is proportional to its surface. Bergmann's work was entirely comparative and theo- retical. While Rameaux in his final memoir brought together and analyzed considerable series of data for pulse-rate, respiration-rate, and limg-capacity, the first experimental evidence seems to have been that presented by Muntz ^^ who in discussing the maintenance food requirement for horses as investigated in a series of experiments made in 1879 gives a clear statement of the conception of the relationship between body-surface and metabolism. Although his experiments contribute nothing of importance to the general problem, his concep- tion is of sufficient importance, historically at least, to be quoted infuU: "II nous semble, d^s k present, que la quantity d'aliments n^cessaire k ranimal pour s'entretenir sans travailler doit se trouver plut6t en rapport avec la surface qu'avec le poids de son corps. Toutes choses ^gales d'ailleurs, on peut admettre que la quantity de chaleur enlev^e au corps est proportion- nelle k sa surface. Une notable partie de I'aliment est certainement consom- me pour I'entretien de la chaleur vitale qui tend constamment k se perdre, par rayonnement ou par conductibilit6, dans le milieu ambiant. Une autre cause de refroidissement est I'^vaporation cutan^e qui est fonction de la surface du corps, si elle ne lui est pas proportionnelle. L'6vaporation produite par les organes respiratoires peut ^galement 6tre regard^e comme ayant un rapport avec la surface bien plus qu'avec le poids. Nous sommes done, par ces con- siderations, autoris^s k a^ettre I'influence pr^pond^rante de la surface du corps sur la quotit6 de la ration d'entretien. ■ Sarrus and Rameaux, Compt. rend. Acad, sci., Paris, 1838, 6, p. 338; loc. cit., 1839, 9, p. 275. * Rameaux, Bull. Acad. roy. d. sci. de Bruxelles, 1839, 6, (2), p. 121. ' Rameaux, M6m. couron. Acad. roy. d. sci. (etc.) de Belg., Brux., 1858, 39, 64 pp. * Richet, La chaleur animale, Paris, 1889, p. 222. ' Bergmann and Leuckart, Anatomisch-physiologische Ubersicht des Thierreichs, Stutt- gart, 1852 , see especially p. 272. Also Bergmann, Ueber die Verhaltnisse der Warme- okonomie der Thiere zu ihrer Grosse, Gottingen, 1848. An earlier paper in MiiUers' Archiv, 1845, p. 300 is also cited. '" Miintz, in an article entitled "Recherches sur Talimentation et sur la production du travail," in Annates de I'lnstitut National Agronomique, Paris, 1880, 3, pp. 23-61. This quotation is from p. 59. According to a statement on p. 25. "Les experiences de la 3"" 5£rie ont dui£ du 12 Septembre 1879 au 7 Fevrier 1 880, c'est4-dire pendant 148 jours.' • 132 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. "Plus tard nous apporterona k I'appui les experiences que nous faisons dans cette direction et qui sont rendues possibles gr&ce au concours de M. Lavalard et de M. Poret, gr&ce aussi a I'obligeant empressement avec lequel MM. Geoffroy Saint-Hilaire et M6nard ont mis k notre disposition les pr^cieuses ressources du Jardin d'acclimatation." The first experimental data which requires consideration in relation to modem work was published almost simultaneously by Rubner " and Richet " both of whom maintained that the heat lost from living organisms is essentially constant per unit of body-surface. Because of his unusual technique the work of Rubner has rightfully been ac- corded the greater weight by physiologists, and the " body-siurface law " is generally referred to as "Rubner's law." It has unquestionably been one of the most stimulating ideas in nutritional physiology. While this constancy of heat-production per unit of body-surface area is the dominant note in Rubner's papers, in several instances he writes as if a causal relationship between body-surface and heat-pro- duction was by no means thoroughly established. Richet, too, lays stress upon many factors, such as nature of integument and external temperature. After the appearance of Rubner's paper the hjrpothesis of a simple mathematical relationship between body-surface and total metabolism became naturally the subject of much discussion. Magnus-Levy and Falk " referred to Rubner's dictimi as the most important recent contribution in the study of the gaseous metabolism. The range in the animal kingdom over which this supposed law has been assiuned to extend is astonishing. It has been extensively appUed to variations in the heat-productions of the same species. The computations of E. Yoit ^* attempt to show that animals ranging in size from a 2-kilo- gram fowl to a 441-kilogram horse have essentially the same heat- production per square meter of body-surface, namely, 970 calories per 24 hours. Armsby and his collaborators,^^ referring to a series of con- stants for man, cattle, horses and swine say: "They show a rather striking degree of unifonnity and tend to confirm the conclusions of E. Voit that the basal katabolism of different species of animals is substantially proportional to their body-surface." An illustration of the extremes to which strict adherence to the bodynsurface law may lead is afforded by Putter's contention " that the "active" surface, i.e., the cell siu*faces of the various organs of the body, should be taken into account. Putter maintaining that the energy " Rubner, Zeitschr. i. Biol., 1883, 19, p. 635. '' Richet, La chaleur animale, Paris, 1889. Hia earlier writings, some of which appeared at about the same time aa Rubner's paper, are here summarized. " Magnus-Levy and Falk, Arch. f. Anat. u. Physiol., Physiol. Abt., Supp., 1899, p. 314. " Voit, Zeitschr. f. Biol., 1901, 41, p. 120. " Armsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, pp. 3-4. See also Journ. Agric. Research, 1918, 13, pp. 49-55. " patter, Zeitschr. f. aUg. Phys., 1911, 12, p. 125. A CRITIQUE OF THE BODY-SUEFACE LAW. 133 consumption is proportional not to the body-surface but to the area of the lung-surface. A careful study of the large mass of literature on metabolism subse- quent to 1883 will show that there has been at no time a fixed inter- pretation of the relationship between body-surface and heat-production. Even the most ardent advocates of the body-surface law have at times called attention to noticeable abnormalities. But attempts were made to explain these discrepancies by the nature of the integument, the density of the fur and hair coverings, and variations in the amount of body-surface exposed." To attempt to review in any detail the extensive discussions of the earlier writers would be a useless task. Unfort\mately many modem authors are not so conservative in their expressions as to the cause of this relationship between body- surface and heat-production as were earlier students. The attitude maintained in more recent times may be illustrated by the following quotations. In his deservedly oft-cited contribution on respiration in Schaefer's Physiology, Pembrey says: ** "Now, small mammals and birds have a temperature equal to or even higher than that of large animals of the same classes; and, on accoimt of the relatively greater surface which they expose for the loss of heat, they must have a relatively far greater production of heat than the large animals, for there is generally no marked difference in the protective coat of fur or feathers." While Minot '° does not explicitly state that heat-loss and heat- generation are determined by body-siirface, his comparison and dis- cussions woidd seem to have this impUcation. The range of appUcabiUty over which Rubner himself would con- sider the surface law vaUd is perhaps indicated by a quotation from a paper of 1908,*° in which he discusses the metabolism of various mammals after birth. Referring to the values used, he says: "Wenn es auch nicht immer Neugeborene waren, die der Stoffwechsel- untersuchung unterzogen sind, so wissen wir auf Grand des von mir erwiesenen Oberflachengesetzes, dass bei den Saugem ihr Stoffwechsel nicht des Masse, aber genau der Oberfiache proportional verlauft. Man kann daher die gewtinschten Grossen des Energieverbrauchs fiir jede beliebige Kleinheit der Thiere, also auch ftir die Neugeborenen, durch Rechnung finden." Lef 6vre specifically states that the appUcation of the law of Newton to living animals is illusory,*^ but in his discussion of the production of heat per unit of surface the following statement appears: ''^ " For example, we frequently find in the text of the earlier writers such statements as the following: " Warmeabgebende Flache und Hautflache sind zwei sehr verschiedene Dinge." Rubner, Beitrage zur Emabrung im Knabenalter mit besonderer Ber&ckaicht- igung der Fettsucht, Berlin, 1902, p. 40. '• Pembrey, Schaefer's Text-Book of Physiology, London, 1898, 1, p. 720. " Minot, The Problem of Age, Growth, and Death, New York, 1908, pp. 18-20. ''" Rubner, Bitzungsb. d. Kgl. Preuss. Akad. d. Wissensch., phys.-math. Kl., 1908, p. 36. " Lefivre, Chaleur Animate et Bio^nergitique, Paris, 1911, p. 379. '^ Lefgvre, loe. eit., p. 500. 134 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. "La production chez rhom^otherme est en Squation avec la perte calori- que. Or, k pouvoir ^missif 6gal, la d^perdition est 6vldemment proportion- nelle k la surface rayonnante. La production calorique (c'est-Srdire, chez Torganisme en 6quilibre et au repos, le besoin d'^nergie) est done proportion- nelle k l'4tendue de la surface totale du corps." Furthermore, Professor H. P. Armsby, whose more recent conclu- sions have been noted above, states : '^ "The results which we have been considering show that in general the emission constant, i.e., the rate of heat emission per unit of surface, is sub- stantially the same in small and large animals and that the greater loss of heat in the former case is met by an increased production. In this aspect the effect is simply an extension of the influence of falling temperature, the in- creased demand for heat being met by an increased supply, so that the extent of surface appears as the determining factor of the amount of metabolism." Moulton, who (on the basis of a series of graphs) has given a detailed discussion of the interrelationship between body-surface, body-weight, blood-volume, nitrogen-content of body, etc., in cattle in various con- ditions, says:^* "A better conception of the basal needs of animals for food can be obtained from a comparison of the relative surface areas of the animals. Since Rubner and Bichet presented evidence to show that the heat production of living animals was proportional to the body surface, this has been a much used unit of reference." In other cmrent (1915) Uterature we find such statements as the following:^ " 'Rubner's law,' to quote from Lusk, is that 'the metabolism is propor- tional to the superficial area of an animal. In other words, the metabolism varies as the amount of heat loss at the surface, and its variance in accordance with this law is necessary for the maintenance of a constant temperature.' " In a popular text-book on nutrition ^® we also find: "Since the body loses heat in proportion to the extension of its surface it is not strange that this is the determining factor for the metabolism." Du Bois, in his Harvey lecture " of November 27, 1915, said: "Rubner demonstrated many years ago that the metabolism is propor- tional to the surface-area of the body and that for each square meter of skin k.rge men, small men, dogs, horses, and mice have about the same heat pro- '* Armsby, The Principles of Animal Nutrition, New York, 1906, 2d ed., p. 365. Professor Armsby, in a, recent personal communication states that this phraseology does not exactly express his belief: " The true state of the case is, as I conceive it, that the body does not produce heat to any considerable extent to keep itself warm but is kept warm because it produces heat. In other words, heat production is substantially not an end but an incident of metabolism." '* Moulton, Joum. Biol. Chem., 1916, 24, p. 303. " Means, Joum. Med. Research, 1915, 32, p. 139. » Stiles, Nutritional Physiology, Philadelphia, 1915, 2d ed., p. 200. " Du Bois, Am. Joum. Med. Sci., 1916, 151, p. 781. Also Studies Dept. Physiol., Cornell Univ. Med. BuU.. 1917, 6, No. 3, Part II. Also The Harvey Lectures, 1916-1916, p. 106. A CRITIQUE OF THE BODY-SURFACE LAW. 135 duction. Just why this should be we do not know. It reminds us at once of Newton's law that the cooling of bodies is proportional to their surface-area, but the metabolism does not follow this law when the external temperature is raised or lowered." The foregoing review, while fragmentary, may give a general idea of the attitude of physiologists toward the problem of body-surface area in relation to metabolism. One essential distinction has not always been clearly drawn by those who have written on the so-called body-surface law. One may inquire whether the law holds for the different species of animals which vary greatly in size, or he may inquire whether it is vaUd when applied to individuals differing in size within the same species. In brief the interspecific and the intra-specific appUcabihty of the so-called law present two different problems. It is quite conceivable that it might be very appUcable intra-specifically but not inter-specificaUy or vice versa. In this volume we shall limit ourselves chiefly to the question of intra-specific applicabiUty. 2. PHYSIOLOGICAL EVIDENCE ON THE BODY-SURFACE LAW. Direct physiological evidence of an experimental nature of two sorts are available. The first is that afforded by determinations of metabolism in similar organisms subjected to different external tem- perature. The second is that afforded by measures of metabolism seciu-ed on individuals of like body-surface but in different physio- logical state. The physical basis of the body-surface law has often been stated to be Newton's "law of cooling." Some of the earlier physiological writers seem to have fidly understood the nature of Newton's law, but in recent years a confused and inadequate conception of this law has estabhshed itself in physiological literatxire. Physiologists have stated the physical law as they would Uke it to be rather than as it really is. For example the immediately foregoing quotation from one of the Harvey lectures ^^ is quite typical of the conception of Newton's law which has been held by physiologists, including the workers at the Nutrition Laboratory. But Newton's law is not primarily a surface law at all, but a law of the rate of cooling, now known to have only a limited applicabiUty even in the simpler cases of controlled physical experimentation. Heat is lost by cooling bodies by convection, conduction, and radiation. The relative importance of these three methods depends upon the nature of the surface and the nature of the surrounding medium. In the majority of cases of transference of heat all these modes are simultane- ously operative in a greater or less degree, and the combined effect is generally of great complexity. The different modes of transference ' The Harvey Lectures, 1915-1916, p. 106. 136 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. are subject to widely different laws, and the difficulty of disentangling their effects and subjecting them to calculation is often one of the most serious obstacles in the experimental investigation of heat imder the controlled conditions of the physical laboratory. If one assxmies the appHcability of Newton's law to hving organisms it is evident that it might under special conditions reduce to a surface law. Thus in 1898 Richet " wrote: "Supposons, en effet, qu'il s'agisse d'un corps inerte; sa radiation sera, conform^ment k la loi de Newton, 6gale k la difference des deux temperatures, multipliee par sa surface S {t — t'). En supposant t — t' constant, ou peu vari- able, 11 s'ensuit que la radiation calorique est proportionnelle k la surface. Or j'ai pu prouver que les chiffres calorim4triques experimentalement obtenus sont tels que I'unite de surface d^gage toujours k peu pr^s la mSme quantity de calories." In modem discussions of the body-surface law the question of the nature of the integument is generally ignored. Yet in the earlier writ- ings the nature of the surface received detailed consideration. This subject is discussed in detail by Richet,^" who not merely treats it from the comparative side but records experiments with animals in normal condition, with shaved animals, and with those whose fur had been smoothed down by a coating of oil or varnish. He even gives the results of experiments with animals having white, gray, and black coats, and claims differences in their heat loss.^' Since Newton's law is really a law of the rate of cooling dtie to differences in temperature, it should be evident that its validity when applied to organisms could be tested only by having all basal-metab- olism determinations made under comparable conditions of internal and external temperature. Certainly this can not be assumed of the series of determinations on diverse organisms which are brought together for comparison in substantiation of the body-surface law. Among the earlier physiologists who had not yet lost sight of the true significance of Newton's law, studies of metabolism at varjdng temperatm-es were seriously considered. When the influence of en- vironmental temperature was studied, difficulties were immediately encountered. In discussing the fact that certain animals show abnor- mal relationships between the environmental temperature and their body temperatxu"e, d'Arsonval*^ introduces the following significant sentence: Cela tient ^videmment k ce que la surface rayonnante physiologique de I'animal n'est pas constante comme sa surface physique. Aux basses tempera- tures, le phenomdne se complique d'une constriction vasculaire peripherique, qui restreint considerablement le pouvoir rayonnant de ranimal k Igalite de '' Richet, Dictionnaire de Physiologie, Paris, 1898, 3, p. 130. *° Richet, La Cbaleur Animale, Paris, 1889; see especially Chapter XI. " Richet. loc. ciU, p. 237. " d'Anonval, Mem. Soc. de Biol., 1884, 8 ser., 1, p. 723. A CRITIQUE OF THE BODY-SURFACE LAW. 137 surface physique. Cela montre que la connaissance de la surface g^om^trique d'un animal est insuffisante pour qu'on en puisse d6duire la perte par rayonne- ment: il faut encore tenir compte de I'^tat de la circulation p4riph6rique. In 1888 V. Hoesslin ^^ pointed out that while in warm-blooded animals variations in the external temperature are followed by varia- tions in metabolism, the change in heat-production is not proportional to the change in external temperatiu-e. Thus heat-loss is not deter- mined solely by difference iu body-temperature and air-temperature, I.e., by differences in potential, v. Hoesslin considers this a valid refutation of Rubner's theory. Richet, in his volume of 1889,^* treated the problem of metabolism imder varying external temperature. The reader interested in details may refer to this work or to a more recent discussion of the problem.*' We now turn to the question of the influence of internal condition on metabolism in its relation to the problem of the validity of the body- surface law. We shall here consider the problem as to whether, when body-surface remains practically constant but other conditions vary, the heat-production per square meter of body-surface area is a constant.** Against this line of argument is to be urged the fact that in an early consideration of the body-surface law Rubner insisted upon uniformity of physiological state.*^ While in more recent writings the constancy or equality in the nutritional level has from time to time been emphasized as a prerequisite for the applicability of the law of surface-area, this has by no means been generally considered, and current practice has tended to accept the universality of this law irrespective of whether the individual is poorly or well nourished. As early as 1888 v. Hoesslin *' pointed out that a dog (studied in the respiration chamber by Pettenkofer and Voit) required 1600 calories per day for maintenance of body-weight. On the sixth day of inanition it used only 1190 and on the tenth day only 940 calories. Body-weight decreased from 33 to 30 kg. If the body-surface law holds, the heat- production of the two periods should stand in the ratio "^SS' : '^30' or 10.288 : 9.655, or there should be a decrease in heat-production of 100(v^-'^30«) „,. — ^^ = =6.15 per cent. ^33« As a matter of fact there is a decrease of 41.25 per cent. M V. Hoesslin, Arch. f. Anat. u. Phys., Phys. Abt., 1888, pp. 327-328. " Richet, La Chaleur Animale, Paris, 1889; especially Chapter XI. " Richet, Chaleur, in Dictionnaire de Physioloeie, 1898, 3, p. 138. ^' Hera only published materials are taken into account. An extensive series of under- nutrition experiments made on a group of 25men was carried out through the winter of 1917-1918 by the Nutrition Laboratory. The problem of the relation of nutritional state to metabolism is considered in detail in the report of these experiments. See Benedict, Miles, Roth, and Smith, Human vitality and efSciency under prolonged restricted diet, Carnegie Inst. Wash. Pub. No. 280. (In press.) " Rubner, Archiv. f. Hyg., 1908, 66, p. 89. u V. Hoesslin, Arch. f. Anat. u. Phys., Phys. Abt., 1888, p. 331. 138 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. A discrepancy in Von Hoesslin's reasoning should be pointed out here, in that the value of 1600 calories was that found during feeding and thereby unquestionably included the stimulating effect of the meat. Consequently the true basal value would be somewhat lower and the decrease on the tenth day is undoubtedly somewhat less than 41.5 per cent, but in any event probably of much greater magnitude than the 6.15 per cent computed on the ratio of the body surfaces. Again, v. Hoesslin points out that Rubner's own dogs show the same decrease in metabohsm with inanition. Rubner introduced a table to show "dass sich der Stoffwechsel bei Himger fast gar nicht andert." Yet this table shows a decrease in the metabolism in absolute terms of 33 per cent, in relation to body-weight of 20 per cent, and in relation to body-surface of 25 per cent. In an experiment upon a dog which was confined to the laboratory for several months and which did not lose weight,'® the metabolism decreased very considerably (19 per cent). When the dog was again allowed country life, her metaboUsm returned to essentially its original value, but the body-weight was imchanged. Here evidently is con- stancy in body-surface area, but variation in heat-production per square meter. Information with regard to the metaboUsm of hiunan individuals who are well or poorly nourished is, for the most part, obtained by observations on different subjects. But during prolonged fasting we may observe in the same person changes in the plane of nutrition fully comparable to those roughly characterized as poorly or well nourished. It is thus seen that dming prolonged fasting simulta- neous measurements of the body-surface and the basal metabolism of the subject have an imusual value. A 31-day fasting experiment made in the Nutrition Laboratory has a particular interest in this connection.*" A study of the relationships of body-weight, body-surface, and basal metabolism during fasting is all the more important when it is remembered that it is commonly believed that the fasting animal rapidly adjusts itself to the minimum metabolism. The results of earUer experiments on the dog, the cock, and the guinea pig *^ indicate that per kilogram of body-weight the fasting metabolism is constant. With the fasting man the metaboUsm per kilogram of body-weight was not constant. Furthermore, calculation of the metabolism per square meter of body-surface on the basis of the Meeh formula — ^the only one available at the time of the experiment — vindicated a large loss in heat- production during the progress of the fast. ReaUzing the desirabiUty "> Liuk, Journ. Biol. Chem., 1915. 20, p. 565, « Benedict, Carnegie Inst. Wash. Pub. No. 203, 1915. "Armsby, The Principles of Animal Nutrition, New York, 1906, 2d ed., p. 34S. A CRITIQUE OF THE BODY-SURFACE LAW. 139 of checking the results, a photographic method *^ of measuring surface- area was developed and the values of heat-production per square meter of body-surface *^ were recomputed. The subject took no food and only about 900 c.c. of distilled water per day for 31 days.** The heat-production during the night was measured directly with the bed-calorimeter for each of the 31 nights.*^ As the fast progressed there was a very noticeable decrease in heat- production from night to night. This would naturally be expected since weight decreased from about 60 kg. to about 47.5 kg. But the metabohsm when computed on the basis of body-weight showed a decided loss as the fast progressed. There was also a loss in metabolism per square meter of body-siuface. This is shown by the data in table 45, which gives the body-weight, the body-surface as computed by the Meeh formula*® and from the measurements of the anatomical photographs, and the heat-production per square meter of body-surface per 24 hom^ as based upon the observations with the bed-calorimeter during the night. Disregarding the last food day prior to the fast, the heat-production per square meter per 24 hours as given in the last column of the table ranges from 927 calories on the third day to 664 calories on the twenty- first day of the fast, representing a decrease of 28 per cent in the heat- production per square meter of body-surface. Thereafter a distinct tendency for the heat-production to increase was apparent. In the absence of any marked change in body-temperatm-e the diffi- culty of considering the loss of heat from the surface of the body as the determining factor in the metabolism of this fasting man is very « Benedict, Am. Journ. Physiol., 1916, 41, p. 275. " Benedict, loc. cit., p. 292. " The fasting man remained (so far as ocular evidence is concerned) for the most part physio- logically normal during the progress of the fast. Strength tests made with the hand dynamometer showed practically no change with the right hand and but a slight decrease with the left hand, although there was an almost immediate evidence of fatigue in the first two or three days of the fast. While there was naturally a certain amount of weakness observable in the last few days, the subject, after having been without food for 31 days, spoke extemporaneously before a body of physicians for approximately three-quarters of an hour, standing during the whole period and vigorously gesticulating. Later in the day he sang and danced. It is thus clear that we have here to do not with a fasting man who is in the last stage of emaciation and in a moribund condition but with an individual who, judged from ocular evidence, would appear not at all unlike the norm- ally emaciated type of individual. Furthermore, the body-temperature did not materially alter. His average body-temperature in the bed-calorimeter experiment on the night of the last day of the fast was but 0.3° C. below that of the night of the second day, a difference which indicates no marked disturbance of the body-temperature. While the pulse-rate was distinctly lower at the end of the period than at the beginning, it will be seen that the subject underwent the 31-day fast without great loss of muscular strength or material alteration of body-temperature. " It was likewise computed indirectly from the carbon-dioxide excretion and oxygen con- sumption during the same period. Reference must be made to the original publication for the methods of calculation and for a discussion of the heat-production per kilogram of body-weight, in which an attempt was made to reduce the observation of each night to a common standard. ** It will be seen from the figures that, using as a standard the body-surface values obtained with the photographic method, the body-surface as computed from the Meeh formula is invariably too large and consequently the heat-production per square meter computed from this measure of the body-surface is too small. 140 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. great. Had the body-temperature fallen materially the explanation of the decrease in heat-production could easily be made on the basis of difference in temperature potential. No such explanation is, how- ever, at hand. Fully confirmatory results in experiments on a squad of 12 men, maintained for a long period on a much reduced diet have been briefly stated in Chapter IV, p. 103. Table 45. — Heat produced by fasting iuhject during experiments in bed calorimeter at night. Body-surface. Heat produced per square meter Day of Body- Com- puted from per 24 hours. Date. weight without By fast. clothing Meeh formula. photo- graphic Meeh formula. Photo- graphic measure- method. ments. 1912 kilos. «g. meters sq. meters cats. cats. Apr. 13-14 60.87 1.91 *1.71 858 958 14-15 iBt 69.86 1.88 1.70 817 904 15-16 2d 58.91 1.86 1.68 830 918 16-17 3d 58.01 1.84 ♦1.66 836 927 17-18 4th 57.22 1.83 1.66 827 912 18-19 6th 56.53 1.81 1.66 764 833 19-20 6th 56.01 1.80 1.65 774 845 20-21 7th 65.60 1.79 1.65 760 825 21-22 8th 65.18 1.78 1.66 790 852 22-23 9th 64.74 1.77 1.66 720 772 23-24 10th 64.25 1.77 ♦1.65 725 778 24-26 11th 53.94 1.76 1.64 715 767 25-26 12th 53.64 1.75 1.64 712 760 26-27 13th 53.48 1.75 1.63 709 761 27-28 14th 53.22 1.74 1.62 658 749 28-29 ISth 62.92 1.74 1.62 649 698 29-30 16th 52.40 1.73 1.61 639 687 Apr. 30-May 1 17th 61.91 1.71 *1.60 642 686 May 1- 2 18th 61.57 1.71 1.60 653 698 2- 3 19th 61.21 1.70 1.60 676 719 3- 4 20th 50.97 1.69 1.60 666 704 4- 5 21at 50.60 1.69 1.59 625 664 5- 6 22d 60.22 1.68 1.59 653 690 6- 7 23d 50.00 1.67 1.59 655 688 7- 8 24th 49.70 1.67 ♦1.59 661 684 8- 9 2Sth 49.40 1.66 1.68 637 670 9-10 26th 49.10 1.65 1.57 695 731 10-11 27th 48.78 1.64 1.57 673 703 11-12 28th 48.52 1.64 1.66 676 711 12-13 29th 48.19 1.63 1.65 691 726 13-14 30th 47.79 1.62 1.54 698 734 14-15 31st 47.47 1.61 •1.53 701 737 * Body surface for days on which photographs were obtained, i.e., April 13, 16, 23, 30, apd May 7 and 14. Other values obtained by interpolation. Turning from the results of prolonged starvation experiments on man to those obtained by Armsby and Fries " for a fattening experi- ment on a steer, we note that they observed an increase of 36 per cent *' Armsby and Fries, Journ. Agric. Research, 1918, 11, p. 461. A CRITIQUE OF THE BODY-SURFACE LAW. 141 in the basal katabolism ** in the fattened state. This they attribute in part to the greater body-weight to be supported in standing, but they point out that the increase in heat-production with fattening is more rapid than the increase in body-weight or in body-surface as estimated by the Meeh formula. "Apparently the accumulation of fat tended in some way to stimulate the general metabolism." 3. MEASUREMENT OF BODY-SURFACE AREA. When one thinks of a physical or biological "law" he naturally assumes that the measurements upon which it is grounded are adequate in number and reUability to justify fully the formulation of the general- ization under consideration. Du Bois and Du Bois *® freely admit that the whole question of the vaUdity of Rubner's Law "rests on the accuracy of the determinations of the basal metabolism and of the siutface-area." They also point out that "The methods of determining the metabohsm have been greatly improved, leaving the smf ace-area the doubtful factor." It seems worth while, therefore, to summarize briefly the actual measure- ments of body-surface area upon which the comparisons underljang the body-surface law rest. In much of the work which has been done on the inter-specific appUcability of the "law" the measures of body-surface can hardly be dignified as approximations. Richet ^° compared the surfaces of his rabbits on the assiunption that they were spheres. Certain investi- gators have used the constant term for the horse in estimating the body-surface of svnne by the Meeh formula. Finally Piitter®^ has ap- parently used the same formula for mammals ranging in form from the camel to the walrus ! Even when we turn to so intensively studied an organism as man, we find that, to quote the Du Boises again, "the number of formulae for surface-area determination is large, the number of individuals whose area has been measured is small." Du Bois and Du Bois give a list and brief discussion of at least the chief of the various formulas which have been proposed. In view of the fact that most of these have received practically no attention from physiologists, it seems unnecessary to discuss them here where we are concerned primarily with the question of the adequacy of the actual measurements upon which formulas have been based. Meeh *^ in 1879 published the results of his painstaking measure- ments of 6 adults and 10 children, using a variety of methods. M Basal katabolism in ruimnants must be determined under conditions in some regards essentially different from those obtaining in investigations on man and the camivora. For the details the special literature of animal metabolism must be considered. « Du Bois and Du Bois, Arch. Intern. Med., 1916, 15, p. 868. "> Richet, La chaleur animate, Paris, 1889, p. 222. " Putter, Zeitschr. f. Allg. Biol., 1911, 12, p. 201. " Meeh, Zeitschr. f. Biol., 1879, IS, pp. 425-458. 142 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Fubini and Ronchi " measured one man, marking out the anatomi- cal regions of the body and determining the areas geometrically. Bouchard " measured five adults. lissauer" measured 12 dead babies, only one of which he con- sidered a normal child, by covering the body with silk paper and then measuring the area of the paper geometrically or with a planimeter, Sytscheff *® measured 10 infants imder one year of age but com- puted no constants. Du Bois and Du Bois " measured the surface-area of 5 individuals with great care. Table 46. — "Ccnstant" term of Meehformvla as determined by direct measurement. Subject. Observer. Age in years. Height in centi- meters. Weight, in kilos. Meas- ured body- surface, sq. cm. Constant for Meeh formula. Benny L Hagenlocher Very thin woman. Korner D. B. and D. B.. . Meeh 36. 13.1 15.7 36. 45.' 17.7 26.2 21. 22. 66. 32. 36. 110.3 137.5 152.' 158. 160.' 169. 170. 162." 164.3 178. 172. 179.2 in.' 149.7 24.20 28.30 31.80 35.38 50.00 50.00 51.75 65.75 59.50 61.60 62.25 64.00 64.08 65.50 74.05 76.50 78.25 88.60 93.00 140.00 8473 11883 12737 14988 17415 16067 18158 19206 18695 18930 19204 16720 18375 20172 19000 19484 22435 21925 18592 24966 10.13 12.80 12.69 13.17 12.96 11.84 12.96 13.16 12.27 12.13 12.01 10.45 11.49 12.48 10.55 10.81 12.26 11.03 9.06 9.26 Bouchard Meeh Schneck Meeh Adult man Nagel Fobini and Ronchi Meeh Fr. Brotheck Naser Meeh Meeh Bouchard Meeh Normal man Fr. Haug Morris S R. H. H Forstbauer E. F. D. B Normal woman . . . D. B. andD. B.... D. B. andD. B.... Meeh D. B. and D. B.. . Bouchard Meeh Large man Mrs. Mc. K Very fat man Bouchard D. B. and D. B.. . Bouchard In the development of a graphic method of determining body- surface area,*® 20 individuals were photographed in different selected positions and the areas of the prints were determined by means of the planimeter. Du Bois and Du Bois *® give a table which we reproduce in a some- what modified form herewith, table 46, showing that actual surface- area measurements have been made on a total of 20 adult individuals. " Fubini and Ronchi, Moleschott's Untersuchungen z. Naturlehre, 1881, 12. M Bouchard, Traits de patbologie g6n6rale, Paris, 1900, 3, p. 200, 384. » Lissauer, Jahrb. f. KinderheUk, N.F., 1903, 58, p. 392. " Sytscheff, Measurement of volume and surface of children of varying ages. Diss., St. Peters- burg, 1902. (From the Clinic of Children's Diseases of Professor Gundobin). See also Gundobin, Die Besonderheiten des Kindesalters, Berlin, 1912, pp. 53-54 (section on body surface of children; quotes Sytscheff and gives table of Sytscheff 's measurements on p. S4 " Du Bois and Du Bois, op. cit. " Benedict, Am. Joum. Physiol., 1916, 41, p. 275. " Du Bois and Du Bois, loe. cU., p. 871. A CRITIQUE OF THE BODY-SURFACE LAW. 143 To what extent do these measurements justify the formulas which have been based upon them? The constant term of both the Meeh and the Lissauer formula is given by Table 47. — Constanls of lAsaauer's babies. Child. K* K No. 1 10.985 2 10.278 9.881 3 9.921 4 10.387 S 8.922 6 10.926 10.245 7 10.284 9.245 8 12.402 10.732 9 10.130 9.530 10 9.953 9.377 11 (10.287) (8.472) 12 10.30 where a' is the directly measured body-surface area. Meeh's observations gave constants entered in the final column of table 46.®° Those for Lissauer's group of 12 babies ** are given in table 47. Now the "constants," both those for adults whose surface-area was measured by Meeh, Fubini and Ronchi, Bouchard, and Du Bois and Du Bois, and those for infants whose surface-area was measiu"ed by Lissauer, show great differences among themselves. Thus in the adult series we find the actually de- termined "constant" terms ranging from 9.06 to 13.17. Yet Meeh in his original pub- lication retained six or seven significant figures in recording his constants, notwithstanding the fact that constants obtained when both sides of the body were actually measured differed from those in which one side only was measured in the third or fourth signifi- cant figure in every case. In Lissauer's in- fants the "constants" range from 8.92 to 12.40. This great discrepancy was fully recognized by Lissauer who, emphasizing the great variation in the individual determinations, chose 10.3 as that most free from criticism. If we determine the standard deviation and the coefficients of varia- tion of these "constant" terms we have the following results: For 20 adults, measured by Meeh and others: ifc = 11.676 (rA = 1.2400 7^ = 10.62 For 12 infants measured by Lissauer: k = 10.398 ^i = 0.7834 F» = 7.53 The coefficients of variation express the results in the most easily comprehensible form. We see that there is a variation of 10.6 per cent in the adults and of 7.5 per cent in the infants. In other words ■0 In 5 cases the constants recomputed by ourselves do not agree exactly with those given by Meeh. We have, however, used the values given by him. " These are the constants given by Lissauer. Their calculation has not been rechecked.^The first column (£*) givest he constant determined from the weight just before or after death. The second (£) gives the constant calculated from the baby's maximum weight. 144 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. the variability about (that is above and below) the mean value is 10.6 and 7.5 per cent of this mean value in adults and infants respectively. What is the real significance of this result? It shows that physiolo- gists have been regarding as a constant a figure which when actually determined shows a variability about two or three times that of stature in man ! Surely no careful observer would consider the statures of the men he passed on the street identical. Yet physiologists have been using a selected value from series two or three times as variable and dignifjring it as a "constant." Wliile the present discussion is limited to the problem of the validity of the surface law in man, it is not without interest to note that Moul- ton, in his investigation of the surface area of cattle,"^ has foimd a wide variation in the value of k. The formulas which he proposes touse differ according to the fatness of the animals. Determining the statistical constants of the values of k entered in table 5 of Trowbridge, Moulton and Haigh, we have : Ic =9.097 (T* =0.8915 7» = 9.80 Again we find a variation in the values of the "constant" which is relatively large, that is about 10 per cent of the average value. The futility of using a "constant" which is so little constant as this k is fully admitted by Trowbridge, Moulton and Haigh when they use different values for animals in different conditions. Thus the Meeh method is no more satisfactory in its application to animal than to human calorimetry. Fortxmately conditions in work on human metaboUsm have been much improved by the studies of Du Bois and Du Bois, residting in the development of the linear formula and of the height-weight chart which has been used throughout this chapter and which is destined to replace entirely the Meeh formula. Computations based upon the latter have, however, been given along with those based on the height- weight chart in many of the tables of the following discussion, since historically the theories considered date from the time when the Meeh formula was the only one available. 4. INADEQUACY OF CRITERIA OF VALIDITY OF BODY-SURFACE LAW HITHERTO EMPLOYED. There has been in the past and prevails at present great diversity of opinion concerning the validity and range of applicability of the surface law. These differences of opinion are foimded in part on tradi- tion. In so far as they rest upon study of the available facts concerning •' Trowbridge, Moulton, and Haigh, Univ. Mo. Agric. Expt. Sta., Research Bull. No. 18, 1916, p. 14. Moulton, Joum. Biol. Chem., 1916, 24, pp. 303-307. A CRITIQXTE OF THE BODY-SURFACE LAW. 145 the measured metabolism of individuals of known or estimated body- surface, the situation seems to be about the following. Series of measurements of basal metabolism have been made and expressed in calories per individual, per kilogram of body-weight, and per square meter of body-surface for definite periods of time. The number of calories produced by individuals varies greatly. When reduced to a standard of calories per square meter of body surface, the heat-production varies much less widely than when the original meas- urements are left entirely imcorrected for the size of the individual experimented with. Workers of one group look at such series of values and seeing the great increase in uniformity of results which has been secured by the correction for body-siu^ace exclaim, "The heat production of an indi- vidual per unit of body-surface is a physiological constant." Workers of another group, however, see the differences which still obtain be- tween the measurements based upon a number of individuals and reply, "Certainly, with differences of such magnitude, no one can speak of calories per square meter of body-surface as a physiological constant." Thus the two groups are apparently in a state of controversial dead-lock which can not be broken by the willingness of one or the other, or of both, parties to look at the other side of the shield, for both groups are already examining the same surface. One group sees in it regularity, the other irregularity. What constitutes regularity as contrasted with irregularity is a matter of personal opinion and must always remain so until some quantitative criterion is adopted. The expression of the amount of heat produced in terms of number of calories per square meter of body-surface is, in its final analysis, merely an attempt to correct for the most significant proximate factors in the determination of heat-production. Since body-surface has the weight of tradition in its favor, it is perhaps naturally assumed to be the most significant factor. But suppose that body-surface is not the most significant variable physiologically? Certainly, it should not then be used as the corrective term. The first step in determining the most potent physiological factor underljring heat-production would seem to be the actual measurement of the intensity of relationship between the various body measurements that may reasonably be suggested as influencing metabolism and total heat-production. We shall then be in a position to consider what measurement of this kind, or what combination of measurements, is most suitable for use as a corrective term to be applied to gross values of basal metabolism obtained from series of human individuals. As far as we are aware, the most quantitative test*^ which has ever " After this manuscript was nearly completed a paper by Armsby and his associates, in which correlations for body-weight and heat-production and body-surface and heat-production were given for the original Nutrition Laboratory series, appeared. Armsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918,4, pp. 3-1. See also Joum. Agr. Res., 1918, 13, pp. 49-55. 146 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. been applied toward the solution of the problem of the relative value of body-weight and of body-surface as a means of correcting for differ- ences in the total metabolism due to differences in the size of the indi- vidual has been the simple determination of the average percentage deviation from the mean value for the whole series of individuals of the measures of heat-production per kilogram of body-weight and per square meter of body-surface. Thus Gephart and Du Bois ®* give the values shown in table 48 for the percentage deviation of calories per kilogram per hour from the mean number of calories per kilogram per hour and of calories per square meter of body-surface per hour from the mean of calories per square meter of surface per hour. TABtE 48. — Comparison of percentage variation of heal-production per kilogram of body-weight and per square meter of body-surface. Subject. Calories per kilogram per hour. Calories per meter per hour. Percentage variation from average. Calories per kilogram. Calories per sq. meter. F.G.B G. L 1.01 1.00 0.95 1.00 0.92 0.96 1.00 1.18 1.11 1.10 1.21 1.13 35.8 34.8 32.4 34.1 30.9 31.7 32.8 37.9 35.1 34.2 36.7 33.8 - 4 - 5 - 9 - 6 -12 - 8 - 5 + 14 + 6 + 5 +16 + 8 + 6 + 2 - 5 -10 - 7 - 4 +11 + 3 + 7 - 1 F.A. R E. F. D. B.... John L J. J. C J. R R. H. H L. C. M F. C. G Louis M T. M. C Average 1.05 34.2 ±8.1 ±4.6 The average of the percentage deviations of the individual measures of heat production in terms of calories per kilogram of body-weight from the general mean of this measure is clearly higher than the average of the percentage deviations of the measures in units of calories per square meter of body-siu^ace from the mean of all of the measures by this method. The means given by Gephart and Du Bois stand in the ratio of 8.1 to 4.6. If instead of using average deviations without regard to sign, as Gephart and Du Bois have done, we compute the standard deviations and coefficients of variation of the number of calories per kilogram of body-weight and per square meter of body-surface, we find the following values. M Gephart and Du Bois, Arch. Intern. Med., 1915, IS, p. 852. A CRITIQUE OF THE BODY-SURFACE LAW. 147 For calories per kilogram per hoiir : a = 0.0908 F = 8.67 For calories per square meter per hour: a = 1.962 V = 5.74 The results confirm those obtained by the average deviation in indicating greater variability in measures of heat-production per unit of weight. The same point may be brought out in a somewhat different and not altogether satisfactory manner by comparing the coefficients of variation for number of calories per kilogram of body-weight with the coefficients of variation for calories per square meter of body-surface in our various adult series. This is done in table 49.®* Table 49. — Comparison of coefficients of variation of heal-production expressed in various units. Series. N CoefBcient of variation of heat per kilogram of body-weight. Coefficient of variation of heat per square meter, Meeh formula. Coefficient of variation of heat per square meter, height- weight.chart. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 10 136 68 35 103 6.99 10.60 9.73 8.07 7.79 9.30 9.64 9.36 11.90 16.84 14.14 3.92 7.76 7.48 6.68 6.40 7.25 8.63 7.44 8.21 12.27 10.29 3.97 6.95 8.26 6.75 7.04 7.10 8.13 8.05 7.51 11.13 9.17 On first consideration these results would seem to fully justify the assertion that among groups of men of varsring weight metabolism is proportional to surface-area according to Rubner's law and is not proportional to body-weight. Extreme caution must, however, be exercised in the physiological interpretation of such a relationship. The fact that the measures in terms of calories per square meter of surface show a smaller percentage of variation from their average value than do measures in terms of calories per kilogram of body-weight does not necessarily have any relationship whatsoever to physiological constants or to causal physiological relationships. Consider this question somewhat more minutely. A series of meas- urements of total heat-production, h,mn individuals are made. These are hi, hi, hz, . . . . h„. The body-surfaces Si, Si, Ss, . • . . s„ and the " This method of analysis has the disadvantage that coefficients of variation are calculated from ratios of heat-production to body-weight and to body-surface. Thus an index of an index is used. 148 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. body-weights lOi, Wt, Wi, . . . . w„ for each individual are available; the following ratios are determined : hi hi hi hn hi hi hi h„ Wi Wi Wz ' ' ' ' W^ Si' Si' S3 ' ' " s„ Clearly enough the variabiUty of the ratios will be determined not merely by the variability of the values of h but by the variabiUty of the values of w and s as well. If the relationship between w and a be such that one of them is necessarily more variable than the other, the ratio in which the more variable measure is employed must of necessity be more variable also. Now this is precisely the condition which obtains in the relationship between body-weight and body-siuiace. In computing body-surface by the Meeh formula, the deviation of the surface-area of an individual from its mean bears only the ratio of •<^w^ to the deviation of the weight from the average weight of the series. Tabij: 50. — Comparison of coefficients of variation for body-xeeight and two measures of body-surfcux. Seiiee. N Coefficient of variation for body- weight. Coefficient of variation for body- surface by Meeh formula. Coefficient of variation for body- surface by height-weight chart. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 136 68 35 103 17.43 14.32 16.68 13.22 16.72 16.73 11.22 16.06 19.78 19.61 20.35 11.44 9.43 10.92 8.74 11.40 11.03 7.43 10.60 12.76 12.97 13.24 10.15 7.55 9.05 7.76 10.15 9.26 6.14 8.89 8.80 9.63 9.34 Thus a lower variability of surface-area as compared with body- weight is an arithmetical necessity. Conversely, a higher variabiUty of the ratio of total heat to body-weight (i.e., of the measures of heat- production in terms of calories per kilogram) is a statistical consequence of the use of the Meeh formula or of direct measurement of body- siu-face in individuals reasonably similar in physical configuration. It is presumably a necessary consequence of the use df the body-surfaces given by the Du Bois height-weight chart also. How great may be the differences in the variability of the physical measurements themselves is readily seen by expressing the variabilities of body-weght and surface-area in relative terms as in table 50. A CRITIQUE OF THE BODY-SURFACE LAW. 149 Here comparison is made of the coefficients of variation, „ _100ffy y _ lQO(r. 'to ~ '« — — w s where a denotes the standard deviations and the bars indicate the means, for body-weight and body-s\u-face as measured by the two methods. Without exception the measures of body-surface show a lower percentage of variation than do the measures of body-weight. It is inevitable that the greater variabiUty of body-weight — ^a purely mathematical phenomenon, not physiological — should influence any ratios into which body-weight enters. It is quite possible that the difference in the variability of calories per kilogram and in calories per square meter of body-siu-face due to this factor may be so great as to invalidate any judgment concerning the physiological significance of ratios to body-weight or body-surface based on inspection and per- sonal judgment merely.*' Objections essentially similar to the above may be raised against one of the earUest series of calorimetric experiments, those of Richet, " who, working with rabbits of weights ranging from about 200 to nearly 4,000 grams, concluded "La perte de chaleur est fonction de la sur- face." Richet arranged his animals according to weight and calculated the average heat-production per kilogram for the ascending weight classes. The constants in this table lead to the "R^sultat des plus int^ressants et des plus nets, puisqu'il nous montre combien, avec I'augmentation de volume, diminue la production de chaleur par kilo- gramme du poids de ranimal." He also arranges the same animals according to weight and determines the loss of heat per unit of surface on the assimiption that the areas of the animals bore to each other the relationship of surfaces of spheres of comparable weights. From these figures he concludes "On voit quelle ressemblance il y a entre ces chiffres, irks proches les uns des autres." But close examination shows that the heat-production per imit of body-surface decreases with the increasing weight of the animals, though apparently at a far lower rate than in the case of that per kilogram of weight. Without more detailed information and closer analysis it is impossible to say to what extent the greater decrease (when heat-production is expressed in calories per kilogram) is due to the fact that the volume of a solid is necessarily more variable than its surface. There is a statistical difficulty in classifying animals by weight and computing the average heat per unit of weight for each weight " The logical fallacy of deciding between weight and surface as a basis of reference has appar- ently been overlooked by even so keen an analyst as Moulton (Joum. Biol. Chem., 1916, 24, p. 320), who says: "On this basis the smallest variations are shown in the heat-consumption perunit of body-surface and the greatest variations in the heat-consumption per unit of body-weight." " Richet, La chaleur animale, Paris, 1889; see pp. 219-221. 150 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. group.®* Suppose, for purposes of argument, that the Nutrition Labora- tory tenet that metabolism is proportional to the active protoplasmic mass, stimulus being considered constant, is valid. Let mi, rrh, mt . . . . OT„ be the active protoplasmic masses of a series of individual animals of weights Wi, w^, W3, . . . . w„ and heat-productions in total calories per unit of time hi, h, ht, . . . . K respectively. Then nil rrii mj or the ratio of the total heat-production to the active protoplasmic mass (the unknown and undoubtedly highly complex and variable stimuli being taken as the same in all cases) is a constant. But practically m is never known, and the ratio which has been used is hi A2 — > — > Wi Wi Wn The observed fact that this ratio is not a constant has been the ground for the rejection of weight as a basis for expressing heat-production and in part the reason for the adoption of body-surface as a standard for this p\irpose. Table 51.— CorrelcUiUm between hody-weight and hetU-production per kilogram of body-weight. Series. Men. Original series Gephart and Du Bois selection First supplementary series. . . . Second supplementary series. . All men of three series Women. Original series Supplementary series Both aeries N 89 72 28 19 136 68 35 103 ^wh. -0.6284=»=0.0433 -0.5552 ±0.0550 -0.6143 ±0.0794 -0.4977±0.1164 -0.6076±0.0365 -0.7742 ±0.0328 -0.7684*0.0467 -0.7852 ±0.0255 ''wh. 14.51 10.09 7.74 4.28 16.65 23.60 16.45 30.79 'Nowwi=mi+Xi, W2=nh+X2, .... , where x denotes the amount of non-active substances which can not contribute to the total metab- olism. The ratios - will be influenced by m and x to an extent pro- w portional to their respective values. Since in the later stages of growth of the vertebrate organism there is a continuous increase in the amount "* In passing, it may be noted that there is another objection to these data. The differences in size are in part due to differences in age. Statements in regard to this factor are not explicit in all cases. The smaller animals were those which produced the most heat, both per unit of weight and per unit of surface. But the smaller animals are probably on the whole younger animals and, as pointed out in the chapter on age, there is (in man at least) a decline in the rate of metabolism during the later periods of growth. A CKITIQUE OF THE BODY-SURFACE LAW. 151 of the inert tissue, and since the increase in weight subsequent to maturity is largely dependent upon the deposition of fat, it is quite clear that in a series of individuals of the same species the metabolism per kilogram of body-weight should decrease as the body-weight increases. Metabolism as measured in units of body-weight decreases as body-weight increases. That metabolism as measured in units of body-surface decreases at a lower rate is perhaps attributable merely to the fact that the values of a;' increases less rapidly than x. This type of relationship has long been familiar to statisticians. If we correlate between x and y/x we get a negative relationship which has been designated as a spurious correlation between indices.*® The relationship may be easily demonstrated on our own data. In table 51 we have given the correlation between body-weight and heat-produc- tion in calories per kilogram of body-weight for certain of our series. The coefficients are negative and of a rather large size throughout. 5. STATISTICAL TESTS OF RELATIVE VALUE OF THE MEEH FORMULA AND OF THE DU BOIS HEIGHT- WEIGHT CHART. From table 50 the reader may have noted that without exception the Du Bois height-weight chart gives a lower percentage variability for body-surface than does the Meeh formula. This point brings up the question of the relative value of these two measures of body-surface. Quite incidentally to carrying out the calculations for this chapter, we have been able to secure certain statistical tests of the relative value of the Meeh formula and of the Du Bois height-weight chart; it there- fore seems desirable to insert these data in this place, after which we shall retiuTi to the discussion of our main problem of the validity of the body-surface law as applied to human individuals. There are two distinct sources of error in the Meeh formula. First, the validity of the use of V u;' as a measure of the surface-area of differ- ent bodies rests on the two assmnptions (a) that the two bodies have the same specific gravity, and (6) that they are comparable in form. Neither of these assumptions can be considered strictly valid when appUed to men and women of different weights. The specific gravity of a very fat individual is certainly sensibly different from that of a lean one. The relative proportions of length of trunk and of leg differ according to the stature of the individual.'" Finally a study of profile photographs of very fat and very lean individuals should suffice to convince any one that as far as form is concerned the two extremes can not be regarded as "comparable solids." Secondly, the constant factor of the Meeh formula is determined empirically. It carries with it, therefore, both the errors of measurement and the probable errors of random sampling attaching to any direct measurements of variable " Pearson, Proc. Roy. Soc. Lond., 1897, 60, p. 492. '° Hums, unpublished constants. 152 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. quantities. The extent of error due to this source has been indicated on page 144 above. We agree with the fundamental correctness of the statement of Du Bois and Du Bois '^ that "In any discussion as to whether metab- olism is proportional to body-weight or to surface-area it is essential to apply a method of measuring the surface which does not depend entirely on weight." A comparison of the correlation between body-weight and body- surface as determined by the two formulas will throw some further light upon the value of the two methods of estimating body-surface. Table 52. — Comparison of relations between weight and body-surface by the Meeh formula with the correlatums between weight and body-surface by the Du Bois height-weight chart. Series. N Correlation between weight and body-surface by Meeh formula. rva M Correlation between weight and body-surface by height- weight chart rv:aj) Differences '■|rO£-'"u!oj|f Men. Origiiial series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series All men of three series Women. Original series Supplementary series Both series 16 62 89 72 28 117 19 136 68 35 103 0.9993 0.9996 0.9986 0.9996± 0.9957 0.9988 0.9994 0.9988 0.0002 0.0001 0.0002 0.0001 0.0011 0.0001 0.0002 0.0001 0.9629 0.9275 0.9466 0.9577 0.9618 9495 0.9632 0.9505 0.0123 0.0120 0.0074 0.0066 0.0096 0.0061 0.0112 ±0.0056 - 0.0364 i -0.0721 = -0.0520 = -0.0419 = - 0.0339 =J -0.0493 = -0.0362^ - 0.0483 =i 0.0123 0.0120 0.0074 0.0066 0.0096 0.0061 0.0112 0.0056 0.9982 ±0.0003 0.9992 ±0.0002 0.9989 ±0.0001 0.9578 ±0.0067 0.9792 ±0.0047 0.9683 ±0.0041 -0.0404 ±0.0067 -0.0200 ±0.0047 -0.0306 ±0.0041 From the constants in table 52, it appears that the correlations between body-weight and body-surface as determined by both methods are large, but that in each group of individuals the correlation between body-weight and body-surface as determined from the Du Bois height- weight chart is lower than that between body-weight and body-surface as determined by the Meeh formula. This must be taken as evidence for the greater value of the Du Bois height-weight chart, since it shows that the body-surface is less a function of body-weight than in the case of the Meeh formula. 6. CORRELATION AS A CRITERION OF THE VALIDITY OF THE BODY-SURFACE LAW. Since it is clear that a mere comparison by inspection of the sets of constants for metaboUsm measured in calories per kilogram of body- " Du Bois and Du Bois, Arch. Intern. Med., 1915, 15, p. 880. A CRITIQUE OF THE BODY-SURFACE LAW. 153 weight and in calories per square meter of body-surface, or even simpler tests of the relative variabiUty of the two sets of measures, are quite inadequate as criteria for selecting the best method of correcting for the size of the individual, a detailed treatment of this question is in order. In the past the physiologist has been seeking to determine whether metabolism is proportional to body-weight or to surface-area. The difl5culty has lain in the fact that body-weight and body-surface area are correlated characters. If individuals varied in weight only, and not in physical configuration, body-surface would be given at once by kyc-^v^. This is, indeed, the basis of the lissauer and the Meeh formulas. Thus if heat-production be in any degree correlated with one of these physical meas\irements, it must be in some degree corre- lated with the other. The degree of correlation between metabolism and either of the physical measurements due to its correlation with the other will depend upon the intensity of the correlation between the two physical measurements. Thus the problem of the physiologist is not so simple as has been suggested when it is said that he must determine "whether metaboUsm is proportional to body-weight or to surface-area." What he has to do is to determine whether it is more nearly proportional to body-surface or to body-weight. The difficulty in doing this has not been due solely to the fact that large series of actual measurements of body-surface and metabolism have not been available, but also to the fact that the physiologist has had no means of comparing directly the degree of interdependence of body-weight measiu-es and metabolism and body-surface measures and metabohsm. Results expressed in calories per kilogram of body-weight are imquestionably better than those expressed in calories per indi- vidual irrespective of size for standard periods of time. Results expressed in calories per square meter of body-surface are also more nearly comparable from individual to individual than those expressed merely in number of calories per individual for the same standard periods of time. The fundamental question is : Are results expressed in calories per square meter of body-surface so constant from individual to individual as to justify the statement that heat-production per square meter of body-surface is a constant? Or, in other words, to justify the statement that it is a physiological law that organisms have a heat-production proportional to their body-surface? Now the closeness of agreement of a series of figures which shall be demanded to justify their designation as representing a constant must depend, in the last analysis, upon the judgment of the workers in a particular field. Specifically, in the case of metabolism investigations, physiologists, not physical chemists or astronomers, must decide how great a variation in the number of calories per square meter of surface 154 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. may be regarded as due to uncontrollable experimental error and hence not be considered as invalidating the generalization that heat-produc- tion per square meter of body-surface is a constant. While only the physiologist can determine the amount of variation allowable in the measures of heat-production per kilogram of body- weight or per square meter of body-surface, the statistician may fimiish certain criteria of value in formulating the decisions. While the statis- tician as such can not pass judgment upon the question of the degree of consistency in a set of constants which must be demanded if they are to be regarded as the expression of a biological law, he can furnish absolute criteria of the degree of consistency. What is really needed, first of all, is a measure of the closeness of interdependence of the total calories of heat produced by an individual, imder the selected standard conditions for measuring basal metabolism, and the other character- istics of the individual with which metabolism may be reasonably assumed to be bound up. Table 5S.— Comparison of correlation between body-weight and total heat-prodttction with the correlations between body-surface by the two formulas and total heat-production. Seriea. N Weight and total heat per 24 hours Twh Surface by Meeh formula and total heat '"if* Difference ra^h-rwh Surface by height-weight chart and total heat Difference Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supple mentary series Second supplementary series All men of three series. . Women. Original series Supplementary series. . . Both series 16 62 89 72 28 117 19 136 68 35 103 0.9577=1 0.6251=1 0.8012=1 0.7879=i 0.8664^ 0.0139 0.0522 0.0256 0.0301 0.0318 0.8175 =t 0.0207 0.5758=1 0.7960=1 0.1034 0.0212 0.7575 =fc 0.0348 0.4536:1=0.0906 0.6092*0.0418 0.9551*0.0148 0.6311*0.0515 0.7997 =fc 0.0257 0.7896*0.0299 0.8747*0.0299 0.8196*0.0205 0.5772*0.1032 0.7980*0.0210 0.7612*0.0344 0.4698*0.0888 0.6170*0.0412 -0.0026*0.0203 +0.0060*0.0733 -0.0015*0.0363 +0.0017*0.0424 +0.0083*0.0436 +0.0021*0.0291 +0.0014*0.1460 +0.0020*0.0298 +0.0037*0.0489 +0.0162*0.1269 +0.0078*0.0587 0.9671*0.0109 0.6632*0.0479 0.8303*0.0222 0.7862*0.0304 0.8636*0.0324 0.8383*0.0185 0.6274*0.0938 0.8196*0.0190 0.7438*0.0365 0.4789*0.0878 0.6111*0.0416 +0.0094*0.0177 +0.0271*0.0707 +0.0291*0.0339 -0.0017*0.0428 -0.0028*0.0454 +0.0208*0.0278 +0.0516*0.1396 +0.0236*0.0285 —0.0137*0.0504 +0.0253*0.1262 +0.0019*0.0590 We now turn to a consideration of the problem of the selection of a suitable measure of the degree of interdependence between the physical character and metabolism. Following the discussion in the preceding chapter, we shall first consider the coefl&cient of correlation.^'* If the du-ect measures of metaboUsm are far more closely correlated with body-surface than with any other physical measurements, it seems " After the manuscript for this volume was practically completed a paper by Armsby, Fries, and Braman (Proc. Nat. Acad. Sci., 1918, 4, p. 1 ; Joum. Agrio. Research, 1918, 13, p. 43) appeared in which the method of correlation here employed was used. A CRITIQUE OF THE BODY-SURFACE LAW. 155 clear that body-surface is the best single factor for predicting basal metabolism. If heat-production shows approximately the same corre- lation with body-weight as with body-surface, the conclusion must be drawn that the two are of practically equal significance for estimating basal metabolism. If the correlation between body-surface and the measure of metabolism be actually smaller than that for other physical characters, it must be relegated to a minor place as a means of predict- ing metabolism. BODY WEIGHT DiAOBAM 23. — ^Relationship between body-weight and daily heat-production by men. The constants are arranged for a comparison of the correlations between weight and heat-production and siirface and heat-production in table 53. The first problem which we have to consider on the basis of these constants is that of the existence of a physiological law. That total heat-production is related to body-weight and to body-surface is clearly shown by the constants. We doubt, however, whether such a quantitative law is what physiologists in general have had in mind when they have stated that heat-production is proportional to body- surface but not proportional to body-weight. Our constants show that 156 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. it is in some degree proportional to both body-surface and to body- weight and they furnish a measure of this closeness of agreement on a universally applicable scale of —1 to +1. They further show that the EODY WEIGHT IN KILOGRAMS Diagram 24. — ^Relationship between body-weight and total heat-production by women. interrelationship is in no case a perfect one. We are not, therefore, dealing with a law in the sense that the term is used in the exact sciences. Knowing the number of seconds which a body has been falling towards the earth, we can state its velocity at this moment or at any future moment of time. Knowing the volume of a gas at temperature t and pressure p, we can state its volume at temperature t' and press- ure p'. These theoretical laws hold in the individual instance with as high a degree of precision as can be demonstrated by the most exact ex- perimental method. Such is not the case in human metabolism. In- stead of having a perfect correlation between body -weight and total heat-production, as we should if ""'iZV^i^^^'l^t^^^^^'oi heat-production were proportional body-surface of women as estimated by to body-Weight, we have only about the Du Bois height-weight chart. gQ p^j. ^gj^^. ^f perfect correlation. The true significance of these correlations may be best understood by looking at them in a quite different way. If heat-production were actually proportional to body-weight, or to body-surface, we should ■nss • • ■J6as • • • ■ISBS • • • J ■lASS • ••■ ■I3SI a •• ^^ • • -y^r. '. - ■i^ns . .:. ?^.'.' ' * • j/^ uas y^ : . ,* " , •• ■loes . 'so l.*0 l£0 1.60 /.70 1.80 1.30 B.OO BODY SURFACE A CRITIQUE OF THE BODY-SURFACE LAW. 157 find a correlation of unity. For any given weight (or surface) there would then be only one possible heat-production. But as a matter of fact the coefficient of correlation, here being less than unity, shows that for any given body-weight or body-siu-face a variety of heat constants may be secured. How widely the heat-productions of individuals of sensibly identical body-weight may vary is well shown by diagram 23 for men and diagram 24 for women, in which each dot represents on BODY SURFACE Diagram 26. — ^Relationship between total heat-production and square meters of body-surface of men as estimated by the Du Bois height-weight chart. the scale at the left the heat-production of an individual whose weight is given by the lower scale.^^ That body-surface is not much better than body-weight as a basis for prediction is evident from the wide scatter of the heat-productions for individuals of like superficial area in diagrams 25 and 26. Now it is quite possible to determine from the correlation coefficient approximately the amoxmt of variation which will be found on the average within the different weight or body-surface classes. This " The Btraight lines in these diagrams are drawn from the equations in Chapter IV, p. 91. 158 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. variability of the subgroups defined by a given grade of weight or body- surface is given by o-A„=o-aV^1- 'fwh '^ha=<^kVl-r, ah' where o-^ is the standard deviation of heat-production in individuals at large and c^^ and o-^^ the standard deviation of heat-production in groups of individuals of the same weight or surface. The results for the major series are summarized in table 54. Table 54. — Percentage of the total variation in heai-prodiLClion which remains after individuals are classified according to body-weight and body-surface by two formulas. Series. Clasaified by body-weight. Correla- tion ''mk Percent- age vari- ability. Clasaified by Meeh formula. Correla- tion Percent- age vari- ability. Classified by height-weight chart. Correla- tion Percent- age vari- ability. Men. Original series Gephart and Du Bois selection Original and first supplementary series All men of three series Women. Original series Supplementary series Both series 0.801 0.787 0.817 0.796 0.757 0.453 0.609 59.84 61.58 57.59 60.53 65.28 89.12 79.30 0.799 0.789 0.819 0.798 0.761 0.469 0.617 60.04 61.36 57.29 60.27 64.S5 88.80 78.70 0.830 0.786 0.838 0.819 0.743 0.478 0.611 55.73 61.79 54.52 57.29 66.84 87.79 79.15 The entries in the body of this table show the relative amount of variation in metabohsm which remains after individuals are sorted into groups according to body-weight or body-surface by the two formulas.^* To faciUtate comparison merely, the variabiUties (standard deviations) of the subgroups of like weight or surface-area have been expressed as percentages of the standard deviation of heat-production in all individuals irrespective of body-weight or body-surface. A cursory inspection of the body of the table shows that the metabolism measurements for any given grade of body-weight or body-surface in the male series exhibit (roughly speaking) 55 or 60 per cent as much variation as measurements made on individuals irrespective of these characters, while in the female series they show from 65 to 90 per cent of the population variability. We now turn to a consideration of the actual magnitudes of the correlations for body-weight and heat-production, r,„A, and body- surface area and heat-production, rah, as given in table 53. Since body-surface is the character upon which such great emphasis has been laid as a standard in metabolism studies for the past quarter " These are the theoretical values derived from the formulas just discussed. It is useless to compare them with the values computed directly when the number of individuals is so small as it is here. A CRITIQUE OF THE BODY-SURFACE LAW. 159 of a century and more, it is important to make the comparisons between the results of different correlations in such a way as to show whether the surface area gives larger (i.e., closer) correlations with total heat- production or other measures of metaboUsm than the other measures tested, or whether it gives sensibly the same or smaller values. Our differences have, therefore, been taken (correlation for body- surface and measure of metabolism) less (correlation for other physical character and measure of metabolism). Thus, when the constant measuring the correlation for body-surface and a given measure of basal metabolism is larger than another constant with which it is compared, the difference is given the positive sign. In men the correlation between body-surface by the Meeh formula and total heat per 24 hours is slightly higher in all but 2 cases (but in no case significantly higher) than that between body-weight and total heat-production. In women the correlation between surface as estimated by the Meeh formula and total heat is in all 3 series slightly but not significantly higher than that between body-weight and total heat-production. Taking these constants as they stand they indicate, therefore, that body-weight gives practically as good a basis of prediction for heat- production as does body-surface by the Meeh formula. To this point we shall return later. When the Du Bois height-weight chart is used the differences are not so regular. In 8 cases the chart measures of body-surface give the higher correlation, whereas in 3 cases the weight gives the higher correlation. Thus apparently surface as estimated by the Du Bois height- weight chart furnishes a better corrective measure than weight. Since the differences between r^^ and r^h are in no case significant in comparison with their probable errors, one can not assert on the basis of the individual series that there is an actually significant physiological difference in the relationships between these two physical measure- ments and metaboUsm. The fact that the majority of the series indi- cate closer correlation of body-surface and total heat-production is evidence in favor of its closer correlation with total metabolism. After the constants in table 53 were computed, Armsby, Fries, and Braman ^* pubUshed correlations for body-weight and total heat- production and body-surface as estimated by the Meeh formula and total heat-production for the constants published by Benedict, Emmes, Roth, and Smith ^^ and by Means." They find: For 98 men 0.7263 =t 0.0320 0.7747 ± 0.0272 For 75 women 0.7759 ±0.0310 0.7447 ±0.0347 " Annaby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, p. 3; Joum. Agric. Research, 1918, 13, pp. 50-51. " Benedict, Emmes, Roth, and Smith, Joum. Biol. Chem., 1914, 18, p. 139. " Means, Journ. Biol. Chem., 1915, 21, p. 263. 160 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. From these results they conclude that the constants "fail to show any greater correlation with the body-surface as computed by the Meeh formula than with the body-weight." Notwithstanding this clear evidence against the body-surface law as appUed to the individuals of the same species, Armsby, Fries, and Braman conclude^* that their assemblage of data for man, cattle, hogs, and horses "tend to confirm the conclusions of E. Voit, that the basal katabolism of different species of animals is substantially pro- portional to their body surface." Total heat which is used as the final expression of basal metabolism may be either directly or indirectly determined. In the case of indirect calorimetry it is calculated from the total amounts of CO2 or O2, taking into account the calorific value of the gas which varies with the respira- tory quotient, i.e., the ratio COj/Oj. Table 55. — Comparison of correlatum between hody-weight and oxygen-eonsumption with the correlations between body-surface by the two formvlas and oxygen-consumption. Series. Men. Original series: Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series All men of three series Women. Original series Supplementary series Both series N 16 62 89 72 28 117 19 136 68 35 103 Surface by Meeh formula and oxygen consimiption 0.9574*0.0141 0.6312^:^0.0515 0.7997*0.0258 0.7845*0.0306 0.8777*0.0293 0.8207*0.0204 0.5771*0.1032 0.7978*0.0210 0.7634*0.0354 0.4741*0.0884 0.6019*0.0424 Difference -0.0021*0 +0.0057*0 -0.0010*0 +0.0016*0, +0.0058*0 +0.0028*0 -0.0008*0, +0.0023*0. 0195 0733 0364 0434 0424 0290 1459 0298 +0.0026*0.0503 +0.0158*0.1262 +0.0069*0.0608 Surface by Du Bois height-weight chart and oxygen con- simiption 0.9661 >i 0.6647 =i 0.8294 d 0.7838=i 0.8632 =i 0.8386^ 0.6369 =< 0.8196=^ 0.7355 =i 0.4836 i 0.5972 =i :=0.0112 =0.0478 =0.0223 =0.0306 = 0.0325 =0.0185 =0.0919 =0.0190 =0.0375 1 0.0873 1 0.0428 Difference ra^o~^V)m +0.0066=1 +0.0392=1 +0.0287 d +0.0009 :J - 0.0087 =i +0.0207=1 +0.0590=1 +0.0241=1 0.0176 0.0707 0.0340 0.0434 0.0446 0.0277 0.1381 0.0285 -0.0153*0.0618 +0.0253*0.1255 +0.0022*0.0608 We tiUTi, therefore, to a consideration of the correlations between body-weight and oxygen consumption and carbon-dioxide production in comparison with those for the two measures of body-surface and oxygen consumption and carbon-dioxide production. The results are given for oxygen consumption in table 55 and for carbon-dioxide output in table 56. The value of r„a and r„<, are taken from table 24. While the differences in the correlations are very small a great majority are positive in sign, i.e., they indicate that the correlations for surface-area and metabolism are higher than those for weight and metabolism. Thus these results seem to indicate that body-surface ''Armsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, p. 3-4. A CRITIQUE OF THE BODY-SURFACE LAW. 161 gives a slightly better criterion of total heat-production than does body-weight. We shall now approach the problem from a somewhat different angle. 7. THE PREDICTION- VALUE OF BODY- WEIGHT AND BODY-SURFACE. When the physiologist asserts that heat-production is proportional to body-surface he states that knowing the body-surface of an indi- vidual we also know his basal metabolism. Of course there are tacitly assumed reservations. Pathological factors, the differentiation due to sex, and a number of other as yet intangible influences are supposed to be neglected. Nevertheless it must be admitted that if the assertion that heat-production is proportional to body-surface is of any practical significance, it is tantamoimt to the assertion that knowing the body- siu^ace of the individual we have the best possible index of his basal metabolism. Table 56. — Comparison of the correlation between hody-weight and carbon-dioxide production with correlations between body-surface by the two formulas and carbon-dioxide production. Series. N Surface by Meeh formula and carbon- dioxide pro- duction Difference Surface by Du Boia height-weight chart and carbon-dioxide production Difference Men. Original series ; Athletes Others Whole series Gephart and Du Bois selection First supplementary series Original and first supplementary series Second supplementary series AU men of three series Women. Original series Supplementary series Both series 15 62 88 71 28 116 19 135 66 35 101 0.9295=1 0.5807=1 0.7703=1 0.7687 =i 0.8187=1 0.7808=1 0.5128=^ 0.7582 d 0.0236 0.0570 0.0292 0.0327 0.0420 0.0244 0.1140 0.0247 - 0.0059 =tO. -1-0.0066 =1=0. -0.0033=1=0. -f-0.0017=t0. -1-0.0121 =fcO. - 0.0003 =fcO. -f0.0086=fc0. -1-0.0007*0. 0321 0809 0410 0464 0612 0345 1622 0349 0.9378 0.6047 0.8043 0.7689 0.8283 0.8024 0.5240 0.7884 =fc 0.0144 0.0543 0.0254 0.0339 0.0400 0.0223 0.1123 0.0229 -1-0.0024 -(-0.0306 -1-0.0307 -0.0081 -1-0.0217 -1-0.0213 -1-0.0198 -1-0.0309 =t 0.0260 0.0790 0.0384 0.0472 0.0598 0.0331 0.1610 0.0337 0.7392=fc 0.0376 0.4427*0.0917 0.6366=1=0.0399 -f-0.0060 =1=0.0537 -f0.0176±0.1309 4-0.0100=1=0.0571 0.7386*0.0377 0.4503*0.0909 0.6357*0.0399 -1-0.0054*0.0538 -f-0.0252±0.1303 4-0.0091*0.0571 We shall start out from the assumption that the best measure of the heat-production of an individual is that which gives the best prediction for an unknown series. Concretely, suppose that we predict the total heat-production of a series of individual men under standard conditions by three different methods. Surely it seems reasonable to regard the method which predicts the metabolism of the individuals most exactly as the best measure. Otherwise the whole contention for normal control series for use in pathological research or in other fields of prac- tical nutrition work is stultified. We shall, therefore, predict the daily heat-production of a series 162 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. of individuals of given weight, of given body-surface as approximated by the Meeh formula, and of given body-surface as estimated by the Du Bois height-weight chart, and shall determine which of these meas- ures actually permits the closest prediction in the case of subjects whose metaboUsm is unknown so far as the development of the prediction formulas is concerned. The arithmetical routine is illustrated in tables 57-59, to be discussed below. To avoid all criticism concerning the selection of measurements to be used as the fundamental series, we shall take those for the 72 indi- viduals chosen by Gephart and Du Bois, and designated in this volume as the Gephart and Du Bois selection. From equations based upon this series we shall compute the total heat-production which should be found in indiAdduals of three other series and compare the results of predicting these values by three different methods with the metabolism constants actually found. The individuals used for the test series are in no case included in the series upon which the prediction formulas are based. The grouping of the individuals has been determined by factors which are entirely beyond our present control. The groups were selected before the prediction equations were calculated, and no change has been made subsequently. The following groups have been used, (a) The 17 men rejected by Gephart and Du Bois from the 89 published by Benedict, Emmes, Roth, and Smith, (b) The first supplementary series of 28 men. (c) The second supplementary series of 19 men. Thus it is possible to test the results of prediction in three separate series of men and (upon the combination of these series) on a general series of 64 individuals. Now all students of metabolism might not agree fully with Gephart and Du Bois in their selection of the 72 indi- viduals as a basis for metabolism constants. It seems worth while, therefore, to base prediction formulas on a quite different series and to compare the predicted values of the metabolism of the 72 individuals of the Gephart and Du Bois selection with their actually determined heat-production. Such a procedure has not merely the merit of furn- ishing a more stringent criterion of the value of the various methods of calculating check series, but has the advantage of emphasizing in a clear-cut manner the fact that data are still inadequate for the most advantageous selection of control values for use in clinical calorimetry. The most natural procedure is, of course, to base prediction form- ulas on the 64 individuals not included in the Gephart and DuBois selection and to test the results secured by these formulas against the observed values for the individuals of the Gephart and Du Bois selection. These series of comparisons cover only men. Turning to women, it has seemed desirable to predict the results for the supplementary A CRITIQUE OF THE BODY-SURFACE LAW. 163 series of 35 from the original series of 68 women, and in turn to predict the heat-production of the original series from constants or equations based on the supplementary series. Thus a very comprehensive test of the validity of the different methods of forming check series is secured. Two methods of calculating the metabolism of an individual whose actual heat-production is unknown suggest themselves. First, one may merely multiply the body-weight or body-surface of the subject by the average heat-production per unit of weight or per unit of surface in the standard series. This has been the method hitherto employed in the calculation of the control values to be used in clinical calorimetry. Second, one may use a mathematical prediction equation based on the standard series. So far as we are aware, this method has not hitherto been employed in studies on basal metabolism. While the second method seems the more logical of the two, we shall give the results of both. WTien prediction of the heat-production of an individual is made by either of the methods a value is obtained which may be identical with the actually determined constant, but which in general deviates somewhat from it. Deviation may, therefore, be either positive or negative in sign. We shall, in consequence, have to consider whether the predictions made by a given method are on the whole too large or too small. Since we are in this case testing methods of prediction against actual observation, we have taken the differences (calculated heat-production) less (actually determined heat-production). Thus when a given prediction method gives results which are on the average too high, the mean deviation (with regard to sign) of the calculated from the actual heat-production will have the positive sign. When it is too low, it will have the negative sign. Dividing the sum of the deviations with regard to sign by the total number of individuals in the series in hand we have a measure of the average deviation in the direction of too high or too low prediction. But the question as to whether a given prediction method gives on the whole too high or too low values is not the only one to be answered. One wishes to know the extent of deviations both above and below the observed value in the case of each of the methods used. One measure of such deviation is obtained by ignoring the signs and simply regarding a difference between observed and predicted values as an error of a given magnitude. Dividing the sum of these errors for the whole series by the number of individuals in the series, we have, in terms of average deviation without regard to sign, a measure of the rela- tive precision of the different methods of prediction employed. This method has two disadvantages. First, it does \'iolence to sound mathe- matical usage with regard to signs. Second, it gives the deviations 164 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. weight proportional to their magnitudes. But one may consider that very great deviations should be given proportionally more weight in testing different prediction methods than very slight deviations. The magnitudes of the deviations may be logically weighted and the transgression against the law of signs avoided by squaring the devia- tions before they are summed. The square root of the mean of these summed squares will then furnish a logical measure of the deviation of the calculated from the observed productions. For the sake of completeness in the investigation of a problem which has the contro- versial status of the "body-surface law" we shall use both of these methods. The deviations of the predicted from the actually determined heat- production is expressed in two different ways in the accompanying tables: (1) The differences are expressed in the absolute terms of calories per 24 hours. (2) The differences are reduced to a relative basis by expressing them as a percentage of the mean heat-production in calories per 24 hours of the specific group of individuals dealt with. We now turn to the actual data. The average heat-productions for the 72 individuals of the Gephart and Du Bois selection and for the 64 other individuals for the three imits of body-measurements adopted are as follows: Heat-production per kilogram of body-weight: 72 of Gephart and Du Bois selection 25.7944*0.1655 calories. 64 others 25.5875*0.2292 calories. Di£Ference 0.2069*0.2827 calories. Heat-production per square meter of body-surface by Meeh formula: 72 of Gephart and Du Bois selection 831.639* 4.413 calories. 64 others 828.203 * 5.742 calories. Difference 3.436* 7.242 calories. Heat-production per square meter of body-surface by Du Bois height-weight chart: 72 of Gephart and Du Bois selection 926.653 * 4.975 calories. 64 others 924.141 * 6.063 calories. Difference 2.512* 7.843 calories. While the results for the two sets of individuals are not exactly identical, as shown by the differences, the probable errors of these differences show that the two groups of men can not be considered to differ significantly. Thus, while the constants of these two series will not give exactly identical results if used for the calculation of control values as a basis of comparison in applied calorimetry, the differences between them are so small that they can not be asserted to have any physiological significance. The results for the two series of women are: Heat-production per kilogram of body-weight: 68 Original women 25.3500*0.2467 calories. 35 Supplementary women 22.7229*0.4103 calories. Difference 2.6271*0.4788 calories. A CRITIQUE OF THE BODY-SURFACE LAW. 165 Heat-production per square meter of body-surface by Meeh formula: 68 Original women 772.397* 5.184 calories. 35 Supplementary women 715.057 =fc 10.004 calories. Difference 57.340*11.267 calories. Heat-production per square meter of body-surface by Du Bois height-weight chart: 68 Original women 865.324 ± 5.317 calories. 35 Supplementary women 820.257*10.410 calories. Difference 45.067*11.690 calories. The agreement of the means for the two series of women is not as good as that for the two series of men. Possibly this is partly due to the fact that the larger female series has only about as many individuals as the smaller male series, while the smaller female series comprises only about half as many individuals as the smaller of the two male series. Whatever the cause of the difference in the two female series, the consequence must necessarily be a larger error of prediction than in the case of males. Table 57. — Comparison of actual heat-production and heat-production calculated (a) from the mean heat per kilogram of body-weight and (b) from the equation for the regression of total heat on body-weight in the Gephart and Du Bois selection. Individual. Body- weight. Measured heat- production. Calculated from mean. Calculated from equation. Heat. Difference. Heat. Difference. H.F Prof. C W. s O. F. M M.H.K H. W F. A. R F. E. M R. I. C W.W.C L. D.A F. M. M E. J. W 82.1 83.0 88.5 85.8 79.0 108.9 74.4 75.0 56.8 56.3 57.1 59.7 50.0 49.3 54.3 55.1 50.6 1615 1655 2017 1827 1944 2559 1704 1698 1687 1629 1539 1739 1158 1591 1632 1421 1510 2118 2141 2283 2213 2038 2809 1919 1935 1465 1452 1473 1540 1290 1272 1401 1421 1305 -1-503 4-486 4-266 4-386 4- 94 4-250 4-215 4-237 -222 -177 - 66 -199 -H32 -319 -231 ±000 -205 1937 1952 2044 1999 1885 2385 1808 1818 1514 1506 1519 1563 1401 1389 1473 1486 1411 4-322 4-297 4- 27 4-172 - 59 -174 4-104 4-120 -173 -123 - 20 -176 -H243 -202 -159 4- 65 - 99 F. P v. G C.H.H B. N. C MuItipljTng body-weight and body-surface by the two formulas by these values, we obtain the predicted values. Upon a comparison of the computed values with those obtained by actual measurement, we may base our conclusions concerning the relative merit of various methods of prediction. The arithmetical routine is naturally somewhat extensive. It will be illustrated for only the smallest series — ^the 17 men omitted by Gephart and Du Bois from the original Nutrition Laboratory series. The actual and calculated values and their differences are given for the individual subjects in the third, foiuiih, and fifth sections of tables 57-59. 166 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. ji. — Comparison of actual heat-production and heai-prodv^ion calculated (a) from the mean heat per square meter 0/ body-surface by the Meeh formula and (b)from the equation for the regression of total heat on body-surface by the Meeh formula in the Gephart and Du Bois selection. Individual. Body- aurface by Meeh formula. Measured heat- production. Calculated from mean. Calculated from equation. Heat. Difference. Heat. Difference. H.F Prof. C W. S O.F.M M. H. K H. W F. A. R F.E.M R. I. C W. W. C L.D.A F. M. M E. J.W F. P V.G C. H. H B. N. C 2.33 2.34 2.45 2.40 2.27 2.81 2.18 2.19 1.82 1.81 1.83 1.88 1.67 1.66 1.77 1.78 1.69 1615 1655 2017 1827 1944 2559 1704 1698 1687 1629 1539 1739 1158 1591 1632 1421 1610 1938 1946 2038 1996 1888 2337 1813 1821 1514 1505 1522 1563 1389 1381 1472 1480 1405 +323 +291 + 21 + 169 - 56 -222 + 109 + 123 -173 -124 - 17 -176 +231 -210 -160 + 59 -105 1934 1942 2032 1991 1884 2328 1810 1819 1515 1506 1523 1564 1391 1383 1474 1482 1408 +319 +287 + 15 +164 - 60 -231 +106 + 121 -172 -123 - 16 -175 +233 -208 -158 + 61 -102 Table 59.— Comparison of actu/il heat-production and heat-production calculated (o) from the mean heat per square meter of body-surface by the Du Bois height-weight chart arid (b) from the equation for the regression of total heat on body-surface by the Du Bois height-weight chart in the Gephart and Du Bois selection. Individual. Body- surface by Du Bois height- weight chart. Measured heat- production. Calculated from mean. Calculated from equation. Heat. Difference. Heat. Difference. H. F 1.90 1.93 1.96 1.98 2.04 2.43 1.80 1.81 1.76 1.67 1.67 1.72 1.47 1.50 1.57 1.62 1.63 1615 1655 2017 1827 1944 2559 1704 1698 1687 1629 1539 1739 1158 1591 1632 1421 1510 1761 1788 1816 1835 1890 2252 166S 1677 1631 1548 1548 1594 1362 1390 1455 1601 1510 +146 +133 -201 + 8 - 54 -307 - 36 - 21 - 56 - 81 + 9 -145 +204 -201 -177 + 80 =fcO00 1774 1805 1836 1856 1918 2318 1672 1682 1631 1538 1538 1590 1333 1364 1436 1487 1497 + 159 +150 -181 + 29 - 26 -241 - 32 - 16 - 56 - 91 - 1 -149 + 176 -227 -196 + 66 - 13 Prof. C W. S O.F.M M. H. K H. W F.A. R F. E. M R. I. C W. W. C L.D.A F. M. M E. J. W F. P V. G C. H. H B.N.C The average deviation vrith regard to sign of the calculated from the observed values are given in table 60. These show that in all series except one the values predicted from the Gephart and Du Bois selection average somewhat too high. The prediction of the value of the metab- A CRITIQUE OF THE BODY-SURFACE LAW. 167 olism of the Gephart and Du Bois selection from the means for the 64 other men is for each method somewhat too low. Similarly, in dealing with women we note that the values predicted for the supple- mentary series from the original female series are on the average too high, while those predicted for the original series are on the average too low. Such differences in sign are of course a necessary result of the differ- ences in the constants of the two standard series of each sex. The point will receive further consideration below. In prediction from the Gephart and Du Bois selection, the average deviation with regard to sign given by using the mean metabolism Table 60. — Average deviation with regard to sign of total heat-prodiuiion as predicted by mean heat-production per unit of body-weight or surface in standard series from the actual heat-production. Series A- Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height^weight chart. III. Men. Averages based on Gephart and Du Bois selection: I. First supplementary series II. Second supplementary series III. Individuals omitted by Gephart and Du Bois 28 19 17 64 72 35 68 + 11.8= 0.74 p. ct. + 38.3= 2.34 p. ct. + 67.6= 3.97 p. ct. + 34.5= 2.10 p. ct. - 3.0= 0.18 p. ct. + 191.7 = 14.32 p. ct. -116.6= 8.61 p. ct. + 6.5 = 0.40 p. ct. -f 14.6 = 0.89 p. ct. + 4.9 = 0.29 p. ct. + 8.5 = 0.52 p. ct. - 6.6 = 0.40 p. ct. -1-119.0=8.89 p. ct. - 93.9 = 6.93 p. ct. -1-25.0= 1.56 p. ct. 4- 4.7 = 0.29 p. ct. -41.1 = 2.42 p. ct. -H 1.4 = 0.09 p. ct. - 3.5 = 0.22 p. ct. -1-77.9 = 5.82 p. ct. —69.9 = 5.16 p. ct. IV. All individuals Averages based on 64 individuals not in Gephart and Du Bois selection : V. Gephart and Du Bois selection. . . . Women. Averages based on original series: VI. Supplementary series Averages based on supplementary series: VII. Original series per square meter of body-surface as calculated by the Du Bois height- weight chart is less than that given by the use of the mean metabolism per kilogram of body-weight in every case except the first supplement- ary series. The total series of 64 individuals shows an average plus deviation of only 1.4 calories per day by the Du Bois height-weight chart, of 8.5 calories by the Meeh formula, and of 34.5 calories by body- weight. In predicting the values of the 72 individuals from the means based on the 64 other men, the Du Bois height-weight chart gives better results for deviation with regard to sign than does the Meeh surface formula, but slightly worse results than prediction from body-weight. In predicting the total heat-production in the two female series, the Du Bois height-weight chart gives much smaller deviations than either of the other methods. Apparently, therefore, the Du Bois height- weight chart gives the smallest average deviation above or below the 168 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. ideal zero deviation, and so far as this test is concerned must accord- ingly be regarded as fumishing the best basis for predicting the metab- olism of an imknown subject. Turn now to the average deviations without regard to sign. These show the average error either above or below the actually observed values. The averages are given in table 61. For the whole series of 64 individuals in which prediction is based on the averages per unit in the Gephart and Du Bois selection ^* the average error is 100 calories by the Du Bois height-weight chart as compared with 141 calories by body-weight, or 6.08 per cent as compared with 8.57 per cent of the average heat-production of the individuals tested. In predicting the Table 61. — Average deciaiion vnthotU regard to sign of total heat-production as predicted from the mean heat-production per unit of body-weight or surface in standard series from the actual heat-production. Series. N Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. n. Prediction from body-surface, height-weight chart. III. Men. Averages based on Gephart and Du Boie selection: I. First supplementaiy series 28 19 17 64 72 35 68 92.8= S.78p. ct. 127.0= 7.75 p. ct. 234.6 = 13.79 p. ct. 140.6= 8.57 p. ct. 106.4= 6.55 p. ct. 243.7 = 18.21 p. ct. 169.8 = 12.63 p. ct. 86.8= 5.40 p. ct. 90.5= 6.52 p. ct. 151.1= 8.88 p. ct. 105.0= 6.40 p. ct. 86.9= 6.36 p. ct. 178.4 = 13.33 p. ct. 115.4= 8.52 p. ct. 94.1= 6.86 p. ct. 99.7= 6.08 p. ct. 109.4= 6.43 p. ct. 99.8= 6.08 p. ct. 88.7= 5.46 p. ct. 149.9 = 11.20 p. ct. 94.6= 6.98 p. ct. II. Second supplementary series III. Individuals omitted by Gephart and Du Bois IV. All individuaU Averages based on 64 individuals not in Gephart and Du Bois selection: V. Gephart and Du Bois selection Women. 1 Averages based on original series: {Averages based on supplementary series: 1 metabolism of the 72 individuals of the Gephart and Du Bois selection from averages based on the 64 other individuals, the average deviations range from 87 to 106 calories, or 5.35 per cent for surface by the Meeh formula, 5.46 per cent for surface by the Du Bois height-weight chart, and 6.55 per cent for body-weight. Errors are much larger in the female series, ranging from 6.98 per cent to 18.21 per cent, but with the order of errors always lowest for prediction from body-surface by the Du Bois height-weight chart, highest by body-weight, and intermediate in " In working with the subgroups great irregularity must be expected because of the limited numbers of individuals. In the case of the 17 individuals discarded from the original Nutrition Laboratory series by Gephart and Du Bois the results of predicting from body-weight are partic- ularly bad. The error is 6.43 per cent in the case of the height-weight chart and 13.79 per cent in the case of body-weight. In the first supplementary series prediction from body-weight gives slightly greater error than prediction from body-surface by the Meeh formula, but slightly less error than prediction from the Du Bois height-weight chart. In all other series the error by the height-weight chart is considerably less than by the body-weight method, and in all but two cases it is less than prediction by the use of means for heat-production per unit of surface-area by the Meeh formula. A CRITIQUE OF THE BODY-SURFACE LAW. 169 prediction from area by the Meeh formula. Again the results indicate the superiority of the Du Bois height-weight chart as a basis of pre- dicting the metabolism of an unknown. Table 62 gives (in terms of the square root of mean-square devia- tion of the predicted from the actual values) a comparison of the results of predicting by the three different means. The square root of the mean-square deviation of the calculated from the actually measured metabolism is in all series greater in prediction from weight than it is in prediction from the height-weight chart. This method, like the two preceding, therefore, justifies the conclusion that (as an empirical basis for the prediction of the heat-production of an individual, on the Table 62. — Square root of mean-square deviation of total keat-production as predicted from the mean heat-production per unit of body-u}eight and surface in standard series from the actual heat-production. Series. A' Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height-weight chart III. Men. Averages based on Gephart and Du Bois ■election: 28 19 17 64 72 35 68 136.2= 8.49 p. ct. 171.3 = 10.45 p. ct. 268.1 = 15.76 p. ct. 189.5 = 11.55 p. ct. 132.2= 8.14 p. ct. 327.8 = 24.49 p. ct. 201.1 = 14.85 p. ct. 107.7= 6.71 p. ct. 135.3= 8.26 p. ct. 173.5 = 10.20 p. ct. 136.0= 8.29 p. ct. 109.1= 6.72 p. ct. 218.7 = 16.34 p. ct. 142.0=10.48 p. ct. 117.3= 7.31 p. ct. 134.4= 8.20 p. ct. 139.1= 8.18 p. ct. 128.5= 7.83 p. ct. 110.6= 6.81 p. ct. 174.0=13.00 p. ct. 122.1= 9.01 p. ct. 11. Second supplexnentaiy series III. Individuals omitted by Gephart and Du Bois IV. All individuals Averages based on 64 individuals not in Gephart and Du Bois selection: V. Gephart and Du Bois selection Womm. Averages based on original series: VI. Supplementary series Averages based on supplementary series: VII Original series ctssumption that heat-production bears a definite ratio to some physical character) the Du Bois height-weight chart measure of body-surface area furnishes distinctly better means of prediction than does body- weight. In the series of 64 individuals in which prediction is made from the Gephart and Du Bois selection the square root of mean square errors expressed as a percentage of the mean of the measured heat-production of the individuals stand as 11.5 : 7.8; in the Gephart and Du Bois selection they stand as 8.1 : 6.8; in the first female series as 14.9 : 9.0; and in the second female series as 24.5 : 13.0 per cent. We now turn to the prediction of metabolism by means of a mathe- matical equation fitted to a series of observations. Because of its simphcity and its direct relation to the correlation coefficient we have naturally first availed ourselves of the linear regression equation. These follow: 170 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Equations based on 72 individuals chosen by Gephart and Du Bois: For total heat on body-weight, ^1= 565.390+ 16.707 u). For total heat on body-surface by Meeh formula, /i = 19.463 +821.567 a^^. For total heat on body-surface by Du Bois height-weight chart, A = - 175.338+1026.173 o^. Equations based on 64 men not included in the Gephart and Du Bois selection: For total heat on body-weight, A = 641.261 +15.392 lo. For total heat on body-surface by Meeh formula, A = 126.334+763.680 a^^. For total heat on body-surface by Du Bois height-weight chart, h= -310.884+1101.230a^. Equations based on 68 women of original Nutrition Laboratory series: For total heat on body-weight, A =781.408+10.522 u;. For total heat on body-surface by Meeh formula, A = 461. 758 +506.428 aj„. For total heat on body-surface by Du Bois height-weight chart, A =88.493+808.401 o^. Equations based on the 35 supplementary women: For total heat on body-weight, A =957.468 +6.313 uj. For total heat on body-surface by Meeh formula, A =741.987+316.101 a^ For total heat on body-surface by the Du Bois height-weight chart, A =519.673 +500.252 a^. Again we may use the 17 individuals omitted by Gephart and Du Bois from the original Nutrition Laboratory series to illustrate the method of calculation. The values are given in the sixth and seventh columns of tables 57, 58, and 59. Space does not permit the publica- tion of the calculated values and their deviation from the actually observed constants in the other series. Before taking up the question of the relative precision of prediction of heat-production from equations based on body-weight and on body- surface by the two formulas, we may consider the relative closeness of prediction by means of average measures in the standard series and by means of equations. In doing this we shall draw the comparisons solely between the results of prediction from means alone and from equations for the same unit of bodily measurement. In the tables, 63-65 the differences are given in calories per day and in percentages of the average heat-production of the group of individuals dealt with. The positive sign indicates that the prediction from means gives a larger error, the negative sign that it gives a smaller error than prediction by the use of the regression equation. In com- paring the deviations with regard to sign it has been necessary to con- sider the magnitudes of the deviations only in these difference tables. The differences show, therefore, which method gives the numerically larger average error, but give no information concerning the sign of this error. The latter can, of course, be obtained from tables 60 and 66. The differences between the average deviations with regard to sign in table 63 show that in 6 out of the 7 cases prediction by equations based on body-weight gives a smaller average deviation than prediction from mean heat-production per kilogram of body-weight. In the exceptional case the difference is very small (i.e., 4.4 calories or 0.28 per cent), whereas in 5 of the 6 cases in which the differences are posi- A CRITIQUE OF THE BODY-SURFACE LAW. 171 tive in sign they are also of a very material order of magnitude, ranging from 24.9 to 113.8 calories or from 1.51 to 8.50 per cent of the average heat-productions of the groups of individuals. In predictions involving body-surface as estimated by the Meeh formula the use of equations gives a smaller net deviation than computation of heat-production by considering it proportional to body-surface. The differences are not so large when measures of body-surface by the Du Bois height-weight chart are used, but here 4 out of the 7 comparisons indicate by the positive sign of the differences the superiority of the regression-line method of prediction. Table 63. — Differences in calories between the average deiricUions with regard to sign resulting from the use of rneans and straight-line equations for prediction. Series. N Prediction from body-weight in kilograms. I- Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height-weight chart. III. Mm. PredictionfromGephartandDuBois selection: 28 19 17 64 72 35 68 + 4.3 = 0.27 p. ct. +25.8 = 1.68 p. ct. +57.9 = 3.40 p. ct. +24.9 = 1.51 p. ct. - 4.4-0.28 p. ct. +113.8 = 8.60 p. ct. +63.3 = 4.68 p. ct. + 0.2=0.01 p. ct. + 0.5 = 0.03 p. ct. + 1.3 = 0.08 p. ct. + 0.6=0.04 p. ct. + 0.4-0.02 p. ct. +40.1 = 3.00 p. et. +38.6=2.85 p. ct. + 0.2 = 0.02 p. ct. - 1.4=0.08 p. ct. + 2.9 = 0.17 p. ct. - 1.1 = 0.08 p. ct. - 0.6 = 0.03 p. ct. + 4.7 = 0.35 p. ct. + 18.4=1.36 p. ct. III. Individuals omitted by Gephart and Du Bois IV. All individuals Prediction from 64 individuals not in Gephart and Du Bois selection: V. Gephart and Du Bois selection Women. Prediction from orig;inal series: VI . Supplementary series Prediction from supplementary aeries: If we consider together all of the tests of prediction by equations as compared with prediction from the average values of metabolism per unit of body-weight or body-surface area made in table 63, we note that 17 out of the 21 differences are positive. In other words, predic- tion from the mean heat-production per unit in the standard series gives a larger average deviation with regard to sign than prediction from equations. Turning now to comparison of the average deviations without regard to sign, we have the results set forth in table 64. The first column of constants shows the differences between the average devia- tions (without regard to sign) of the predicted from the actually ob- served heat-productions when the predictions are made by the use of equations and when they are made from the average heat-productions per unit of body-weight in the check series as a whole. The positive signs (indicating a greater error of prediction when average heat- production per kUogram of body-weight is used as a standard) show that the equations give better results in every instance. 172 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. In comparing the results of predicting total heat-production from body-surface by equations and by considering it proportional to the average heat-production per square meter of body-surface, we note that the differences are far smaller than those found when body-weight is used. It is not, therefore, so essential to use the equations when body-surface is to be employed as a basis of prediction as when body- weight is used. But in predicting from body-surface the equations give better results in 8 out of the 14 comparisons. Table 65 gives the comparison of the square root of mean square deviation of the calculated from the actual values for the prediction by the use of means only and by the use of linear regression equations. In prediction from body-weight, the straight line gives far more satis- Table 64. — Differences in calories between the average deviations imthout regard to sign resulting from the use of means and straight-line equations for prediction. SerieB. JV Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height-weight chart. III. Mm. Prediction from Gephart and Du Bois aelec- tion: I. First supplementary genes 28 19 17 64 72 35 68 + 1.7 = 0.11 p. ct. +27.6=1.69 p. ct. +85.5 = 5.03 p. ct. +31.6 = 1.92 p. ct. +18.3-1.12 p. ct. +93.7=7.00 p. ct. +73.7 = 5.44 p. ct. - 0.7=0.05 p. ct. - 9.5=0.58 p. ct. + 1.0=0.06 p. ct. - 2.8 = 0.17 p. ct. - 0.5 = 0.03 p. ct. +29.4=2.20 p. ct. + 19.9 = 1.47 p. ct. +4.5 = 0.28 p. ct. -1.1 = 0.07 p. ct. +3.0=0.18 p. ct. +2.4=0.14 p. ot. ±0.0=0.00 p. et. +3.8-0.28 p. ct. +1.5 = 0.11 p. ct. 11. Second supplementazy series in. Individuals omitted by Gephart and Du Bois IV. All individuals Prediction from 64 individuals not in Gephart and Du Bois selection: V. Gephart and Du Bois selection Women. Prediction from original series: VI. Supplementary series Prediction from supplementary series: VII. Original series factory results. In the case of the two body -surface measurements there is less difference. It is important to note that in the case of the Du Bois height-weight chart, in which body-surface is not merely a function of weight, the evidence for accuracy of prediction is in favor of the linear prediction formula. This is shown by the fact that in 6 of the 7 cases prediction from the mean heat-production in the standard series gives a larger square root of mean square deviation than prediction by the use of linear equations. Taking all the three lines of evidence together, a material superiority of the linear regression equation over the method heretofore used for purposes of prediction is evident. We now turn to a comparison of the results of predicting metabo- lism by means of straight-line equations based on body-weight and based on body-surface. We shall compare the results of such prediction A CRITIQUE OF THE BODY-SURFACE LAW. 173 in three ways : by the determination of the mean error with regard to sign, by the determination of the mean error without regard to sign, and by the determination of the square root of mean square deviation of the predicted from the actually measured values. The mean deviations with regard to sign appear in table 66. With one exception they indicate that in the nine comparisons with the three subseries (I-III) prediction from the constants of the Gephart and Du Bois selection is on the average too high. This is also true of the whole series of 64 individuals. The actual amount of the deviation is not large. It ranges from 3.6 to 38.2 calories in the subseries and from 2.5 to 9.6 calories in the combination series. In terms of per- centages of the mean heat-production of the groups dealt with these Table 65. — Differences in calories betweeri square root of the mean-square errors of prediction by iise of means and by use of straight-line equations. Series. ff Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-suriace, height-weight chart. III. Men. Predictionfrom Gephart and Du Bois selection: 1. First supplementary series 28 19 17 64 72 35 68 + 24.4= 1.52 p. ct. + 27.6= 1.68 p. ct. + 97.2= 5.72 p. ct. + 60.3= 3.06 p. ct. + 22.0= 1.35 p. ct. +154.3 = 11.53 p. ct. + 80.9= 6.98 p. ct. - 0.3 = 0.02 p. ot. - 8.2 = 0.60 p. ct. + 0.9 = 0.06 p. ct. - 2.3 = 0.14 p. ct. - 0.4 = 0.03 p. ct. -1-46.9=3.50 p. ct. +22.2 = 1.64 p. ct. +3.4 = 0.21 p. ct. -0.5 = 0.03 p. ct. +6.2 = 0.37 p. ct. +2.9 = 0.18 p. ct. +0.4-0.02 p. ct. +4.9 = 0.37 p. ct. +1.7 = 0.12 p. ct. III. Individuals omitted by Gephart and Du Bois IV. All individuals Prediction from 64 individuals not in Gephart and Du Bois selection: V. Gephart and Du Bois selection Women, Prediction from original series: VI. Supplementary series Prediction from supplementary series: average deviations with regard to sign range from 0.15 to 2.25 per cent, but only 2 of the subseries show a percentage deviation of over 1 per cent, and the 3 constants for the whole series of 64 individuals show a deviation of less than 0.6 per cent. Since the constants based on the Gephart and Du Bois selection give shghtly too high results when used to predict the heat-production of other individuals, it is necessary that the constants of this other series give values which are too low when they are used to predict the heat-production of the individuals of the Gephart and Du Bois selection. We note, therefore, that the average deviations for the predicted values of the Gephart and Du Bois selection are negative in sign throughout. The actual values are roughly comparable with those already con- sidered, ranging from 4.1 to 7.4 calories, or from 0.25 to 0.46 per cent of the mean heat-production. This difference in the sign of the average deviation in the two 174 A BIOMETKIC STUDY OF BASAL METABOLISM IN MAN. series emphasizes the fact that even series comprising over 60 individ- uals each are not large enough to give wholly accurate mean predictions of metabolism. Metabolism constants are highly variable, and this has as a necessary consequence a high probable error of a mean constant based on a number of individuals which to the experimental physiol- ogist would seem to be very large. The reader will of course note that since the average deviations of predicted values differ in sign in these two series, the result of combining the two series for the purpose of predicting standard control values, as we shall do later in this volume, will be an average deviation much more nearly the theoretical zero in amoimt. How close to the theoretical the average of values predicted from these combined series will lie can, of course, be determined only in the future when the necessary experimental data have been collected. Table 66. — Average deviation with regard to sign of total heat-prodttciion as predicted by linear equations from the actual heat-production. Series. JV Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height-weight chart III. Mm. Equations based on Gephart and Du Bois selection: I. First supplementary series .... 28 19 17 64 72 35 68 + 7.5-0.47 p. ct. + 12.5 = 0.76 p. ct. + 9.7 = 0.57 p. ct. -1- 9.6 = 0.58 p. ct. — 7.4 = 0.46 p. ct. +77.9 = 5.82 p. ct. -63.3 = 3.93 p. ct. + 6.3 = 0.39 p. ct. + 14.1=0.86 p. ct. + 3.6 = 0.21 p. ct. + 7.9 = 0.48 p. ct. — 6.1 = 0.38 p. ct. +78.9 = 5.89 p. ct. -55.3 = 4.08 p. ct. +24.8 = 1.54 p. ct. + 6.1 = 0.37 p. ct. —38.2 = 2.25 p. ct. + 2.5 = 0.15 p. ct. - 4.1 = 0.25 p. ct. +73.2 = 5.47 p. ct. -51.5 = 3.80 p. ct. III. Individuals omitted by Gephart and Du Bois IV. All individuals Equations based on 64 individuals not in Gephart end Du Bois selection: V. Gephart and Du Bois selection Women. Equations based on original series: Equations based on supplementary series: VII. Original series Comparable results, as far as the opposite signs are concerned, are found in the two feminine series. The magnitudes of the deviations are, however, much greater. We find, in fact, averages ranging from about 50 to about 80 calories, instead of from 2.5 to 9.6 calories, aa in the general male series. Expressed in percentages of the mean, the deviations are of the order 3.8 to 5.9 per cent, instead of generally lower than 1 per cent. The conclusion to be drawn from this result is obvious. Prediction of the metabolism of women can not be carried out by these equations with the degree of certainty that is possible in dealing with men. To what extent this may be due to the smaller number of records of women as yet available, and to what extent it may be looked upon as due to age heterogeneity or as indicating real biological differences between the sexes, must remain a problem for further investigation and consideration. A CRITIQUE OF THE BODY-SURFACE LAW. 175 Confining our attention to the four general series, IV-VII, in which the number of individuals is reasonably large, it is apparent that in every case prediction from the linear equations based on body-surface as determined by the Du Bois height-weight chart gives lower average deviations with regard to sign than do those based on either body- surface by the Meeh formula or body-weight. Thus the Du Bois height-weight chart gives the best prechction, in so far as accuracy of prediction can be measured by the average deviation of the predicted from the actually observed value. There seems to be little difference between the results of prediction from body-weight and from body- surface as estimated by the Meeh formula. Table 67. — Average deviation without regard to sign of total heat-production as predicted by linear equations from actual heat-production. Series. N Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height-weight chart. III. Men. Equations based on Gephart and Du Bois selection : 28 19 17 64 72 35 68 91.1= 5.67 p. ct. 98.4= 6.06 p. ct. 149.1= 8.76 p. ct. 109.0= 6.64 p. ct. 88.1 = 5.43 p. ct. 150.0 = 11.21 p. ct. 96.1= 7.09 p. ct. 87.5= 5.45 p. ct. 100.0= 6.10 p. ct. 150.1= 8.82 p. ct. 107.8= 6.67 p. ct. 87.4= 5.38 p. ct. 149.0=11.13 p. ct. 95.5= 7.05 p. ct. 89.6= 5.58 p. ct. 100.8= 6.15 p. ct. 106.4= 6.25 p. ct. 97.4= 5.93 p. ct. 88.7= 5.46 p. ct. 146.1 = 10.92 p. ct. 93.1= 6.87 p. ot. II. Second supplementary series III. Individuals omitted by Gephart and Du Bois IV. All individuals Equations based on 64 individuals not in Gephart and Du Bois selection : V. Gephart and Du Bois selection Women. Equations based on original series: VI. SuDolementarv series Equations based on supplementary series: Turning to the average deviations without regard to sign, we note from table 67 that in the whole series of 64 individuals the three methods give deviations of only 109, 108, and 97 calories or stand in the ratio 6.64 : 6.57 : 5.93 per cent. Thus the difference in the per- centage error of predicting from body-weight and body-surface by the Du Bois height-weight chart is only 6.64—5.93 = 0.71 per cent. For the 72 individuals of the Gephart and Du Bois selection the average deviations for the three methods of prediction are 88.1, 87.4, and 88.7 calories, or stand as 5.43 : 5.38 : 5.46 per cent. Thus body- weight is a little better than body-surface by the height-weight chart as a basis of prediction. In the two feminine series the absolute error in calories is considerably larger, the percentages ranging from 6.87 to 11.21. In both feminine series the Du Bois height-weight chart gives the lowest and body-weight the highest average deviation. The height-weight chart is therefore the best and body-weight the worst basis for prediction. 176 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Tximing to the square root of mean-square deviation as given in table 68 for our most critical test of the three methods, we find that for the first series of 64 men and for the supplementary series of women the Du Bois height-weight chart gives closer prediction than body-weight. The differences in terms of percentages of the mean heat-production of the groups dealt with are 8.48-7.65=0.83 per cent for the men and 12.96 — 12.63=0.33 per cent for the women. In the Gephart and Du Bois selection, body-weight and body- surface by the Du Bois height-weight chart are equally good as a basis for prediction, differing by only 6.79 - 6.79 = 0.00 =±= per cent. The origi- nal women also show practical identity in the results of the two methods of prediction, the difference being only 8.87— 8.89 = —0.02 per cent. Table 6S.— Square root of meari-squaTe deviation of total heat-production as by Imear equations from the actual heat-production. predicted Series. N Prediction from body-weight in kilograms. I. Prediction from body-surface, Meeh formula. II. Prediction from body-surface, height-weight chart. III. Men. Equations based on Gephart and Du Bois selection: 28 19 17 64 72 35 68 111.8= 6.97 p. ct. 143.8= 8.77 p. ct. 170.9 = 10.04 p. ct. 139.2= 8.48 p. ct. 110.2= 6.79 p. ct. 173.5 = 12.96 p. ct. 120.2= 8.87 p. ct. 108.0= 6.73 p. ct. 143.5= 8.75 p. ct. 172.6 = 10.14 p. ct. 138.3= 8.43 p. ct. 109.6= 6.75 p. ct. 171.8 = 12.84 p. ct. 119.8= 8.84 p. ct. 113.9= 7.10 p. ct. 134.9= 8.23 p. ct. 132.9= 7.81 p. ct. 125.6= 7.65 p. ct. 110.2= 6.79 p. ct. 169.1 = 12.63 p. ct. 120.4= 8.89 p. ct. 11. Second supplementary series III. Individuals omitted by Gephart and Du Bois rV. All individuals Equations based on 64 individuals not in Gephart and Du Bois selection: V. Gephart and Du Bois selection Women. Equations based on original series: Equations based on supplementary series: Possibly the results slightly favor the prediction of heat-production from the Du Bois height-weight chart, but the differences are by no means so large as would be implied by the statements of those who have urged that heat-production is proportional to body-surface but not to body-weight. Thus, in the instance among the larger series (IV-VII) most favorable to the body-surface theory, i.e., that in which there is a square root of mean-square deviation of 7.65 per cent in predicting the metabolism of the individuals of an unmeasured series from body surface and of 8.48 per cent in predicting from body-weight, the error of prediction is only 8.48—7.65=0.83 per cent greater when body- weight is used as a base. We shall return to these problems in a subsequent section. Summarizing the results of these tests of body-surface as measured by the Du Bois height-weight chart in comparison with body-weight A CRITIQUE OF THE BODY-SURFACE LAW. 177 as a basis of the prediction of the heat-production of a subject, we note the following points from the two major series of each sex (series IV-VII, tables 60-62, 66-68). 1. In testing the two bases of prediction, body-weight and body- sxirface, by the average deviation with regard to sign of the predicted from the actually observed values, we find that in predicting by the use of mean heat-production per unit of weight and of mean heat- production per unit of surface area, body-surface gives the lower average deviation in three of the four series (table 60). When pre- diction is made by means of the linear regression equations, body- surface gives the lower average deviation in all four series (table 66). 2. In testing the two bases of prediction by means of the average deviation without regard to sign of the predicted from the observed values, we find that in predicting from mean heat per unit of weight and from mean heat per unit of area, body-surface is the better basis of prediction in all four cases (IV-VII, table 61). In predicting by the use of equations we find that surface is the better basis of prediction in three of the four cases, but slightly worse than body-weight in series V, table 67. 3. In testing the two bases of prediction by the square root of mean-square deviation of the predicted from the observed values, we find that in predicting from mean heat-production per unit, body- surface gives lower deviations from the actually measured heat- productions than body-weight (table 62). In predicting by equations, body-sm-face gives the closer agreement of prediction with observation in two of the series (IV, VI), but the two methods are, practically speaking, equally good in the other two series (V, VII, table 68). The net result of this analysis seems to be that metabolism can be predicted more accurately from body-surface than from body-weight. The difference between these two means of prediction depends in a very large degree upon the method of calculation used, and somewhat upon the criterion of accuracy of prediction adopted. With the best methods of calculation the difference between the accuracy of prediction from body-weight and that from body-surface is not very large. 8. FURTHER TESTS OF THE VALUE OF BODY-WEIGHT AND BODY-SURFACE FOR ESTIMATING TOTAL HEAT-PRODUCTION. The practical importance of the solution of the problem of predict- ing the metabolism of the individual with the highest attainable degree of accuracy is so great that we shall apply one further test of the rela- tive value of body-weight and body-surface area as measured by the Du Bois height-weight chart. In the preceding tests we have adhered strictly to the procedure which is theoretically the best and which fulfills exactly the conditions to be met in practice. That is, in the case of a subject whose metabolism is assumed to be unknown, we have 178 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. predicted the heat-production from constants based on other series of individuals taken as the bases of standard constants. The compari- son of heat-productions thus calculated with those which have been actually determined furnishes a test of the accuracy of prediction by the several methods to be tested. From the theoretical side it is evident that in testing the value of any method of predicting metaboUsm, the measurement of an indi- vidual subject should not be included in the series upon which the constant or equation used in predicting his own metabolism is based. In other words, the metabohsm of an individual should not be predicted from itself. This error has in essence been made by earlier writers in tests of the validity of the body-surface law. But while a single aberrant subject might have great weight in determining a standard constant based on a small group of individuals, the importance of any single metabolism measurement rapidly de- creases as the number included in the group becomes larger. Thus in our series of males one individual has a weight of only 1/136 and in our series of females one individual has a weight of only 1/103 in determining the constant for the whole series. In predicting the metabolism of really, and not merely supposedly, unknown subjects in the hospital ward the clinician should naturally use the constants based on oiu- 136 men, not on the 72 of the Gephart and Du Bois selection or the 64 others. The same is true of the 103 women as com- pared with the two subseries of 35 and 68 individuals. Since prediction constants based on these series, the largest avail- able up to the present time, will be used in the calculation of controls, it seems desirable to determine the error of prediction of the heat- productions of the individual subjects, considered unknown, from prediction constants based on the series as a whole. If we follow the old practice of estimating the metabolism of a subject by multiplsdng his body-weight by the average heat-production per kilogram of body- weight, or his body-surface by the average heat-production per square meter of body-surface, we employ the following average values per 24 hours : Formen, iV^=136: Mean calories per kilogram 25.697 Mean calories per square meter of body-surface by height-weight chart 925.471 For women, N = 103: Mean calories per kilogram 24.457 Mean calories per square meter of body-surface by height-weight chart 850.010 If, on the other hand, we desire to use the method proposed in this paper of predicting heat-production by use of regression equations, we have the following: For men: A = 617.493 -1-15.824 w A= -254.546-M070.454o . D For women: A = 884.528-1- 8.227tc h= 333.618-(- 638.610o . A CRITIQUE OP THE BODY-SURFACE LAW. 179 The results of predicting the heat-production of the 136 individual men and of the 103 individual women by these four methods are shown in table 69. Here the deviations of the calculated heat-production in calories per day are shown in units of 75 calories per day range as indi- cated in the first colimm. The frequencies of deviations of given grade are shown for the four different methods of calculation and for the two sexes in the following eight columns. This table brings out various facts which are not shown by the other methods of comparison hitherto employed. 1. The deviations of the predicted from the actually observed heat-productions may be very great. Differences of 188 calories and over, either above or below the observed values, occur in many cases. Table 69. — Comparison of amounts and frequencies of error by different methods of prediction based on all men and women. Deviation of calculated from observed heat- production in Men. Women. li .CO S 2 egression heat on eight. egression licat on irface. 2:2 a % egression heat on weight. egression fieat on irface. calories per day. £■" S S *■_ S "^ « «t E S •s ' "-Z g >> S >. a >. o >> >• s >i "=• >, ° >, o pq p. a « C5 pa =• a n a +863 to +937 1 +788 to +862 +713 to +787 +638 to +712 +563 to +637 3 +488 to +562 1 2 +413 to +487 2 2 +338 to +412 2 . 3 +263 to +337 5 2 2 2 3 4 + 188 to +262 7 5 9 5 7 4 7 7 + 113 to +187 16 14 13 15 7 13 12 13 + 38 to +112 20 34 24 36 12 20 22 21 - 37 to + 37 31 34 39 30 16 24 23 26 - 38 to -112 23 26 22 29 20 22 23 18 -113 to -187 14 11 19 9 15 8 8 10 -188 to -262 13 6 7 9 6 5 3 5 -263 to -337 1 3 1 6 3 5 3 -338 to -412 1 1 1 2. The distribution of the errors of estimation is not chaotic, but remarkably regular in all cases. The errors form monomodal more or less symmetrical distributions, i.e., they are distributed around a maximum control frequency. 3. The errors of estimation in the case of prediction from average heat-production per kilogram of body-weight are obviously far greater in both men and women than those resulting from any other method. The errors by this method tail off in the positive direction with a number of errors beyond the 338-412 calories class in the women. Obviously, prediction from mean calories heat-production per kilo- gram of body-weight gives bad results in both sexes, and particularly 180 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. bad results in (he case of the women. From mere inspection of the frequency distributions of this series of errors it is impossible to dis- criminate between the value of the three other methods of prediction. Having recourse to the three tests of accuracy of prediction used in the foregoing discussion we find the following results from the ungrouped deviations. The average deviations of the predicted from the actually observed values voith regard to sign are the following : Calculated from body-weight W«"- Womm. Diference. By means +15.346 +32.243 +16.897 By equations - 0.007 - 0.019 + 0.012 Difference +15.339 +32.224 Calculated from body-surface By means -0.919 +2.816 +1.897 By equations + 0.015 + 0.029 + 0.014 Difference + 0.904 + 2.787 This comparison brings out with great clearness three important results. 1. The average error with regard to sign of prediction from average heat-production per unit is enormously greater than that in prediction by the use of regression equations. This is true whether body-surface or body-weight be used as a basis of prediction. 2. The errors in predictions from body-surface by use of the mean heat per imit of body-surface in the standard series is far lower than that resulting from prediction from body-weight. 3. The errors of prediction are in all cases larger in the calculations for women than the comparable values for men. As far as it goes, therefore, this test indicates the superiority of body-surface over body-weight as a basis of prediction. The superiority of the regression equations for purposes of predic- tion over the old method of considering heat-production directly proportional to body-weight or body-surface is the most striking, and doubtless the most valuable, feature of this table. The old method of estimation gives average errors of from 0.9 of a calorie to over 32 calories per day, depending on the sex and method of prediction used. The new method of prediction does not in any case give an average error of as much as 0.03 calorie per day! Turning now to the average deviations without regard to sign of the predicted from the observed values we have the following results: Calculated from body-weight ^"*- Women. Difference. By means 122.5 165.3 +42.8 By equations 97.6 98.0 +0.4 Difference + 24.9 + 67.3 Calculated from bodynsurface By means 93.7 99.7 + 6.0 By equations 92.0 97.2 + 5.2 Difference + 1.7 + 2.5 A CRITIQUE OF THE BODY-SURFACE LAW. 181 The constants in this table show: 1. That in all four comparisons prediction from means gives a higher error than prediction by use of equations. 2. That prediction from body-surface gives lower average devia- tions than prediction from body-weight. This is true whether predic- tion is made by considering the production proportional to body- weight or body-surface, or as given by a linear equation. 3. That by all methods the error of prediction is larger in the women than that due to comparable methods in the men. In prediction from body-weight the disadvantage of the method of estimation from average heat per unit is particularly conspicuous. It gives an average error of 24.9 calories in men and 67.3 calories per 24 hours in women greater than prediction from equations based on body-weight. In the case of prediction from body-surface the differ- ence between the error resulting from the use of means and the use of equations is not so great, but amounts to 1.7 calories in men and 2.5 calories in women. Results secured by the use of equations are conspicuously more consistent than those reached by prediction from means of heat- production per unit of surface. For example, in the men the mean error of the prediction of heat-production from the mean heat-produc- tion per kilogram in the series as a whole is 28.8 calories per 24 hoiu's greater than prediction from the mean heat-production per square meter of body-surface in the whole series. For the women the differ- ence is 65.6 calories. But when equations are used the excess error of 28.8 calories in the men shrinks to 5.6 calories and the excess error of 65.6 calories in the women shrinks to 0.8 calorie. Again, in comparing the men and the women we note differences of 42.8 and 6.0 calories when prediction is made by considering heat-production proportional to body-weight or body-surface, but these differences are only 0.4 and 5.2 calories per day when prediction is made by equations. Turn now to our third and final standard of comparison — the square root of mean-square error of prediction. Calculation from body-weight ^"'- Wonun. Difference. By means 160.99 225.74 +64.75 By equations 123.88 123.03 - 0.85 Difference + 37.11 +102.71 Calculation from body-surface By means 119.44 126.81 + 7.37 By equations 117.21 122.86 + 5.65 Difference + 2.23 +3.95 The conclusions to be drawn from this table are in essential agree- ment with those drawn from the preceding tests. Prediction from body-surface gives a far lower error than prediction from body-weight when heat-production is considered directly proportional to weight 182 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. and surface, but the errors of prediction are much more nearly equal when equations connecting body-weight and body-surface on the one hand and daily heat-production on the other are used. Thus differ- ences of 41.55 and 98.93 calories in the results of prediction of metab- olism by the use of mean calories per kilogram and mean calories per square meter are reduced to 6.67 and 0.17 calories when equations are used; and differences of 64.75 and 7.37 calories in the deviation of pre- dicted from the observed standards in men and women when mean heat per kilogram and per square meter are used as a basis of predic- tion reduce to 0.85 and 5.65 calories when equations are employed for prediction. Finally, comparing body-weight and body-surface as bases of prediction when the more satisfactory equation method is used for prediction, one finds surprisingly little difference between them. For men body-weight gives a square root of mean-square deviation of 123.88 calories per day, while body-surface gives 117.21 calories or only 6.67 calories less. For women the difference is only 123.03 — 122.86 = 0.17 calorie per 24 hours. The reader must note that these differ- ences are based on an average metabolism of 1631.74 calories per 24 hours in men and 1349.19 calories in women. Thus the differences are less than 0.5 per cent of the total metabolism in each case. On the basis of such differences, who is prepared to assert that metabolism is proportional to body-surface but not to body-weight? 9. PREDICTION OF HEAT-PRODUCTION FROM TWO PHYSICAL CHARACTERS. We shall now approach the problem of the basis of comparison of the metabolism of various individuals along what we believe to be an entirely novel line of attack. In a preceding section we have empha- sized the view that the true test of any method for the reduction of the metabolism of individuals of different size and shapes to comparable terms is its capacity for predicting an unknown metabolism. This we believe to be not merely a logically sound position, but the one upon which the results of the greatest practical importance can be based. Aside from the purely physiological problem of the value to be assigned to the basal metabolism coefficient for the human species, the precise determination of the metaboUsm of the normal individual underlies a wide range of practical medical, economic, and social problems. Take one illustration merely. A tj^jhoid or goitre subject is placed in the respiration chamber and basal metabolism is calcidated from gaseous exchange. This is merely a technical matter. The theoretical question which must be solved before these observational data have any medical significance is: What value should be assigned to the metaboUsm of this individual on the basis of his measurable bodily characters on the assumption that he is in normal health? In short, we A CRITIQUE OF THE BODY-SURFACE LAW. 183 are forced to use his predicted metabolism in health as a basis of com- parison with his measured metabohsm in disease, in order to reach any conclusion of value concerning the influence of disease on metabolism.*" We shall now consider the possibility of predicting the basal metab- olism of an individual by the simultaneous use of two physical charac- ters. Should the method of the use of two or more characters prove more advantageous than the use of a single character, the selection of the most suitable physical characters for use in the estimation of the normal metabolism of the individual will present a problem of some practical importance. At present, it is quite natural to take the two measurements which are most easily and generally made, namely stature and body-weight. Let s= stature, ti;= weight, ^ = total heat-production. Then the prediction of h from both s and w will be carried out by the formula " h = h V"'~'''"^'- . -^ (w -w) + ^"' ~''*-^'° ' . -* js-l) or in terms more convenient for purposes of calculation n = n— — ; — ■ — w ~ —z ; — • - s 1— r 2 +3.237 «. For aU women, i\r = 103 h= 713.016+ 8.063 u»+1.116 «. These equations have been used for purposes of prediction and the calculated heat-productions compared with the actually observed pro- ductions, just as was done in the preceding sections in prediction from standard average values or by means of a linear equation based on one bodily measure only. Thus we have predicted the total heat-production of the 64 indi- viduals not included in the series selected by Gephart and Du Bois from equations based on stature and body-weight in the Gephart and Du Bois selection. Conversely, to secure a more exhaustive test of the value of our prediction formulas, we have estimated the total heat- production of the 72 individuals constituting the Gephart and Du Bois selection from the data of the 64 other males. Similarly, the total heat-production of the 35 supplementary women has been predicted from equations involving the constants for stature and body-weight in the original feminine series, and the values for the individuals of the original series have been predicted from the data of the supplementary series of women. Details are given on pages 161-176, tables 60-68. The reader will bear in mind the fact that these predictions and comparisons with actually observed constants have been made for the purpose of determining the most suitable method for estimating the metabolism of a subject. The division of our materials to make this test possible naturally increases somewhat the probable errors of the constants of the prediction formulas. After the most suitable method for the calculation of the metabolism of an unknown subject has been determined, the constants for actual use in the establishment of stand- ard control or check values will be based upon all the data at our disposal. In examining the results of the prediction of the metabolism of series of individuals by means of equations involving both body- weight and stature, our object has been to ascertain whether this method gave sensibly better results than other methods of prediction hitherto employed. Since it has been shown in a preceding chapter that the correlation between stature and metabohsm is relatively small as compared with that between body-weight and metabolism, it will be unnecessary to compare the results of prediction by the use of equations involving both stature and body-weight with those based on stature only. A more valuable test of the possible superiority of prediction from both A CRITIQUE OF THE BODY-SURFACE LAW. 185 stature and body-weight may be obtained by a comparison with the results of prediction from body-weight only. Since it has appeared that the prediction from body-surface as estimated by the Du Bois height-weight chart gives more reliable results than prediction from body-surface as computed from the Meeh formula, it seems superfluous to make the comparisons of the prediction methods here under consideration with those involving body-surface as measured by this now antiquated formula. In the following tables we shall, therefore, compare the errors of estimation found in predicting metaboUsm from multiple regression equations involving stature and body-weight with those found by considering it proportional to body-weight and to body-surface by the Table IQ.—Cormparison of average deviation {in calories, with regard to tign) from the actual calorie- output, of heat-prodiuUion calculated on the one hand from multiple regression equations invohing body-weight and stature and on the other from (a) the mean heat-production per unit of body-weight and of surface by the Du Bois height-weight chart and from (6) the regression of total heat on body- weight and on surface area by the Du Bois height-weight chart. Series. Prediction from regreesion equations involving stature and weight, I. Comparison with results obtained by other methods.* Difference from prediction from average heat per square meter of body-surface. II. Difference from prediction from regression equation for total heat on body-surface. III. Difference from prediction from average heat per kilogram of body-weight. IV. Difference from prediction from regression equation for total heat on body-weight. V. I II III.... IV.... V VI.... VII .. . Men. . Women +14.8=0.92 p. ct. +10.0=0.61 p. ct. — 5.1 = 0.30 p. ct. + 8.1 =0.50 p. ct. — 6.5 = 0.40 p. ct. +77.7=5.80 p. ct. -49.8=3.68 p. ct. ± 00.0 =0.00 p. ct. ± 00.0 =0.00 p. ct. -10.2 = 0.64 p. ct. + 6.3 = 0.32 p. ct. -36.0=2.12 p. ct. + 6.7=0.41 p. ct. + 3.0=0.18 p. ct. - 0.2=0.02 p. ct. -20.1 = 1.48 p. ct. - 0.9=0.06 p. ct. - 2.8 = 0.21 p. ct. -10.0=0.62 p. ct. + 3.9 = 0.24 p. ct. -33.1 = 1.96 p. ct. + 6.6=0.36 p. ct. + 2.4=0.15 p. ct. + 4.5=0.33 p. ct. - 1.7=0.12 p. ct. =*= 0.0=0.00 p. ct. ± 0.0=0.00 p. ct. + 3.0=0.18p. ct. - 28.3 = 1.73 p. ct. - 62.5=3.67 p. ct. - 26.4= 1.60 p. ct. + 3.6=0.22 p. ct. -114.0=8.52 p. ct. - 66.8 = 4.93 p. ct. - 16.4=0.94 p. ct. - 32.2 = 2.39 p. ct. +7.3=0.46 p. ct. -2.5=0.15 p. ct. -4.6=0.27 p. ct. -1.5 = 0.08 p. ct. — 0.9=0.06p. ct. -0.2=0.02 p. ct. —3.6=0.26 p. ct. ±0.0=0.00 p. ct. =*=0.0=0.00p. ct. * The differences in these colimins are obtained from the first column of this table and the entries of pre- ceding tables as follows: column II from III of table 60; column III from III of table 66; column IV from I of table 60; column V from I of table 66. Du Bois height-weight chart, and when given by a linear-regression equation in which heat is predicted from body-weight or from body- surface by the height-weight chart. Table 70 gives the average deviations with regard to sign of the theoretical heat-productions calculated by the multiple-prediction equation from the observed values and compares these deviations with those computed by the four other methods. Comparing the average deviations with regard to sign of the constants computed by the various methods in table 70, we note that in 2 of the 4 larger series (IV-VII), in which the prediction of the metabolism of the individuals of one series is made from the equations based on another series of individuals of the same sex, prediction by the simultaneous use of stature and 186 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. body-weight gives a slightly larger average error than prediction from body-surface by the Du Bois height-weight chart when prediction from body-surface is made by considering that the heat-production of an individual is given by where ao is the superficial area of the individual by the Du Bois height- weight chart and h^ the average heat-production per square meter in the standard population. In two cases, VI and VII, it gives a smaller average deviation from the ideal zero error. When the best measure of heat-production on the basis of a single physical measurement is supposed to be given by as we have demonstrated to be the case, the multiple regression equa- tion gives sUghtly higher error in three of the four larger series. The difference between the results of predicting heat-production by the use of multiple regression equations involving stature and weight and those due to the use of linear equations for prediction from body-surface by the DuBois height-weight chart is, however, very slight indeed. In only 1 of the 8 comparisons is the difference over 7 calories. The difference in the percentage value of the average deviations with regard to sign of the two methods of prediction is in only 1 case over 0.5 per cent in the 8 comparisons based on larger series. When the values of the individual subjects are computed from equations based on the entire material for each sex (136 men and 103 women, as given in the two lower rows of the table) the average devia- tion with regard to sign is theoretically 0, and for all practical purposes empirically in our actual observational data. As far as this criterion can show, all three regression methods seem equally good when predic- tions of individual values are made from the constants of the population to which they belong. Therefore, either of these three methods neces- sarily gives better results as measured by this criterion than either of the two methods of calculation from average heat-production per unit of weight or per unit of body-surface area in the standard series. Turning now to the average deviations without regard to sign, as shown in table 71, we note practically the same relationship between the results for the 3 sets of formulas as in the preceding comparisons. Confining our attention to the 4 larger groups (IV-VII), in which prediction is made from the constants of another series of individuals, we note that in 5 of the 8 comparisons the multiple prediction equation shows (as indicated by the positive sign) a slightly larger, but only slightly larger, error than prediction from body-surface. The difference is in no case as much as 4.5 calories. In percentages of the average A CRITIQUE OF THE BODY-SURFACE LAW. 187 measured heat-productions for the group under consideration, the differences in the errors of prediction range from 0.00 per cent to 0.29 per cent. If the test be based upon the whole series of men and of women we find that the multiple regression equations give better results in every case but one. In this case prediction from the linear equation for total heat on body-surface area gives a mean deviation 0.2 calorie per day less in the men than the multiple regression equations. This represents a difference of 0.01 per cent only. The comparison on the basis of square root of mean-square devia- tion is made in table 72. The results show that in 6 of the 8 larger series (IV-VII) in which prediction is made from constants based upon Table 71. — Comparison of average deviation (in cahries, without regard to sign) from the actual caloric-output, of heat production calculated on the one hand from multiple regression equations involving body-weight and stature and on the other from (a) the mean heat-production per unit of body weight and of surface by the Du Bois height-weight chart and from (6) the regression of total heat on body-weight and on surface area by the Du Bois height-weight chart. Prediction from Comparison with results obtained by other methods,* regression Difference from Difference from Difference from Difference from Series. equations prediction from prediction from prediction from prediction from involving stature average heat per regression equation average heat regression equation and weight. square meter of for total heat on per kilogram of for total heat on body-surface. body-surface. body-weight. body-weight. I. 11. III. IV. V. I 87.9= 6.48 p. ct. — 6.2 = 0.38 p. ct. - 1.7 =0.10 p. ct. - 4.9 = 0.30 p. ct. - 3.2=0.19 p. ct. II 99.1= 6.04 p. ct. 127.2= 7.48 p. ct. - 0.6=0.04 p. ct. +17.8= 1.06 p. ct. - 1.7 = 0.11 p. ct. +20.8= 1.23 p. ct. - 27.9 = 1.71 p. ct. -107.4 = 6.31 p. ct. - 0.3 = 0.02 p. ct. -21.9 = 1.28p.ct. Ill IV 101.7= 6.20 p. ct. + 1.9=0.12 p. ct. + 4.3 = 0.27 p. ct. - 38.9 = 2.37 p. ct. - 7.3 = 0.44 p. ct. V 88.6= 6.46 p. ct. - 0.1 = 0.00 p. ct. - 0.1 = 0.00 p. ct. - 17.8= 1.09 p. ct. + 0.5 = 0.03 p. ct. VI 160.0 = 11.21 p. ct. + 0.1 = 0.01 p. ct. + 3.9 = 0.29 p. ct. - 93.7 = 7.00 p. ct. =fc O.0=0.00p.ot. VII 94.0= 6.94 p. ct. - 0.6=0.04 p. ct. + 0.9 = 0.07 p. ct. — 75.8 = 6.59 p. ct. - 2.1 = 0.15 p. ct. Men 92.2= 6.65 p. ct. - 1.6 = 0.10 p. ct. + 0.2 = 0.01 p. ct. - 30.3 = 1.86 p. ct. — 5.3 = 0.33 p. ct. Women 93.6= 6.94 p. ct. - 6.1=0.45 p. ct. — 3.6=0.26 p. ct. - 71.7 = 6.31 p. ct. - 4.4 = 0.32 p. ct. * The differences in these columns are obtained from the first column of this table and the entries of preceding tables as follows: column II from III of table 61; column III from III of table 67; column IV from I of table 61; column V from I of table 67. a different group the error of prediction is greater by the equations here being tested than by prediction from body-surface by the Du Bois height-weight chart. The difference between the two methods is, how- ever, very slight. In working units, it ranges from 1.1 to 4.7 calories per day. In terms of percentages of the average daily heat-production of the series of individuals dealt with, the differences in the errors of estimation by the multiple-regression equations and the prediction method based on body-surface range from 0.04 to 0.33 per cent. Turning to a comparison of the various methods of calculation when the whole series of men and women are used, it appears in every case except one that the multiple regression equations give the more accurate prediction of metabolism. 188 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Now, if we retiim to the differences in these three tables and con- sider together the three criteria of excellence of prediction — each of which has some advantages but neither of which is perfect — ^as a basis for a generalization concerning the value of the two methods under consideration, we note the following points: 1. The results in the first difference column show that prediction from the two direct measurements stature and body-weight gives more accurate results than the method of calculation from body-surface area by the Du Bois height-weight chart heretofore employed. 2. The second difference colmnn suggests that when the more accurate method of prediction by means of linear regression equations suggested in this volume is substituted for the old method slightly more Table 72. — Comparison of square root of mean-square deviation (in calories) from the actual cahric-ovtput, of heai-production, calculated on the one hand from multiple regression equations involving body-weight and stature and on the other from (a) the mean heat-production per unit of body-weight and of surface by the Du Bois height-weight chart and from, (6) the regression of total heat on body-weight and on surface area by the Du Bois height-weight chart. Prediction from Comparison with results obtained by other methods.* regression Difference from Difference from Difference from Difference from Series. equations prediction from prediction from prediction from prediction from involving stature average beat per regression equation average heat regression equation and weight. square meter of for total heat on per kilogram of for total heat on body-surface. body-surface. body-weight. body-weight. I. II. III. IV. V. I 110.7= 6.90 p. ct. -6.6=0.41 p. ct. - 3.2 = 0.20 p. ct. - 25.5= 1.59 p. ct. - 1.1=0.07 p. ct. 11 139.4= 8.50 p. ct. +5.0=0.30 p. ct. + 4.6 = 0.27 p. ct. - 31.9= 1.95 p. ct. - 4.4=0.27 p. ct. m 148.6= 8.73 p. ct. +9.5 = 0.55 p. ct. +15.7=0.92 p. ct. -119.5= 7.03 p. ct. -22.3 = 1.31 p. ct. IV 130.3= 7.94 p. ct. +1.8=0.11 p. ct. + 4.7=0.29 p. ct. - 59.2= 3.61 p. ct. - 8.9=0.54 p. ct. V 111.3= 6.86 p. ct. +0.7 = 0.05 p. ct. + 1.1=0.07 p. ct. - 20.9= 1.29 p. ct. + 1.1 =0.07 p. ct. VI 173.5= 12.96 p. ct. -0.5 = 0.04 p. ct. + 4.4=0.33 p. ct. - 154.3 = 1 1.53 p. ct. * 0.0=0.00 p. ct. VII 121.0= 8.93 p. ct. -1.1=0.08 p. ct. + 0.6=0.04 p. ct. - 80.1= 5.92 p. ct. + 0.8=0.06 p. ct. Men 117.4= 7.19 p. ct. -2.0=0.13 p. ct. + 0.2 = 0.01 p. ct. - 43.6= 2.68 p. ct. — 6.5=0.40 p. ct. Women... 117.4= 8.70 p. ct. -9.5 = 0.70 p. ct. - 5.5 = 0.41 p. ct. -108.4= 8.03 p. ct. - 5.7 = 0.42 p. ct. 1 * The differences in these columns are obtained from the first column of this table and the entries of the pre- ceding tables as follows: column II from III of table 62; column III from III of table 68; column IV from I of table 62; column V from I of table 68. accurate predictions may be made from body-surface area than from multiple regression equations involving height and weight. 3. The third difference column shows that practically without exception (25 out of 27 tests) better prediction can be made from multiple regression equations than by considering heat-production in the individual as given by (body-weight X mean heat-production per kilogram in the control series). 4. Even when the superior method of predicting from the regression of heat-production on body-weight introduced in this paper is employed instead of the older method, the multiple regression equation in which prediction is based on both stature and body-weight gives far better results (as shown by the preponderance of negative signs in the final difference column) than prediction from weight alone. A CRITIQUE OF THE BODY-SUBFACE LAW. 189 10. PREDICTION OF HEAT-PRODUCTION FROM TWO PHYSICAL CHARACTERS (STATURE AND BODY-WEIGHT) AND ACE. In the foregoing section we demonstrated the eflSciency of equations involving stature and body-weight for the prediction of the heat- production of the individual. From the analyses in the preceding chapter it is clear that age is another factor which should be taken into account in estimating the basal metabolism of the individual. Our problem in this section is therefore twofold: First, we must determine some means of including an age factor in our prediction equation. Second, we must, on the basis of the available observational data, replace the symbols in these equations by numerical constants and determine empirically whether equations involving age as well as body-weight and stature show a superiority for the prediction of the heat-production of the imknown subject. While Du Bois has given a tentative correction for age we have not considered it worth while, in view of the very approximate nature of his terms as given on page 123 to apply his age correction in drawing a comparison between equations based on body-surface and those based on stature, weight, and age. Working in terms of partial correlations and variabilities, the multiple-prediction formvilas for the estimation of total heat-production from stature, body-weight, and age require: Partial correlation between weight and total heat-production for constant stature and age, laTwh. Partial correlation between stature and total heat-production for constant weight and age, Ti/aTjkt Partial correlation between age and total heat-production for constant weight and stature, v/sTakf Partial correlation between age and stature for constant body-weight and daily beat-pro- duction, h-JTa,. Partial correlation between stature and weight for constant age and daily heat-production, These are: Tmk — • ta'wh TmH — V(l -rj -rj' -raJ+2ra,ra„r^) V(l -r,.^ -r,^' -raA*+2r„r„fcr.*) va* »h ts'ah hw'aa OA^MP — V(l -ra„2-r„,2-.r„2+2r„„r„OV(l -r^J-r^h^-rah^+2rav;rahru,h) \/(l -r,„=-r„a='-r„«-|-2r.„7-„r„J ^(1 -r^^-r^h^-r,h''+2r,^r.^r„^) y,a(l —rhi/) —'''h,'''ha—i'w,rv,a-\-THv,{n,r^a+rkary„) ^^(1 -r*,* -r„.» -rA,«-|-2r*„r».r„,) V(l - ri„« - r.,^ - r*,«-i-2rA„rA„r„„) r„{l —rat") — ra,ra»— rA.rt«,-frai(rn,rt,-|-ra„rfc,) V(l -r„»*-rA.» -ra,'-|-2raAra.rJ V(l -ra»*-r».*-ra,*-|-2raAra„0 190 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN, The first three lead to the partial regressions which are required for computing the variations in heat-productions associated with differ- ences in weight, stature, and age. The last two are useful in checking the partial variabilities. The partial regressions are: •a' IT* '^ah~vt'ah tah^w wah^t tUMh^a where the partial variabilities are given by ,a*ff„ = +1.8496«-4.6756o The testing of these formulas is carried out in precisely the same manner as that employed in dealing with those in which total heat- production was predicted from body-weight and stature in the preced- ing section. Thus tables 73 to 75 are quite comparable with tables 70 to 72. The first column gives the results of predictions of total heat- production from weight, stature, and age. The five following colunms show the differences between these results and those obtained by other methods. The final column shows the difference between prediction from weight and stature as given in the first column of tables 70 to 72 and that from weight, stature, and age as given in the first column of tables 73 to 75. The subtractions are so made that a minus sign denotes a smaller error of prediction when the equation involving weight, stature, and age is used. In taking these differences in the case of A CRITIQUE OF THE BODY-SURFACE LAW. 191 the average deviation of the calculated total heat-production with regard to signs, the signs of the constants in the first column of table 70 and in the first column of table 73 are disregarded, and the differences represent merely the difference in the numerical magnitudes of the discrepancy between observation and prediction. Considering the values in table 73, we see that in some cases the equations involving weight, stature, and age give closer and in some cases slightly wider average deviations above or below the true value. In the larger series (IV-VII and total men and women) the equations Table 73. — Comparison of average deviation {in caUniea. with regard to sign) from aUual, caloric-output of heal-production calculated on the one hand from multiple regression equations invoking stature, body-weight, and age and on the other from (a) the mean heat-production per unit of body-weight and body-surface by Du Bois height-weight chart, from (6) the regression of total heat on body-weight and on boay-surface by the Du Bois height^weighl chart, and from (c) the regression of total heat-produxtion on stature and body-weight. Series. Prediction from regression equations involving stature, weight, and age. I. Comparisons with results obtained by other methods.* Difference from prediction from average heat per square meter of body-surface. II. Difference from prediction from regression equation for total heat on body-surface. III. Difference from prediction from average heat per kilogram of body-weight. IV. Difference from prediction from regression equation for total heat on body-weight. V. Difference from prediction from regression equation for total heat on stature and weight. VI. I II Ill ... . IV V VI VIZ.... Men... Women col. pel. +20.0=1.25 -51.0 = 3.11 -36.8 = 2.16 -16.2 = 0.99 + 7.6=0.47 +30.8 = 2.30 - 2.7 = 0.20 ± 0.0=0.00 ± 0.0=0.00 col. p.et. - 5.0=0.31 +46.3=2.82 - 4.3 = 0.25 +14.8 = 0.90 + 4.1 = 0.25 -47.1 = 3.52 -67.2=4.96 - 0.9=0.05 - 2.8 = 0.21 cal. p.cl. - 4.8 = 0.30 +44.9 = 2.74 - 1.4 = 0.08 + 13.7 = 0.83 + 3.5 = 0.22 -42.4 = 3.17 -48.8 = 3.60 =t 0.0=0.00 =fc 0.0=0.00 col. p.ct. + 8.2= 0.61 + 12.7= 0.77 - 30.8= 1.81 - 18.3= 1.11 + 4.6= 0.28 -160.9 = 12.02 -113.9= 8.41 - 15.3= 0.94 - 32.2= 2.39 col. p.ct. +12.6 = 0.78 +38.5 = 2.35 +27.1 = 1.59 + 6.6 = 0.40 + 0.2 = 0.01 -47.1 = 3.52 -50.6=3.74 =fc 0.0=0.00 =fc 0.0=0.00 cat. p.cl. + 5.2 = 0.32 +41.0=2.50 +31.7 = 1.86 + 8.1 = 0.49 + 1.1 = 0.07 -46.9 = 3.50 -47.1 = 3.48 ±00.0=0.00 ±00.0=0.00 * The differences in these columns are obtained from the first column of this table and the entries of pre- ceding tables as follows: column II from III of table 60; column III from III of table 66; column IV from I of table 60; column V from I of table 66; column VI from I of table 70. which take into account weight, stature, and age give somewhat better results than those in which prediction is made by the other methods employed. The figures set forth in tables 74 and 75 are so striking that they require but few words of discussion. Consider table 74 showing the average deviations without regard to sign of the calculated from the actually determined heat-productions in the several series of individuals when the former are computed in various ways. With one single and numerically insignificant (-1-0.7 =0.04 per cent) exception the 45 differ- ences are negative in sign, showing that the error of prediction is smaller when multiple regression equations involving wei^t, stature, and age are used than when any of the other 5 methods of estimating the heat- production of a subject is employed. In the larger series (IV-VII and 192 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. Table 74. — Comparison of average deviation {in calories, uithout regard to sign) from the actual caloric- output, of heat-prodiKtion calculated on the one hand from multiple regression equations invohing body-weight, stature, and age and on the other from (a) the mean heaUproduction per unii of body- weighi and of surface by the Du Bois height-weight chart, from (6) the regression of total heat on body-weight and on body-surface, and from (c) the regression of total heat-production on stature and body-weight. Series. Prediction from leEression equations involving stature, weight, and age. I. Comparisons \iith results obtained by other methods.* Difference from prediction from average heat per square meter of body-surface. II. Difference from prediction from regression equation for total heat on body-surface. III. Difference from prediction from average heat per kilogram of body-weight. IV. Difference from prediction from regression equation for total heat on body-weight. V. Difference from prediction from regression equation for total heat on stature and weight. VI. I II III... IV V VI VII... . Men... Women cal. p.ct. 88.6=5.52 98.8=6.02 86.8=5.10 81.1=5.55 79.1=4.87 109.7=8.20 75.8=5.60 81.2=4.98 84.6=6.27 cal. p.ct. - 5.6 = 0.34 - 0.9 = 0.05 -22.6=1.33 - 8.7 = 0.53 - 9.6=0.59 -40.2 = 3.00 -18.8 = 1.39 -12.5 = 0.77 -15.1 = 1.12 cal. p.ct. - 1.0=0.06 - 2.0=0.12 -19.6=1.15 - 6.3 = 0.38 - 9.6 = 0.59 -36.4=2.72 -17.3 = 1.28 -10.8=0.66 -12.6=0.93 cal. p.ct. - 4.2= 0.26 - 28.2= 1.72 -147.8= 8.69 - 49.5= 3.02 - 27.3= 1.68 -134.0=10.01 - 94.0= 6.93 - 41.3= 2.53 - 80.7= 5.98 ad. p.ct. - 2.5=0.16 - 0.6=0.04 -62.3=3.66 -17.9=1.09 - 9.0=0.55 -40.3=3.01 -20.3 = 1.50 -16.4 = 1.01 -13.4 = 0.99 coJ. p.ct. -f- 0.7 = 0.04 - 0.3 = 0.02 -40.4=2.37 -10.6=0.65 - 9.6=0.59 -40.3 = 3.01 -18.2=1.34 -11.0=0.67 - 9.0=0.67 * The differences in these columns are obtained from the first column of this table and the entries of the preceding tables as follows: column II from III of table 61; column III from III of table 67; column IV from I of table 61 ; column V from I of table 67; column VI from I of table 71. Table 75. — Comparison of square root of mean-square deviation (in calories) from the actual caloric-output of heat-production calcukUed on the one hand from multiple regression equations involving body-weight, stature, and age, and on the other from (a) the mean heat-production per unit of body-weight and of surface by the Du Bois height-weight chart, from (b) the regression of total heat on body-weight and on body-surface by the Du Bois height-weight chart and from (c) the regression of total heat on sUUure and body-weight. Series. Prediction from regression equations involving stature, weight, and age. I. Comparisons with results obtained by other methods.* Difference from prediction from average heat per square meter of body-surface. II. Difference from prediction from regression equation for total heat on body-surface. III. Difference from prediction from average heat per kilogram of body-weight. IV. Difference from prediction from regression equation for total heat on body-weight. V. Difference from prediction from regression equation for total heat on stature and weight. VI. I II III... IV V VI VII... . Men... Women eal. p.ct. 104.3= 6.50 137.5= 8.38 94.4= 6.56 112.9= 6.88 98.3= 6.05 136.4 = 10.19 94.2= 6.95 101.7= 6.23 106.3= 7.88 cal. p.ct. -13.0=0.81 -1- 3.1 = 0.19 -44.7 = 2.63 -16.6=0.95 -12.3 = 0.76 -37.6 = 2.81 -27.9=2.06 -17.7=1.08 -20.6 = 1.52 cal. p.et. - 9.6=0.60 -1- 2.6 = 0.16 -38.5 = 2.26 -12.7=0.77 -11.9 = 0.73 -32.7 = 2.44 -26.2 = 1.93 -15.5 = 0.95 -16.6 = 1.23 eal. p.ct. - 31.9= 1.99 - 33.8= 2.06 -173.7 = 10.21 - 76.6= 4.67 - 33.9= 2.09 -191.4 = 14.30 -106.9= 7.89 - 59.3= 3.63 -119.4= 8.86 eoJ. p.ct. - 7.6 = 0.47 - 6.3-0.38 -76.5=4.50 -26.3 = 1.60 -11.9 = 0.73 -37.1 = 2.77 -26.0=1.92 -22.2 = 1.36 -16.7 = 1.24 cal. p.et. - 6.4 = 0.40 - 1.9 = 0.12 -54.2 = 3.19 -17.4=1.06 -13.0=0.80 -37.1 = 2.77 -26.8=1.98 -16.7=0.96 -11.1 = 0.82 * The differences in these columns are obtained from the first column of this table and the entries of pre- ceding tables as follows: column II from III of table 62; column III from III of table 68; column IV from I of table 62: column V from I of table 68; column VI from I of table 72. A CRITIQUE OF THE BODY-SURFACE LAW. 193 totals) the differences range from 6.3 to 134.0 calories, or from 0.38 to 10.01 per cent of the average (24-hoiir) heat-production of the group of subjects imder consideration. If one prefers to base his judgment concerning the value of the different means of estimating the basal metabolism of an unknown subject upon the square root of the mean-square deviation of the computed from the actually observed values, he may examine the results set forth in table 75. Here again the 45 tests of the suitability of the multiple regression equation involving stature, weight, and age with two trivial exceptions (+2.6 calories =0.16 per cent and +3.1 calories =0.19 per cent) indicate the superiority of these equations over the 5 other methods which have been tested. The values for the larger series (IV-VII and totals) range from 0.73 to 14.30 per cent. Considered in their relation to the problem of the present chapter, that of the body-surface law, the tables of this and the preceding section show that results as good as or better than those obtainable from the constant of basal metabolism per square meter of body-surface can be obtained by Mometric formulas involving no assumption concerning the derivation of surface-area but based on direct physical measurements. To the practical application of these formulas we shall return in the two following chapters. II, COMPARISON OF BODY- WEIGHT AND BODY-SURFACE AS BASES OF PREDICTION IN MALE AND FEMALE INFANTS. Unfortunately our series of new-bom infants are not large enough to justify division into subseries for the purpose of testing the suita- bility of different methods of prediction by the treatment of the indi- viduals of one subseries as unknown. We must, therefore, test the value of the different methods of predicting the total heat-production of an infant by comparing the actually measured heat-production with that computed from constants based on the series to which it belongs.*' It seems worth while to test only the methods of predicting total heat-production from body-weight and from body-surface by the linear regression equations, and by multiple-regression equations based on both weight and stature. The linear equations required are: For male babies: For female babies: h= 25.156+ 34.517 U) h= 26.184+ 34.229 w ft = -31.703+749.914 ot A = -32.048+751.548 ai " Unfortunately the Du Boises have not as yet prepared a height-weight chart for infants and we are in consequence limited to the Lissauer formula, which may in time be discarded like the Meeh formula for adults. An extensive series of measurements made in conjunction with Dr. Fritz B. Talbot and according to the Du Bois plan of measurement has shown quite re- markable agreement between the surface areas of infants computed (1) by the Lissauer formula (2) by the Du Bois linear formula, t. e., so far as normal infants weighing up to approximately 10 kilograms are concerned. For infants weighing more than 10 kilograms the Lissauer for- mula gives results unquestionably too small. Measurements are now being collected for under- nourished and atrophic infants. 194 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. In male and female infants the deviations of the heat predicted by use of these equations from the actually measured heat-productions are: Boy babiet. Girl babie6 Average deviations with regard to sign: Prediction from weight —0.020 —0.093 Prediction from surface +0.118 +0.047 Average deviations without regard to sign : Prediction from weight 11.04 11.16 Prediction from surface 11.10 11.02 Square root of mean-square deviations: Prediction from weight 13.81 13.77 Prediction from surface 13.80 13.61 These results show how slender is the evidence furnished by infants for the assertion that "heat-production is proportional to body-surface and not proportional to body-weight." By the first criterion, surface- area is slightly better in the females but slightly worse in the males. The average deviations without regard to sign show that in the females prediction from body-surface there is an average error of 0.14 calorie per day less than in prediction from body-weight, but that in the males prediction from body-surface area by the Lissauer formula gives 0.06 calorie worse prediction ! Relying upon the square root of mean-square deviation for the most critical test, we note that there is a difference between the two methods of only 0.01 and 0.16 calorie per day! The differences are trivial in comparison with the average daily metabolism of over 140 calories for infants of both sexes. In short, body-weight and body-surface area are equally good for purposes of prediction. Turning now to the prediction of total heat-production from mul- tiple regression equations based on the whole series, we have the equations, For boy babies ;i= -22.104+31.050 t»+1.162s For girl babies fc= -44.901 +27.836 w+1.842» The theoretical heat-production for each infant has been cal- culated by these formulas and compared with the actually observed heat-production. The theoretical average deviation with regard to sign is zero and is actually —0.078 calorie per day in the males and —0.047 calorie per day in the females. The average deviation without regard to sign is 11.02 calories in the males and 10.84 calories per 24 hours in the females. Measuring the suitabiUty of the formulas by the square root of mean-square deviations we find 13.78 calories for the males and 13.53 calories for the females. Comparing these results with those secured by prediction from body-weight and body-surface above, we note that prediction from stature and body-weight simultaneously has given slightly better results than prediction from either body-weight or body-surface alone. A CRITIQUE OP THE BODY-SURFACE LAW. 195 12. RECAPITULATION AND DISCUSSION. According to Rubner's "law" or the body-surface "law" the heat- production of an organism is proportional to its superficial area. Otherwise stated, heat-production measured in calories per square meter of body-surface is a constant. In this chapter we have outlined the historical development of the physiologist's behef in the validity of this "law," have discussed certain experimental evidences for its inappUcability to man, and have tested its validity by the application of statistical criteria to the largest available series of data on human basal metabolism. Historically, the idea of proportionality between body-surface and heat-production was originally based upon the assumed physical law, confused by many physiologists with Newton's law of cooling, that heat-loss is proportional to the surface-areas of similar solids, and upon the further assumption that heat is produced to maintain the body- temperature constant. The idea of a causal relationship between body-surface and heat-production has frequently been strongly empha- sized in foreign writings and is distinctly to be inferred from those of a number of American writers. The vaUdity of the body-surface law has long been held in question by the workers at the Nutrition Laboratory. In a series of papers ^* its universal appUcability was challenged and it was stated that the loss of heat from the body-surface could not be considered as the deter- mining factor of metabolism. Certain factors, such as sex, age, and athletic training, were shown to affect the basal metabolism, even when measured on the basis of calories per square meter of body-surface, thus affording illustrations of exceptions to the so-called law. In dealing with the problem of the constancy of heat-production per square meter of body-surface in the hxunan species two pha ses must be recoguissed. The first is that of the constancy of heat-produc- tion within the same individual at different tim,es. The second is that of the constancy of heat-production per square meter of body-surface from individual to individual. From the side of controlled individual experimentation it has been ) shown That animals at different nutritional levels, or under varying <, external conditions, differ in their heat loss to a degree which can not ^ be explained by differences in body-surface. A man who fasted 31 days showed a decrease of 28 per cent in heat- production per square meter of body-surface. Squads of college men recently investigated on prolonged reduced diet at the International Y. M. C. A. College at Springfield gave ample corroborative evidence. Such experiments can be interpreted only as proof of the inappUcability ■* Benedict, Emnies, Roth, and Smith, Joum. Biol. Chem., 1914, 18, p. 139; Benedict and Roth, ibid, 1915, 20, p. 231; Benedict and Smith, ibid., 1915, 20, p. 243; Benedict and Emmes, Und., 1915, 20, p. 253: Benedict, ibid., 1915, 20, p. 263. 196 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. °ij!''\® ^^^c,6-area law to subjects in widely varying states of nutrition. Criticism will of course be at once directed against the use of such evidence. It will be contended that prerequisite conditions for the application of the surface law as outlined by Rubner ^ are like physio- logical conditions, such as nourishment, climatic influences, tempera- ture, and capacity for work. Just such adverse criticism has been made of conclusions drawn at the Nutrition Laboratory concerning the basal metabolism of normal and atrophic infants. In reply to such comment it is necessary to point out merely that the physiological states of the fasting man are by no means incompar- able with the conditions commonly existing in pathological subjects. Notwithstanding the fact that enormous variations in the previously mentioned physiological factors are invariably found, their metaboUsm has been treated by authors just as though the body-surface law were fully applicable. For example, in a report on a series of observations made in the Nutrition Laboratory on patients with severe diabetes ^ the metabolism of the diabetics was, compared with that foiuid in noimial individuals of like height and weight, i.e., of a somewhat thin and'emaciated type. The marked difference in metabolism found with diabetics when acidosis was present as compared with that when it was diminished or absent ®^ led to the conclusion that diabetes increases the metabolism approximately 15 to 20 per cent above that of the normal individual. When a wholly arbitrary normal standard value (obtained with a large number of individuals of whom the greater proportion were in full vigor) was used for comparison, Graham Lusk concluded *' that the emaciated diabetics with acidosis showed little or no increase in metaboUsm. If it is erroneous to apply the sxirface- area law to an individual normal subject throughout a prolonged fast, it is difficult to see the validity of applying it when there are such marked variations in conditions of noxirishment and bodily vigor as exist between the large group of normal persons and the group of emaciated diabetics. We must, however, in this connection, refer to the detailed discussion of the influence of rapid changes in nutritional level upon the basal metaboUsm on pp. 102-103. With the fasting individual it is evident that the body-surface law does not obtain. The differences in the fasting man at the beginning and end of the fast are by no means so great as the differences between pathological individuals, including diabetics, and the average normal vigorous individuals from whom the standard of comparison proposed by other writers has been derived. » Rubner, Arch. f. Hyg., 1908, 66, p. 89. " Benedict and Joslin, Carnegie Inst. Wash. Pub. No. 176, 1912. " It has been demonstrated that when the diabetics are without acidosis (for example, when following the remarkable Allen treatment), the metabolism is distinctly lower (Joslin, Am. Joum. Med. Sci., 1915, ISO, p. 485) than with acidosis, so that unquestionably the acidosis per le materially increases the metabolism. " Lusk, Science, 1911, n. n. 33, p. 434; ibid., Joum. Biol. Chem., 1915, 20, p. 599; Ibid., Science, 1916, n. s. 42, p. 818. A CRITIQUE OF THE BODY-SURFACE LAW. 197 There are even very real purely physical difficulties in the way of assuming that the superficial body-area can be considered a true meas- ure^of the heat-loss which is assumed ito bear a causal relation to heat- production. Heat-loss does not occur exclusively from the skin. A considerable proportion of the total heat generated is given off from the lungs through the warming of the air and through the vaporization of water. From a large number of experiments with human subjects at rest^ either with or without food, it is found that on the averagers per cent of the total heat for 24 hou^ is required to warm the inspired air; 10 per cent is lost as the result of vaporization of water from the luiiga-and 12.3 per cent from the vaporization of water from the skin.*' A recent critical study by Soderstrom and Du Bois *° indicates that with normal individuals somewhat more than 25 per cent of the total heat is lost in the vaporization of water from the lungs and skin. Turning from purely experimental tests to those in which the results of experimentation are subjected to statistical analysis, we may first note that the estimates of body-surface area upon which most of the conclusions have been based have been shown to be open to serious criticism. It is to the credit of D. and E. F. Du Bois that they have made possible greater precision in this phase of the work. In testing by statistical methods the validity of this "law" which has held a conspicuous place in the Uteratiire of metabolism for over a quarter of a century, we have started out from two interdependent fundamental assumptions which seem axiomatic. (a) The primary requisite in testing any biological law is to deter- mine quantitatively the degree of interdependence of the magnitudes of the variables which it connects. (6) The true test of the validity of a law is its capacity for predict- ing an unknown result. The chief argument used in the past in support of the body-surface law has been that heat-production shows the least variation from individual to individual when expressed in calories per square meter of body-surface. We have shown that this argument is nullified by the simple physical relationship between body-weight and body-surface. The surface areas of similar solids are not directly proportional to their weights, but to the two-thirds powers of their weights. Thus, in a series of individuals whose body-surface area has been determined by the Meeh formula, body-surface area must necessarily be less variable than body-weight. The ratio Body^urface ™^s*» therefore, also be less . , , . , Total heat vanable than Body-weight ' Since the body-surface measurements by the Meeh formula and by the Du Bois height-weight chart are very closely correlated, the •» Benedict, Carnegie Inst. Wash. Pub. No. 77, 1907, p. 476. M Soderstrom and Du Bois, Arch. Intern. Med., 1917, 19, 946. 198 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. same conclusion must also apply for the more modern method of body- surface measurement. The question as to whether heat-production is more closely related to body-weight or to body-sm^ace can be answered only by (a) deter- mining the correlation between each of these two characters and heat- production, or by (6) determining which of these two characters will give the closest prediction of the heat-production of an individual. The correlations between body-weight, body-surface as approxi- mated by the Meeh formula, and body-surface as indicated by the Du Bois height-weight chart on the one hand and gaseous exchange and total heat-production on the other have been determined. The correla- tions between body-weight and heat-production are of approximately the same magnitude as those between body-surface and heat-production. These results do not, therefore, justify the conclusion that metabolism is proportional to body-surface and not proportional to weight. Metab- olism is not proportional to either of these physical characters in an absolute sense. It is correlated very closely indeed with all three bodily measurements, stature, weight, and surface. While the differences between the constants are very slight and can in no case be looked upon as statistically significant in comparison with their probable errors, the correlation coefficients indicate a some- what closer relationship between body-surface and total heat-produc- tion than between body-weight and total heat-production. That this closer relationship between area and heat-production can not be taken as proof of the validity of "Rubner's law" as applied to human indi- viduals has been indicated. This point will receive attention below. In the past many physiologists have assumed that the heat- production of an individual should be given by h=whk where h =the heat-production of the individual, w =the weight of the individual, and h^ the mean heat-production per kilogram of body- weight in the standard series, or by h=aha where a = superficial area and ha =mean heat per square meter of body- area in the standard series. We have shown that far better results are given by the use of equations of the type {h-h) =r^H- {w-w) (h-h) ^ra,^'(a-a) where h, w, and a denote total heat, body-weight, and surface-area, the bars denote means, the sigmas standard deviations, and r the coefficient of correlation between the characters. When these equa- tions are used the heat-production of an individual can be calculated A CRITIQUE OF THE BODY-SURFACE LAW. 199 from body-weight with essentially the same degree of acciiracy as when body-surface is used as a basis of prediction. Since it has been shown in Chapter IV that both stature and body- weight have independent significance in determining the amount of the metabolism, we have attempted to predict heat-production by the simultaneous use of stature and body-weight. With such equations the errors of prediction from stature and weight are about the same as when using body-surface as a basis of pre- diction. Apparently there may be a slight superiority of prediction from body-surface area as estimated from the Du Bois height-weight chart, especially when the superior methods of prediction by the use of linear equa- tions developed in this volume are employed, but on the basis of the data at hand this superiority can not be asserted to be more than apparent. The investigation of the vaUdity of the body-surface law has not merely a theoretical interest but possesses material practical impor- tance. While of recent years Rubner's law has taken on the nature of an empirical formula to be practically applied, in origin it was groimded on the hjrpothesis that thermogenesis is determined by thermolysis. Or, it was assumed that coohng obtains as a cause of heat-production in the organism. As we look at the matter, the "body-surface law" is at best purely an empirical formula. It has furnished a somewhat better basis for the prediction of the metabolism of an unmeasured subject than does body-weight. The demonstration in the course of this investigation that by the use of proper biometric formulas the metabolism of an individual can be predicted from stature and body-weight with practically the same accuracy as from body-surface area robs "Rubner's law" of its imique empirical significance in clinical and other applied calorimetry. It also casts grave doubts upon any evidence which its superior power of prediction as compared with body-weight may be supposed to furnish in favor of its being a real physiological law. We have shown that the great supposed difference between body- surface area and body-weight as bases of predicting the metabolism of an unknown subject is largely due to the fact that fallacious methods of calculation have been employed. In so far as body-surface area, as estimated from the Du Bois height-weight chart, has any superiority as a basis of prediction, we believe that this has not been due to any causal relationship between body-surface area as such and metabolism, but that it is merely incidental to the fact that body-surface takes somewhat into account both body-weight and stature, each of which we have shown to have independent significance as proximate factors in determining the total metaboUsm. In this volume we have limited our investigation of the body-surface law strictly to its appUcability to variations within the human species, in short to its intra-spedfic and not its interspecific appUcabiUty. It is 200 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. proper, however, to point out that since the long existing doubts as to the validity of the older methods for the measurement of body- surface have been fully substantiated by the development of the linear formula of the Du Boises for adults and the photographic method, it is quite possible that more intensive work will draw into question the validity of the surface measurements upon which the evidence of the applicability of the law to animals in general depends. If the errors in the Meeh formula are as large as those pointed out by the Du Boises, one may also reasonably question the formulas for lower animals. It is thus probable that the computations of E. Voit, recently approved by Armsby, will need a radical revision. What influence this revision may have upon the general acceptance of the wider applicability of the so-called body-surface law awaits determination. Finally, in view of the facts that (o) the equations developed in this volume and the convenient tables ®^ which have been provided for the prediction of the basal metabolism of the individual from stat- ure, weight, and age deprive the "body-surface law" of its unique practical significance, and that (6) the evidence of an actual physio- logical nexus between body-s\irface area and metaboUsm is altogether inconclusive, it seems to us that the "body-surface law," as far as its ; supposed application to the hiunan individual is concerned, must play a very minor rdle indeed in future physiological discussions. The equations which we have given were designed primarily for the most exact work in the problem of metaboUsm during the period of adidt hiiman life. While for this period they are decidedly superior to prediction by means of the average heat production per unit of body surface in a standard series we would not at present recommend the discarding of the older methods of correcting for body size in compara- tive studies of metaboUsm. Body-weight, the two-thirds power of body-weight, and the more recent attempts at actual surface measurement must be considered in comparing organisms of very different physical configuration. We must, however, point out that our experience with the "body- surface law" in its application to the human individual indicates that extraordinary caution must be used in regard to aU of these methods. Eventually they will probably have to be replaced by standards similar to those developed for human adults in this volume. Until this can be done on the basis of adequate physical and experi- mental data we do not desire to have our results for adults generaUzed beyond the range of physical characters and age to which we have ourselves applied them. If this were done they might tend to hinder rather than to assist in the advancement of research. For the present at least, the older methods of comparison must stiU be appealed to in the inter-specific comparisons. " See Chapter VIII for a full discussion of these tables. Chapter VII. A COMPARISON OF BASAL METABOLISM OF NORMAL MEN AND WOMEN. I. HISTORICAL. Consideration of the problem of the relative metabolism of men and women dates from 1843, when Scharling,* whose results have been recalculated by Sond6n and Tigerstedt,^ found that a girl 19 years of age excreted a considerably smaller amount of carbon dioxide and a considerably smaller amount of carbon dioxide per kilogram of body- weight than a boy 16 years of age. Her actual carbon-dioxide produc- tion was less than that of two men of 28 and 35, but her carbon dioxide per kilogram of body-weight lay between that of the two adult men. He also foimd that a girl of 10 produced both absolutely and relatively less carbon dioxide than a boy of about the same age. Scharling con- cludes from these observations that there is a greater production of carbon dioxide by men than by women of the same age. Andral and Gavarret ^ worked with 37 men and 22 women. They conclude that throughout the whole of life there is a greater production of carbon dioxide by men than by women, and that between the ages of 16 and 40 men produce about twice as much carbon dioxide as women do. Unfortimately Andral and Gavarret have not recorded the weights of their men and women; it is therefore, impossible to make comparisons on the basis of relative heat-production, i.e., on the num- ber of calories per kilogram of body-weight or on the basis of the number of calories per square meter of body-surface. The data of Speck,* restated by Sond^n and Tigerstedt,* show higher metabolism in men than in women over 17 years of age, but the difference is reversed in the case of a boy of 10 and a girl of 13. In their classical monograph on the respiratory exchange and metabolism, Sond6n and Tigerstedt ° published an extensive series of observations on both men and women, in which the large respiration chamber in Stockholm was used. These results are comparable for the two sexes, although the observations were made under such conditions ' Schailing, Ann. d. Chem. u. Fhann., 1843, 45, p. 214. Kepiinted in detail in Ann. de chim. et phys., 1843, 3 B^r., 8, p. 478. ' Sonden and Tigerstedt, Skand. Arch. f. Physiol., 1895, 6, p. 54. * Andral and Gavarret, Ann. d. chim. et phys., 1843, 3 B6r., 8, p. 129. * Speck, PhysioloKie des menschlichen Athmens, Leipzig, 1892. * Sond£n and Tigerstedt, Joe. cit., p. 67. * SondSn and Tigerstedt, loc. at., p. 58. 201 202 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. as to exclude them for use as indices of basal metabolism. These authors based their comparisons on the carbon-dioxide excretion per hour per kilogram of body-weight and per square meter of body-surface. They express the relationship between the gaseous exchange of men and women as a proportion. Their end results are summarized in table 76. They conclude that in youth the carbon-dioxide production of boys is considerably greater than that of girls of about the same age and body-weight, but with increasing age this difference gradually becomes less and less, and finally in old age it disappears entirely. It must be noted here that the authors specifically state that it appears to them that new experiments are necessary before this problem can be completely solved. Table 7G.— Comparison of carbon-dioxide prodvction in men and women: data of Sondin and Tigerstedt. Age of males. , Age of females. COj per kilogram per hour, males. COj per kilogram per hour, females. Relative CO, production per kilogram. CO, per hour per square meter, males. CO, per hour per square meter, females. Relative CO, production per square meter. 7 7 1.149 1.133 100 : 101 26.27 26.61 100 : 99 9 9 1.207 0.850 100 : 142 26.89 20.78 100 : 144 10 to 11 11 1.0S5 0.845 100 : 131 27.88 21.75 100 : 128 12 12 0.997 0.743 100 : 134 26.49 20.14 100 : 132 13 to 14 14 0.980 0.661 100 : 148 27.12 18.22 100 : 149 15 15 0.813 0.601 100 : 135 23.54 17.16 100 : 137 17 17,30 0.814 0.522 100 : 156 24.18 15.53 100 : 156 30 to 50 40 to 50 0.499 0.554 100 : 90 16.55 17.94 100 : 90 67 65 0.407 0.390 100 : 104 14.24 12.04 100 : 113 In 1899 Magnus-Levy and Falk ^ published an extended series of observations on both men and women in which the Zuntz-Geppert respiration apparatus was employed. Although Johannson* had shortly before emphasized the importance of controlling muscular repose and had outhned his experience in the voluntary exclusion of muscular activity, these observations of Magnus-Levy and Falk represent the first comparative observations made upon both men and women in which particular attention was given to complete muscular rest; hence they are more nearly comparable with our experiments than any series published previous to 1899. The series with men comprise observations on 16 boys, 10 men between 22 and 56 years of age, and 5 men 64 years old and over. The series of women include observations on 9 girls, 15 women between 17 and 57, and 7 women of 71 years or older. The data as to age, weight, and height are recorded. The authors have Ukewise computed the values per kilogram per minute and per square meter of body-surface per minute. In their comparisons of the values obtained with men and women on the basis ' Magnus-Levy and Falk, Arch. f. Anat. u. Physiol., Physiol. Abt., Suppl., 1899, p. 314. ■ Johannson, Skand. Arch. f. Physiol., 1898, 8, p. 85. BASAL METABOLISM OP NORMAL MEN AND WOMEN. 203 of body-weight, they conclude that in middle life the gaseous metab- olism of women is approximately the same as that of men of the same age and body-weight. With children and old men and women, the females have a slightly less (5 per cent) metabohsm than the men. The authors also point out that, owing to the larger proportion of body-fat, women would have a metabolism per unit of active pro- toplasmic tissue greater than would men. Following the work of Magnus-Levy and Falk there was a period of about 16 years in which little was done on the problem of the differ- ences in the metabolism of men and women. Many observations were made on men, but there were relatively few determinations of basal metabolism on normal women. In 1915, however, Benedict and Emmes® returned to the problem, basing their calculations on the 89 men and the 68 women designated as the original Nutrition Labora- tory series. In this study they introduced what we have here called the selected-group method of comparison, a method which marked a distinct advance in the comparison of the metabolism of classes of individuals. This method, in a somewhat modified form, we shall employ extensively in this chapter. 2. COMPARISON OF METABOLISM OF MEN AND WOMEN ON THE BASIS OF GENERAL CONSTANTS. In this section we shall base our comparisons of the basal metabol- ism of the sexes upon the constants for the series of individuals as a whole. This method of testing the existence of a sexual differentiation in metabohc activity is not, in our opinion, so valuable as the further development of the selected-group method of Benedict and Emmes in the following section. For the sake of completeness, however, both methods of analysis must be employed. Consider, first, the average gross heat-production in calories per 24 hours in series of adults. For the 72 individuals of the Gephart and Du Bois selection, the 64 others, and the 136 men the averages are 1623, 1641, and 1632 calories, respectively. For the 68 original, the 35 sup- plementary, and the total 103 women the daily heat-productions are 1355, 1339, and 1349 calories, respectively. Thus the heat-production of the average woman is roughly 300 calories per day less than that of the average man, when both are measured in muscular repose and at a period 12 hours after the last meal. Thus in adults gross metabolism is markedly less in women than in men. Note, however, that these values are uncorrected for weight, stature, and age in both sexes. But women are on the average smaller than men. In either sex large individuals produce on the average more heat than smaller ones. In any discussion of the relation of metabolism to sex it is necessary to correct for this difference in size. Turning to average heat-produc- ' Benedict and Emmea, Joum. Biol. Chem., 1915, 20, p. 253. 204 A BIOMETKIC STUDY OF BASAL METABOLISM IN MAN. tion per unit of body-weight or body-surface, we note that in the 72 men constituting the Gephart and Du Bois selection the average heat- production is 25.8 calories per kilogram of body-weight, in the 64 other men it is 25.6 calories, while for the total 136 men it is 25.7 calories. In the 68 original women it is 25.4 calories, in the 35 supplementary women it is 22.7 calories per kilogram, while in the whole series of 103 women it is 24.5 calories. On the basis of body-surface area the average heat-productions per square meter as estimated by the Meeh formula are 832 calories in the Gephart and Du Bois selection, 828 calories in the 64 men not included in the Gephart and Du Bois selection, and 830 calories in the whole series of 136 men. The comparable values for the women are 772 calories for the 68 original women, 715 calories for the 35 supplementary women, and 753 calories for the whole series of 103 women. With the measurement of body-surface area furnished by the height-weight chart we find average heat-productions per square meter of body-surface area of 927 calories for the Gephart and Du Bois selection, 924 calories for the 64 other men, and 925 calories for the whole series of men. For women the values are 865 calories for the 68 original women, 820 calories for the 35 supplementary women, and 850 calories for the whole series. If we extend the comparison to the 8 men and 7 women studied by Palmer, Means, and Gamble,'" we find that the average daily heat- production of men is 1657.4 calories, whereas in women it is 1468.7 calories. In men the average heat-production per kilogram of body- weight for a 24-hoiU' period is 23.36 calories, whereas in women it is 21.77 calories. Expressing heat-production in calories per square meter of body-surface per 24 hours we find that the results for men and women stand in the ratio 784 : 718 calories when siirface is estimated by the Meeh formula and in the ratio 941 : 919 calories when surface is estimated by the Du Bois method. These results, due to the experi- ence of other investigators, will be tested by other criteria on p. 217, and shown to be in full accord with oiu* own findings throughout. It is now desirable to look at the evidence from a quite different angle. Instead of depending upon average heat-production or average heat-production per unit of body-weight or body-surface for a basis of comparison of men and women, we may inquire what amount of change in heat-production would be associated with a variation of a definite amoimt from the mean body-weight or the mean body-surface in the two sexes. If women show a smaller change in heat-production associated with a variation of the same amount in a physical dimension we must conclude that metabohsm is less in women than in men. If we consider these variations in quantity of heat set free per unit of body- "> Palmer, Means, and Gamble, Joum. Biol. Chem., 1014, 19, p. 239; Means, Und., 1015, 21, p. 263. BASAL METABOLISM OF NORMAL MEN AND WOMEN. 205 weight or body-surface we note from equations on page 170 that in the 72 individuals of the Gephart and Du Bois selection heat-production increases 16.7 calories per 24 hours for each increase of 1 kilogram of body-weight above the average. In the 64 men not included in the Gephart and Du Bois selection the increase is 15.4 calories. In the 136 men it is 15.8 calories. For comparison we note that in the 68 original women the increase is 10.5 calories, in the supplementary series it is 6.3 calories, and in the whole series of women it is 8.2 calories. Turning to the change in heat-production with variation in body- siuf ace, we note from the variable term of the appropriate equations (page 170) that the change for body-siurface as measured by the height- weight chart is very different from that for body-surface as measured by the Meeh formula. Working, therefore, with each of the two formulas separately, we find that with surface measured by the Meeh formula the two groups of men show a change of 822 and 764 calories for a variation of 1 square meter of body-surface, while for the 136 men the change is 783 calories. In the 68, 35, and 103 women the values are 506, 316, and 400 calories respectively. When superficial area is measured by the height-weight chart the change in heat-production for a variation of 1 square meter of body- surface is 1026, 1101, and 1070 calories in the 72, 64, and 136 men of the three groups compared, whereas in the groups of 68, 35, and 103 women the values are 808, 500, and 639 calories respectively. Turning back to the diagrams of preceding chapters showing the heat-production of subgroups of men and women, we note that the smoothed averages, and generally the actually observed averages as well, are higher in men than in women. This is clearly shown in dia- grams 13 and 17 of Chapter IV, in which the individuals are arranged according to stature and according to body-weight. Again in diagrams 20-22 of Chapter V, showing the gross heat- production and heat-production per unit of body-weight and body- surface in men and women of different ages, the lines for the men are consistently higher than those for the women. The same is true, with few exceptions, of the empirical means. Now the highly important result of all these methods of comparison is this: Without exception the tests based on general population constants indicate higher metabolism in the man. 3. COMPARISON OF METABOLISM OF MEN AND WOMEN BY USE OF GRADUATION EQUATIONS. We now turn to a comparison of men and women on the basis of a method which is in essence an extension and modification of the selected- group method of Benedict and Emmes." Instead of comparing the " Benedict and Emmes, loc. cit. Magnus-Levy and Falk, loe. cit., used essentially the se- lected-group method but with wholly inadequate data. 206 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. averaged constants of a group of women with the empirical average of a group of men selected for their approximate agreement in stature and body-weight, we compare the averages for the groups of women selected for stature, body-weight, or both stature and body-weight, or for stature, body-weight, and age with the smoothed or theoretical averages for men of the specified physical dimensions. The method is essentially the same as that which has been followed in certain preceding sections. We calculate the theoretical heat- production of female individuals from constants based on the series of men, and by comparison of the empirical means with the average of the theoretical values we determine whether the women have a higher or a lower metabolism than would be expected if they were men of the same physical dimensions. For a first test of the existence of sexual differentiation we classify the women according to (o) body-surface area as determined from the Du Bois height-weight chart, (6) body-weight, (c) stature, and (d) age. The predicted total heat-production has been estimated by means of the regression equations for total heat on physical characters and age in the total male series.^'' In using these equations we have started from the simplest and advanced to the more complex, laying the results attained by each of the methods before the reader, who may therefore trace the growth of the underlying conceptions of our methods and convince himself that the results due to the more complicated processes are not attributable to some error in the more recondite reasoning. We first of all compare the values of the metabolism constants actually obtained for women with those which are calculated from their weight, from their stature, and from their body-surface area considered independently of each other and of age. Thus in working with body-surface we determine whether women as a class have a higher or a lower basal metabolism than men of the same superficial area. In doing this we disregard body-weight, stature, and age. Similarly, in dealing with equations in- volving constants for body-weight we disregard stature, body-surface, and age. In the second attack upon the problem we base our predictions of heat-production in women upon an equation involving the con- stants for body-weight and stature in men. Thus body-surface (which is of course largely determined by stature and weight) and age have been disregarded. " The analysis in Chapter VI has fully demonstrated the fallacy of predicting total heat- production by multiplying body-weight or body-surface by the average heat-production per unit weight or per unit surface in the standard series. We shall not, therefore, give the results of com- parison on that basis further than to say that with individuals grouped according to body-weight and body-surface area, as in tables SO and 81, the average actual heat-production of the groups of women is lower than that based on male constants in all the 12 subgroups classified with respect to body-surface and lower than that calculated from the average production per kilogram of body-weight in the men in 10 of the 13 groups of women classified according to body-weight. BASAL METABOLISM OF NORMAL MEN AND WOMEN. 207 Finally we have employed an equation in which prediction of heat- production is made from weight, stature, and age. The characteristic equations for the calculation of total heat- production from age, surface, weight, and stature considered alone are: ft= 1823.80-7.15 o h = -254.546-h 1070.454 o. h= 617.493-1-15.824 u) A =-1237.637-1-16.589 8 where A = total heat, a=age, ac= body-surface area by the Du Bois height-weight chart, w= body-weight, and s= stature. Employing these equations, we have calculated the theoretical heat-production of each individual woman on the assumption that she is a man of like character. The difference between her observed metabohsm (24-hour period) and her theoretical metabolism has then been determined by taking (measured metabolism) less (theoretical metabohsm) Thus a negative sign denotes a deficiency in the actual as com- pared with the normal heat-production. Table 77. — Differences in the metabolism of men and women, women classified according to age. Age. N Mean total heat- produc- tion. Prediction from age. Prediction from weight and stature. Prediction from weight, stature, and age. Mean predicted total heat. Actual les9 pre- dicted. Percent- age differ- ence. Mean predicted total heat. Actual less pre- dicted. Percent- age differ- ence. Mean predicted total heat. Actual leas pre- dicted. Percent- age differ- ence. 15 to 19 20 to 24 25 to 29 30 to 39 40 to 64 55 to 74 12 35 20 13 13 10 1371.4 1370.9 1334.7 1347.3 1368.0 1253.1 1698.0 1666.1 1635.6 1569.2 1487.2 1379.3 -326.6 -295.2 -300.9 -221.9 -119.2 -126.2 19.2 17.7 18.4 14.1 8.0 9.1 1392.9 1444.3 1399.9 1466.6 1600.2 1540.1 - 21.5 - 73.3 - 65.2 -119.2 -232.2 -287.0 1.5 5.1 4.7 8.1 14.5 18.6 1464.7 1487.1 1412.0 1416.6 1479.3 1313.2 - 93.3 -116.2 - 77.3 - 69.3 -111.3 - 60.1 6.4 7.8 5.5 4.9 7.5 4.6 In basing our conclusions concerning the existence of a sexual difference in metabohsm upon these differences we have examined them in three ways: (o) We have compared the average values of observed and theoretical metabolism in groups of women classified with respect to age, stature, body surface, and weight. (6) We have compared the average values of observed and of theoretical heat- production in groups of individuals classified by both stature and body- weight. Finally, (c) we have arranged the differences in order according to sign and magnitude and considered the evidence furnished by the frequency distributions of the individual deviations. The results of a comparison of the total heat-productions with those computed from age and classified according to the age of the women are shown in the first panel of table 77. The differences are without exception negative in sign, thus indicating that the metabol- 208 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. ism of^the women is lower than it would be in men of the same age if physical differences were disregarded. The differences range from 119.2 to 326.6 calories, or from 8.0 to 19.2 per cent. The results are represented graphically in the lower figure, A, of diagram 27. In this and the following four diagrams the upper row of dots represents the theoretical and the lower row the actually observed average basal metabolism for the groups of individuals." DiAGBAM 27. — Comparison of metabolism of men and women, classified according to age. Women [The differences between the theoretical and the actual heat- production is not as great in the older groups of women as in the younger. This point will be touched upon later. " In this and the following diagrams the theoretical heat-productions calculated from the linear equations should of course lie in a straight line except for the divergences due to the devia- tions of the individuals in the subgroups from the mid-ordinate values for age, stature, body- weight, and body-surface due to the errors of random sampling. The remarkable agreement of the best-fitting straight line and the calculated mean theoretical heat-production of the several groups of women furnishes a most gratifying justification of the system of grouping adopted. BASAL METABOLISM OF NOKMAL MEN AND WOMEN. 209 For the sake of a further comparison on the basis of an age grouping of the women we have used the metabohsm calculated from the equa- tion for the regression of heat-production on body-surface as estimated by the Du Bois height-weight chart in the men. The comparison is made in table 78. The results, which are represented graphically in the uppermost figure, D, of diagram 27, fully confirm the preceding. Without exception the groups of women show average values of metabohsm from 13 to 273 calories or from about 1 to 18 per cent lower than values computed on the assumption that their heat-production is identical with that of men of Uke weight, stature, and age. Table 78. — Differences in the metabolism of men and women, women cUutified according to age. Age. N Mean total heat- production. Prediction from body-surface. Mean predicted total heat. Actual less predicted. Percentage difference. 15 to 19 20 to 24 25 to 29 30 to 39 40 to 64 65 to 74 12 35 20 13 13 10 1371.4 1370.9 1334.7 1347.3 1368.0 1253.1 1384.1 1432.2 1391.8 1464.2 1568.6 1525.6 - 12.7 - 61.3 - 57.1 -106.9 -200.6 -272.5 0.9 4.3 4.1 7.4 12.8 17.9 Table 79. — Differences in the metabolism of men and women, women classified according to stature. Stature. N Mean total heat- produc- tion. Prediction from stature. Prediction from weight and stature. Prediction from weight, stature, and age. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. Mean predicted total beat. Actual less predicted. Per- cent- age differ- ence. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. 149 to 151 152 to 164 155 to 157 158 to 160 161 to 163 164 to 166 167 to 169 170 to 172 173 to 175 176 to 178 2 6 14 18 24 19 12 6 1 1 1259.5 1316.7 1310.8 1298.2 1376.8 1367.3 1379.0 1413.2 1430.0 1383.0 1267.0 1300.7 1353.9 1403.9 1450.7 1494.4 1550.7 1591.0 1666.0 1682.0 - 7.5 H- 15.0 - 43.1 -105.8 - 75.0 -127.1 -171.7 -177.8 -236.0 -299.0 0.6 1.2 3.2 7.5 5.2 8.5 11.1 11.2 14.2 17.8 1295.0 1327.2 1352.4 1407.8 1478.7 1531.5 1632.7 1645.2 1661.0 1894.0 - 36.5 - 11.5 - 41.6 -109.6 -103.0 -164.2 -153.7 -132.0 -131.0 -511.0 2.7 0.9 3.1 7.8 7.0 10.7 10.0 8.5 8.4 27.0 1336.0 1374.6 1346.6 1406.0 1445.4 1494.1 1603.4 1613.8 1680.0 1786.0 - 75.5 - 58.9 - 35.7 -107.8 - 69.6 -126.8 -124.4 -100.6 -160.0 -403.0 6.7 4.3 2.7 7.7 4.8 8.6 8.3 6.6 9.6 22.6 The results of a comparison of the actual heat-production in the women with that computed from stature in groups of women classified with respect to stature are shown in table 79. With one single excep- tion, that of the 6 subjects 152 to 154 cm. in height, the women of each grade of stature show a smaller actual average metabolism than that computed on the assumption that they were men of like stature. The lower figure. A, in diagram 28, which represents these results brings 210 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. out clearly the difference between the actual metabolism in women and the metabolism which would be found in men of the same stature. The width of the shaded zone increases from the lower to the higher statm-es. Thus the taller women show a greater deficiency in their metabolism than the shorter ones. ISO isj lis Diagram 28. — Comparison of metabolism of men and women, classified according to stature. Women Calculating the total heat-production of the women from the equa- tions for the regression of total heat-production on body-surface in men, and classifying with respect to body-surface, we have the mean calculated and the mean actual heat-production in the first section of table 80. Again the actual heat-productions of the women are without exception lower than those which they would have if they were men of like body-surface area. BASAL METABOLISM OF NORMAL MEN AND WOMEN. 211 The graphic representation of the results for the grouping by sur- face area in the lowermost figure, A, of diagram 29, shows a deficiency in metaboHsm throughout the whole range of variation in body-surface area. Apparently the difference between the actual and the computed metabolism is greater in the women of larger as compared with those of smaller area. Table 80. — Differences in the metabolism of men and women, women classified according to surface. Body- Burface. N Mean total heat- produc- tion. Prediction from body-surface. Prediction from weight and stature. Prediction from weight, stature, and age. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. 1.28 to 1.34 1.35 to 1.41 1.42 to 1.48 1.49 to 1.55 1.66 to 1.62 1.63 to 1.69 1.70 to 1.76 1.77 to 1.83 1.84 to 1.90 1.91 to 1.97 1.98 to 2.04 1 9 13 26 18 11 12 7 1 2 3 985.0 1191.8 1276.1 1285.1 1368.4 1463.4 1447.0 1416.6 1334.0 1673.5 1521.7 1137.0 1223.9 1299.3 1371.0 1443.8 1514.5 1592.1 1657.0 1769.0 1822.5 1890.0 -152.0 - 32.1 - 23.2 - 85.8 - 76.4 - 51.2 -145.1 -240.4 -435.0 -149.0 -368.3 13.4 2.6 1.8 6.3 5.2 3.4 9.1 14.5 24.6 8.2 19.5 1167.0 1246.2 1313.6 1380.8 1450.6 1518.5 1599.7 1677.0 1797.0 1895.0 1945.7 -182.0 - 54.4 - 37.5 - 95.7 - 82.2 - 65.1 -152.7 -260.4 -463.0 -221.5 -424.0 16.6 4.4 2.9 6.9 6.7 3.6 9.5 15.5 25.8 11.7 21.8 1006.0 1257.2 1294.1 1390.5 1439.4 1526.5 1552.0 1666.7 1621.0 1966.0 1834.3 - 20.0 - 65.4 - 18.0 -106.4 - 71.0 - 63.1 -105.0 -150.1 -287.0 -291.5 -312.6 2.0 6.2 1.4 7.6 4.9 4.1 6.8 0.6 17.7 14.8 17.0 Table 81. — Differences in the metabolism of men and wom.en, women classified according to body-weight. Body- weight. N Mean total heat- produc- tion. Prediction from body-weight. Prediction from stature and weight. Prediction from weight, stature, and age. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. Mean predicted total heat. Actual less predicted. Per- cent- age differ- ence. 34.6 to 39.6 39.6 to 44.5 44.6 to 49.5 49.6 to 54.5 54.6 to 69.5 59.6 to 64.5 64.6 to 69.6 69.6 to 74.6 74.6 to 79.5 79.6 to 84.6 84.6 to 89.6 89.6 to 94.6 2 8 18 27 19 11 4 7 1 2 1 3 1063.0 1197.9 1255.8 1303.8 1422.2 1449.2 1491.3 1381.7 1334.0 1494.5 1591.0 1646.0 1195.0 1284.0 1370.4 1441.3 1626.1 1597.7 1677.6 1745.7 1861.0 1905.0 2015.0 2083.7 -132.0 - 86.1 -114.6 -137.6 -102.9 -148.6 -186.3 -364.0 -527.0 -410.5 -424.0 -437.7 11.0 6.7 8.4 9.6 6.8 9.3 11.1 20.9 28.3 21.6 21.0 21.0 1203.0 1253.4 1324.8 1400.5 1477.9 1552.5 1628.5 1658.0 1797.0 1817.0 1873.0 1963.3 -140.0 - 55.6 - 69.0 - 96.7 - 56.7 -103.3 -137.3 -276.3 -463.0 -322.5 -282.0 -307.3 11.6 4.4 5.2 6.9 3.8 6.7 8.4 16.7 25.8 17.7 15.1 15.7 1060.5 1264.8 1308.8 1411.0 1484.9 1552.9 1552.0 1502.8 1621.0 1728.0 1944.0 1901.0 + 2.5 - 66.9 - 63.0 -107.2 - 62.7 -103.7 - 60.7 -121.1 -287.0 -233.5 -353.0 -265.0 0.2 5.3 4.0 7.6 4.2 6.7 3.9 8.1 17.7 13.5 18.2 13.4 The results of predicting the total heat-production of women from the regression of total heat on body-weight in men are shown in com- parison with the average actual heat-productions of women in the first section of table 81. 212 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. In every group the observed total production of the women is distinctly lower than it would be if the group were composed of men of Uke body-weight. The graphic representation of these results for grouping by body- weight in the lowermost figure, A, of diagram 30, shows the widest divergence of the actual from predicted heat-productions found in any of DiAGBAM 29. — Comparison of metabolism of men and women. Women classified according to body-surface. the four groupings, i.e., by age, stature, body-surface, and body-weight. The discrepancy is particularly great in the case of the heavier women. The largest divergence between the theoretical and the actual heat- productions is found when the theoretical values for the women are computed by assuming that the heat-production of a woman should BASAL METABOLISM OF NORMAL MEN AND WOMEN. 213 be the same as that of a man of like weight. The greatest increase in the amount of divergence between the theoretical and the actual heat- production is apparently found toward the upper limit of the range of the bases of classification. It seems reasonable, therefore, to assume (as a working hypothesis for further investigation) that body-weight DiAOKAM 30. — Comparison of metabolism of men and women, classified according to body-weight. Women rather than stature or body-surface is the primary proximate factor in bringing about this observable tendency for the women with greater stature and greater body-surface to show a relatively greater deficiency in metabolism. If this view be correct, the observed relationships for stature and body-surface would be the resultant of this primary inter- relationship and the correlations of both stature and area with weight. 214 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. We now apply a further test of the existence of a sexual differentia- tion with respect to metabolic activity in the human adult. In Chapter VI the value of multiple-regression equations, involving both stature and body-weight, for purposes of prediction has been conclusively demonstrated. We may now make use of equations of this type for predicting the amount of heat in calories per 24 hours which a woman would produce if she were a man of the same stature and body-weight. We shall thus avail oiurselves of all the advantages of the selected-group method employed in earUer papers from the Nutrition Laboratory," but by the use of suitable statistical methods shall avoid certain real difficulties encountered, but not overcome, by them. What we have done is in effect this: We have expressed the rela- tionship between heat-production and stature and weight in men as a mathematical plane, the coordinates of which give the most probable heat-production in individuals of any combination of statm-e and weight. Using this plane to predict the heat which a woman of given weight and stature would produce if she were a man, we have a series of check or control values which is free from the disadvantages of the empirical selected-group system. Using the equation /i = -314.613-f-13.129w-1-6.388s based on men we have computed the theoretical heat-production for each woman. We have treated the differences between the actual and the cal- culated heat-production in three ways. The distribution of the deviation of the actual heat-production of each woman from her computed production is shown in table 84, to be discussed below. The mean theoretical and actual heat-productions for groups of individuals classified by age, stature, body-surface by the Du Bois height-weight chart, and body-weight have been calculated, and the differences between theoretical and actual heat-production are recorded imder the caption "Prediction from weight and stature" in tables 77, 79, 80, and 81. Without a single exception the 39 comparisons indicate a lower metabolism in women. The differences between observed and theo- retical values range from 1.5 to 18.6 per cent in the case of groups classified according to age, from 0.9 to 27.0 per cent in the case of women grouped according to stature, from 2.9 to 25.8 per cent in the case of subjects arranged according to their body-surface, and from 3.8 to 25.8 per cent in the case of groups of women assembled on the basis of body-weight. " Benedict and Emmes, op. eit. BASAL METABOLISM OF NORMAL MEN AND WOMEN. 215 These results are expressed graphically in the second figure, B, of diagrams 27 to 30. These figures differ from those representing pre- diction from linear equations (A) in that the mean theoretical heat- productions do not lie in sensibly a straight line. The discrepancy is especially great in the classification by stature, where the disturbing influence of weight is very obvious. The difference between the graphs for body-weight and body-sur- face area is not quite so clearly marked as in the case of the hnear equations, but the more conspicuous deficiency in the metabolism of the heavier women is manifest. The results fully confirm the analysis on the basis of the linear equations. We now turn to the results secured when age as well as body-weight and stature is taken into account ia determining the theoretical heat- productions of the women. The equation, based on the 136 men, is ;i = 66.4730+13.7516 w;+5.0033s-6.7550 a By the evaluation of this equation for each woman by inserting her weight w, stature s, and age a, we obtain her probable heat-production on the assumption that she is a man of like weight, stature, and age. A comparison of the calculated average heat-productions of women grouped by age, weight, body-surface, and by stature is made in the final sections of tables 77, 79, 80, and 81. With one exception — that of the lowest-weight group containing only 2 women — ^which is niunericaUy insignificant, the 39 comparisons indicate that the actual heat-production is lower than it would be if these individuals were men of the same age, stature, and body-weight. The amount by which the women fall short of their computed metab- olism is measiu-ed by differences ranging from 4.9 to 7.8 when the classi- fication is on an age basis, from 2.7 to 22.6 when grouping is made by stature, from 1.4 to 17.7 when body-surface serves as a basis of classi- fication, and (disregarding the one exceptional case) from 3.9 to 18.2 per cent when the women are thrown into groups of like body-weight. The results are represented graphically in the third figure, C, of diagrams 27 to 30. Correction for age has perhaps tended to reduce slightly the differences between the observed and predicted-heat productions, but (with the one sUght exception already noted) they are nevertheless conspicuous and persistent throughout the whole range of whatever scale of classification is employed. The reader will note that when the correction for age, stature, and weight is made and the individuals are classified by age, the theoretical and the empirical heat-productions are separated by roughly the same distance throughout the whole age range. As far as this method of analysis is concerned, more conclusive proof of the existence of a sexual difference in the metabolism of male 216 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. and female adults could not be obtained. We now turn to another method of analysis. For p\irposes of comparison by group averages we have classified the women in a table of double entry, table 82. The entries with signs in this table are the differences between the theoretical and the actual average heat-productions for the groups of individuals having the weights and statures, indicated by the marginal columns. The differ- ences are given in calories and in the average percentage of the com- puted heat-production of each individual. The percentages follow the Table 82.- -Differences in metabolism of men and women, women classified according to stature and weight. Weight in kilogramE. Stature in centimeters. General averages. 149 to 157. 158 to 160. 161 to 163. 164 to 166. 167 to 178. 34.6 to 44.5 44.6 to 49.5 49.6 to 54.5 54.6 to 59.5 59.6 to 69.5 ■■ 69.6 to 94.5 General averages . - 76.6= 6.4 - 84.6= 6.7 JV=5 - 48.5= 3.8 - 67.5= 5.2 N=2 JV=b -131.0=10.1 - 53.0= 4.3 A- = l - 56.5= 4.5 + 40.0= 3.4 ^■=2 - 72.4= 5.9 - 53.1= 4.1 N=VO - 61.4= 4.7 - 6.66= 5.1 JV=7 — 6.2= 0.4 - 32.6= 2.3 JV=5 - 32.0= 2.4 - 64.0= 4.6 Ar=2 -172.0 = 12.6 =*= 00.0= 0.3 A'=3 -201.0=14.7 -198.0=14.5 N=l - 69.0= 5.1 - 53.5= 3.9 Ar=i8 - 39.5= 2.9 - 53.5= 3.8 N=4. -102.2= 7.4 -148.2 = 10.5 Ar=6 - 90.8= 6.4 - 75.7= 5.4 JV=9 -105.0= 7.4 -129.3= 8.8 JV=6 -196.5 = 13.4 -168.5 = 11.8 N=2 - 96.7= 6.8 -107.3= 7.5 N=27 + 48.3= 3.2 + 9.0= 0.4 Ar=4 -222.0=15.1 -209.0 = 14.4 JV=2 - 91.0= 6.3 - 38.6= 2.6 - 44.0= 2.9 - 94.0= 6.1 A' = 3 — 44.2= 2.9 - 67.2= 4.3 Ar = 5 — 55.7= 3.8 - 62.8= 4.2 Ar=19 + 189.0=12.8 +125.0= 8.1 'Ar='o -103.7= 6.7 - 38.5= 2.3 A'=6 -165.0=10.5 -187.0 = 11.7 Ar=l -155.3= 9.7 -155.9= 9.7 N=7 -112.3= 7.0 - 92.3= 5.7 Ar=i5 -134.0= 7.7 - 64.0= 3.8 N=l -263.0=15.9 -112.0= 7.0 -256.5 = 14.6 -220.0=11.2 //=2 -309.4 = 16.9 -222.4 = 12.7 A^=5 -421.0=23.3 -256.0 = 15.2 iV=3 -303.3 = 17.1 -194.3 = 11.3 Ar=i4 - 32.9= 2.7 - 45.7= 3.6 N = 22 -109.7= 7.3 -107.8= 7.5 iV=18 -103.0= 6.8 - 69.7= 4.5 iV=24 -164.3 = 10.3 -126.8= 7.9 Ar=i9 -163.9 = 10.1 -132.5= 8.3 A-=20 -112.3= 7.3 - 94.0= 6.2 AT =103 equality sign. A negative sign indicates that the women show a lower heat-production than would men of like characteristics. The theoretical heat-productions were calculated in two ways. The entries with signs in ordinary type are the differences between the observed and the theoretical heat-productions when the latter are computed from weight and stature only. The entries with signs in black-faced type are the differences between the actual and the theoretical heat-productions when the latter are calculated from weight, stature, and age. In arranging the data for this table the individuals have been assembled into somewhat larger and more arbitrarily limited groups for both stature and weight than when they were classified with respect BASAL METABOLISM OF NORMAL MEN AND WOMEN. 217 to one of these physical characters merely. This has been necessary in order to secure a number of individuals in the several compartments of the table. With the grouping of weight and stature adopted in the accompanying table, 28 of the 30 different combinations of stature and weight are represented by from 1 to 9 individuals each. When the theoretical heat-productions are computed from weight and stature, 26 of the 28 groups of women classified with regard to both stature and weight show lower average heat-productions than they would if they were composed of men falling in the same range of stature and weight. When weight, stature, and age are all taken into account, 24 of the 28 groups of women show lower average heat-productions than they would if they were men of similar weight, stature, and age. The general averages for all the individuals of given stature-groups or weight-groups are by both methods without exception smaller than would be found in men of Uke physical dimensions. The average defici- ency for the whole series of women is 94.0 calories per 24 hours when stature, weight, and age are taken into account, and 112.3 calories when stature and weight only are considered. The differences for the subgroups naturally vary widely because of the small numbers of indi- viduals. The general average percentage deficiency when weight and stature only are considered in the calculations of the theoretical heat- productions is 7.3 per cent. When age is taken into account as well as stature and body-weight, the deficiency is 6.2 per cent. Table 83. — Differences in the metabolism of men and women. Test based on data of Palmer, Means, and Gamble. Subject. Age. Weight. Height. Total calories per 24 hours. Calcu- lated heat. Actual less calcu- lated. Percent- age differ- ence. MiBsM.A. H Mias R. R 21 24 22 21 20 21 23 57.9 70.9 48.1 76.0 77.7 79.8 67.5 157 169 155 168 166 170 170 1434 1648 1143 1497 1635 1480 1444 1506 1725 1355 1810 1830 1853 1690 - 72 - 77 -212 -313 -195 -373 -246 4.8 4.5 15.6 17.3 10.7 20.1 14.6 MissH Misa D. L Miss F. M. R Miss L. F. W Miss R. Rob More conclusive proof of the existence of a sexual differentiation with respect to metaboUsm could hardly be expected. As a further test of our method we may compute the daily heat- productions of the 7 young women studied by Palmer, Means, and Gamble '® from the equation, based on our total men. The results appear in table 83. For every individual the actual heat-production is lower than it would have been in men of the same weight, stature, and age. The differences range from 72 to 373 calories per 24 hours. " Palmer, Means, and Gamble, Joum. Biol. Chem., 1914, 19, p. 239; Means, ibid., 1915, 21, p. 263. 218 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. In percentages of the theoretical heat-production they range from 4.5 to 20.1 lower than in men of the same weight, stature, and age. Thus this series of measurements by another group of observers, whether analyzed by the simple method of averages, as on page 204, or by the special methods here employed, fully confirms the conclusions drawn from our own data. We must however in this connection refer to certain considerations to be taken up in the following chapter (p. 232). A discussion of the data on the metabolism of German men and women recorded by Magnus-Levy and Falk is reserved for the following chapter (page 232). Table 84. — Deviations of metabolism of individtuil women from the masculine standard. (Note the high proportion of cases in which metabolism is lower.) Deviations from the male standard. Prediction from age. Prediction from body- surface. Prediction from stature. Prediction from body- weight. Prediction from stature and weight. Prediction from stature, weight, and age. +338 to +412 +263 to +337 +188 to +262 +113 to +187 + 38 to +112 1 4 3 3 9 1 4 1 4 7 1 8 2 3 9 1 3 9 - 37 to + 37 9 19 14 11 17 22 - 38 to -112 -113 to -187 -188 to -262 -263 to -337 -338 to -412 -413 to -487 -488 to -562 -563 to -637 -638 to -712 9 5 21 18 20 10 5 1 22 20 16 6 2 2 1 22 20 14 10 5 1 22 18 20 12 5 2 3 1 22 21 17 7 1 2 2 22 25 12 6 2 1 In the foregoing discussion comparisons have been made on the basis of differences in the empirical and theoretical average metabolism of individuals of various ages, statures, body-weights, body-surfaces, of various statures and body-weights, and of various statures, weights, and ages. As far as we know, these methods of comparison are free from all objections and give conclusive results. They fail, however, to give the distribution of the individual errors of predicting female from male metabolism due to the sexual differentiation which has been shown to exist. These errors we have seriated in a grouping of 75 calories range in table 84. The entries in the first four frequency columns of this table show the distribution of the deviations of the actual heat-productions of oiu" women from the values which would most probably be found if they were men of like age, stature, body-weight, or body-surface area BASAL METABOLISM OF NORMAL MEN AND WOMEN. 219 as measured by the Du Bois height-weight chart. The fifth column shows the deviations of the observed from the theoretical values when the latter are calculated by the simultaneous use of stature and body- weight. Finally, the last colmnn shows the deviations of the observed from the theoretical values when body-weight, stature, and age are simultaneously taken into account. Taking deviations of —37 to -|-37 as representing a central "zero" class, we note that by all methods there is a large excess of negative differences — i.e., of differences indicating a lower metaboUsm in women. Thus, on the basis of computation involving age there are only 5 individuals showing a metabolism more than 37 calories per day above their theoretical heat-production as compared with 89 showing a metabolism of over 37 calories below their theoretical heat-production. When computation is based on body-surface area, only 15 women show more than 37 calories per day above their theoretical heat- production as compared with 69 who are in defect by the same amount or more. On the basis of stature the individuals of the two classes stand in the ratio of 17 to 72; on the basis of body-weight in the ratio of 9 to 83; on the basis of both weight and stature in the ratio of 14 to 72, and on the basis of weight, stature, and age in the ratio of 13 to 68. Thus the results for individuals fully substantiate the conclusions based on averages above. 4. COMPARISON OF BASAL METABOLISM OF MALE AND FEMALE NEW-BORN INFANTS. The foregoing analysis of the data for adults has demonstrated beyond all question the differentiation of the adult male and female individual in man in respect to metabohc activity. From the stand- point of the student of the physiology of sex it is important to inquire whether this differentiation obtains only during the period of adult life or whether it is demonstrable in infancy. To test this matter, we naturally turn to Dr. Fritz B. Talbot's series of new-bom infants." The method to be followed is identical with that used above. We shall predict the metabolism of girl infants from constants based on the boys and determine the sign and the magnitude of the difference between the observed and calculated values. We require, therefore, equations showing the regression of total heat on stature (body-length), on weight, and on body-surface in the male infants. These are A =25.156-1-34.517 w, ft = -229.576 -K7.340s, ft = -31.703-1-749.914 a^ where ft = total heat per 24 hours, w = weight, s = stature (length), and 02,= body-surface area computed by the Lissauer formula. The results for the infants grouped by body-length are shown under the caption "Prediction from linear equations" in table 85. In three u Benedict and Talbot, Carnegie Inst. Wash. Pub. No. 233, 1915. 220 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. groups the average heat-productions predicted on the assumption that the subjects were boys of like body-length are higher and in three groups they are lower than the actual mean values. Thus, as far as this test goes, it furnishes no CAadence of a sexual differentiation in metabolism in new-bom infants. Table 85. — Tests for differences in metabolism of male and female infants. Prediction from Prediction from Female Mean linear equations. planar equations. infants actual classified total Mean Actual Percent- Mean Actual Percent- by stature. heat. predicted less age of predicted less age of total heat. predicted. predicted. total heat. predicted. predicted. 46.0 to 47.0 111.3 112.0 -0.8 0.7 118.3 -7.0 6.9 47.5 to 48.5 120.1 121.1 -1.0 0.8 119.7 +0.4 0.4 49.0 to 60.0 139.7 134.6 +5.1 3.8 133.5 +6.2 4.7 50.5 to 61.5 142.0 145.3 -3.3 2.3 146.9 -4.9 3.3 52.0 to 53.0 161.1 155.7 +5.4 3.5 158.4 +2.7 1.7 63.5 to 64.6 168.0 167.8 +0.3 0.1 172.3 -4.3 2.6 The differences between the actual heat-production and the theo- retical heat-production as calculated from the regression of total heat on body-surface in the boys are shown for groups of girl infants classi- fied according to body-surface by the Lissauer formula in the first section of table 86. Those calculated from the equation for the rela- tionship between total heat-production and body-weight in the boys appear in groups of various body-weights in the first part of table 87. Table 86. — Tests for differences in metabolism of male and female infants. Prediction from Prediction from Mean linear equations. planar equations. infants classified by actual total Mean Actual Percent- Mean Actual Percent- body-surface. beat. predicted less age of predicted less age of total heat. predicted. predicted. total heat. predicted. predicted. 0.170 to 0.186 109.0 106.0 +3.0 2.8 106.0 +3.0 2.8 0.187 to 0.203 122.1 116.4 +5.7 4.9 115.3 +6.9 6.9 0.204 to 0.220 120.8 125.3 -4.5 3.6 124.3 -3.5 2.8 0.221 to 0.237 137.6 140.3 -2.7 1.9 138.4 -0.8 0.6 0.238 to 0.254 153.1 150.9 +2.3 1.5 150.6 +2.6 1.7 0.255 to 0.271 163.1 164.9 -1.7 1.0 164.9 -1.7 1.0 0.272 to 0.288 181.5 177.0 +4.5 2.5 178.0 +3.5 2.0 By both of these methods of computation and analysis, the results are very similar to those found in the grouping by stature above. Some of the groups show a lower, others a higher, metabolism than the computed value. Taking these data as a whole they afford no evidence that the sexual differentiation in metabolic activity demon- strated for the adults obtains in new-bom infants. Using the multiple-regression equation, A =22.104 -l-31.049w-f-l.162s, for the boy babies, to predict the heat-productions of the girl babies BASAL METABOLISM OF NORMAL MEN AND WOMEN. 221 we have the deviations of the average actual from calciilated heat- productions shown under the caption "Prediction from planar equa- tions" in tables 85 to 87. These differences are sometimes positive and sometimes negative in sign. They show, therefore, that the actually observed heat-productions of the girl babies are sometimes higher and sometimes lower than they would be expected to be if they were boys of the same physical dimensions. As far as our data go they indicate, therefore, that on the average there is no sensible difference between the heat-productions of the two sexes in the first week of life. Table 87. — Tests for differences in metabolism of male and female infants. Prediction from Prediction from Female Mean linear equations. planar equations. infants actual classified by total Mean Actual Percent- Mean Actual Percent- body-weight. heat. predicted less age of predicted less age of total heat. predicted. predicted. total heat. predicted. predicted. 2.12 to 2.46 109.0 107.0 +2.0 1.9 106.0 +3.0 2.8 2.47 to 2.81 123.6 117.1 +6.5 5.6 116.1 +7.5 6.5 2.82 to 3.16 118.9 125.1 -6.3 5.0 124.6 -5.7 4.6 3.17 to 3.51 137.6 139.7 -2.1 1.5 138.4 -0.8 0.6 3.52 to 3.86 153.1 150.5 +2.6 1.7 150.6 +2.5 1.7 3.87 to 4.21 163.1 164.9 -1.7 1.0 164.9 -1.7 1.0 4.22 to 4.56 181.5 178.0 +3.5 2.0 178.0 +3.5 2.0 5. RECAPITULATION. Our analysis of the available data to ascertain whether men and women differ in the level of their metabolism has fully confirmed and considerably extended the conclusions reached by Benedict and Emmes in the first critical investigation of the problem. Our finding that the metabolism of women is significantly lower than that of men is based on three hnes of evidence. 1. The general averages are higher in men than in women. The average woman shows a daily heat-production about 300 calories less than the average man. If correction be made for body-size by expres- sing heat-production in calories per kilogram of body-weight, she shows an average heat-production of about 1.2 calories per unit of weight less than the man. If body-surface area be used as the basis of correc- tion, the woman shows daily heat-production of 77 calories per 24 hours per square meter as measured by the Meeh formula and 75 calories per square meter as measured by the Du Bois height-weight chart less than that of the man. 2. The deviation of heat-production of the individual woman from the general average associated with a deviation in her body-weight from the general average is less than comparable deviations in the man. When changes in heat-production associated with changes in other characters in men and women are compared by means of equations 222 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. based on the data as a whole, the line for the men is found to lie above that for the women. 3. When the theoretical heat-production of women is calculated by inserting their actual physical measurements in equations based on series of men, the actual heat-production is generally lower than the theoretical value. Larger women show a relatively larger deficiency in heat-production than smaller ones. The suggestion is made that body-weight is the primary factor in determining the greater deficiency in the heat-production of larger women, and that it is observable in the case of stature and body-surface area primarily because these are correlated with body-weight. The most critical test shows that when body-weight, stature, and age are taken into account women show about 6.2 per cent lower metabolism than men. Our results show that the differentiation of the sexes in metabolism is not evident in new-bom infants. The researches of Sond6n and Tigerstedt suggest that it is well marked in youth. Our findings are not in accord with the conclusion of Sond^n and Tigerstedt *^ "dass sich der im Kindes - und Jugendalter so deuthch imd scharf hervortretende Unterschied zwischen den beiden Ge- schlechtem aUmahlich verwischt, um endlich bei herannahendem Greisenalter ganz zu verschwinden." Instead we find the difference between the metaboUsm of men and women well marked throughout the period of adult life. " SoDdte and Tigerstedt, Skand. Arch. f. Physiol., 1895, 6, p. 96. Chapter VIII. STANDARD BASAL METABOLISM CONSTANTS FOR PHYSIOLOGISTS AND CUNICIANS. 1. THE NECESSITY FOR AND FUNDAMENTAL NATURE OF STANDARD METABOLISM CONSTANTS. While the discussions in the foregoing chapters should show that the determination of basal metabolism, or of variations in metabolism, in normal men and women presents a series of important physiological problems, it is quite evident that investigations of metabolism will receive the widest recognition and be of the greatest practical im-? portance if they can be extended to include measurements based on I individuals performing different amounts or kinds of work, subsisting <, on different diets, or suffering from various diseases. All such studies must be comparative. The metabolism of a group of individuals affected by any special condition has httle interest imless it can be shown to be the same as or to differ sensibly from the basal metabolism of a comparable group of normal individuals. For example, before any discussion of metaboUsm in individuals suffering from disease can be of value a series of non-pathological controls must be established to serve as a basis of comparison. The need for such control constants has been recognized with varying degrees of clearness by all those who have worked on the problem of the metab- olism of individuals suffering from disease.' While, as far as we are aware, it is now universally considered that the value of a metaboUsm determination on a pathological subject is strictly limited by the trustworthiness of the normal control with which it is compared, the establishment of suitable controls has been the subject of serious disagreement. "Controversies have raged more > Magnus-Levy and Falk (Arch. f. Anat. u. Phya., Physiol. Abt., 1899, Suppl., p. 315) stated one of the purposes of their lesearch begun in 1895 to have been the determination of nonnal metabolism data for comparison with their pathological records. Benedict and Joslin (Camegje Inst. Wash. Pub. No. 136, 1910) in 1910 published such determinations on normal subjects as were then available as a basis of comparison with their diabetic individuals. Lusk (Science, n. s. 1911, 33, p. 433) in reviewing this publication, emphasizes indirectly the importance and the inadequacy of control series. Again, in reference to investigations of respiratory metabolism in disease, Du Bois (Am. Joum. Med. Sci., 1916, 151, p. 785: also Studies Dept. Physiol., Cornell Univ. Med. BuU., 1917, 6, No. 3, Part II) says: "The main object of all investigators has been to determine the heat- pioduction of the patient while at complete rest 14 hours or more after the last meal. This is the so-called basal metabolism, and is of interest only when compared with the figures obtained on normal individuals. Since it is impossible to measure the metabolism of many of our patients when they are entirely recovered, it is necessary to calculate what the man's metabolism would be were he normal." 223 224 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. fiercely about the normal controls than about the pathological cases." '^ The difficulty has been twofold. First, the measurement of an ade- quately large series of individuals has been a very heavy undertaking. Second, the selection of the proper measure of metabolism in the control series has presented theoretical difficulties. In relation to the first of these we may quote a statement made as late as 1914: ^ "The impetus given to th^ study of gaseous and gross metabolism during the past decade has resulted in a large number of observations, both in the domain of physiology and pathology. Investigators in pathology are, how- ever, continually confronted by the paucity of normal data with which to compare their observations." Somewhat later Gephart and Du Bois * wrote : " The importance of the normal control has been emphasized so strongly by the serologists and the management of the control has been developed by them to such an art that it has seemed advisable to apply some of their methods of critique to the study of the respiratory metabolism These precau- tions .... have been made necessary by the fact that the normal control is usually the point of attack in serological controversies. Likewise in the study of metabolism the normal control is coming to be recognized as the weakest part of the experiment The literature is notoriously filled with false theories, of which by far the greater part would never have been promulgated if sufficient attention had been given to normal controls." Notwithstanding the confidence which has generally prevailed in the validity of the expression of metaboUsm in calories per square meter of body-surface area, the theoretical difficulties in the selection of control series have not passed unrecognized. "The selection of the proper normal base-line is a matter of extreme difficulty."® The detailed discussion in the preceding chapters of the factors associated with variations in basal metabolism suggests that the difficulties of the selection of proper controls has been underestimated rather than overestimated in the past. A brief consideration of the fundamental principles of the estab- lishment of standard or control constants to be used as a basis of com- parison in experimental work is in order. In the simplest cases the metabolism of an individual under any exceptional condition may be compared with his own basal metabolism which serves, therefore, as a standard or control. This is true, for example, in the case of variations in muscular activity, in rationing or in prolonged fasting. Even in the case of protracted illness, sugges- tion has been made of the possibility of using basal metabolism deter- minations upon the same individual, obtained subsequent to recovery, as a basis of comparison with the constants secured when the subject < Du Bois, Am. Joum. Med. Sci., 1916, 151, p. 785. * Benedict, Emmea, Roth, and Smith, Joum. Biol. Chem., 1914, 18, p. 139. * Gephart and Du Bois, Arch. Intern. Med., 1915, IS, p. 835. ' Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 858. STANDAHD BASAL METABOLISM CONSTANTS. 225 was in the pathological state. Such a course is, however, obviously impracticable in the vast majority of instances, since the duties or inclinations of the former patient may preclude periods of study sub- sequent to those made during confinement in a hospital. Furthermore, subsequent to a period of severe illness, there is no assurance in any single period of determinations that the subject has returned, or indeed that he ever will return, to the normal condition, or at least to the condition antecedent to the disease. Finally, because of the great variations in basal metabohsm from individual to individual, or under experimentally controllable conditions within the same indi- vidual, single comparisons have Uttle crucial value as a basis for generalization concerning the influence of special conditions on metab- ohsm unless the influence be very great. Practically, therefore, one is reduced in the great majority of cases, and especially in those of the greatest medical interest, to the statis- tical method of comparing observations on a group of individuals of a special class (the metabolism of which is being investigated) with those on individuals which do not possess the characteristics under considera- tion, or with "normal" individuals. In experimental work there are two ways in which control constants maybe determined : (1) The control observations may be made simul- taneously with those on the individuals of the special class under investigation. This method is necessarily followed when it is impossible to regulate external conditions with exactness and when individuals which are exactly comparable except for the particular characteristics under investigation must be employed — for example, in cases in which two mammals from the same litter, two groups of birds from the same clutch, or two lots of seedlings from the same parent plant must be utilized. (2) Standard determinations may be used as a basis of com- parison for all special groups. This method may be followed in cases in which it is impossible to obtain for simultaneous observation indi- viduals which are more nearly alike than those which can be obtained at other times, and in which the experimental technique is so highly perfected that there is no question but that measurements made at different times or by different observers are comparable within the limits of a very slight physical experimental error. In work on metabolism the second method is not merely justified but necessary. The jvLstification for the estabhshment of a standard control series instead of making normal control measurements for each pathological case lies in the fact that respiration chambers, calorimeters and other apparatus and technique essential for investigating basal metabolism have been brought to such a stage of perfection that, with proper chemical and physical standardizations at frequent intervals, technical errors may be disregarded. Furthermore, subjects upon whom basal metabolism determinations are made must comply so 226 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. exactly with a generally adopted set of conditions that there is no advantage in carrying out a normal control determination coincident- ally with the measurement of the metabolism of subjects suffering from any disease which may be under investigation. The necessity for estabUshing a standard control series rests upon two fundamental considerations. First, variation in basal metabolism from subject to subject is so great that to be of critical value a control series must comprise a relatively large number of individuals. Sec- ondly, the very limited equipment available in all the scientific insti- tutions of the world for carrjdng out trustworthy metabolism deter- minations and the great expenditure in time and effort necessary for making these determinations render it practically essential that data which may be regarded as standard for long periods of time be secured once for all, in order (in so far as possible) to set the limited equipment free for investigating the many pressing problems of metaboUsm under special conditions of exercise, nutrition, and disease. Hitherto control values have been established in two ways. First, the average value of metaboUsm per unit of body-weight or body-surface in a selected group of subjects has been used as a control value, and the observed metaboUsm of the hospital patient or other subject, expressed in terms of the same units, has been compared directly with this value. This is the method used by the majority of investigators in the past. Second, the average of the constants secured from a group of normal individuals as nearly as possible comparable, in physical characters, with the subjects of the special group under consideration is used as a standard of comparison. This is the selected-group method employed at the Nutrition Laboratory in a study of diabetes, of vegetarians and non-vegetarians, of athletes and non-athletes, and of men and women. The obvious objection to the population-average method of com- puting control values is that, in obtaining the fundamental constant, individuals of the most diverse physical characters are lumped together indiscriminately. From the physiological standpoint it is quite imrea- sonable to compare a standard value obtained from a large number of normal robust individuals with that derived from an emaciated patient in the clinic; this is evidenced by the fact that an individual imdergoing a prolonged fast may show a decrease of 28 per cent in his metaboUsm, as measured in relation to body-siuface, simultaneously with the assimiption of an emaciated condition quite comparable with that observed in some pathological subjects. The selected-group method in which pathological or other special groups are compared with normal individuals of Uke height and weight, i.e., of general anatomical and morphological similarity, is free from this very serious criticism, but is open to two others. (1) There is considerable opportunity for personal equation in the selection of the STANDARD BASAL METABOLISM CONSTANTS. 227 series of individuals to be used as a control in any specific instance; (2) because of the well-known and large variations in the metabolism constant from subject to subject the average value based on a small group of individuals may be either too large or too small by an amount determined by the probable errors of random sampling. It seems clear that some form of the selected-group method will fm*- nish the most satisfactory basis of comparison. Ideally one should find a method which will combine all the advantages, and reduce to a mini- mum all of the disadvantages, of the two methods hitherto employed. The results of the analysis in the preceding chapters have shown that four factors need to be taken into account in estimating the basal metabolism of a subject: sex, body-weight, stature, and age. The importance of body-weight in the selection of controls has been very generally recognized, at least tacitly, by all those who have expressed metaboUsm in terms of oxygen consumption, carbon-dioxide excretion, or calories produced per kilogram of body-weight. While the relation of stature to metabolism is not so obvious as that of body- weight, it has been shown in Chapter IV to be a character of independ- ent significance in the determination of metabolism. It has long been known that metabolism is related to age. In Chapter V this relation- ship has been expressed quantitatively. The method used here for the establishment of standard normal metabolism constants is essentially an extension of the selected-group method used earlier for various comparisons at the Nutrition Labora- tory. Instead of using the empirical average heat-production of an actually observed group of individuals, we shall give the "smoothed" or "graduated" values for groups of given age, stature, and body- weight as determined from equations based on all the available data. We thus obviate, as far as possible, the two main objections to the selected-group method: (c) the possibility of the influence of personal equation in the selection of the normal values to be used as controls in any specific case, and (6) the probable errors of random sampling attached to the control constants. The rather detailed application of the method in Chapters V, VI, and VII should have made the whole theory perfectly clear. There remains, therefore, merely the restate- ment of the equations and the tabling of a series of standard constants to be derived from them in the form most convenient for practical use. As shown in Chapter VI, p. 190, the multiple prediction equations based on the total adults of the two sexes are For men ^ = + 66.4730+13.7516u)+5.0033«-6.7550a For women ^ = +655.0955+ 9.5634 u)+1.8496s-4.6756o where h = total heat-production per 24 hours, w = weight in kilograms, s=stat\u*e in centimeters, and a=age in years. The evaluation of these equations, which are used in the calculation of the theoretical 228 A BIOMETEIC STUDY OF BASAL METABOLISM IN MAN. heat-production for any individual, requires merely the substitution of the actually measured weight, stature, and age. The tabling of these equations for a range of body-weight, stature, and age which will be encountered in practice results in a multiple-prediction normal standard, or an adult standard normal, with which the observed basal metabolism (daUy heat-production) of individual subjects may be compared. While the standard values are so arranged as to facilitate the comparison of individual subjects the reader must remember that because of the great variability of metabolism from subject to subject a comparison of a single subject of any special class furnishes a very slender basis for generalization concerning that class. It is only when reasonably consistent results are obtained from series of individual comparisons that generalizations can satisfactorily be drawn. The vaUdity of these formulas has been exhaustively tested in comparison with the methods hitherto employed in calorimetry in the section devoted to the body-surface law. It has there been shown that, when applied to the individual subjects of the largest series of basal metabolism data yet secured by a single group of observers, these formulas give the most satisfactory prediction of the basal metalsolism of an unknown subject of any method hitherto employed. With certain reservations concerning the range of age over which these formulas may be legitimately applied, we have the highest confidence in their validity. 2. TABLES OF MULTIPLE PREDICTION STANDARD METABOLISM CONSTANTS. For the convenience of those who have to estimate the metabolism of subjects from physical characteristics either in the clinical ward or in the physiological laboratory, we have prepared tables of the values of these equations for the various grades of body-weight, stature, and age. The form adopted for these tables has been determined by purely practical considerations. Because of the large number of permutations of weight, stature, and age, it is obviously out of the question to publish constants for each possible combination of these characters; but two tables of constants may be constructed from which the worker may obtain the most probable metabolism of a man (i.e., the average metabolism of a group of individuals of like weight, stature, and age) by simply adding together the entry for body-weight in table I and that for stature and age in table II. For women the comparable entries in tables III and IV will be used. These tables have been constructed to be entered by body-weight recorded to the nearest tenth of a kilogram, stature recorded to the nearest centimeter, and age to the nearest year. In following this course we have been under no illusions concerning these physical meas- urements, but have used the units which have become conventional among physiologists. A measurement of statiu-e to the nearest centi- STANDARD BASAL METABOLISM CONSTANTS. 229 meter is about the limit of accuracy. To retain tenths of kilograms is certainly weighing with a degree of refinement hardly justified by the continually changing state of the experimental object. Finally, when individuals are recorded to the nearest year of age we may remember that they are on an average a quarter of a year older or younger than the age to which they are assigned. Against these objections is to be urged the fact that measurements which are not made with great refinement are very apt to lack essential accuracy. Since these are the divisions of the scales which have been most generally employed by physiologists it has certainly not seemed desirable to replace them by coarser ones. Furthermore, it must be noted that our equations are not based upon a few observations, but upon over 100 determinations for each sex. Therefore, as a basis of generalization, they have a much higher degree of accuracy than any single observation or group of a small number of observations. The sources of error in using the multiple prediction tables are two. (1) The tables themselves are based upon a finite number of observations. In comparison with physiological measurements as a class, the number of measurements is very large; biometrically con- sidered it is small. Every constant in these equations is therefore, somewhat too large or somewhat too small because of the innate varia- bility of human individuals. If another group of subjects were added to the series upon which these tables are based the factors would be tlightly changed. The constants are subject to revision with increasing intensiveness or extensiveness of work, just as all physical and chemical constants are.® Until more data are available they must be taken as they are, with the xmderstanding that the standard has its probable error, just as have the individual metabohsm measurements which will be compared with it. (2) As we have repeatedly emphasized in the foregoing pages, every individual metabolism measurement considered as a basis for general- ization concerning the peculiarities of the individual upon which it is based (e.g. physical characteristics, pathological state, etc.) has a large probable error. Thus one can not compare the metabolism of a single individual of any specified type with the standard constant and use it as a basis of generalization. It is only when a series of individuals of the specified type are considered that generaUzations may be drawn. From the standpoint of arithmetical technique, the tables probably correctly represent the residts of the largest series of determinations on normal men and women with an error of not over 1 calorie per 24 hours.^ * We plan later to prepare a revised edition of these tables based upon more extensive data. ' The results could have been given in such a form that the final constants would have been arithmetically correct to less than a single calorie per 24 hours had decimal places been retained in the tables. This seemed a quite needless refinement. Those who desire may derive the theo- retical values to more places directly from the equations. The theoretical values in the scries of illustrations in this chapter were determined in this way. 230 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. In constructing these tables the constant term of the equation and the corrective term for body-weight are combined in table I for men and table III for women. The corrective term for stature and age is given in table II for men and table IV for women. These tables must be used in conjunction only. Thus table I or III must not be used to esti- mate the metabolism of an individual whose weight only is known. Tables II or IV must not be used to estimate the metabolism of an individual whose weight is unknown. The use of the tables presents no difficulty whatever. Three exam- ples follow: Man 27 years Woman 22 yean Woman 66 years old, 172 cm. in old, 166 cm. in old, 162 cm. in height, 77.2 height, 77.2 height, 62.3 kilos, weight. kilos, weight. kilos, weight. Prom table I 1128 From table III 1393 From table III 1251 From table II 678 From table IV 204 From table IV - 9 Predicted calories 1806 Predicted calories 1597 Predicted calories 1242 3. ILLUSTRATIONS OF PRACTICAL APPLICABILITY OF STANDARD MULTIPLE PREDICTION TABLES OF BASAL METABOLISM. In a foregoing chapter (VII) the practical usefulness of the equa- tions upon which these tables are based has been fully demonstrated in their application to a specific problem, that of the sexual differentiation in metabolic activity. It now remains to supply further illustrations of their range of usefulness by applying them to certain cases in which the individuals were measured by workers outside of the Nutrition Laboratory, in which the individuals fall outside the range of age or of physical form upon which the equations were based, or in which the subjects were in a particular physiological or pathological state, the influence of which upon metabolism is imder investigation. Illustbahon A. Txsts of Nobmalitt of Series of Determinations. In applied calorimetry the need to be met is practically always the same. One requires to know whether a special series of metabolism measurements agrees with a larger series of determinations taken as a standard. If the special series is made up of individuals characterized by some specific condition, e.g., rationing, exercise, or disease, the result of the comparison shows whether this specific peculiarity may or may not be considered to have a determining influence on the basal metabolism. Some special cases of this sort will be examined. As a first illustration of the practical usefulness of our multiple- prediction equations, we may consider the agreement between certain series of measurements by other observers and the standard which has been based upon the Nutrition Laboratory experience. Take first a series of young men and women studied by Palmer, Means, and Gamble * aijd discussed in relation to the problem of the body-surface ■ Palmer, Means, and Gamble, Joum. Biol. Chem., 1914, 10, p. 239. STANDARD BASAL METABOLISM CONSTANTS. 231 law by Means." The data for the application of the equations and the results of their application are shown in table 88 for the 8 men and in table 89 for the 7 women. In these and the following comparisons the differences are taken (actual metabolism) less (calculated metabolism) so that a positive sign indicates supernormal and a negative sign subnormal metaboUsm in a subject. In this regard the constants of this chapter differ from those in Chapter VI. The reason for the differ- ence seems a logical one. In that place we were seeking to determine empirically which of a series of methods proposed for predicting metab- Tabie 88. — Comparison of metabolism of men stiidied by Palmer, Means, and Gamble with normal (multiple prediction) standard. Subject. Age. Weight. stature. Actual daily heat- production. Calculated daily heat- production. Actual less calcu- lated meta- bolism. Percentage difference. Dr. W. W. P Mr. H. L. H Dr. W. S. W Dr. L. W. H Dr. P. H. P Dr.J.H.M Dr. J. L. G Dr. L. H.N 32 27 25 25 27 29 30 31 93.9 62.0 73.8 68.4 77.2 70.7 68.1 68.1 187 172 177 169 172 175 181 169 2004 1574 1660 1671 1620 1599 1679 1452 2077 1597 1798 1684 1806 1718 1706 1502 - 73 - 23 -138 - 13 -186 -119 - 27 - 50 - 3.5 - 1.4 - 7.7 - 0.8 -10.3 - 6.9 - 1.6 - 3.3 Table S9.— Comparison of metabolism of women studied by Painter, Means, and Gamble with normal (multiple prediction) standard. Subject. Age. Weight. stature. Actual daily heat- production. Calculated daUy heat- production. Actual less calcu- lated meta- bolism. Percentage difference. MissM.A.H Miss R. R 21 24 22 21 20 21 23 57.9 70.9 48.1 76.0 77.7 79.8 67.5 157 169 155 168 166 170 170 1434 1648 1143 1497 1635 1480 1444 1401 1534 1299 1594 1612 1634 1508 -1- 33 -1-114 -156 - 97 + 23 -154 - 64 + 2.4 + 7.4 -12.0 - 6.1 + 1.4 - 9.4 - 4.2 MissH Mies D. L Miss F. M. R MissL.F.W Miss R.Rob olism actually gives the closest approximation to the true value in a large series of subjects. We therefore determined which predicted with the Hnallest error, i.e., which gave the lowest value of (calculated metabolism) less (actual metabolism). But having established the best method and utilized the largest avail- able series of data uniformally obtained as the basis of our constants, we feel fully justified in taking these equations as our standard, and in considering that smaller series either do or do not agree with this * Means, Joum. Biol. Chem., 1915, 21, p. 263. 232 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. standard, as the actual constants may indicate. The differences are therefore taken (actual metabolism) less (calculated metabolism) to give the proper sign to the difference. Without exception the 8 men are subnormal in their daily heat- production. The differences range from 13 to 186 calories and are on an average 78.6 calories. Expressed as a percentage of the calculated heat-production, the differences range from 0.8 to 10.3 with a general average of 4.4 per cent. In the case of the women, in which the theoretical heat-production is calculated by inserting the values for weight, stature, and age of the individual under consideration in our equation based on 103 women, the deviation of the actual from the theoretical values is not so great. In 3 cases metabohsm is higher and in 4 cases lower than would be expected. The average difference is (-I-170 — 471)/7 = —43.0 calories. Thus while the young women are more nearly typical than the yoimg men studied by Palmer, Means, and Gamble, their individuals of both sexes show a tendency to a defective metabohsm rate. We have no suggestion to offer concerning the technical or physio- logical explanation of the apparent tendency of this series to subnormal metabolism. The suggestion may of course be offered that it is our standards which are at fault. There are various evidences that this is not the case. First of all, the observations upon which our standards are based have been made by a carefully standardized technique but by a nimiber of observers. Thus the probabiUty of an influence of personal equation is to a considerable extent reduced. The large nimiber and great diversity of individuals dealt with furnishes a strong guarantee for the validity of the constants. Furthermore the apphca- tion of our method to other series of data indicates supernormal metab- olism in comparison with our standards. Thus we have abstracted from the classical paper of Magnus-Levy and Falk ^° the ages, weights, and statiu-es of a nimiber of men and women and have calculated the total calories per 24 hours from their measurements of the respiratory exchange. The essential values are given in table 90. Of the 10 men 7 show a heat-production above standard as compared with 3 which show heat-production below standard. The deficiencies range from — 13 to —61 calories, whereas the excesses range from -f6 to -f-203 calories. With one exception the 14 women show a daily heat-produc- tion above normal. The excess ranges from 22 to 359 calories per 24 hours or from 1.6 to 25.7 per cent. The average excess for the 10 men is 54.5 calories, while for the 14 women it is 110.2 calories per 24 hours. The average percentage deviation from standard without regard to sign is 5.3 for men and 8.5 '» MagnuB-Levy and Falk, Arch. f. Anat. u. Phyaiol., Physiol. Abt., Suppl. 1899, pp. 314-381. Tables I and III. STANDARD BASAL METABOLISM CONSTANTS. 233 for women. Regarding signs, the men show an excess of 3.7 per cent and the women an excess of 8.5 per cent. Thus the adult series of Magnus-Levy and Falk show supernormal metabolism when compared with the standard which we have adopted, whereas the subjects examined by Palmer, Means, and Gamble show a subnormal metabolism. If, as judged by the Palmer, Means, and Gamble series, our standards predict a metabolism somewhat too high, when judged by the Magnus-Levy and Falk series they predict a basal metaboUsm somewhat too low. Oiu' standards can not be changed without making the results of one or the other of these groups of observers appear much more abnormal than they now seem. Table 90. — Metabolism of the German men and women studied by Magnus-Levy and Falk compared with American normal (multiple prediction) standard. Name and number. Age. Weight. Stature. Actual daily heat- production. Calculated daily heat- production. Actual less calcu- lated meta- bolism. Percentage difference. Men. 1. Rud 2. L 3. Hutt 4. W 5. B 6. Piof. Z 7. Dr. M.-L 8. Dr.L.-Z 0. Sp 10. Schm Women. 1. B.K 2. G.D 3. W. Spr 4. O.K 6. L. Gr 7. M.W 8. H.M 9. H. Sch 10. M. Kl 11. E. Spl 12. L. W 13. Schw. M 14. A. Sche 15. Br. K 43.2 50.8 53.0 56.6 58.0 65.0 67.5 67.5 82.7 88.3 31.0 32.2 37.9 39.0 47.2 49.4 51.2 54.0 54.0 61.3 61.0 62.7 68.2 76.5 148(=i=) 153 153 170(=fc) 161 161(*) 167 167 175 176 135 133 142 139 147 159 157 152 156 156 167 155(?) 159 169 1333 1315 1527 1519 1510 1498 1608 1621 2030(?) 2019(?) 1073 1109 1204 1344 1345 1355 1466 1529 1403 1758 1508 1602 1612 1571 1239 1328 1385 1316 1453 1475 1661 1682 1883 2013 1014 1031 1117 1168 1280 1328 1304 1368 1381 1399 1454 1420 1499 1573 -1- 94 - 13 +142 -1-203 + 57 -I- 23 - 53 - 61 -1-147 + 6 -t- 59 -I- 78 + 87 -t-176 -I- 65 + 27 -t-162 -H61 + 22 -1-359 -1- 54 -1-182 -M13 - 2 -1- 7.6 - 1.0 +10.3 + 13.4 + + + + 3.9 1.6 3.2 3.6 7.8 0.3 + 5.8 + 7.6 + 7.8 +15.1 + 5.1 + 2.0 +12.4 +11.8 + 1.6 +25.7 + 3.7 +12.8 + 7.6 - 0.1 Possibly such tendencies to subnormal or supernormal metabolism as those seen in the two groups of men and women just studied may be due merely to errors of random sampling in the selection of the subjects. This seems, however, highly improbable. To another possible explana- tion we shall return in a moment. That such tendencies are not necessarily characteristic of subseries is evident from the following further illustration. Table 91 contains the physical data and the actual and computed heat-production of a number of men studied at the Nutrition Labora- 234 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. tory after the tables for the present volume were closed." For per- mission to use the constants of these men in advance of their publi- cation elsewhere we are indebted to our associates Dr. T. M. Carpenter, Mr. L. E. Emmes, Miss M. F. Hendry, and Dr. P. Roth. In 13 cases these subjects showed a basal metaboUsm of from 24 to 328 calories less than would have been expected from their stature, weight, and age, whereas in 18 cases they were characterized by a basal metab- Table 91. — Comparison of metabolism of series of men recently investigated by Carpenter, Em,mes, Hendry, and Roth, with normal (multiple prediction) standard based on earlier Actual Calculated Actual Subject. Age. Weight. Stature. daily beat- production. daily beat- production. less calcu- lated meta- bolism. Percentage difference. W. G. S 19 63.5 171 1704 1667 -1- 37 + 2.2 E.R.K 20 69.0 168 1812 1721 + 91 + 5.3 A.S.P 21 69.3 169 1733 1723 + 10 + 0.6 J.L.G.* 21 65.5 163 1600 1641 - 41 - 2.5 G.C.G 22 71.3 171 1874 1754 -t-120 + 6.8 R.T.V 22 65.S 175 1610 1698 - 88 - 5.2 H.H.H 22 71.5 173 1793 1767 -f- 26 + 1.6 J.F.T 22 63.8 188 1750 1736 + 14 + 0.8 P.G.H 22 62.1 176 1549 1515 + 34 + 2.2 R.K.B 22 65.8 179 1694 1718 - 24 - 1.4 C.A.C 22 64.9 180 1656 1711 - 55 - 3.2 A.C.B 22 77.6 175 1533 1861 -328 -17.6 H. A. M 23 23 63.5 60.8 174 178 1702 1827 1655 1638 + 47 +189 + 2.8 +11.6 S.N.G W.J.S 23 56.5 172 1330 1549 -219 -14.1 H. O 23 23 67.2 51.1 172 161 1628 1258 1696 1419 - 68 -161 - 4.0 -11.3 C.F.M O.A.G 24 66.8 166 1788 1653 +136 + 8.2 T.H.N 24 69.1 190 1868 1805 + 63 + 3.5 A.G.N 24 59.9 172 1600 1589 + 11 + 0.7 F. S 24 24 24 67.4 76.1 61.4 172 181 174 1515 1863 1632 1554 1857 1619 - 39 + 6 + 13 - 2.6 + 0.3 + 0.8 W. F. M C.S.B L.J.T 25 59.6 176 1471 1696 -125 - 7.8 L.F.F 25 67.5 167 1606 1524 + 82 + 6.4 J.A.C 25 59.6 177 1663 1603 + 60 + 3.7 H. B 25 26 64.6 61.8 166 167 1482 1493 1617 1576 -135 - 83 - 8.3 - 5.3 G.A.B K.B.C 26 79.8 177 1759 1874 -115 - 6.1 K. G. M 32 44 68.8 64.3 171 170 1889 1572 1652 1504 +237 + 68 +14.3 + 4.6 R.W.P * J. L. G., aged 20 yeara and 6 months b considered 21. olism from 6 to 237 calories higher than the theoretical value. Had the sample been exactly tjrpical of the standard control series the ratio should have been 15.5 : 15.5 instead of 18 : 13. Thus there is a devia- tion of only 13 — 15.5 = 2.5*1.9 from the equality which should result if prediction could be made without a bias toward too high or too low values. " These aubjects will be included with such others as may become available in any subse- quent revision of our prediction tables. STANDARD BASAL METABOLISM CONSTANTS. 235 The most widely divergent individuals are A. C. B. with a metab- olism which is subnormal by 17.6 per cent and K. G. M. with a metab- olism which is supernormal by 14.3 per cent. Of the remaining 29 men only 3 deviate more than 10 per cent from the standard. Taking the series as a whole, the average observed heat-production is 1653.35 calories whereas the average calculated heat-production is 1661.03 calories. Thus for 31 individuals the average error of our multiple prediction formula is only -|-7.68 calories per day. This is only 4-0.46 per cent of the predicted value. If the individual differences between the predicted and the measured daily heat-productions of these men be considered without reference to their sign, i.e., without regard to the fact that some are subnormal while others are super- normal, we find that there is an average difference of ±87.87 calories. Thus by the use of our equations we have been able to predict the heat-production of 31 subjects with an average (±) error of 5.30 per cent. This series may therefore be regarded as quite typical of the standard, and might in consequence be legitimately employed for any rationing or other metabolism experiment. Returning to the discrepancy between the series of measxirements by Magnus-Levy and Falk and our standard basal constants, we may note that in addition to the two possible explanations suggested above — i.e., faulty technique and errors of random sampling in the selection of the subjects — another must be considered. It is quite possible that the German and American populations from which these subjects were drawn are differentiated with respect to the magnitude of their metab- olism. Some further light may be thrown upon this question by com- puting the metabolism of the German girls, women, and old women from the equation based on the 136 American men. In doing this we are determining what the heat-productions of these individuals should be if they were American men of Uke stature, weight, and age. As fully discussed in Chapter VII, comparison of the actual with the theo- retical heat-productions will then show whether German women show a higher or a lower metabohsm rate than American men. The results are set forth in table 92. Leaving the girls out of consideration for the moment we note that of the 17 women from 17 to 86 years of age all but 5 show a daily heat- production in excess of that computed on male standards. The deficiencies range from —39 to —211 calories with an average of —94.2 calories, whereas the excesses range from +3Q to -|-369 calories with an average of 152.0 calories. For all the women the average daily excess is (1824- 471)/17= 79.6 calories. Expressing these differences in relative terms, we note that the German women range from 11.8 per cent below to 39.3 per cent above the standard male values. The average for the 5 women who fall below the masculine standard is 5.8 per cent, while the average for the 236 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 12 women who have a metabolism above this standard is 14.0 per cent. For the whole series, regarding signs, the average excess is 8.2 per cent. Now data are not as yet available for determining the real signifi- cance of these actually demonstrated differences. They may be due to defective technique, although we beheve that other students of human metabohsm will agree with us in holding the manipulative features of Magnus-Levy's work in the highest regard. They may represent real physiological differentiation, possibly due to differences in plane of nutrition ^^ or in muscular training (to be discussed under Table 92.— Comparison of metabolism of German girls and women studied by Magnus-Levy and Folk with ike American masculine normal {multiple prediction) standard. Actual Calculated Actual Subject. Age. Weight. Stature. daily daily less calcu- Percentage heat- heat- lated meta- difference. production. production. bolism. GirU. 1. A. K... 7 15.3 107 866 765 -1-101 -1-13.2 3. A. M... 12 24.0 129 962 961 + 1 + 0.1 4. Ft. W.. 12 25.2 128 938 972 - 34 - 3.6 5. E.Gl... 13 31.0 138 1217 1095 -t-122 -1-11.1 6. H.Sch.. 11 35.0 141 1313 1179 -f-134 -1-11.4 7. Fr.Th.. 14 35.5 143 1299 1176 -M23 -1-10.5 9. M. P... 11 42.0 149 1459 1315 4-144 + 11.0 Women. 1. B. K... 40 31.0 135 1073 898 -M75 -1-19.5 2. Gd 38 32.2 133 1109 918 -1-191 -1-20.8 3. W. Spr. 35 37.9 142 1204 1062 -f-142 -(-13.4 4. O. K... 25 39.0 139 1344 1129 -1-215 -1-19.0 6. L. Or... 21 47.2 147 1345 1309 -f- 36 -\- 2.8 7. M.W... 20 49.4 159 1355 1406 - 51 - 3.6 8. H. M... 28 61.2 157 1466 1367 + 99 + 7.2 9. H.Sch.. 18 64.0 152 1529 1448 + 81 + 5.6 10. M. Kl . . 17 64.0 156 1403 1475 - 72 - 4.9 11. E. Spl . . 28 61.3 156 1758 1501 -(-257 +17.1 12. L. W. . . 20 61.0 167 1508 1606 - 98 - 6.1 13. Schw. M 26 62.7 155(?) 1602 1529 -f 73 + 4.8 14. A. Sche. 22 68.2 159 1612 1651 - 39 - 2.4 15. Br.K... 27 76.5 169 1571 1782 -211 -11.8 Old women. 4. Kl 71 49.5 145 1088 993 -1- 95 + 9.6 6. Schm... 83 61.0 146 1307 938 -(-369 +39.3 7. Scha.... 86 59.3 160 1143 1052 + 91 + 8.7 Illustration D, below) in the women of the German and the men of the American classes from which the subjects were drawn. The solution of this question must be a problem for the future. The results show with the greatest clearness the value of standard tables based upon three characters for the direction of future research. Again the results exemplify the importance of large groups as a basis for conclusions. Five of the 17 women show heat-productions less than the male standard. Had a smaller number been examined, one or more of these might have been included and the result have been far less conclusive than it seems with 17 determinations. " See Chapter VI, p. 196. STANDARD BASAL METABOLISM CONSTANTS. 237 Illustration B. Metabolism in Cbildhooo and Youth and in Extreme Old Age. In Chapter V we discussed in detail the changes in metabolism which occur with increasing age during the period of adult life. As we indicated there, the limits which mark ofif the stages of development from the period of maturity and the period of old age from that of extreme old age are very indefinite, or at least are determinable only with difficulty. Our equations do not fully represent the metaboUsm of the develop- mental period. Neither do the observations upon which they are based contain numbers of very old men or women adequately large to justify using them as a standard for determining the influence of special conditions {e.g. the incidence of a specific disease) upon the metabolism of advanced old age. For these very reasons our equations are par- ticularly adapted to determining whether the metabolism of individuals in these extremes of the life-cycle differs from that characteristic of the wide central range of mature Hfe. In applying them to this problem we calculate the metabolism of the individuals of extreme age on the assumption that it is given by inserting the weight, stature, and age of the subjects in the equations based on our adult series. Comparison of the values obtained by actual measurement with that given by the equations then shows whether the metabolism of the age in question differs from that in adult life. Table 93. — Comparison of metabolism of Du Bois hoy scouts with the advlt masculine normal (multiple prediction) standard. Name. Age Weight in kilo- grams. Height in centi- meters. Actual daily heat- production. Calculated daily heat- production. Actual less calcu- lated meta- bolism. Percentage difFerence. J. D. D. B Leslie B Raymond M . . . Reginald F F. R. S Arthur A Hany B Henry K 34.5 28.5 30.4 35.4 32.1 30.6 36.6 36.0 153 141 141 148 142 147 146 148 1340 1300 1415 1485 1375 1348 1401 1432 1225 1076 1102 1206 1131 1128 1206 1207 -H15 +224 +313 +279 +244 +220 +195 +225 + 9.4 +20.8 +28.4 +23.1 +21.6 +19.5 +16.3 +18.6 Consider first the boy scouts studied by Du Bois." The essential details are given in table 93. The computed values are in all cases lower than the observed. The differences range from 115 to 313 calories per 24 hours, with an average of 227 calories. Thus boys of 12 or 14 years of age have a basal metabolism from 115 to 313 calories per day higher than would be expected if they were adult individuals of the same weight and height. Expressing these results in terms of percentages of the adult standard, as must be done in comparing boys with men, we note that the boys have a metabolism from 9.4 to 28.4 " Du Bois, Arch. Intern. Med., 1916, 17, p. 887. 238 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. per cent higher than they would be expected to have if they were adults of the same height and weight. The average superiority of the boys is 19.7 per cent of the standard. Thus if the boys were able to remain in complete muscular repose during the experimental periods, and if the light breakfast had no measureable influence on their metab- olism, so that the constants may be looked upon as truly basal, it is evident that the metabolism is relatively high at the onset of puberty, and that the decrease from this period to that of maturity is more rapid than during adult life. Table 94. — Comparison of metabolism of German boys and girls studied by Magnus-Leoy and Falk with American normal {multiple prediction) adult standards. Actual Calculated Actual Name and Age. Weight. Stature. daily daily less calcu- Percentage number. heat- heat- lated meta- difference. production. production. bolism. Boys. 2. M.N... 6 14.5 110 926 776 -M50 + 19.3 3. Fr. H... 6 18.4 110 970 829 -1-141 + 17.0 4. G. H... 7 19.2 112 1067 844 -1-223 +26.4 5. K. W... 7 20.8 110 1153 856 -1-297 +34.7 6. E. J.... 9 21.8 115 1036 881 -1-155 +17.6 7. P. Oe... 11 26.5 129 1151 1002 -1-149 +14.9 8. A. T.... 10 30.6 131 1338 1075 -f263 +24.6 9. O. Gr... 14 36.1 142 1310 1179 -1-131 +11.1 10. E. K. . . 14 36.8 142 1285 1188 + 97 + 8.2 11. K. Ke.. 16 39.3 149 1352 1244 4-108 + 8.7 12. R. D... 17 40.0 154 1397 1272 + 125 + 9.8 13. A. N. .. 14 43.0 149 1525 1309 +216 +16.5 14. K. W... 17 44.3 154 1525 1331 + 194 +14.6 15. L. Z.... 16 57.5 160 1636 1550 + 86 + 5.5 16. B 16 57.5 170 1681 1600 + 81 + 5.1 Girls. 1. A. K... 7 15.3 107 866 967 -101 -10.4 3. A. M... 12 24.0 129 962 1067 -105 - 9.8 4. Fr. W . . 12 25.2 128 938 1077 -139 -12.9 5. E. Gl... 13 31.0 138 1217 1146 + 71 + 6.2 6. H.Sch.. 11 35.0 141 1313 1199 + 114 + 9.S 7. Fr.Th.. 14 35.5 143 1299 1194 + 105 + 8.8 9. M. P. . . 11 42.0 149 1459 1281 + 178 +13.9 Turning to the data for youth presented by Magnus-Levy and Falk, the comparison of observed and theoretical values in table 94 shows that without exception the boys are characterized by a higher heat-production than would be expected if metabolism showed the same rate of change from childhood to maturity as it does from matur- ity to old age, and if the relationship between physical dimensions and metabolism were the same in developing as in mature individuals. The excess ranges from 81 to 297 calories and on the average is 161.1 calories for the 15 boys and youths. On a relative scale, the differences between observation and theory are from 5.1 to 34.7 per cent of the latter, with a general average of 15.6 per cent. The results for the few girls are not so consistent. As to the reason STANDARD BASAL METABOLISM CONSTANTS. 239 for this difference between boys and girls we have no suggestion to offer. It emphasizes the need for more numerous and more minutely recorded data. It appears that the metabolism is much higher in boyhood than in manhood, but in passing we must note that practically all of Magnus- Levy and Falk's determinations are higher than the American stand- ard. Thus the values of their constants for youth are probably too high (when used in connection with American values for adults) for the plotting of a curve of metabolism throughout life, as has been done by Du Bois." To avoid all possible misunderstanding concerning the line of reasoning employed in this section, we may reiterate that the age factor in these immature subjects has for purposes of investigation been assumed to be given by an extension of the line found vaUd for the period of adult life. If the measiired metabolism of the growing sub- jects is higher than the value predicted by the standard equation for adult life, we conclude that (if all sources of experimental error were ruled out) the decrease in metabolism rate is much more rapid in the period of growth than in the period of maturity. This seems to be the indication of the series of measurements by Du Bois" and Magnus- Levy and Talk. To show how large an influence correction for age by the adult formula has had upon these metabolism constants we have predicted the metabolism of the young subjects by means of the equations for adult life ignoring the influence of age changes during adult life itself. The equations are *® For all men h= -314.613+13.129 u)+6.388 8 For all women h= 713.016+ 8.063ic+1.116 8 The results are given in table 95. The first difference column shows that the age term in our equations has made a difference in the predicted value of from 74 to 199 calories per 24 hours. The second section of the table shows the percentage excess of the measured over the theoretical heat-production when the latter is computed in the two ways. Here there is an influence not merely of the actual differences in calculated and measured heat-production, but of the theoretical heat-productions used as bases for the calculation of the percentage excesses. "DuBois, Am. Journ. Med. Sci., 1916, 151, p. 781. Also Stud. Dep. Physiol., Cornell Univ. Med. Biill., 1917, 6, No. 3, part II, p. 1. " Just as this manuscript was being completed for the press, a second paper on the same sub- jects appeared (Olmstead, Barr and Du Bois, Arch. Intern. Med., 1918, 21, p. 621). In this investigation they find that the boy scouts had shown a material decrease in metabolism during the two years since they were last studied. The influence of a small breakfast upon metabolism has also been investigated (Soderstrom, Barr, and Du Bois, Arch. Intern. Med., 1918,21, p. 613), and the authors conclude that it has no aiguificant influence upon the metabolism constant. " See Chapter VI, p. 184. 240 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. The final difference column shows how much greater the excesses are when the age term is ignored and the regression equation involv- ing stature and weight only is used. We now turn to the problem of the metabolism rate at the other extreme of the life cycle, and shall consider the metabolism of the 6 old men studied by Aub and Du Bois." Table 96 contains the essen- tial measurements and the comparison of the observed heat-production Table 95. — Comparison of metabolism of 'pays calculated from aduU normal (multiple predic- tion) standard when the age factor is considered and when it is ignored. Name. Calculated metabolism in calories per 24 hours. Age considered. Age ignored. Difference. Percentage excess on basis of standard. Age considered. Age ignored. Difference American boys. J. D. D. B . . .., . . . Leslie B Raymond M Reginald F F. R. S Arthur A Hany B Henry K German boya. M.N. 2. 3. Fr. H . 4. G. H.. 5. K. W . 6. E.J... 7. P. Oe . 8. A. T. . 9. O. Gr . 10. E. K.. 11. K. Ke. 12. R. D.. 13. AN.. 14. K. W . 15. L. Z . . 16. B 1225 1076 1102 1206 1131 1128 1206 1207 776 829 844 856 881 1002 1075 1179 1188 1244 1272 1309 1331 1550 1600 1116 960 985 1096 1014 1026 1099 1103 578 630 653 661 706 857 924 1066 1076 1153 1194 1202 1251 1462 1526 + 109 +116 +117 +110 + 117 + 102 + 107 + 104 + 198 + 199 + 191 + 195 + 175 + 145 +151 + 113 + 112 + 91 + 78 +107 + 80 + 88 + 74 9.4 20.8 28.4 23.1 21.6 19.5 16.2 18.6 19.3 17.0 26.4 34.7 17.6 14.9 24.6 11.1 8.2 8.7 9.8 16.5 14.6 5.5 5.1 20.1 35.4 43.7 35.5 35.6 31.4 27.5 29.8 60.2 54.0 63.4 74.4 46.7 34.3 44.8 22.9 19.4 17.3 17.0 26.9 21.9 11.9 10.2 + 10.7 +14.6 + 15.3 +12.4 + 14.0 +11.9 +11.3 +11.2 +40.9 +37.0 +37.0 +39.7 +29.1 +19.4 +20.2 + 11.8 + 11.2 + 8.6 + 7.2 +10.4 + 7.3 + 6.4 + 5.1 in calories per 24 hoiu^ (indirect calorimetry) with the values predicted by the use of our formula from the constants for body-weight, stature, and age. The difference column shows that our formula has in all cases but one predicted a lower metabolism for these subjects than that found by actual observation. The difference between observation and theory in these 5 cases is rather large, amounting to about 245 calories per 24 hours. For comparison we may show the results of applsang our equations to the physical measurements of the old men and women studied by " Aub and Du Bois, Arch. Intern. Med., 1917, 19, p. 823. STANDARD BASAL METABOLISM CONSTANTS. 241 Magnus-Levy and Falk.^* The comparison of observed and theo- retical values in table 97 shows that with one exception the observed are higher than the calculated values. The differences range from 2.2 to 27.5 per cent higher than the standard. The results tend, therefore, to confirm those of Aub and Du Bois. At first glance this might seem to indicate that our formula is erroneous, at least when applied to individuals falling quite outside the age range covered by the series of observations upon which it is based. We make no claim whatever for the strict validity of our formula in extreme old age. Such a claim can only be made when far more extensive series of old men and women are included in the standard series. Table 9^.— Comparison of metabolism of old men studied by Avb and Du Bois with adult normal (multiple prediction) standard. Name. Age. Weight in kilo- grams. Height in centi- meters. Actual daily heat- production. Calculated daily heat- production. Actual less calcu- lated meta- bolism. Andrew O'C Henry L Charles H Charles W William C John B 77 78 79 80 83 83 69.7 68.9 52.9 69.1 62.9 50.5 171 167 163 164 163 158 1600 1568 1416 1220 1426 1240 1360 1323 1076 1297 1186 991 -1-240 -f245 -f340 - 77 -1-240 -f249 Table 97. — Comparison of metaboliim of old men and women (German) measured by Magnus- Levy and Falk with American ruyrmal (multiple prediction) standard. Name and number. Age. Weight. Stature. Actual daily heat- production. Calculated daily heat- production. Actual leas calcu- lated meta- bolism. Percentage difference. Old mm. 1. A.Kr.... 2. Be 3. Ki 4. Wa 5. He Old viomen. '4. Kl J6. Schm 7. Seha 71 70 78 77 64 71 83 86 47.8 60.0 68.5 69.3 70.4 49.5 61.0 59.3 164 165 162 172 160 145 146 150 1124 1320 1215 1479 1760 1088 1307 1143 1065 1244 1292 1360 1403 1065 1025 1098 + 59 + 76 - 77 -1-119 +357 + 23 +282 + 45 + 5.6 + 6.1 - 6.0 + 8.8 +26.4 + 2.2 +27.5 + 4.1 In emphasizing the fact that our equations predict a metabolism for these octogenarians below their observed heat-productions we must point out that exactly the same relationship is found if the original line as drawn by Du Bois is used. Thus in the explanation of their figure 1, Aub and Du Bois remark :" "In accordance with the findings in^the present series, the Une is somewhat higher in old age than in " Magnus-Levy and Falk, 2oc. cit. " Aub^and Du Bois, Arch. Intern. Med., 1917, 19, p. 824. 242 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. the curves published in previous papers." Thus their earlier diagram agrees with our equation in indicating that the observed metabolism of these old men is abnormally high. The remarkable agreement of 5 of the men in their figure 2 with the old-age portion of their line and the obvious bad results with our equation are, therefore, due to the fact that their prediction line has been redrawn to fit the special observations, while our own has not. The explanation of these results is a problem of considerable diffi- culty. Of course, one thinks first of all of the question of muscular repose. Were these octogenarians as quiet as the younger individuals with whom they are compared? We must note that even for the years of matiirity the constants of Magnus-Levy and Falk are higher than the American standards. If this result be due to faulty technique it may account for the high values of the old men and women measiu*ed by them. It seems to us quite as possible that the discrepancy indicates not the invalidity of oiu: formula but the selected character of the 6 old men studied by Aub and Du Bois, In the coiirse of their discussion they remark: "It will be noted that the metabolism of Charles W. was unusually low. This may be accounted for by the fact that he was much more senile than the others. While this finding is of importance in showing the great depression in metabolism which may occur in old age, we are not justified in using it to obtain the average figure which represents the heat-production of men of his age The results on Charles W. show a deviation of 21 per cent from the average of the other old men. He is therefore excluded from the averages as the result of the rule which debars an observation in which the deviation from the mean is greater than 4 times the average deviation." Our formula gives the metabolism of Charles W. within slightly more than 77 calories per day, or with an error of only 5.9 per cent of the calculated metabolism. On purely general grounds there seems to be no more reason to exclude Charles W. because he was too senile for his age than to exclude the other 5 men because they were too juvenile for their age.^° It must not be forgotten that men who reach 75 or 80 years are by virtue of this very fact a selected class. By this time a large pro- portion of humanity has succumbed to the wear and tear of life. Few are able to totter forward many paces further. Those who march with vigor are not typical of their age. But in selecting subjects for metabolism work, individuals in presumably good health are chosen. In examining the case-histories of the old men studied by Aub and Du Bois one is rather impressed by the idea that they must have been physically very remarkable individuals. Certainly in reading that '"' If Charles W. is to be excluded, this should certainly have been done before his metabolism was measured. STANDARD BASAL METABOLISM CONSTANTS. 243 Andrew O'C. had never been sick until 75 years of age, and that during most of his Ufe he drank about a pint of whiskey a day, that ten of the brothers and sisters of Charles H. lived to be over 70 years of age, that Charles W. at 80 "was formerly very alcoholic," that the health of William C. has always been good, and that the mother of John B., 83 years old, died at 93, the biologist must feel that the octo- genarians upon whom this series of determinations was based must have been in their prime men of rare physical capacity. If this suggestion of the strong influence of selection in the case of old men and women be vaUd, one might expect that a standard based on a period of life in which selection is not such an important factor would give values lower than the actually measured heat-productions of old age. The anomalous results (in comparison with oiu* standards) of these two independent series of measurements on old people show the pressing need for further investigations of metabolism at the maximum age. We of course freely admit the possibility that our standards may be inadequate for this period. If so, the equations must be modi- fied. We hope that data on this problem may be secured at an early date. Divergence of results of diflferent observers has shown by a comparison with our normal standards of illustrations A and B, how great is the danger of combining the results of different series in order to obtain a curve of the change of metabolism with age as has been done by Du Bois. Illustration C. Metabolism or Individuals of Aberrant Physical Form. We now turn to the problem of the basal metabolism of individuals of highly aberrant physique. For this purpose we avail ourselves of Table 98. — Comparison of the melabolism of dwarfs as studied hy AiA, Du Bois, McCrudden, and Lusk with normal (multiple prediction) standard for men. Name. Subject. Age. Height in centi- meters. Weight in kilo- grams. Actual daily heat- production. Calculated daUy heat- production. Actual less calculated metab- olism. Patrick W... Raphael De P Samuel G.... Irwin E George F J. P.* Rachitic dwarf. Achondroplasia Achondroplasia Myxedema .... fHjrpopituitary. IHypothyroid.. . /Intestinal Ilnfantiliem .... 38 35 29 32 124 135 124 134 149 113 37.31 40.86 34.92 37.37 53.05 21.3 1180 1256 1266 828 1159 733 943 1067 971 1035 1217 810 -237 -189 -295 +207 + 58 + 77 * J. P. was studied by McCrudden and Lusk, the others are due to Aub and Du Bois. the data for dwarfs published by Aub and Du Bois ^^ and the single dwarf studied by McCrudden and Lusk.'*^ Table 98 gives the essential data and the comparison of the theoretical and measured heat-produc- " Aub and Du Bois, Arch. Intern. Med., 1917, 19, p. 840. " McCrudden and Lusk, Joum. Biol. Chem., 1912-13, 13, p. 447. 244 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. tions for 24-hour periods. In 3 instances our formula has predicted too large and in 3 cases too small a daily heat-production. The average error without regard to sign is 177 calories, but with regard to sign it is —63 calories per day. Thus, while in the individual instance the error of prediction may be fairly large, the average result is, considering the small number of subjects, reasonably close. Physiologically the comparison suggests that the metabolism of dwarfs is essentially the same as that of normal adults. Illustration D. Metabolism op Athletes. As an example of the application of these equations, or tables, in the solution of a specific physiological problem, we may take the data for a series of 16 athletes ^ studied in the Chemical Laboratory of Syracuse University by Dr. H. Monmouth Smith, now of the Nutri- tion Laboratory staff. These all fall well within the age range of our equation, and an observed deviation from the standard values can not in this case be attributed to a distinct difference in metabolism due to age, as is certainly the case in the series of boy scouts studied by Du Bois, or to possible inadequacy of our formulas for extreme old age, as in the octogenarians recorded by Aub and Du Bois. Table 99. — Comparison of basal metabolism of H. Monmouth Smith's athletes with adult male normal (multiple prediction) standard. Actual Calculated ActualleBs Subject. Age. Weight. Stature. daily daily calculated Percentage beat- heat- metab- difference. production. production. olism. M.A. M... 29 66.0 177 1695 1664 + 31 -1-1.9 F. G. R. . . . 20 74.0 179 1914 1845 -1- 69 -1-3.7 W. F. M . . . 21 62.4 180 1816 1683 -1-133 -1-7.9 E.G 20 78.9 184 2126 1937 -1-189 -f9.8 D. H. W... 22 82.1 186 2034 1977 + 57 -f2.9 J. H. R 23 82.2 187 1978 1977 + 1 -t-0.1 M. H. K. . . 19 79.0 188 1944 1965 - 21 -1.1 H.W 19 108.9 198 2559 2426 -(-133 -1-5.5 C.J.D 27 56.7 160 1524 1464 -t- 60 +4.1 W.S 22 88.5 165 2017 1960 + 57 +2.9 W. A. S . . . . 21 56.3 169 1562 1544 + 18 +1.2 R. D. S. . . . 21 63.5 170 1619 1648 - 29 -1.8 M.Y. B... 20 63.5 172 1677 1665 + 12 +0.7 C. D. R. ... 22 74.0 173 1908 1801 4-107 +6.9 H. R. W. . . 24 73.9 175 1842 1796 + 46 +2.6 P.D.F.... 23 71.2 176 1810 1771 + 39 +2.2 Table 99 gives the age, weight, and stature, from which the theo- retical basal metabolism of the men has been calculated and entered in the fifth column of the table. As is clearly shown by the entries in the sixth and seventh columns, the athletes are, with two slight exceptions, supernormal in their metabolism. The excesses over the standard values range from 1 to 189 calories per 24 hours, or from 0.1 to 9.8 per cent 3 Benedict and Smith, Joum. Biol. Chem., 1916, 20, p. 243. STANDARD BASAL METABOLISM CONSTANTS. 245 of the standard value. On an average the athletes show an excess of 56.37 calories or 3.03 per cent over the standard. These results fully confirm the conclusions concerning the influence of athletic training already drawn, although the percentage differences are materially lower by the new methods of analysis. The authors ** expressed their results for selected groups of athletes and of non-athletic individuals in terms of heat-production per 24 hours per square meter of body-surface as estimated by the Meeh formula and on the average found for athletes 863 calories and for non-athletes 807 calories. Thus athletes were 6.84 per cent higher. Subsequent revision of these calciilations on the basis of the Du Bois height-weight chart shows 978 calories for athletes and 912 calories for non-athletes. Thus the athletes are 7.24 per cent higher. By the method of analysis here employed we find a difference of only 3 per cent. This difference in percentage results is probably due to (1) the inherent defects in the selected-group system of comparison which have been pointed out above; and (2) to including athletes in the data from which the normal standard was derived. Had athletes been excluded from the standard normal series the differences would have been greater. Why, therefore, were they not excluded? Because athletic training is in some degree characteristic of men at large. Blacksmiths, riveters, stone-masons, lumbermen, cowboys, miners, and stevedores are quite as tjrpically men as are bar-tenders, book-keepers, floor-walkers, and college professors. Out of 136 men, 16 with special athletic training is perhaps not too large a proportion for a series which is intended to serve as a standard for normal men, in good health, as a class. IlXUSTItATION E. MeTABOUSM OF VeOETABIANB. As a further illustration of the applicability of these equations in human physiology, we may consider the metaboUsm of vegetarians, a question which has already been discussed elsewhere ^® on the basis of a series of men and women well within the age-range over which our equations may be held to apply. The observed daily heat-produc- tions are compared with the standard productions in table 100 for men and in table 101 for women. Of the 11 men, 6 show a subnormal and 5 show a supernormal metabolism. Of the 11 women, 5 are character- ized by a subnormal and 6 by a supernormal metabolism. Disregarding sex, as we may quite properly do since it has been taken into account in the equations used, we note that 11 vegetarians have a subnormal and 11 have a supernormal metabolism. The average metabolism of the 11 men is subnormal by 24.64 calories per 24 hours, whereas that of the women is supernormal by 5.91 calories per 24 hours. Disre- garding sex, the metaboUsm of vegetarians differs from the multiple " Benedict and Smith, Joum. Biol. Chem., 1915, 20, p. 251, Table II. ^ Benedict and Roth, Joum. Biol. Chem., 1915, 20, p. 231. 246 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. prediction standard values for individuals of like sex, age, weight, and stature, on the average by 9.37 calories per 24 hours. These results furnish a full substantiation for the conclusion already drawn: *® "We may, therefore, fairly conclude that living upon a vegetarian diet for a longer or shorter period does not fundamentally alter the basal gaseous metabolism." Table 100. — Comparison of basal metabolism of Roth's male vegetarians with normal {multiple prediction) standard for men. Subject. Age. Weight. Stature. Actual daily heat- production. Calculated daily heat- production. Actual less calcu- lated meta- bolism. Percentage difference. B. K 39 32 27 58 21 41 38 29 22 25 25 1 58.2 50.6 60.0 50.0 49.3 55.2 75.0 59.3 59.2 64.7 55.4 178 179 179 155 163 164 164 164 169 170 171 1393 1510 1530 1158 1365 1341 1698 1451 1605 1499 1545 1494 1442 1605 1138 1418 1369 1662 1507 1578 1638 1515 -101 + 68 - 75 + 20 - 53 - 28 + 36 - 56 + 27 -139 + 30 -6.8 +4.7 -4.7 +1.8 -3.7 -2.0 +2.2 -3.7 +1.7 -8.6 +2.0 B. N. C L. H. W E. J. W v. E. H Dr.P. R F. E. M W.B.L T. H. Y E. H. T O.N. A Table 101. — Comparison c / metabolism of Roth's female vegetarians with normal {multiple prediction) standard for women. Subject. Age. Weight. Stature. Actual daily heat- production. Calculated daily heat- production. Actual less calcu- lated meta- bolism. Percentage difference. Miss O. A 21 53 26 27 44 27 27 22 29 36 39 90.2 58.0 53.8 47.0 93.6 49.1 44.8 56.8 44.9 40.0 67.2 164 163 ' 160 167 165 151 157 166 159 168 170 1756 >415 1215 1168 1765 1178 11S9 1365 1272 1269 1521 1723 1263 1344 1287 1650 1278 1248 1402 1243 1180 1430 + 33 + 152 -129 -119 +115 -100 - 59 - 37 + 29 + 89 + 91 + 1.9 +12.0 - 9.6 - 9.2 + 7.0 - 7.8 - 4.7 - 2.6 + 2.3 + 7.5 + 6.4 Mrs.E.B MissJ. N. B Miss L. B Dr.M.D Miss M. H Miss M.J Miss L. K Mrs. A. L Miss J. T Miss C. Z Illustration F. Metabolism in Disease. The purpose of many clinical calorimetric researches is to determine whether a significant modification of metabolism is associated with the specific disease under investigation. To solve this problem one must compare the actually measured calories of the subject with the calories calculated from weight, stature, and age on the assumption that he is in normal health. To illustrate the applicability of these equations (or tables) to such pathological problems, we may avail ourselves of Dr. Elliott P. Joslin's series of diabetics.^^ " Benedict and Roth, loc. cit., p. 240. " Benedict and Joslin, Carnegie Inst. Wash. Pub. No. 176, 1912. STANDARD BASAL METABOLISM CONSTANTS. 247 Table 102 gives the key number of the subjects,*^ their age, weight, stature, and actually measured basal heat-production for 24-hour periods. The fifth column gives the theoretical heat-production, the sixth the absolute deviation of the measured from the calculated, and the seventh the relative deviation of the actually determined from the theoretical (normal) heat-production. Table 102. — Metabolism of Joslin's series of diabetics in comparison vnth normal (multiple prediction) standard. Subject. Age. Weight. Stature. Actual daily heat- production, Calculated daily heat- production. Actual leas calcu- lated meta- bolism. Percentage difference. Men. A(2) A(l) C(l) C(2) D G I J K(2) K(l) L(2) L(l) N P Q R S T V Women. B H O U 49 50 30 30 31 34 25 21 46 47 22 24 14 17 15 48 57 44 36 40 38 16 37 51.6 46.1 55.5 62.7 48.8 67.1 40.0 64.0 59.1 55.6 63.0 66.5 31.5 40.0 51.7 55.3 58.0 51.4 60.0 41.4 52.4 52.6 39.5 171 171 166 166 173 178 176 171 180 180 183 183 146 173 168 181 177 180 173 158 159 173 160 1481 1255 1610 1728 1382 1978 1608 1670 1596 1728 1898 1884 1186 1414 1538 1812 1428 1553 1894 1195 1440 1498 13S5 1301 1218 1458 1557 1394 1650 1328 1523 1469 1414 1700 1734 1136 1367 1517 1408 1365 1377 1514 1156 1273 1403 1156 -t-180 -t- 37 -(-152 -1-171 - 12 +328 4-280 -t-147 -1-127 -1-314 -1-198 -1-150 -I- 60 + 47 + 21 4-404 4- 63 4-176 4-380 4- 39 4-167 4- 96 4-229 4-13.8 4- 3.0 4-10.4 4-11.0 - 0.9 4-19.9 4-21.1 4- 9.7 4- 8.6 4-22.2 4-11.6 4- 8.7 4- 4.4 4- 3.4 4- 1.4 4-28.7 4- 4.6 4-12.8 4-25.1 4- 3.4 4-13.1 4- 6.8 4-19.8 With one single exception of 12 calories per 24- hours in the case of subject D, the observed are all higher than the theoretical metabolism constants. The excess ranges from 21 to 404 calories per 24 hours in men and from 39 to 229 calories in women. In relation to the computed heat-production taken as a standard, the excess in the men ranges from 1.4 to 28.7 per cent. In the women the range is from 3.4 to 19.8 per cent. The average deviation of the 19 male determinations is 169.11 calories, while the average deviation of the 4 female determinations is 132.50 calories. On the average the heat productions of the men are 11.55 per cent above normal, whereas those for the women are 10.78 per cent above normal. These results are fully confirmatory of the general conclusions " Obaervations on the same patient at different ages or different body-weights are in some cases available. These are recorded as 1 and 2. 248 A BIOMETRIC STUDY OP BASAL METABOLISM IN MAN. already drawn.'*^ Here the application of the formulas to diabetics serves merely as a particular example of a general method. It may not be out of place, however, to look at certain quantitative aspects of the subject more closely. On examining the increments in metabolism due to diabetes found by this method, we note that they are on the average only about 11 per cent as compared with 15 to 20 per cent as asserted in earlier publications from the Nutrition Labora- tory.^" In partial explanation of this percentage difference we may note that our prediction equation for men includes about 16 athletes. This represents about 12 per cent of the whole control series. But in a preceding illustration we have shown that athletes themselves have a higher metabolism than normal men at large. Our reasons for including athletes in our standard series have been given above. It should be a fixed scientific principle that standards should not be changed whenever convenience demands.^' The inevitable conse- quence of this inclusion of the athletes has been to reduce the per- centage difference between diabetics and non-diabetics. In short, it has made the comparison as disadvantageous as possible to the views concerning diabetes long held at the Nutrition Laboratory. Notwith- standing this fact, the validity of the general conclusions already drawn is fully supported. A study of the individual entries in this table has considerable value as indicating the limits of trustworthiness of conclusions from single subjects even when compared with a standard control based on large nimibers. For example, had the one subject examined chanced to be D the incautious clinician might have concluded that diabetes decreases metabolism. Had the second subject chanced to be Q he might have concluded that a defect of 12 calories in one case and an excess of 21 calories in the other indicated no relationship at all between diabetes and metabolism. Had V or R been the only subject examined, a qmte exaggerated impression of the influence of diabetes might have been drawn, for these men show an excess of 25.1 and 28.7 per cent. It is only when a considerable number of pathological cases are available for comparison tvith the standard that dependable con- clusions concerning the influence of any disease can be dravm. This principle is a fundamental one, and must be applied in all comparisons of special groups with standard control series in all nutritional research. '9 Benedict and Joslin, loc. cit., p. 121. " Benedict and Joalin, Camesie Inst. Wash. Pub. No. 136, 1910, p. 193; also Carnegie Inst. Wash. Pub. No. 176, 1912, p. 121. " Criticism has been made from the Nutrition Laboratory of the Du Bois method of excluding undersized individuals in obtaining their normal, and the specific statement has been made that we should not compare standard normals based primarily upon robust, vigorous individuals with emaciated, weak, under-weight diabetics. We still hold these criticisms to be valid, and we have avoided them in the comparisons in table 102 by utilizing equations which enable one to compare each diabetic with a standard value for an individual of like height, weight, and age. But in determining the equations for these standard values we have included athletes among the normals, even though their inclusion has minimized the difference between diabetic and non-diabelie individiutla. STANDARD BASAL METABOLISM CONSTANTS. 249 Illustration G. Rationinq in Periods of Emergenct. The problem of rationing in national crises involves so many factors (biological, social, and economic) that general principles only can be established. It is evident, however, that the fairest and the most advantageous plan for the allotment of rations is that which is based on the physio- logical needs of the individuals of the population under consideration. For instance in an editorial ^^ on the Inter-Allied Scientific Food Commission we read : "The basal heat production of an average man weighing 156 pounds (70 kg.) will be 70 calories an hour at rest and without food, or 1680 calories in twenty-four hours." Body-weight is not, however, an adequate standard. The analysis in the present volume shows that stature, weight, and age must all be taken into account in determining the basal metabolism of the indi- vidual, and hence in determining most exactly the food requirements of a population. Our 136 men show an average weight of 64.1 kilograms instead of the 70 kilograms ordinarily assumed as an average value. They show an average basal metabolism of 1632 calories as compared with 1680 calories. Our men are on the average 26.9 years of age and 173 centimeters in height. If we assume that the men of a population average 70 kg. in weight, 170 cm. in stature, and 35 years of age, we find from tables I and II a basal requirement of 1029 -{-614 = 1643 calories. If we are considering a population of adult women weighing on the average 56.0 kg., 162 cm. in height, and 35 years of age the values from tables III and IV are 119H-136 = 1327 calories. These factors must, in practical rationing, be multiplied by the requisite factors for the increased metabolism due to muscular and other activity. 4. RECAPITULATION. The purpose of this chapter, in which the principles imderlying the establishment of standard control series have been discussed, has been three-fold. 1. To emphasize the necessity for the establishment of statistical normal basal metabolism standards, which may serve as a basis of comparison in all special nutritional investigations. 2. To supply convenient tables of such standards based on the most extensive series of normal data as yet available. 3. To illustrate the practical use of such tables in the solution of problems in nutritional physiology. The analysis of this and the preceding chapters leads to the conclu- sion that biologically the most rational and practically the most satis- "Journ. Am. Med. Ass., 1618, 71, p. 1660. Incompletely quoting Lusk, Journ. Am. Med. Ass., 1918, 70, p. 821. 250 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. , factory standard is that secured by taking into account the body- , weight, stature, and age of the subject in predicting basal metabolism. I, This method is therefore an extension and modification of the selected group method, employed earlier at the Nutrition Laboratory. In the new method, which we have designated as the multiple -pre dict ion method, we replace the empirical determinations of the metaboiism of individuals of specific weight, stature, and age by values given by multiple prediction equations based on the statistical constants of all available normal data. These equations have been tabled for both men and women for a f range of weight, stature, and age which will be met in practical work ''^ with adult subjects, and give a set of multiple prediction tables of standr- )ard normal adult basal metabolism constants. The illustrations of the practical application of these multiple pre- diction tables show first of all their great usefulness in the detection of differences between series of metaboUsm measurements. Thus, as far as we are aware, the anomalous nature of the series of determina- tions by Magnus-Levy and Falk and those by Palmer, Means, and Gamble, has heretofore quite escaped the notice of physiologists, and their data have been combined freely with other series for the purpose of generalization. The aberrant nature of these series becomes evident as soon as comparison of the actual measurements with the theoretical values from the multiple prediction tables is made. The use of the tables shows the clear differentiation of athletes and diabetics from other individuals in their metaboUc level, thus confirm- ing conclusions already drawn at the Nutrition Laboratory. The use of the standards shows the existence of a well-marked differentiation in the level of metabolism of men and women, and shows that the differences are persistent throughout adult life instead of disappearing in later years as maintained by Sond^n and Tigerstedt. There is no evidence for such differentiation in new-bom infants. While the novelty of the conception underlying these standards will probably limit somewhat their immediate adoption by physiolo- gists, the illustrations show that for purposes of more refined analysis they have great practical value. We believe that ultimately the great convenience of these multiple prediction tables will result in their general adoption as standards of reference in all work on human nutritional physiology. When larger series of basal data are available we expect to revise these tables so that they may represent the broadest and most secure foundation for comparative nutritional investigation. APPENDIX. STANDARD MULTIPLE PREDICTION TABLES FOR NORMAL BASAL METABOUSM (For method of use see page 230. Chapter VIII gives illustiations of practical application). PREDICTION TABLES FOR BASAL METABOLISM. 253 Table I — Fatiiar Jar body-weCght in men. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 25 410 412 413 414 416 417 419 420 421 423 26 ■424 425 427 428 430 431 432 434 435 436 27 438 439 441 442 443 446 446 447 449 450 28 452 453 46^ 456 457 458 460 461 463 464 29 465 467 468 469 471 472 474 476 476 478 30 479 480 482 483 485 486 487 489 490 491 31 493 494 496 497 498 500 601 602 504 506 32 507 508 509 511 512 613 615 616 618 619 33 520 622 523 524 526 527 629 630 531 633 34 534 535 637 538 540 541 542 544 545 546 35 548 549 661 552 553 666 556 657 559 560 36 562 663 564 566 567 568 570 671 673 674 37 575 577 578 579 581 582 584 586 686 688 38 589 590 692 693 595 596 597 699 600 601 39 603 604 606 607 608 610 611 612 614 615 40 617 618 619 621 622 623 626 626 628 629 41 630 632 633 634 636 637 639 640 641 643 42 644 645 647 648 650 651 652 654 655 656 43 658 669 661 662 663 666 666 667 669 670 44 672 673 674 676 677 678 680 681 683 684 45 685 687 688 689 691 692 694 696 696 698 46 699 700 702 703 705 706 707 709 710 711 47 713 714 716 717 718 720 721 722 724 725 48 727 728 729 731 732 733 735 736 738 739 49 740 742 743 744 746 747 749 760 751 753 50 754 765 767 758 760 761 762 764 766 766 51 768 769 771 772 773 776 776 777 779 780 52 782 783 784 786 787 788 790 791 793 794 53 795 797 798 799 801 802 804 806 806 808 54 809 810 812 813 815 816 817 819 820 821 55 823 824 826 827 828 830 831 832 834 835 56 837 838 839 841 842 843 846 846 848 849 67 860 862 863 854 866 857 859 860 861 863 58 864 866 867 868 870 871 872 874 875 876 59 878 879 881 882 883 885 886 887 889 890 60 892 893 894 896 897 898 900 901 903 904 61 905 907 908 909 911 912 914 916 916 918 62 919 920 922 923 925 926 927 929 930 931 63 933 934 936 937 938 940 941 942 944 945 64 947 948 949 961 952 953 955 966 958 969 65 960 962 963 964 966 967 969 970 971 973 66 974 976 977 978 980 981 982 984 985 986 67 988 989 991 992 993 995 996 997 999 1000 68 1002 1003 1004 1006 1007 1008 1010 1011 1013 1014 69 1015 1017 1018 1019 1021 1022 1024 1025 1026 1028 70 1029 1030 1032 1033 1035 1036 1037 1039 1040 1041 71 1043 1044 1046 1047 1048 1060 1061 1052 1054 1065 72 1067 1058 1069 1061 1062 1063 1066 1066 1068 1069 73 1070 1072 1073 1074 1076 1077 1079 1080 1081 1083 74 1084 1086 1087 1088 1090 ,1091 1092 1094 1095 1096 254 PREDICTION TABLES FOR BASAL METABOLISM. Table I. — Factor for body-weight in men. — Concluded. 75 .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1098 1099 1101 1102 1103 1105 1106 1107 1109 1110 76 1112 1113 1114 1116 1117 1118 1120 1121 1123 1124 77 1125 1127 ^128 1129 1131 1132 1134 1135 1136 1138 78 1139 1140 11£2 1143 1145 1146 1147 1149 1150 1151 79 1153 1154 1156 1157 1158 1160 1161 1162 1164 1165 80 1167 1168 1169 1171 1172 1173 1175 1176 1178 1179 81 1180 1182 1183 1184 1186 1187 1189 1190 1191 1193 82 1194 1195 1197 1198 1200 1201 1202 1204 1205 1208 83 1208 1209 1211 1212 1213 1215 1216 1217 1219 1220 84 1222 1223 1224 1226 1227 1228 1230 1231 1233 1234 85 1235 1237 1238 1239 1241 1242 1244 1245 1246 1248 86 1249 1250 1252 1253 1255 1256 1257 1259 1260 1261 87 1263 1264 1266 1267 1268 1270 1271 1272 1274 1275 88 1277 1278 1279 1281 1282 1283 1285 1286 1288 1289 89 1290 1292 1293 1294 1296 1297 1299 1300 1301 1303 90 1304 1305 1307 1308 1310 1311 1312 1314 1315 1316 01 1318 1319 1321 1322 1323 1325 1326 1327 1329 1330 92 1332 1333 1334 1336 1337 1338 1340 1341 1343 1344 93 1345 1347 1348 1349 1351 1352 1354 1355 1356 1358 94 1359 1360 1362 1363 1365 1366 1367 1369 1370 1371 95 1373 1374 1376 1377 1378 1380 1381 1383 1384 1385 96 1387 1388 1389 1391 1392 1394 1395 1396 1398 1399 97 1400 1402 1403 1405 1406 1407 1409 1410 1411 1413 98 1414 1416 1417 1418 1420 1421 1422 1424 1425 1427 99 1428 1429 1431 1432 1433 1435 1436 1438 1439 1440 100 1442 1443 1444 1446 1447 1449 1450 1451 1453 1454 101 1455 1457 1458 1460 1461 1462 1464 1465 1466 1468 102 1469 1471 1472 1473 1475 1476 1477 1479 1480 1482 103 1483 1484 1486 1487 1488 1490 1491 1493 1494 1495 104 1497 1498 1499 1501 1502 1504 1505 1506 1508 1509 105 1510 1512 1513 1515 1516 1517 1519 1520 1521 1523 106 1524 1526 1527 1528 1530 1531 1532 1534 1535 1537 107 1538 1539 1541 1542 1543 1545 1546 1548 1549 1550 108 1552 1553 1554 1556 1557 1559 1560 1561 1563 1564 109 1565 1567 1568 1570 1571 1572 1574 1575 1576 1578 110 1579 1581 1582 1583 1585 1586 1587 1589 1590 1592 111 1593 1594 1596 1597 1598 1600 1601 1603 1604 1605 112 1607 1608 1609 1611 1612 1614 1615 1616 1618 1619 113 1620 1622 1623 1625 1626 1627 1629 1630 1631 1633 114 1634 1636 1637 1638 1640 1641 1642 1644 1645 1647 115 1648 1649 1651 1652 1653 1655 1656 1658 1669 1660 116 1662 1663 1664 1666 1667 1669 1670 1671 1673 1674 117 1675 1677 1678 1680 1681 1682 1684 1685 1686 1688 118 1689 1691 1692 1693 1695 1696 1697 1699 1700 1702 119 1703 1704 1706 1707 1708 1710 1711 1713 1714 1715 120 1717 1718 1719 1721 1722 1724 1725 1726 1728 1729 121 1730 1732 1733 1735 1736 1737 1739 1740 1741 1743 122 1744 1746 1747 1748 1750 1751 1752 1754 1756 1757 123 1758 1759 1761 1762 1763 1765 1766 1768 1769 1770 124 1772 1773 1774 1776 1777 1779 1780 1781 1783 1784 PREDICTION TABLES FOR BASAL METABOLISM. 255 Table II. — Facterfor ttaiure and age in men 21 22 23 24' 25 26 27 28 29 30 151 614 607 600 593 587 580 673 566 660 553 152 619 612 605 598 592 686 578 571 565 558 153 624 617 610 603 697 690 583 576 670 563 154 629 622 615 608 602 695 688 681 675 568 155 634 627 620 613 607 600 693 586 580 573 156 639 632 625 618 612 605 698 591 586 678 167 644 637 630 623 617 610 603 596 590 583 158 649 642 635 628 622 616 608 601 595 588 159 654 647 640 633 627 620 613 606 600 593 160 659 652 645 638 632 625 618 611 605 598 161 664 657 650 643 637 630 623 616 610 603 162 669 662 655 648 642 635 628 621 616 608 163 674 667 660 653 647 640 633 626 620 613 164 679 672 665 658 652 645 638 631 625 618 165 684 677 670 663 657 650 643 636 630 623 166 689 682 675 668 662 665 648 641 636 628 167 694 687 680 673 667 660 663 646 640 633 168 699 692 685 678 672 666 658 651 645 638 169 704 697 690 683 677 670 663 656 650 643 170 709 702 695 688 682 676 668 661 665 648 171 714 707 700 693 687 680 673 666 660 653 172 719 712 705 698 692 686 678 671 665 658 173 724 717 710 703 697 690 683 676 670 663 174 729 722 715 708 702 695 688 681 675 668 175 734 727 720 713 707 700 693 686 680 673 176 739 732 725 718 712 705 698 691 686 678 177 744 737 730 723 717 710 703 6% 690 683 178 749 742 735 728 722 715 708 701 695 688 179 754 747 740 733 727 720 713 706 700 693 180 759 752 745 738 732 725 718 711 705 698 181 764 757 750 743 737 730 723 716 710 703 182 769 762 755 748 742 735 728 721 716 708 183 774 767 760 753 747 740 733 726 720 713 184 779 772 765 758 752 745 738 731 725 718 185 784 777 770 763 757 750 743 736 730 723 186 789 782 775 768 762 755 748 741 735 728 187 794 787 780 773 767 760 753 746 740 733 188 799 792 785 779 772 765 758 761 746 738 189 804 797 790 784 777 770 763 756 760 743 190 809 802 795 789 782 775 768 761 765 748 191 814 807 800 794 787 780 773 766 760 763 192 819 812 805 799 792 785 778 771 765 758 193 824 817 810 804 797 790 783 776 770 763 194 829 822 815 809 802 795 788 781 775 768 195 834 827 820 814 807 800 793 787 780 773 196 839 832 825 819 812 805 798 792 786 778 197 844 837 830 824 817 810 803 797 790 783 198 849 842 835 829 822 815 808 802 795 788 199 854 847 840 834 827 820 813 807 800 793 200 859 852 845 839 832 825 818 812 805 798 256 PREDICTION TABLES FOR BASAL METABOLISM. Table II. — Factor for stature and age in men. — Continued. 31 32 33 34 35 36 37 38 39 40 151 546 539 533 526 519 512 506 499 492 486 152 551 544 538 531 524 517 611 604 497 490 153 556 549 543 536 529 522 516 609 502 495 154 561 554 548 541 534 627 521 514 607 500 155 566 559 553 546 539 532 526 519 512 505 156 571 564 558 551 544 537 531 524 617 610 157 576 569 563 556 549 542 636 629 522 515 158 581 574 568 561 554 547 541 634 627 520 159 586 679 573 566 559 552 546 539 632 526 160 591 584 578 571 564 557 551 544 537 630 161 596 589 583 576 569 562 556 549 542 635 162 601 594 588 581 574 567 561 654 547 540 163 606 599 593 586 579 572 566 569 552 646 164 611 604 598 591 584 577 571 664 557 650 165 616 609 603 596 589 582 576 569 562 556 166 621 614 608 601 594 587 581 674 567 560 167 626 619 613 606 599 592 586 579 572 565 168 631 624 618 611 604 597 591 584 577 570 169 636 629 623 616 609 602 596 689 582 575 170 641 634 628 621 614 607 601 594 587 580 171 646 639 633 626 619 612 606 599 592 685 172 651 644 638 631 624 617 611 604 597 690 173 656 649 643 636 629 622 616 609 602 696 174 661 654 648 641 634 627 621 614 607 600 175 666 659 653 646 639 632 626 619 612 605 176 671 664 658 651 644 637 631 624 617 610 177 676 669 663 656 649 642 636 629 622 615 178 681 674 668 661 654 647 641 634 627 620 179 686 679 673 666 659 652 646 639 632 625 180 691 684 678 671 664 657 651 644 637 630 181 696 689 683 676 669 662 656 649 642 635 182 701 694 688 681 674 667 661 654 647 640 183 706 699. 693 686 679 672 666 659 662 645 184 711 704 698 691 684 677 671 664 667 660 185 716 709 703 696 689 682 676 669 662 655 186 721 714 708 701 694 687 681 674 667 660 187 726 719 713 706 699 692 686 679 672 665 188 731 724 718 711 704 697 691 684 677 670 189 736 729 723 716 709 702 696 689 682 675 190 741 734 728 721 714 707 701 694 687 680 191 746 739 733 726 719 712 706 699 692 686 192 751 744 738 731 724 717 711 704 697 690 193 756 749 743 736 729 722 716 709 702 695 194 761 754 748 741 734 727 721 714 707 700 195 766 759 753 746 739 732 726 719 712 705 196 771 764 758 751 744 737 731 724 717 710 197 776 769 763 756 749 742 736 729 722 715 198 781 774 768 761 754 747 741 734 727 720 199 786 779 773 766 759 752 746 739 732 725 200 791 785 778 771 764 757 751 744 737 730 PBEDICTION TABLES FOB BASAL METABOLISM. 257 Table II. — Factor far atature and age in men — Continued. 41 42 43 44 45 46 47 48 49 50 151 479 472 465 458 462 446 438 431 425 418 152 484 477 470 463 457 450 443 436 430 423 153 489 482 475 468 462 455 448 441 436 428 154 494 487 480 473 467 460 453 446 440 433 155 499 492 485 478 472 465 458 451 445 438 156 504 497 490 483 477 470 463 456 450 443 157 509 502 496 488 482 476 468 461 465 448 158 514 507 500 493 487 480 473 466 460 463 159 619 612 505 498 492 485 478 471 466 468 160 524 517 610 603 497 490 483 476 470 463 161 529 522 616 608 502 495 488 481 475 468 162 534 527 520 513 607 500 493 486 480 473 163 639 532 625 518 612 505 498 491 485 478 164 544 537 630 623 517 510 603 496 490 483 165 549 542 536 528 522 516 608 501 496 488 166 554 647 540 533 527 620 613 506 500 493 167 659 562 545 53« 632 525 618 511 505 498 168 564 557 550 643 637 630 623 516 510 503 169 569 562 555 548 542 635 628 621 516 608 170 574 667 660 553 647 540 533 626 620 513 171 579 672 666 568 562 545 538 631 625 618 172 584 577 570 663 567 550 643 636 530 623 173 589 582 575 568 562 656 548 641 635 628 174 594 687 680 673 667 660 563 546 640 533 176 599 692 686 678 672 665 658 551 546 538 176 604 597 690 583 577 570 563 656 550 543 177 609 602 595 588 582 676 668 561 655 548 178 614 607 600 593 687 580 673 566 560 553 179 619 612 605 598 692 585 678 571 665 558 180 624 617 610 603 697 590 583 576 570 563 181 629 622 615 608 602 695 588 581 576 568 182 634 627 620 613 607 600 593 686 680 673 183 639 632 626 618 612 606 698 691 686 678 184 644 637 630 623 617 610 603 696 690 583 185 649 642 635 628 622 616 608 601 695 688 186 654 647 640 633 627 620 613 606 600 593 187 659 662 645 638 632 625 618 611 606 598 188 664 667 650 643 637 630 623 616 610 603 189 669 662 655 648 642 635 628 621 616 608 190 674 667 660 653 647 640 633 626 620 613 191 679 672 666 658 652 645 638 631 625 618 192 684 677 670 663 657 660 643 636 630 623 193 689 682 675 668 662 666 648 641 635 628 194 694 687 680 673 667 660 653 646 640 633 195 699 692 686 678 672 665 658 651 645 638 196 704 697 690 683 677 670 663 656 660 643 197 709 702 695 688 682 675 668 661 655 648 198 714 707 700 693 687 680 673 666 660 663 199 719 712 705 698 692 685 678 671 666 658 200 724 717 710 703 697 690 683 676 670 663 258 PREDICTION TABLES FOB BASAL METABOLISM. TabIiE n. — Faetorfar ttatwre and age in men. — Continued. 51 52 53 54 55 56 57 68 59 60 151 411 404 397 391 384 377 370 364 357 350 152 416 409 402 396 389 382 376 369 362 365 153 421 414 407 401 394 387 380 374 367 360 154 426 419 412 406 399 392 385 379 372 365 155 431 424 417 411 404 397 390 384 377 370 156 436 429 422 416 409 402 395 389 382 375 157 441 434 428 421 414 407 400 394 387 380 158 446 439 433 426 419 412 405 399 392 385 159 451 444 438 431 424 417 410 404 397 390 160 456 449 443 436 429 422 415 409 402 395 161 461 454 448 441 434 427 420 414 407 400 162 466 459 453 446 439 432 425 419 412 406 163 471 464 458 451 444 437 431 424 417 410 164 476 469 463 456 449 442 436 429 422 415 165 481 474 468 461 464 447 441 434 427 420 166 486 479 473 466 459 452 446 439 432 425 167 491 484 478 471 464 457 451 444 437 430 168 496 489 483 476 469 462 456 449 442 435 169 501 494 488 481 474 467 461 454 447 440 170 506 499 493 486 479 472 466 459 452 445 171 511 504 498 491 484 477 471 464 457 450 172 516 509 503 496 489 482 476 469 462 455 173 521 514 508 501 494 487 481 474 467 460 174 526 619 513 506 499 492 486 479 472 465 175 531 524 518 511 504 497 491 484 477 470 176 536 529 523 516 509 502 496 489 482 475 177 541 534 528 621 614 507 501 494 487 480 178 546 639 533 626 619 512 606 499 492 485 179 551 544 538 531 524 617 611 604 497 490 180 556 649 643 536 529 622 616 509 502 495 181 561 554 548 541 534 627 521 514 507 500 182 566 559 553 546 639 532 526 519 512 505 183 671 564 558 561 644 637 531 524 517 510 184 676 569 563 556 549 642 536 529 522 615 185 581 674 568 561 554 647 541 534 527 520 186 586 579 673 566 559 562 546 639 532 525 187 591 584 678 671 664 557 551 644 637 530 188 596 589 683 676 669 562 656 549 642 535 189 601 594 688 681 574 567 561 564 647 540 190 606 599 593 686 579 572 566 559 662 545 191 611 604 698 691 684 677 571 564 657 550 192 616 609 603 696 689 582 576 569 562 555 193 621 614 608 601 594 687 681 574 567 660 194 626 619 613 606 599 592 586 579 672 666 195 631 624 618 611 604 697 591 584 677 670 196 636 629 623 616 609 602 696 589 582 575 197 641 634 628 621 614 607 601 594 587 580 198 646 639 633 626 619 612 606 699 692 685 199 651 644 638 631 624 617 611 604 697 690 200 656 649 643 636 629 622 616 609 602 696 PREDICTION TABLES FOR BASAL METABOLISM. 259 Table II. — FacUrrfor stature and age in men. — Concluded. 61 62 63 64 65 66 67 68 69 70 151 343 337 330 323 316 310 303 296 289 283 152 348 342 335 328 321 316 308 301 294 288 153 353 347 340 333 326 320 313 306 299 293 154 358 352 345 338 331 325 318 311 304 298 155 363 357 350 343 336 330 323 316 309 303 156 368 362 355 348 341 335 328 321 314 308 157 373 367 360 353 346 340 333 326 319 313 158 378 372 366 358 351 346 338 331 324 318 159 383 377 370 363 366 360 343 336 329 323 160 388 382 375 368 361 365 348 341 334 328 161 393 387 380 373 366 360 353 346 339 333 162 398 392 385 378 371 365 368 361 344 338 163 403 397 390 383 376 370 363 366 349 343 164 408 402 395 388 381 375 368 361 364 348 165 413 407 400 393 386 380 373 366 359 353 166 418 412 405 398 391 385 378 371 364 358 167 423 417 410 403 396 390 383 376 369 363 168 428 422 415 408 401 396 388 381 374 368 169 434 427 420 413 406 400 393 386 379 373 170 439 432 425 418 411 406 398 391 384 378 171 444 437 430 423 416 410 403 396 389 383 172 449 442 435 428 421 415 408 401 394 388 173 454 447 440 433 426 420 413 406 399 393 174 459 452 445 438 431 425 418 411 404 398 176 464 457 450 443 437 430 423 416 409 403 176 469 462 455 448 442 435 428 421 414 408 177 474 467 460 453 447 440 433 426 419 413 178 479 472 466 458 462 446 438 431 424 418 179 484 477 470 463 467 460 443 436 429 423 180 489 482 475 468 462 455 448 441 434 428 181 494 487 480 473 467 460 453 446 440 433 182 499 492 485 478 472 465 458 461 446 438 183 504 497 490 483 477 470 463 456 460 443 184 509 502 495 488 482 476 468 461 466 448 185 514 507 500 493 487 480 473 466 460 453 186 519 512 505 498 492 486 478 471 466 458 187 524 517 510 503 497 490 483 476 470 463 188 529 522 515 508 502 496 488 481 476 468 189 534 527 620 513 507 500 493 486 480 473 190 539 532 526 518 612 505 498 491 485 478 191 544 537 630 623 617 610 503 496 490 483 192 549 542 636 628 622 516 508 601 496 488 193 554 547 640 633 627 520 513 606 500 493 194 559 552 646 638 632 625 518 611 505 498 195 564 567 650 643 637 530 523 516 510 503 196 569 662 666 548 542 635 528 521 616 508 197 574 567 560 553 547 540 533 626 520 513 198 579 572 666 558 562 646 538 631 526 518 199 584 577 570 563 557 660 543 536 630 623 200 589 682 575 568 562 666 648 541 535 628 260 PREDICTION TABLES FOR BASAL METABOLISM. Table III. — Factor far body-vieight in women. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 25 894 895 896 897 898 899 900 901 902 903 26 904 905 906 907 908 909 909 910 911 912 27 913 914 915 916 917 918 919 920 921 922 28 923 924 925 926 927 928 929 930 931 931 29 932 933 934 935 936 937 938 939 940 941 30 942 943 944 945 946 947 948 949 950 951 31 952 953 953 954 955 956 957 958 959 960 32 961 962 963 964 965 966 967 968 969 970 33 971 972 973 974 975 975 976 977 978 979 34 980 981 982 983 984 985 986 987 988 989 35 990 991 992 993 994 995 996 997 997 998 36 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 37 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 38 1019 1019 1020 1021 1022 1023 1024 1025 1026 1027 39 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 40 1038 1039 1040 1041 1041 1042 1043 1044 1045 1046 41 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 42 1057 la-e 1059 1060 1061 1062 1062 1063 1064 1065 43 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 44 1076 1077 1078 1079 1080 1081 1082 1083 1084 1084 45 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 46 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 47 1105 1106 1106 1107 1108 1109 1110 1111 1112 1113 48 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 49 1124 1125 1126 1127 1128 1128 1129 1130 1131 1132 50 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 51 1143 1144 1145 1146 1147 1148 1149 1150 1150 1151 52 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 53 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 54 1172 1172 1173 1174 1175 1176 1177 1178 1179 1180 55 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 56 1191 1192 1193 1194 1194 1195 1196 1197 1198 1199 57 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 58 1210 1211 1212 1213 1214 1215 1216 1216 1217 1218 59 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 60 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 61 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 62 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 63 1258 1259 1260 1260 1261 1262 1263 1264 1265 1266 64 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 65 1277 1278 1279 1280 1281 1281 1282 1283 1284 1285 66 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 67 1296 1297 1298 1299 1300 1301 1302 1303 1303 1304 68 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 69 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 70 1325 1325 1326 1327 1328 1329 1330 1331 1332 1333 71 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 72 1344 1345 1346 1347 1347 1348 1349 1350 1351 1352 73 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 74 1363 1364 1365 1366 1367 1368 1369 1369 1370 1371 PEEDICTION TABLES FOR BASAL METABOLISM. 261 Table III. — Factor for hody-weight in women. — Concluded. .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 76 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 76 1R8? 1383 1384 1385 1386 1387 1388 1389 1390 1391 77 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 78 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 79 1411 1412 1413 1413 1414 1415 1416 1417 1418 1419 80 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 81 1430 1431 1432 1433 1434 1435 1435 1436 1437 1438 82 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 83 1449 1450 1451 1452 1453 1454 1455 1456 1457 1457 84 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 85 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 86 1478 1479 1479 1480 1481 1482 1483 1484 1485 1486 87 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 88 1497 1498 1499 1500 1501 1501 1502 1503 1604 1605 89 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 90 1516 1517 1518 1519 1520 1521 1522 1522 1523 1524 91 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 92 1535 1536 1537 1538 1539 1540 1541 1542 1543 1644 93 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 94 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 95 1564 1565 1566 1566 1567 1568 1569 1570 1671 1572 96 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 97 1583 1584 1585 1586 1587 1588 1588 1589 1590 1591 98 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 99 1602 1603 1604 1605 1606 1607 1608 1609 1610 1610 100 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 101 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 102 1631 1632 1632 1633 1634 1635 1636 1637 1638 1639 103 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 104 1650 1651 1652 1653 1654 1654 1655 1656 1657 1658 105 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 106 1669 1670 1671 1672 1673 1674 1675 1676 1676 1677 107 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 108 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 109 1698 1698 1699 1700 1701 1702 1703 1704 1705 1706 110 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 111 1717 1718 1719 1720 1720 1721 1722 1723 1724 1725 112 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 113 1736 1737 1738 1739 1740 1741 1741 1742 1743 1744 114 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 115 1755 1756 1757 1758 1759 1760 1761 1762 1763 1763 116 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 117 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 118 1784 1785 1785 1786 1787 1788 1789 1790 1791 1792 119 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 120 1803 1804 1805 1806 1807 1807 1808 1809 1810 1811 121 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 122 1822 1823 1824 1825 1826 1827 1828 1829 1829 1830 123 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 124 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 262 PREDICTION TABLES FOR BASAL METABOLISM. Table IV. — Faetorfor stature and age in women. 21 22 23 24 25 26 27 28 29 30 151 181 176 172 167 162 158 153 148 144 139 152 183 178 174 169 164 160 155 150 146 141 153 185 180 175 171 166 161 157 152 147 143 154 187 182 177 173 168 163 159 154 149 145 155 189 184 179 174 170 165 160 166 151 146 156 190 186 181 176 172 167 162 168 153 148 157 192 188 183 178 173 169 164 169 155 150 158 194 189 185 180 175 171 166 161 157 152 159 196 191 187 182 177 173 168 163 158 154 160 198 193 188 184 179 174 170 165 160 156 161 199 195 190 186 181 176 172 167 162 158 162 201 197 192 187 183 178 173 169 164 159 163 203 199 194 189 185 180 175 171 166 161 164 205 200 196 191 186 182 177 172 168 163 165 207 202 198 193 188 184 179 174 170 165 166 209 204 199 194 190 185 181 176 171 167 167 211 206 201 197 192 187 183 178 173 169 168 213 208 203 199 194 189 184 180 175 170 169 214 210 205 200 196 191 186 182 177 172 170 216 212 207 202 198 193 188 184 179 174 171 218 213 209 204 199 195 190 185 181 176 172 220 215 211 206 201 197 192 187 183 178 173 222 217 212 208 203 198 194 189 184 180 174 224 219 214 210 205 200 196 191 186 182 175 225 221 216 211 207 202 197 193 188 183 176 227 223 218 213 209 204 199 195 190 185 177 229 225 220 215 210 206 201 196 192 187 178 231 226 222 217 212 208 203 198 194 189 179 233 228 224 219 214 210 205 200 195 191 180 235 230 225 221 216 211 207 202 197 193 181 237 232 227 223 218 213 209 204 199 195 182 238 234 229 224 220 215 210 206 201 196 183 240 236 231 226 222 217 212 208 203 198 184 242 237 233 228 223 219 214 209 205 200 185 244 239 235 230 225 221 216 211 207 202 186 246 241 236 232 227 222 218 213 208 204 187 248 243 238 234 229 224 220 215 210 206 188 250 245 240 236 231 226 221 217 212 207 189 251 247 242 237 233 228 223 219 214 209 190 253 249 244 239 235 230 225 221 216 211 191 255 250 246 241 236 232 227 222 218 213 192 257 252 248 243 238 234 229 224 220 215 193 259 254 249 245 240 235 231 226 221 217 194 261 256 251 247 242 237 233 228 223 219 195 262 258 253 248 244 239 234 230 225 220 196 264 260 255 250 246 241 236 232 227 222 197 266 262 257 252 247 243 238 233 229 224 198 268 263 259 254 249 245 240 235 231 226 199 270 265 261 256 251 247 242 237 232 228 200 272 267 262 258 253 248 244 239 234 230 PREDICTION TABLES FOR BASAL METABOLISM. 263 Table IV. — Fadarfor stature and age in women. — Continued. 31 32 33 34 35 36 37 38 39 40 151 134 130 125 120 116 111 106 102 97 92 152 136 132 127 122 117 113 108 103 99 94 153 138 133 129 124 119 115 110 105 101 96 154 140 135 131 126 121 117 112 107 102 98 155 142 137 132 128 123 118 114 109 104 100 156 144 139 134 130 125 120 116 111 106 102 157 145 141 136 131 127 122 117 113 108 103 158 147 143 138 133 129 124 119 115 110 105 159 149 144 140 135 130 126 121 116 112 107 160 151 146 142 137 132 128 123 118 114 109 161 153 148 143 139 134 129 125 120 115 111 162 155 150 145 141 136 131 127 122 117 113 163 157 152 147 143 138 133 128 124 119 114 164 158 154 149 144 140 135 130 126 121 116 165 160 156 151 146 142 137 132 128 123 118 166 162 157 153 148 143 139 134 129 125 120 167 164 159 155 150 145 141 136 131 127 122 168 166 161 156 152 147 142 138 133 128 124 169 168 163 158 154 149 144 140 135 130 126 170 169 165 160 155 151 146 141 137 132 127 171 171 167 162 157 153 148 143 139 134 129 172 173 169 164 159 154 150 145 140 136 131 173 176 170 166 161 156 152 147 142 138 133 174 177 172 168 163 158 154 149 144 139 135 175 179 174 169 165 160 155 151 146 141 137 176 181 176 171 167 162 157 153 148 143 139 177 182 178 173 168 164 159 154 ISO 145 140 178' 184 180 175 170 166 161 156 152 147 142 179 186 181 177 172 167 163 158 153 149 144 180 188 183 179 174 169 165 160 155 151 146 181 190 185 180 176 171 166 162 157 152 148 182 192 187 182 178 173 168 164 159 154 150 183 194 189 184 180 175 170 165 161 156 151 184 195 191 186 181 177 172 167 163 158 153 185 197 193 188 183 179 174 169 165 160 155 186 199 194 190 185 180 176 171 166 162 157 187 201 196 192 187 182 178 173 168 164 159 188 203 198 193 189 184 179 175 170 165 161 189 205 200 195 191 186 181 177 172 167 163 190 206 202 197 192 188 183 178 174 169 164 191 208 204 199 194 190 185 180 176 171 166 192 210 206 201 196 191 187 182 177 173 168 193 212 207 203 198 193 189 184 179 175 170 194 214 209 205 200 195 191 186 181 176 172 195 216 211 206 202 197 192 188 183 178 174 196 218 213 208 204 199 194 190 185 180 175 197 219 215 210 205 201 196 191 187 182 177 198 221 217 212 207 203 198 193 189 184 179 199 223 218 214 209 204 200 195 190 186 181 200 225 220 216 211 206 202 197 192 188 183 264 PREDICTION TABLES FOR BASAL METABOLISM. Table IV. — Factor for stature and age in women. — Ck>ntinued. 41 42 43 44 45 46 47 48 49 50 151 88 83 78 74 69 64 60 55 50 46 152 89 85 80 75 71 66 61 57 52 47 153 91 87 82 77 73 68 63 59 54 49 154 93 88 84 79 74 70 65 60 56 51 155 95 90 86 81 76 72 67 62 68 53 156 97 92 87 83 78 73 69 64 59 65 157 99 94 89 85 80 75 71 66 61 67 158 101 96 91 87 82 77 72 68 63 68 159 102 98 93 88 84 79 74 70 65 60 160 104 100 95 90 86 81 76 72 67 62 161 106 101 97 92 87 83 78 73 69 64 162 108 103 99 94 89 85 80 75 71 66 163 110 105 100 96 91 86 82 77 72 68 164 112 107 102 98 93 88 84 79 74 70 165 113 109 104 99 95 90 85 81 76 71 166 115 111 106 101 97 92 87 83 78 73 167 117 113 108 103 98 94 89 84 80 75 168 119 114 110 105 100 96 91 86 82 77 169 121 116 112 107 102 98 93 88 83 79 170 123 118 113 109 104 99 95 90 85 81 171 125 120 115 111 106 101 97 92 87 83 172 126 122 117 112 108 103 98 94 89 84 173 128 124 119 114 110 105 100 96 91 86 174 130 125 121 116 111 107 102 97 93 88 175 132 127 123 118 113 109 104 99 95 90 176 134 129 124 120 115 110 106 101 96 92 177 136 131 126 122 117 112 108 103 98 94 178 138 133 128 124 119 114 109 105 100 95 179 139 135 130 125 121 116 111 107 102 97 180 141 137 132 127 123 118 113 108 104 99 181 143 138 134 129 124 120 115 110 106 101 182 145 140 136 131 126 122 117 112 108 103 183 147 142 137 133 128 123 119 114 109 105 184 149 144 139 135 130 125 121 116 111 107 185 150 146 141 136 132 127 122 118 113 108 186 152 148 143 138 134 129 124 120 115 110 187 154 150 145 140 135 131 126 121 117 112 188 156 151 147 142 137 133 128 123 119 114 189 158 153 149 144 139 134 130 125 120 116 190 160 155 150 146 141 136 132 127 122 118 191 162 157 152 148 143 138 134 129 124 119 192 163 159 154 149 145 140 135 131 126 121 193 165 161 156 151 147 142 137 133 128 123 194 167 162 158 153 148 144 139 134 130 125 195 169 164 160 155 150 146 141 136 132 127 196 171 166 161 157 152 147 143 138 133 129 197 173 168 163 159 154 149 145 140 135 131 198 175 170 165 160 156 151 146 142 137 132 199 176 172 167 162 158 153 148 144 139 134 200 178 174 169 164 160 155 150 145 141 136 PREDICTION TABLES FOR BASAL METABOLISM. 265 Table IV — Factor for statuxe and age in women — Continued. 51 52 53 54 55 56 57 58 59 60 151 41 36 31 27 22 17 13 8 3 -1.2 152 43 38 33 29 24 19 15 10 5 0.6 153 45 40 35 31 26 21 16 12 7 2 154 46 42 37 32 28 23 18 14 9 4 155 48 44 39 34 30 25 20 16 11 6 156 50 45 41 36 31 27 22 17 13 8 157 52 47 43 38 33 29 24 19 15 10 158 54 49 44 40 35 30 26 21 16 12 159 56 51 46 42 37 32 28 23 18 14 160 57 53 48 43 39 34 29 25 20 15 161 59 55 50 45 41 36 31 27 22 17 162 61 57 52 47 42 38 33 28 24 19 163 63 58 54 49 44 40 35 30 26 21 164 65 60 56 51 46 42 37 32 27 23 165 67 62 57 53 48 43 39 34 29 25 166 69 64 59 55 50 45 41 36 31 26 167 70 66 61 56 52 47 42 38 33 28 168 72 68 63 58 54 49 44 40 35 30 169 74 69 65 60 55 51 46 41 37 32 170 76 71 67 62 57 53 48 43 39 34 171 78 73 68 64 59 54 50 45 40 36 172 80 75 70 66 61 56 52 47 42 38 173 82 77 72 67 63 58 53 49 44 39 174 83 79 74 69 65 60 55 51 46 41 175 85 81 76 71 67 62 57 52 48 43 176 87 82 78 73 68 64 59 54 50 45 177 89 84 80 75 70 66 61 56 52 47 178 91 86 81 77 72 67 63 58 53 49 179 93 88 83 79 74 69 65 60 65 51 180 94 90 85 80 76 71 66 62 57 52 181 96 92 87 82 78 73 68 64 59 54 182 98 93 89 84 79 75 70 65 61 56 183 100 95 91 86 81 77 72 67 63 58 184 102 97 93 88 83 78 74 69 64 60 185 104 99 94 90 85 80 76 71 66 62 186 106 101 96 92 87 82 78 73 68 63 187 107 103 98 93 89 84 79 75 70 65 188 109 105 100 95 91 86 81 77 72 67 189 111 106 102 97 92 88 83 78 74 69 190 113 108 104 99 94 90 85 80 76 71 191 115 110 105 101 96 91 87 82 77 73 192 117 112 107 103 98 93 89 84 79 75 193 119 114 109 104 100 95 90 86 81 76 194 120 116 111 106 102 97 92 88 83 78 195 122 118 113 108 104 99 94 89 85 80 196 124 119 115 110 105 101 96 91 87 82 197 126 121 117 112 107 103 98 93 89 84 198 128 123 118 114 109 104 100 95 90 86 199 130 125 120 116 111 106 102 97 92 88 200 131 127 122 117 113 108 103 99 94 89 266 PREDICTION TABLES FOR BASAL METABOLISM. Table IV. — Fadorjar stature and age in tvtnrun. — Concluded. 61 62 63 64 65 66 67 68 69 70 151 -6 -11 -15 -20 -25 -29 -34 -39 -43 -48 152 -4 - 9 -13 -18 -23 -27 -32 -37 -41 -46 153 -2 - 7 -12 -16 -21 -26 -30 -35 -40 -44 154 -0 - 5 -10 -14 -19 -24 -28 -33 -38 -42 155 1 - 3 - 8 -13 -17 -22 -27 -31 -36 -41 156 3 - 1 - 6 -11 -15 -20 -25 -29 -34 -39 157 5 1 - 4 - 9 -14 -18 -23 -28 -32 -37 158 7 2 - 2 - 7 -12 -16 -21 -26 -30 -35 159 9 4 - - 5 -10 -15 -19 -24 -29 -33 160 11 6 1 - 3 - 8 -13 -17 -22 -27 -31 161 13 8 3 - 1 - 6 -11 -15 -20 -25 -30 162 14 10 S - 4 - 9 -14 -18 -23 -28 163 16 12 7 2 - 2 - 7 -12 -16 -21 -26 164 18 13 9 4 - 1 - 5 -10 -15 -19 -24 165 20 15 11 6 1 - 3 - 8 -13 -17 -22 166 22 17 12 8 3 - 2 - 6 -11 -16 -20 167 24 19 14 10 5 - 4 - 9 -14 -18 168 26 21 16 11 7 2 - 3 - 7 -12 -17 169 27 23 18 13 9 4 - 1 - 5 -10 -15 170 29 25 20 15 11 6 1 - 4 - 8 -13 171 31 26 22 17 12 8 3 - 2 - 6 -11 172 33 28 24 19 14 10 5 - 4 - 9 173 35 30 25 21 16 11 7 2 - 3 - 7 174 37 32 27 23 18 13 9 4 - 1 - 6 175 38 34 29 24 20 15 10 6 1 - 4 176 40 36 31 26 22 17 12 8 3 - 2 177 42 37 33 28 23 19 14 9 5 178 44 39 35 30 25 21 16 11 7 2 179 46 41 37 32 27 22 18 13 8 4 180 48 43 38 34 29 24 20 15 10 6 181 50 45 40 36 31 26 22 17 12 8 182 51 47 42 37 33 28 23 19 14 9 183 53 49 44 39 35 30 25 21 16 11 184 55 50 46 41 36 32 27 22 18 13 185 57 52 48 43 38 34 29 24 20 15 186 59 54 49 45 40 35 31 26 21 17 187 61 56 51 47 42 37 33 28 23 19 188 63 58 53 48 44 39 34 30 25 20 189 64 60 55 50 46 41 36 32 27 22 190 66 62 57 52 48 43 38 33 29 24 191 68 63 59 54 49 45 40 35 31 26 192 70 65 61 56 51 47 42 37 33 28 193 72 67 62 58 53 48 44 39 34 30 194 74 69 64 60 55 50 46 41 36 32 195 75 71 66 61 67 52 47 43 38 33 196 77 73 68 63 59 54 49 45 40 35 197 79 74 70 65 60 56 51 46 42 37 198 81 76 72 67 62 58 53 48 44 39 199 83 78 74 69 64 59 65 50 45 41 200 85 80 75 71 66 61 57 52 47 43