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: :':g S. t.EE, 
 
 .i-^VilA COLLi-,.'_ 
 
 New Yobk, 
 
 Transactions of The Academy of Science of St. Louis. 
 
 VOL. VI. No. 12. 
 
 THE GROWTH OF ST. LOUIS CHILDREN. 
 
 WILLIAM TOWNSEND PORTER. 
 
 Issued April 14, 1894. 
 
THE GROWTH OF ST. LOUIS CHILDREN. 
 
 INTRODUCTION. 
 
 In November, 1891, I applied to the Teachers' Committee 
 of the St. Louis Board of Public Schools for permission to 
 make a series of physical measurements of the St. Louis 
 school children. The ends in view were the study of the 
 phenomena of growth, the making of physical standards for 
 each age in the period of school life, and the adjustment of 
 school tasks to the pupil's strength. On the recommendation 
 of Mr. Long, superintendent of the Public Schools, Dr. Hick- 
 man and Mr. Walter F. McEntire, at that time chairman of 
 the committee, it was resolved to lay before the Board a 
 statement of the purpose of the measurements and to advise 
 that the permission to make them be granted. This favorable 
 report, for which thanks are due the gentlemen just named, 
 caused the Board to authorize the measurements at its sitting 
 December 8, 1891. 
 
 The measurements were collected by what statisticians know 
 as the generalizing method. In the generalizing method, a 
 great number of children is measured once, and the measure- 
 ments classified according to age. The mean height of the 
 boys or girls at each age is regarded as the height typical 
 of that age. When these typical heights are arranged 
 in order, they show the increase in the height of the type- 
 child during his period of growth and thus express a 
 law of growth. A similar procedure reveals the growth in 
 ■weight, girth of chest, or any other physical dimension. It is 
 believed that the values got by the generalizing method are 
 the same as would be obtained if a smaller number of children 
 was measured yearly during the growth period. In either 
 case, the accuracy of the result depends on the number of 
 observations at each age, and a high degree of accuracy 
 requires the making of many thousand measurements. 
 
 (263) 
 
264 Introduction. 
 
 So large an undertaking demands great labor and a consid- 
 erable expenditure of money. The labor was in the present 
 instance shared by many hands. Most of the measurements 
 were made by the teachers. The measurements of the head 
 and face were made by undergraduates of the St. Louis 
 Medical College. Other members of the same institution 
 were of the greatest service as " special assistants." Messrs. 
 Taussig, Gooden, Soper, Blair, Gross, Schlossstein, Lemen, 
 Loth, Newcomb and Simmons served in this capacity. 
 To their unwearied and long-continued labors and to the 
 support unselfishly given them by their fellow-students the 
 success of the work is chiefly due. 
 
 The expense of the investigation was for apparatus, printing 
 and the hire of clerks, and was borne by gentlemen of public 
 spirit in St. Louis. Some of the apparatus was given or 
 loaned free of charge. The Simmons Hardware Company 
 gave callipers and measuring tapes ; the Fairbanks Scale Com- 
 pany loaned scales; Mr. F. W. Humphrey loaned a dozen 
 watches; Dr. John Green and Dr. A. E. Ewiug gave cards 
 for testing the acuteness of vision, and the Nixon- Jones 
 Printing Company made special rates for printing. 
 
 The cordial support of Chancellor Chaplin, Professors H. 
 S. Pritchett, G. Hambach and E. A. Engler of Washington 
 University, the valuable advice of Dr. John B. Shapleigh, and 
 the interest of the Academy of Science of St. Louis are 
 gratefully acknowledged. 
 
 The data collected are necessarily of unequal value. Many 
 of the curves constructed from them are highly satisfactory; 
 others present irregularities to be ascribed to an insufficient 
 number of observations at those points. Some investigators 
 have withheld the curves in which such irregularities occur. 
 They have all been printed here, because the wide-spread use 
 of anthropometrical methods in the Public Schools, so much 
 to be desired, seems at present only possible where the meas- 
 urements are made by the teachers, and it is necessary to 
 know by the examination of the total material of such inves- 
 tigations, what degree of accuracy can be expected. 
 
CHAPTER J. 
 
 THE COLLECTION OF THE MEASUREMENTS. 
 
 In collecting anthropometrical measurements on a large 
 scale, a systematic working-plan is evidently of much impor- 
 tance. Many things should be borne in mind in making such 
 a plan. The school routine should be disturbed as little as 
 possible ; the directions to the measurers should be compre- 
 hensive and clear; the apparatus employed should be simple; 
 the measurements should be made during a few months only 
 and in the same season of the year, for the weight of clothing 
 and even the rate of growth differs at different seasons, and 
 measurements collected partly in one season and partly in an- 
 other cannot be so suitable for comparison as those collected 
 only in the winter or only in the summer; the order in which 
 the schools are visited should be governed by their situation, so 
 that no time may be spent unnecessarily in going and coming ; 
 and much care should be taken to collect sufficient data con- 
 cerning the social condition and the nationality of parents. 
 In short, the construction of a serviceable working-plan for 
 anthropometrical measurements of great numbers of children 
 is a difficult task, and it is to be regretted that the literature 
 is all but barren of suggestions as to the best method of 
 collecting such material. It is hoped for this reason that a 
 description of the methods used in this investigation may be 
 not without value. 
 
 The data collected are mentioned in Form A., one of four 
 " forms" employed in this investigation. 
 
 Form A. 
 
 MALE, 
 
 Please Write with Ink. 
 
 -1. Observer 
 
 2. School 
 
 3. Date 
 
 4. Name of pupil 
 
 5. Place of birth 
 
 6. Age at nearest birthday 
 
 (265) 
 
266 Trans. Acad. Sci. of St. Louis. 
 
 7 In what country was father born 
 
 8. In what country was mother born > 
 
 9. Occupation of father 
 
 10. No. of sisters living ; dead 
 
 11. No. of brothers living ; dead 
 
 ] 2. Residence, No Street. 
 
 fDark Brown. 
 Dark Brown. ... , ^ _ 
 
 „ I Light Brown. 
 
 13. Hair ■{ Light Brown. U. Eyes -{ r^^ 
 
 I Red. „ 
 
 ^, I Grey. 
 
 I Flaxen. L •' 
 
 15. Height standing cm. 
 
 16. Height sitting cm. 
 
 17. Span of arms cm. 
 
 18. Strength of squeeze, right hand lbs. 
 
 19. Strength of squeeze, left hand lbs. 
 
 20. Girth of chest, forced expiration cm. 
 
 21. Girth of chest, forced inspiration cm. 
 
 22. Weight lbs. 
 
 23. Acuteness of vision, right eye 
 
 24. Acuteness of vision, left eye 
 
 25. Acuteness of hearing, right ear ft in 
 
 26. Acuteness of hearing, left ear ft in. 
 
 27. Length of head mm. 
 
 28. Width of head mm. 
 
 29. Height of face mm. 
 
 30. Width of face mm. 
 
 31. The height of face from the hair line to ihe point of chin mm. 
 
 32. Grade 
 
 Form B was the same as Form A, except that the paper ou 
 which it was printed was green instead of white, the color of 
 Form A, and the word "Male" was replaced by the word 
 " Female." 
 
 On Jan. 4, 1892, the first school * in the series to be exam 
 ined began to set down the answers 1, 2, 3, 4, 13, 14, 32, and 
 its pupils were directed to carry home Form C in order that 
 it might be filled by the parents. 
 
 * Pupils were measured in the following schools: Ames, Blair, Blow, 
 Branch High, Bryan Hill, Carr, Carroll, Carr Lane, Central High, Charless, 
 Chouteau, Clay, Clinton, Crow, Divoll, Douglass, Eliot, ElleardsvilJe, Frank- 
 lin, Garfield, Hamilton, Hodgen, Humboldt, Irving, Jackson, Jefferson, 
 Laclede, Lafayette, Lincoln, Lowell, Lyon, Madison, Maramec, Mullanphy, 
 O'Fallon, Peabody, Penrose, Pestallozzi, Polytechnic, Pope, Shepard, Shields, 
 Spring Avenue, Stoddard, Webster, New Webster. (The " Branches " of 
 the Clinton and other schools are included.) 
 
Porter — The Growth of St. Louis Children. 267 
 
 Form C. 
 
 THE PHYSIQUE OF THE SCHOOL CHILDREN IN ST. LOUIS. 
 
 The parents or guardians of school children are requested to fill out the 
 following blank, and to return it to the teacher on the next school day : 
 
 4. Name of pupil 
 
 5. Place of birth 
 
 6. Age at nearest birthday 
 
 7. In what country was pupil's father born 
 
 8. In what country was pupil's mother born 
 
 9. Occupation of father 
 
 10. Number of pupil's sisters living ; dead 
 
 11. Number of pupil's brothers living ; dead 
 
 12. Eesidence of pupil, No , Street. 
 
 On the second day, Form C having been returned, answers 
 5, 6, 7, 8, 9, 10, 11 and 12 were written. Some ignorant or 
 prejudiced parents refused to answer the questions in Form C 
 and in such cases the answers were obtained as far as possible 
 from the school registers. While the first school was em- 
 ployed in this way on the second day, another school began 
 to answer questions 1, 2, 3, 4 and 32. On the third day, the 
 first school measured the height standing, height sitting and 
 span of arms, while the second school was busy with the 
 second day's work and the third school with the first. 
 
 Thus the thirty-two questions were divided into groups, and 
 by the ninth day nine schools were working simultaneously, 
 each on a different group. As soon as one school finished 
 with an apparatus, it was taken to the next school on the list, 
 almost always the nearest in point of distance. An extract 
 from " The Chart of Days " will make this clear. 
 
268 
 
 Trans. Acad. Sci. of St. Louis. 
 
 A PORTION OF " THE CHART OF DAYS.' 
 
 NAME OF 
 SCHOOL. 
 
 SPECIAL 
 ASSISTANT. 
 
 
 
 
 Record : 
 
 
 
 
 
 
 
 
 
 
 
 
 
 MS 
 
 
 
 
 
 
 M to 
 
 "^ 
 
 
 
 
 
 
 "la 
 ..a 
 
 o 
 
 CD 
 
 
 N 
 
 a> 
 
 0) 
 
 3 
 
 J3 
 
 
 o 
 
 O 
 
 bo 
 a 
 'S 
 
 ei 
 
 w 
 
 o 
 
 m O 
 
 00 
 
 bo 33 
 
 
 O 
 o 
 
 S 
 
 _bp 
 'S 
 
 tn 
 
 <o 
 a 
 
 CO 
 
 0) 
 
 a 
 
 flO 
 
 fl 
 
 a> 
 
 03 
 
 
 « 
 
 o 
 
 <J^ 
 
 < 
 
 tn 
 
 5 
 
 < 
 
 <! 
 
 Laclede 
 
 Madison and New 
 Madison 
 
 Pestalozzi 
 
 Carroll 
 
 Lafayette and La- 
 fayette Branch.. 
 
 Humboldt 
 
 Lyon 
 
 Shepard 
 
 Meramec 
 
 Blow and Blow 
 Branch 
 
 Lemen 
 
 Simmons. .- 
 Newcomb... 
 Loth 
 
 Taussig. .. . 
 Gooden . ... 
 
 Soper 
 
 Blair... 
 
 Gross 
 
 Schlossstein 
 
 4* 
 
 5 
 
 7 
 
 8 
 
 11 
 
 12 
 
 13 
 
 14 
 
 5 
 
 6 
 
 8 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 6 
 
 7 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 18 
 
 7 
 
 8 
 
 12 
 
 13 
 
 14 
 
 15 
 
 18 
 
 19 
 
 8 
 
 11 
 
 13 
 
 14 
 
 15 
 
 18 
 
 19 
 
 20 
 
 11 
 
 12 
 
 14 
 
 15 
 
 18 
 
 19 
 
 20 
 
 21 
 
 12 
 
 13 
 
 15 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 13 
 
 14 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 25 
 
 14 
 
 15 
 
 19 
 
 20 
 
 21 
 
 22 
 
 25 
 
 26 
 
 15 
 
 18 
 
 20 
 
 21 
 
 22 
 
 25 
 
 26 
 
 27 
 
 18 
 19 
 20 
 
 21 
 22 
 
 25 
 26 
 27 
 
 The Laclede School began Jan. 4 and finished Jan. 15, the 
 Madison School began Jan. 5 and finished Jan. 18, and so 
 through the list. 
 
 Nearly nine thousand pupils were examined each school-day 
 after the ninth, and each day saw the returns of nearly a 
 thousand pupils completed. The collection of material was 
 finished in fifty-four school-days, beginning Jan. 4 and ending 
 March 18. During this period of about 11 weeks, 18059 
 girls and 16295 boys were examined f and nearly one million 
 data collected, about five hundred thousand of which were 
 measurements, a result which would hardly have been possible 
 without the strenuous exertions of my assistants. 
 
 One of the Special Assistants mentioned in the Chart of 
 Days was assigned to each school under investigation. It was 
 his duty to visit the school every day for the purpose of 
 giving any explanation which might be necessary. He was 
 
 * This and the following numbers are the days of the month on which the 
 respective groups of measurements were made. 
 
 t Owing to absentees, the number of returns of any one measurement, 
 e. g., height, was less than the number here given. 
 
Porter — The Growth of St. Louis Children. 269* 
 
 charged also to see that his school finished its allotted daily 
 task and dispatched at the close of the session the apparatus 
 in its hands to the next school on the list. In addition to 
 these nine Special Assistants, thirty Head Measurers were 
 employed. The Head Measurers were divided into five sec- 
 tions named after the days of the school week from Monday 
 to Friday. Each section went on its own day to the school 
 whose turn it was to have heads and faces measured. The 
 remaining measurements were made by the teachers. 
 
 Not even the industry of these many assistants would have 
 accomplished the task in the required time had there not been 
 an abundance of apparatus. Of measuring-rods, measuring- 
 tapes for the chest, double sets of Snellen-Green test letters, 
 spectacle blinders, watches and callipers, there were a dozen 
 each, and five dynamometers and six small platform-scales 
 were also in constant use. Twelve school rooms could thus 
 often work at the same time, and a great many children were 
 measured in a few hours. 
 
 The following printed instructions were given to every 
 measurer. 
 
 Form D. 
 
 INSTRUCTIONS TO OBSERVERS. 
 
 Four printed forms are furnished. Tliese are : 
 Form A. Male (wliite paper) . 
 " B. Female (tinted paper) . 
 " C. For parents. 
 " D. Instructions to observers. 
 
 On Monday, January 4th, a sufficient number of these forms will be taken 
 to school A. The same day answers 1, 2, 3, 4, 13, 14 and 32, Form A or B, are 
 written, and each pupil is given Form C to carry home. The next morning 
 form C is returned by the pupils, and answers 5, 6, 7, 8, 9, 10, II and 12 
 are copied on form A or B. The third day the measurements begin, and are 
 carried out according to the following 
 
 
 
 
 CALENDAR 
 
 
 
 
 Ist^ 
 
 day 
 
 1,: 
 
 2,3, 
 
 4, 
 
 13, 
 
 14, 
 
 32. 
 
 
 2d 
 
 
 5,' 
 
 6,7, 
 
 |8, 
 
 9,: 
 
 10, 
 
 11, 
 
 12. 
 
 3d 
 
 
 15, 
 
 16, 
 
 17 
 
 
 
 
 
 4th 
 
 
 18, 
 
 , 19. 
 
 
 
 
 
 
 5th 
 
 
 20, 
 
 , 21. 
 
 
 
 
 
 
 6th 
 
 
 22. 
 
 
 
 
 
 
 
 7th 
 
 
 23, 
 
 24. 
 
 
 
 
 
 
 8th 
 
 
 25, 
 
 , 26. 
 
 
 
 
 
 
 9 th 
 
 
 27, 
 
 28, 
 
 29, 
 
 , 30 
 
 ,31 
 
 . 
 
 
270 Trans. Acad. Sci. of St. Louis. 
 
 Form C and answers 1 to 12 in forms A and B, require no explanation. 
 Ttie remaining answers are to be sought by the following methods. 
 
 Arrange forms A and B in the order in which the pupils sit at their desks, 
 and preserve this arrangement throughout the measurements. 
 
 13, 14. Color of Hair and Eyes. 
 
 Choose the adjective that most nearly indicates the color; cross out the 
 rest with pen and ink. 
 
 13. Height Standing. 
 
 1. All the pupils unlace their shoes. 
 
 2. The teacher places the measuring rod against the cloak-room door cas- 
 ing, the projections on the rod serving to keep it parallel with the casing, 
 and presumably perpendicular to the floor. 
 
 3. The pupil in the first seat comes forward, removes his shoes, stands 
 on a folded newspaper upon which the rod also rests, his heels, body and 
 head touching the door casing, the mouth closed and the chin somewhat 
 depressed. Hair worn in a high knot must be let down. 
 
 4. Lower the sliding arm until the edge touches the crown of the pupil's 
 head, and dictate the reading to a pupil assistant, who writes it opposite 
 "15. Height standing." Meanwhile, the second pupil gets ready. [The 
 rods are divided in centimetres and half centimetres; it will be easy to read 
 to quarter centimetres. The dictation should be in the decimal system; 
 thus: " One hundred fifteen, seventy-five (written 115.75), not one hundred 
 fifteen and three quarters.] 
 
 5. The first pupil steps to one side, puts on his shoes, returns to his seat, 
 and there laces his shoes. The second pupil removes his shoes and steps 
 on the newspaper. The third pupil comes forward. 
 
 1 6. Height Sitting. 
 
 Place an armless wooden chair with a flat seat sideways against the door 
 casing. The measuring rod is held perpendicularly on the seat, the pro- 
 jections on the rod touching if possible the casing. Pupils come forward 
 as before. 
 
 Take care: 1, that the lower part of the spinal column touches the rod; 
 2, that the mouth is closed and the chin somewhat depressed ; 3, that hair 
 worn in a knot on the back of the head does not introduce an error. Meas- 
 ure, and dictate the reading. 
 
 2 7. Span of Arms. 
 
 1. Draw on the wall a chalk mark parallel with the floor and as high as 
 the chin of a pupil of average height. 
 
 2. Hold the measuring rod parallel to the line and as high as the neck of 
 the pupil to be measured. 
 
 3. The pupil touches one end with the middle finger of one hand and 
 stretches along the rod as far as he can reach; chin up, heels together, body 
 as close as possible to the rod. 
 
 4. Dictate the reading. 
 
 [In this and all other measurements the place of the pupil measured 
 should be instantly taken by another. ] 
 
Porter — The Growth oj St. Louis Children. 271 
 
 18, 19. Strength of Squeeze. 
 
 1. Depress tlie trigger of the dynamometer until the point of the indicator 
 is exactly over the zero line of the scale. 
 
 2. The pupil grasps the oval ring in the right hand and squeezes his 
 best. 
 
 3. Read the outer scale (graduated from to 160) to pounds * as ex- 
 actly as possible. Write the number after <' 18. Strength of Squeeze, right 
 hand." 
 
 4. Reset the instrument, and test left hand. [Please do not touch the 
 indicator. Always use the trigger.] 
 
 20, 21. Girth of Chest. 
 
 1. Take four pupils into the cloak room. They remove clothing over 
 chest down to the garment next the skin. The measurements are made on a 
 level with the nipples, and are dictated in centimetres and decimal frac- 
 tions of a centimetre to a pupil assistant, who writes them opposite 20 
 and 21. 
 
 2. "Forced expiration." Pupil breathes out, makes chest as small as 
 possible, inclines head forwards, draws shoulders slightly together. 
 
 3. "Forced inspiration." Shoulders back, head raised, deepest possible 
 inspiration. 
 
 . [Some children will require to be shown how to do this. As fast as a pupil 
 is measured, dresses and returns to his seat, another pupil enters the cloak 
 room to take his place, and strips for measurement.] 
 
 22. Weight. 
 The upper figures on the beam and the smaller of the two numbers on the 
 iron weights are used with the scale pan. Pay no attention to them. The 
 lower figures on the beam read from 1 to 45 pounds. Place the pupil's 
 approximate weight on the counterpoise at the end of the beam ; move the 
 poise along the latter until the scale balances. Add the larger number on 
 the hanging weight to the number marked on the lower scale by the poise. 
 The sum is the pupil's weight. 
 
 23, 24:. Acuteness of Vision. 
 
 It is necessary to make these tests between 10:30 a. m., or better 11 
 a. m., and 3 p. m., as at other hours the winter light is insufficient. 
 
 A pupil must not see the card before the moment for his test has come. 
 Nor can the pupils who have been tested be allowed to communicate with 
 those yet to be tested. Otherwise the letters will be committed to memory 
 and the test spoiled. 
 
 1. Hang the test card on the wall opposite the windows, in a good light, 
 and level with the pupil's eyes. Turn down the middle leaf of the card, so 
 that only one set of test letters is visible. 
 
 2. Stand the pupil with toes touching a chalk mark 16 feet 5 inches from 
 the card, and cover the left eye with the blinder furnished for that purpose . 
 The head must be held straight, so that the child cannot see the test letters 
 with the blinded eye. 
 
 wo dynamometers were graduated metrically. 
 
272 Trans. Acad. Sci. of St. Louis. 
 
 3. The child reads the test letters beginning with the largest ; the smallest 
 letter which can be read indicates the " acuteness of vision " at 16 feet 5 
 inches (5 metres). Mark the arable figure under this letter opposite 
 " Acuteness of Vision, right eye." 
 
 4. Change the blinder to the right eye. 
 
 5. Turn up the middle leaf of the test card so as to expose the second set 
 of test letters . 
 
 6. Test the acuteness of vision of the left eye in a similar manner. 
 
 25, 26. Acuteness of Hearing. 
 The hearing tests are to be made in the cloak-room with the doors closed. 
 Their success depends primarily on the absence of all noise from the adjacent 
 class-rooms and halls. 
 
 1. The pupil is seated with the right ear towards the observer. 
 
 2. An assistant closes the pupil's left ear by pressing the tragus (the little 
 cartilage in front of the external opening) inwards with her thumb while 
 with the fingers of the same hand she closes the eyelids with a handkerchief. 
 "With the other hand the assistant holds the end of the brass ring of the tape 
 measure against the head just beneath the ear, grasping the ring between 
 thumb and forefinger and keeping the hand entirely below the auditory 
 opening. 
 
 3. The observer stands directly opposite the ear and 11 feet from it, 
 holding the tape parallel with the floor. The watch is held by the chain 
 ring against the median line of the observer's body, just above and not 
 touching the tape. The face of the watch is towards the pupil. 
 
 4. The observer charges the pupil to say " now " when he hears the 
 watch tick, and advances the watch until the pupil replies. The watch is 
 now withdrawn and again advanced until the pupil replies. Marking this 
 point on the tape measure between finger and thumb, the observer puts the 
 watch behind her back, and asks '« Do you hear now? " If the pupil replies 
 " No," the watch is returned to the former position and the inquiry repeated. 
 If the watch is again heard at this distance the test is satisfactory ; if not, 
 it should be repeated. "Write the distance at which the watch is heard in 
 feet and inches opposite "Acuteness of Hearing, right ear." 
 
 5. Turn the pupil around (180°) and test the left ear in a similar manner. 
 The wilfulness of some children will make the accuracy of their tests 
 
 doubtful. In such cases write an interrogation mark after the figures 
 secured. 
 
 27, 28, 29, 30. Head Measurements. 
 The teacher carries the blanks arranged in the order in which the pupils 
 sit in her room, a pen, and a centimetre rule. The medical assistant makes 
 a measurement, places the callipers on the rule which the teacher holds, 
 and reads the number of centimetres and millimetres. The teacher writes 
 these numbers while the assistant makes the next measurement. 
 
 Instructions for Medical Assistants. 
 
 Measurements must be read to millimetres. 
 
 1. Length of head. — Place one point of the callipers on the most prominent 
 point of the forehead, between the eyebrows. Bring the other point of the 
 callipers down to the posterior part of the head and move it along the middle 
 line until the greatest length of the head is found. (A, B.) 
 
Porter — The Growth of St. Louis Children. 
 
 273 
 
 2. Breadth of head. — Take the greatest breadth of the head between the 
 ears wherever it is found. Hold the callipers horizontally and perfectly 
 symmetrically, approximately at F. 
 
 3. Height of face. — Put one point of the callipers in the deepest depression 
 on the nose between the eyes (C) — then press the other point against the 
 chin and find that point at D where the chin turns backwards. Ask the per- 
 son to press his teeth together. 
 
 4. Breadth of face. — This is the greatest breadth between the narrow, bony 
 ridges felt in front of the ears. The ridges ran from the cheek bones to the 
 ears. Hold the callipers horizontally and symmetrically, approximately 
 atG. 
 
 Position of the Points at which Head Measurements are Taken. 
 A-B, length of head. Approximately at F, breadth of head. C-D, Height 
 of face. Approximately at G, breadth of face.* 
 
 6. Hair line. — This is the height of face from the point of the chin to the 
 point where the hair begins to grow above the forehead. 
 
 Further information, if desired, may be had by addressing the Physiolog- 
 ical Laboratory of Washington University, 625 Clark avenue. f 
 
 "W. TowNSEND Porter. 
 Approved Jan. 4th, 1891. 
 E. H. Long, 
 
 Superintendent. 
 
 Some changes were made ia the above instructions during 
 the course of the investigations. The tests of acuteness of 
 hearing were found impracticable because of the unavoidable 
 noise in the schools and were given up after about seven 
 thousand pupils had been tested. It was noticed that the 
 number possessing less than the normal acuteness of hearing 
 was very large, and more than one pupil was found who had 
 been punished for inattention, the result of an unsuspected 
 
 * I am indebted to Dr. Franz Boas for this figure. 
 
 t Since removed to 1806 Locust street. Dr. Porter's present address is 
 Harvard Medical School, Boston, Mass. 
 
274 Trans. Acad. Sci. of St. Louis. 
 
 deafness. Although the returns did not seem sufficiently 
 trustworthy for statistical treatment, they justified the state- 
 ment that not a little deafness exists unknown to both teacher 
 and parents. This hidden infirmity deprives the pupil of 
 much of the benefit of class-room instruction. 
 
 The measurement of the girth of chest over the garment 
 next the skin was also modified after several thousand boys 
 and girls had been measured, and the boys were made to re- 
 move coats and vests while the girls were measured over the 
 indoor dress. The few girls who wore stays laid them aside. 
 
CHAPTER II. 
 
 THE STATISTICAL METHODS EMPLOYED. 
 
 All measurements are accompanied by unavoidable errors. 
 Thus the attempt to measure the height of a man is influenced 
 by the accuracy with which the measuring apparatus is con- 
 structed, the care with which it is used, the position of the 
 man's head on the vertebral column, the thickness of the 
 interveitebral disks and a multitude of other factors. Some 
 of these influences would make the observed height greater 
 than the true height, others would make it less. The one 
 group tends to counteract or compensate the other, and the 
 result of their conflict is the measurement actually observed. 
 The observed height therefore is never, except by chance, the 
 real height, but deviates from it in one or the other direction — 
 is now above and now below the truth — as one or the other 
 group of influences gets the upper hand. The greater the 
 number of influences, the more perfectly does compensation 
 take place and the more nearly does the observed result 
 approach the truth. But the truth itself can never be known, 
 for only when the number of influences is infinite, can the 
 probability of perfect compensation between them rise to a 
 certainty. That which we call true is merely the probable 
 truth and is worthy of confidence in exact proportion to its 
 numerical probability. 
 
 The influences which affect a measurement are of two sorts, 
 the one accidental and varying, such as, taking the measure- 
 ment of height for an example, the degree of inclination of 
 the head to the axis of the body, the placing of the measuring- 
 rod and the like, the other constant and unvarying, such as an 
 inaccuracy in the construction of the measuring-rod or a per- 
 sistent bias in the mind of the observer. In both classes, the 
 degree of compensation varies with the number of influences, 
 for even a constant cause, although not accidental in its nature 
 and found always on one side of the mean, may be compen- 
 sated by another constant cause on the opposite side of the 
 
 (275) 
 
276 Trans. Acad. Sci. of St. Louis. 
 
 mean. The accidental or varying influences, however, are 
 much more numerous than the constant or unvarying, and 
 thus compensation is in their case much more complete. 
 Constant, unvarying influences are therefore more deceptive 
 than varying, accidental influences. 
 
 In practice, the influences determining the result of a single 
 measurement elude all attempts at calculation, and the extent 
 to which the result of a single observation approximates the 
 truth cannot be told. But if many measurements are made 
 of the same thing, for example the height of a man, the 
 individual measurements arrange themselves on either side of 
 the true height. If only accidental influences have been at 
 work in each individual measurement in the series, the dis- 
 tribution of the observed heights on either side of the real 
 height would, if the number of observations were infinite, be 
 symmetrical. Thus the true height would at once appear, and 
 the probability or degree of deviation of any single measure- 
 ment would also be visible. Even with finite numbers a 
 probability so great as to amount to a practical certainty can 
 be secured. If 2,000 measurements of the same physical 
 dimension, e. g. the height of an individual, are made care- 
 fully, the total number of observations will be distributed 
 nearly as follows : — 
 
Porter — The Growth of St. Louis Children, 
 
 277 
 
 TABLE No. 1. 
 
 The Distribution of 2,000 Measurements of the Same Quantity when 
 THE Deviation of the Individual Observations From the Trub 
 Value of the Measured Quantity is due to Purely Accidental 
 
 Causes.* 
 
 d = the Probable Deviation. 
 
 Number of Observations. 
 
 Greater than + 5.0 d 
 
 1 
 
 + 4.5 d to 
 
 + 5.0 d 
 
 1 
 
 + 4.0 d 
 
 
 + 4.5 d 
 
 5 
 
 + 3,5 d 
 
 
 + 4.0d 
 
 11 
 
 + 3.0d 
 
 
 + 3.5d 
 
 25 
 
 -j- 2.5 d 
 
 
 + 3.0d 
 
 49 
 
 + 2.0 d 
 
 
 + 2.5 d 
 
 85 
 
 -\-l.5d 
 
 
 + 2.0d 
 
 135 
 
 + 1.0 d 
 
 
 + 1.5 d 
 
 188 
 
 + 0.5d 
 
 
 + l.Od 
 
 236 
 
 ± .0 
 
 
 + 0.5 d 
 
 264 
 
 — 0.5d 
 
 
 d= .0 
 
 264 
 
 — l.Od 
 
 
 — 0.5 d 
 
 236 
 
 — 1.5 d 
 
 
 — l.Od 
 
 188 
 
 — 2.0d 
 
 
 — 1.5 d 
 
 135 
 
 — 2.od 
 
 
 — 2.0d 
 
 85 
 
 — B.Od 
 
 
 — 2.5d 
 
 49 
 
 — 3.5 d 
 
 
 — 3.0d 
 
 25 
 
 — 4.0d 
 
 
 — S.5d 
 
 11 
 
 — i.od 
 
 
 — 4.0d 
 
 5 
 
 — 5.0d 
 
 
 — 4.5d 
 
 1 
 
 Greater than 
 
 — 5.0 d 
 
 1 
 
 This result is quite independent of the nature of the thing 
 measured, provided that no unvarying influences are at work. 
 
 An examination of Table No. 1 shows (1) that the distribu- 
 tion of the observations is symmetrical about a median point, 
 in other words that equal deviations to one and the other side 
 of this point are equally probable ; (2) that half the whole 
 number of observations fall within ± 1.0 cZ of the most prob- 
 able value, indicating that a small deviation is more probable 
 than a large one; and (3) that there is a limit beyond which 
 no deviation occurs. Such are the peculiarities of a series of 
 observations in which the deviations from the true value 
 are due to purely accidental causes. It is evident that the 
 most probable value of the true measurement is typical of the 
 whole series, and that the degree of probability of any devia- 
 
 * After Thoma : Untersuchungen iiber die Grosse der anatomischea Be- 
 standtheile des menschlichen Korpers im gesunden und kranken Zastande. 
 Leipzig, 1882. Page 28. 
 
278 
 
 Trans. Acad. iSci. of St. Louis. 
 
 tion from the type is easily calculated ; for example in the 
 series of -Table No. 1, the chances are even that any deviation 
 will fall between +1.0 cZ and — 1.0 d, for it has been seen that 
 half the whole number of observations fall within these limits. 
 Quetelet demonstrated that the method of grouping related 
 measurements could be used not only for showing the most 
 probable height of one individual but also for showing the 
 most probable or typical height, i. e., that most often found, of 
 a number of individuals. The Belgian Astronomer Koyal 
 pointed out that the series obtained by measuring a number 
 of individuals of the same type, e. g., men of the same nation- 
 ality, was characterized by the peculiarities that distinguish 
 a series in which the deviations from the typical or most 
 probable value are due to accidental causes. The truth of 
 this statement is obvious when the two are compared. 
 
 TABLE No. 2.* 
 Heights of United States Recruits. 
 
 Height at Intervals of 
 
 One Inch. 
 
 Number of Recruits. 
 
 Between 78 and 79 i 
 
 nches 
 
 2 
 
 «' 77 ' 
 
 ' 78 
 
 
 6 
 
 i( 76 ' 
 
 ' 77 
 
 
 9 
 
 " 75 ' 
 
 ' 76 
 
 
 42 
 
 " 74 ' 
 
 ' 75 
 
 
 118 
 
 u 73 £ 
 
 ' 74 
 
 
 343 
 
 " 72 ' 
 
 ' 73 
 
 
 680 
 
 u 71 < 
 
 ' 72 
 
 
 1485 
 
 70 ' 
 
 ' 71 
 
 
 2075 
 
 " 69 ' 
 
 ' 70 
 
 
 3133 
 
 •' 68 ' 
 
 ' 69 
 
 
 3631 
 
 u 67 < 
 
 ' 68 
 
 
 4054 
 
 " 66 ' 
 
 ' 67 
 
 
 3475 
 
 " 65 ' 
 
 ' 66 
 
 
 3019 
 
 u 64 t 
 
 ' 65 
 
 
 1947 
 
 " 63 ' 
 
 ' 64 
 
 
 1237 
 
 " 62 * 
 
 ' 63 
 
 
 526 
 
 " 61 ' 
 
 ' 62 
 
 
 50 
 
 «' 60 ' 
 
 ' 61 
 
 
 15 
 
 59 ' 
 
 ' 60 
 
 
 10 
 
 " 58 ' 
 
 ' 59 
 
 
 6 
 
 " 57 ' 
 
 • 58 
 
 
 7 
 
 56 « 
 
 ' 57 
 
 
 3 
 
 " 55 < 
 
 ' 56 
 
 
 1 
 
 " 55 ar 
 
 id less 
 
 4 
 
 
 
 
 Total... 25878 
 
 * E. B. Elliott's table in Medical Statistics of the Provost- Marshal-Gen- 
 eral's Bureau, by J. H. Baxter, 1875, Vol. I. Introduction, page Ixxx. 
 
Porter — The Growth of St. Louis Children. 
 
 279 
 
 If the individual heights of a group of adults are found to 
 be approximations of a middle, typical height, it would seem 
 that the heights of children of the same sex, age and class 
 must show a similar relation to a type ; and this inference is 
 justified by observation. 
 
 TABLE No. 3. 
 Observed Distribution of the Heights of 2192 St. 
 
 Girls, Aged 8. 
 
 Louis School 
 
 Heights at Intervals of 2 Centimetres. 
 
 Number of Observations. 
 
 141 and 142 cm. 
 
 1 
 
 139 
 
 
 140 '« 
 
 
 137 
 
 
 138 " 
 
 1 
 
 135 
 
 
 136 " 
 
 5 
 
 133 
 
 
 134 " 
 
 10 
 
 131 
 
 
 132 <« 
 
 2L 
 
 129 
 
 
 130 " 
 
 28 
 
 127 
 
 
 128 " 
 
 79 
 
 125 
 
 
 126 " 
 
 138 
 
 123 
 
 
 124 " 
 
 183 
 
 121 
 
 
 122 " 
 
 243 
 
 119 
 
 
 120 " 
 
 342 
 
 117 
 
 
 118 " 
 
 321 
 
 115 
 
 
 116 «' 
 
 297 
 
 113 
 
 
 114 " 
 
 222 
 
 111 
 
 
 112 " 
 
 137 
 
 109 
 
 
 110 " 
 
 84 
 
 107 
 
 
 108 " 
 
 42 
 
 105 
 
 
 106 " 
 
 27 
 
 103 
 
 
 104 " 
 
 8 
 
 101 
 
 
 102 " 
 
 2 
 
 99 
 
 
 100 <' 
 
 1 
 
 - 
 
 
 
 — 
 
 Total 2192 
 
 The characteristics of a series in which the individual ob- 
 servations are accidental deviations from a typical middle 
 value are established by methods which have long been used 
 by astronomers and mathematicians. These methods seek to 
 determine (1) the middle or typical value and (2) the way in 
 which the individual observations are dispersed on either side 
 of this value. Some statisticians take the average to be the 
 nearest approach to the typical value, others prefer the mean, 
 i. e., median value.* It will be necessary to consider at some 
 length the relative value of average and mean in anthropomet- 
 rical studies of the growth of children, but for the present a 
 
 * Throughout this work the word mean is used as the synonym of median 
 VALUE, and not in the sense of arithmetical mean, which is called here 
 the AVERAGE. The middle value will be employed as meaning either 
 Median or Average value. 
 
280 
 
 Trans. Acad. Sci. of St. Louis. 
 
 statement of the methods by which the mean and average are 
 secured will suffice. 
 
 By AVERAGE (A) is meant the quotient obtained by divid- 
 ins the sum (2" a) of the values (a) obtained in the individual 
 measurements by the whole number of measurements (?i). 
 
 n 
 
 (1) 
 
 The calculation of the average height of girls, aged 9, will 
 serve as an example. 
 
 TABLE No. 4. 
 
 The Calculation of the Average Height of St. Louis School 
 
 Girls, Aged 9. 
 
 Heiglit in 
 Centi- 
 metres. 
 
 Number of 
 Observa- 
 tions. 
 
 Product. 
 
 Height in 
 Centi- 
 metres. 
 
 Number of 
 Observa- 
 tions. 
 
 Product. 
 
 168 
 
 1 
 
 168 
 
 134 
 
 25 
 
 3350 
 
 167 
 
 
 
 133 
 
 31 
 
 4123 
 
 166 
 
 
 
 182 
 
 29 
 
 3828 
 
 165 
 
 
 
 131 
 
 62 
 
 8122 
 
 164 
 
 
 
 130 
 
 78 
 
 10140 
 
 163 
 
 
 
 129 
 
 91 
 
 11739 
 
 162 
 
 
 
 128 
 
 119 
 
 15232 
 
 161 
 
 
 
 127 
 
 132 
 
 16764 
 
 160 
 
 1 
 
 160 
 
 126 
 
 143 
 
 18018 
 
 159 
 
 
 
 125 
 
 162 
 
 20250 
 
 158 
 
 
 
 124 
 123 
 
 141 
 
 17484 
 
 157 
 
 162 
 
 19926 
 
 156 
 
 
 
 122 
 
 145 
 
 17690 
 
 155 
 
 
 
 121 
 
 130 
 
 15730 
 
 154 
 
 
 
 120 
 
 145 
 
 17400 
 
 153 
 
 
 
 119 
 
 97 
 
 11543 
 
 152 
 
 
 
 118 
 
 94 
 
 11092 
 
 151 
 
 
 
 117 
 
 69 
 
 8073 
 
 150 
 
 
 
 116 
 
 59 
 
 6844 
 
 149 
 
 
 
 115 
 
 47 
 
 5405 
 
 148 
 
 
 
 114 
 
 30 
 
 3420 
 
 147 
 
 
 
 113 
 
 18 
 
 2034 
 
 146 
 
 
 
 112 
 
 11 
 
 1232 
 
 145 
 
 
 
 111 
 
 10 
 
 1110 
 
 144 
 
 
 
 110 
 
 10 
 
 1100 
 
 143 
 
 1 
 
 143 
 
 109 
 
 5 
 
 545 
 
 142 
 
 2 
 
 284 
 
 108 
 
 1 
 
 108 
 
 141 
 
 3 
 
 423 
 
 107 
 
 5 
 
 535 
 
 140 
 
 2 
 
 280 
 
 106 
 
 3 
 
 318 
 
 139 
 
 3 
 
 417 
 
 105 
 
 1 
 
 105 
 
 138 
 
 9 
 
 1242 
 
 104 
 
 1 
 
 104 
 
 137 
 
 12 
 
 1644 
 
 103 
 
 1 
 
 103 
 
 136 
 
 15 
 
 2040 
 
 102 
 
 
 
 135 
 
 14 
 
 1890 
 
 101 
 
 
 
 
 
 
 100 
 
 2 
 
 200 
 
 
 Total 
 
 71 = 2122 
 
 r«=262358 
 
 . la 262358 ^^_, 
 
 A = = =123.64 cm. 
 
 n 2122 
 
Porter — The Growth of St. Louis Children. 281 
 
 If the number of observations is very large, the mean 
 (MEDIAN value, M,) may be found with considerable accuracy 
 by a mere inspection of the series. The mean of such a 
 series is the measurement which most frequently recurs. 
 Thus, the mean height of the recruits of Table Xo. 2, page 278, 
 is between 67 and 68 inches. The accuracy with which the 
 mean can thus be found depends not only on the number of ob- 
 servations, but also on the size of the units of measurement. 
 
 For most purposes it is desirable to know not merely at 
 which inch, centimetre, kilogramme or other unit the greatest 
 number of observations is found, but exactly at what fraction 
 of the unit. Again, the relation between the number of 
 observations and the size of the unit may be such that 
 the largest number of observations at one unit will not 
 fall at the true mean, or line dividing the total number 
 of observations into two equal groups. The method by 
 which the mean can be calculated with exactness will be 
 illustrated by the following example. The mean height of 
 the girls in Table No. 4 is obtained by adding the number 
 of observations from below upwards until the sum cannot 
 be' increased by the next number in the column without 
 exceeding half of the total number of observations. Thus 
 1046 is reached opposite 123 cm. ; the next number in 
 the column (141) would make the sum 1187, which is 
 more than the half (1061) of the total number of observa- 
 tions (2122). The mean is, therefore, greater than 123 cm. 
 but less than 125 cm. Its position is found by interpolation. 
 Half of the total number of observations is 1061, which is 15 
 more than the sum of the observations up to 124 cm. ; 15 is 
 11 per cent, of 141, the observations at 124 cm. Hence, the 
 mean is 124.15 cm. 
 
 Neither the mean nor the average can give any information 
 as to the way in which the individual observations in a series 
 are distributed, and it is plain that two series having an iden- 
 tical mean or average may differ greatly in respect of the 
 dispersion of the individuals from the middle value. Thus the 
 two very different series — 
 
 4, 5, 6, 14, 15, 16 
 9, 9, 10, 10, 11, 11 
 
282 Trans. Acad. Sci. of St. Louis. 
 
 have the same average (10). The best measure of the degree 
 of dispersion or deviation of the individual members of a series 
 from their common mean or average is that afforded by the 
 Probable Deviation. The probable deviation is that devia- 
 tion from the middle value, which, in a large series of obser- 
 vations, is as often exceeded as attained (Lexis). In other 
 words, half of the whole number of observations fall short 
 of the probable deviation, while the other half exceed it. A 
 deviation which exceeds is as probable as one that does not 
 reach thia value. The probable deviation can be calculated 
 with the formula — 
 
 d = ± 0.6745^^ -~-^ (2) 
 
 In this formula: 
 
 d = the probable deviation. 
 Id^ = the sum of the squares of the individual deviations 
 from the mean or average. 
 n = the number of observations in the series. 
 
 In the place of this formula, in which the calculation of 
 Sd'^ requires much labor when the number of observations is 
 great, a simpler formula may be safely used in getting the 
 deviation in a large series. 
 
 d = ± 0.8453 — (3) 
 
 n 
 
 The formula says that all the individual deviations from the 
 mean or average of a series must be added together without 
 regard to whether they are plus or minus and divided by the 
 total number of observations. The working of the formula 
 will be illustrated by finding the probable deviation from the 
 average height of girls aged 8. 
 
Porter — The Growth of St. Louis Children. 
 
 283 
 
 TABLE No. 5. 
 
 The Calculation of the Probable Deviation (d) from the Average 
 
 Height (118.36 Cm.) of 2193 Girls, aged 8. 
 
 Height at Intervals of 
 
 V 
 
 
 E S 
 
 2 Centimetres. 
 
 
 
 
 141 and 142 Cm. 
 
 1 
 
 23.64 
 
 23.64 
 
 139 " 140 " 
 
 
 
 
 137 " 138 " 
 
 1 
 
 19.64 
 
 19.64 
 
 135 " 136 " 
 
 5 
 
 17.64 
 
 88.20 
 
 133 " 134 ♦' 
 
 10 
 
 15.64 
 
 156.40 
 
 181 " 132 " 
 
 21 
 
 13.64 
 
 286.44 
 
 129 " 130 '« 
 
 28 
 
 11.64 
 
 325.92 
 
 127 '' 128 " 
 
 79 
 
 9.64 
 
 761.56 
 
 125 «' 126 " 
 
 188 
 
 7.64 
 
 1054.32 
 
 123 " 124 '« 
 
 183 
 
 5.64 
 
 1032.12 
 
 121 " 122 «' 
 
 243 
 
 8.64 
 
 884.62 
 
 119 «' 120 " 
 
 342 
 
 1.64 
 
 560.88 
 
 117 " 118 " 
 
 321 
 
 0.36 
 
 115.56 
 
 115 " 116 " 
 
 297 
 
 2.36 
 
 700.92 
 
 113 " 114 " 
 
 222 
 
 4.36 
 
 967.92 
 
 111 " 112 " 
 
 137 
 
 6.36 
 
 872.69 
 
 109 " 110 " 
 
 84 
 
 8.36 
 
 702.24 
 
 107 " 108 " 
 
 42 
 
 10.36 
 
 435.12 
 
 105 " 106 " 
 
 27 
 
 12.36 
 
 333 72 
 
 103 " 104 " 
 
 8 
 
 14.36 
 
 114.88 
 
 101 " 102 " 
 
 2 
 
 16.36 
 
 32.72 
 
 99 " 100 «' 
 
 1 
 
 18.36 
 
 18.36 
 
 Total 
 
 2192 
 
 
 9487.77 
 
 9487 77 
 d = ± 0.8453 ^^ ^^ = d= 3.698 Cm. 
 
 The distribution of the above series of the heights of girls, 
 aged 8, is therefore characterized by a probable deviation of 
 ± 3.7 cm.; that is, one against one may be wagered that no 
 girl aged 8 will be taller than 122.06 cm. or shorter than 114.66 
 cm. If the number of observations falling between A ziz d, 
 
 A dr 2d, A zb 36? A zh "c? be noted, a complete picture 
 
 of the individual observations in a series will be obtained. 
 This observed distribution may then be compared directly 
 with the distribution of the observations in an hypothetical 
 series constructed according to the calculus of probabilities. 
 The observed and the theoretical series should correspond, if 
 the causes of deviation are purely accidental. It has already 
 been said that such a comparison must be made before it can 
 be known whether the observations in any series can be 
 treated by the methods of the theory of probabilities. It is 
 however not necessary to compare more than one of a num- 
 
284 
 
 Trans. Acad. Set. of St. Louis. 
 
 ber of series in which the distribution follows a common 
 type. It will suffice for our purposes therefore to compare 
 the distribution of the 2192 heights in Table No. 3, page 279, 
 with the distribution of an equal number according to the 
 calculus of probabilities. The method by which this is done 
 permits the construction of a curve from the observations 
 actually made which shall be the probable form of a curve 
 representing the distribution of the entire class from which 
 the observations have been drawn. 
 
 The number of observation (Z) which should be included 
 between the average (A) and any deviation from the average, 
 in other words any multiple {m) of the probable deviation 
 (cZ), is obtained from the equation.* 
 
 t 
 
 viri 
 
 The labor of calculating deviations with the aid of this 
 equation is avoided by the use of such tables as Stieda's, 
 reproduced below. 
 
 -t2 
 
 dt 
 
 (4) 
 
 TABLE No. 6. 
 
 Stieda's Table for Calculating the Number of Observations at any 
 Distance from the Mean or Average within the Limits: M-j- 
 5d AND M — 5d. 
 
 p 
 
 Percent. 
 
 P 
 
 Percent. 
 
 0.1 
 
 5.4 
 
 1.8 
 
 77.5 
 
 0.2 
 
 10.7 
 
 1.9 
 
 80.0 
 
 0.3 
 
 16.0 
 
 2.0 
 
 82.3 
 
 0.4 
 
 21.3 
 
 2.1 
 
 84.3 
 
 0.5 
 
 26.4 
 
 2.2 
 
 86.2 
 
 0.6 
 
 31.4 
 
 2.3 
 
 87.9 
 
 0.7 
 
 36.3 
 
 2.4 
 
 89.5 
 
 0.8 
 
 41.1 
 
 2.5 
 
 90.8 
 
 0.9 
 
 45.6 
 
 2.6 
 
 92.1 
 
 1.0 
 
 50.0 
 
 2.7 
 
 93.1 
 
 l.I 
 
 54.2 
 
 2.8 
 
 94.1 
 
 1.2 
 
 58.2 
 
 2.9 
 
 95.0 
 
 1.3 
 
 61.9 
 
 3.0 
 
 95.7 
 
 1.4 
 
 65.5 
 
 3.5 
 
 98.2 
 
 1.5 
 
 68.8 
 
 4.0 
 
 99.3 
 
 1.6 
 
 71.9 
 
 4.5 
 
 99.8 
 
 1.7 
 
 74.8 
 
 5.0 
 
 99.93 
 
 * Kramp. L'Analyse des refractions astronomiques. 
 
Porter — The Growth of St. Louis Children. 285 
 
 If p is allowed to represent one of the figures in the first 
 column and A the average of all the measurements in a series, 
 the figures opposite p in the second column will give the per 
 cent, of individual measurements lying within the limits : 
 
 K -\- p . d and A — p . d 
 
 Suppose for example it were required to know how many 
 of a series of 2192 girls aged 8 were of a height between the 
 average (118.36 cm.) and a deviation of ± l-'5 d (1.5. 3,7 
 cm. = 5.55 cm.), i. e. between 118.36 cm. + 5.55 cm. = 
 123.91 cm. and 118.36 cm. — 5.55 cm. = 112.81 cm. 
 The number in the table opposite 1.5 is 68.8, which 
 says that 68.8 per cent, of the 2192, or 1508, should fall 
 within the limits stated. Then half this number must fall 
 between A and A + 1.5 cZ (118.36 cm. and 123.91 cm.). In 
 a similar manner it will be found that 50 per cent, of the 
 whole number, or 1096, should fall within the limits Aid 
 (118.36 cm. + 3.7 cm. = 122.06 cm. and 118.36 cm. — 3.7 
 cm. = 116.51 cm.), and 25 per cent, between A and K -\- d 
 (118.36 cm. and 122.06 cm.). Thus may be calculated the 
 number of observations which should occur at any deviation 
 from the average. The theoretical and observed distribution 
 of 2192 girls, aged 8, is compared in Table No. 7. 
 
286 
 
 Trans. Acad. Sci. of St. Louis. 
 
 TABLE No. 7. 
 
 The Theoretical and the Observed Distribution of the Heights 
 OF 2192 Girls, Aged 8. 
 
 Probable 
 Deviation 
 
 d. 
 
 Heights at Intervals of 
 
 Theoretical 
 
 Observed 
 
 of zb 0.5d. 
 
 Distribution, 
 
 Distribution. 
 
 + 5,0 d 
 
 136.86 Cm, 
 
 2 
 
 2 
 
 + 4.5'^ 
 
 135.01 " 
 
 6 
 
 8 
 
 + 4.0 " 
 
 133.26 " 
 
 12 
 
 18 
 
 4-3.5 " 
 
 131.31 " 
 
 27 
 
 27 
 
 + 3.0'' 
 
 129.46 " 
 
 54 
 
 57 
 
 + 2.5" 
 
 127.61 " 
 
 93 
 
 104 
 
 + 2.0'^ 
 
 125.76 " 
 
 148 
 
 150 
 
 + 1.5 " 
 
 123.91 " 
 
 206 
 
 209 
 
 + 1.0 " 
 
 122.06 " 
 
 259 
 
 286 
 
 + 0.5 " 
 
 120.21 " 
 
 289 
 
 300 
 
 0.0 « 
 
 118.36 " 
 
 
 
 
 
 — 0.5" 
 
 116.51 " 
 
 289 
 
 272 
 
 — 1.0 " 
 
 114.66 " 
 
 259 
 
 275 
 
 — 1.5" 
 
 112.81 '* 
 
 206 
 
 196 
 
 — 2.0 " 
 
 110,96 " 
 
 148 
 
 126 
 
 — 2.5 " 
 
 109.11 " 
 
 93 
 
 80 
 
 — 3.0 " 
 
 107.26 " 
 
 54 
 
 40 
 
 — 3.5 •• 
 
 105.41 " 
 
 27 
 
 26 
 
 — 4.0 «' 
 
 103.56 " 
 
 12 
 
 12 
 
 — 4.5 " 
 
 101,71 '• 
 
 6 
 
 3 
 
 — 5,0 '« 
 
 99,86 " 
 
 Total 
 
 2 
 
 2 
 
 
 2192 
 
 2192 
 
 The curves in Plate I * give a graphic representation of the 
 figures in Table No. 7. A glance at these curves shows that 
 there is a close agreement between them, indicating that the 
 individual observations out of which they are constructed are 
 symmetrically grouped about a middle value typical of the 
 whole, and proving that the material with which we have to 
 deal satisfies the requirements of theory. 
 
 The method of showing distribution just described is not 
 the only method used for this purpose. Francis Gallon f 
 determines the actual distribution of the observations in a 
 series at intervals of 5 or 10 per cent, from the median or 
 50 '* percentile grade." The calculation of the median value 
 (mean) or 50 percentile grade has already been described: 
 that for the 5, 10, 20 and other percentile grades is similar in 
 
 * The plates are placed after the index at the end of the number. 
 t Natural Inheritance. London, 1889. 
 
Porter — The Grotvth of St. Louis Children. 
 
 287 
 
 principle. The percentile grades of the heights of girls, 
 aged 9, are as follows: — 
 
 TABLE No. 8. 
 The Percentile Distribution of the Heights of Girls, Aged 9. 
 
 Percentile Grades. 
 
 Number of 
 Observations. 
 
 Heights. 
 
 95 
 
 2015.9 
 
 133.42 Cm. 
 
 90 
 
 1909.8 
 
 130.97 
 
 
 80 
 
 1697.6 
 
 128.62 
 
 
 75 
 
 1591.5 
 
 127.58 
 
 
 70 
 
 1485.4 
 
 126.54 
 
 
 60 
 
 1273.2 
 
 125.53 
 
 
 50 
 
 1061.0 
 
 124.11 
 
 
 40 
 
 848.8 
 
 122.76 
 
 
 30 
 
 636.6 
 
 121.21 
 
 
 25 
 
 530.5 
 
 120.90 
 
 
 20 
 
 424.4 
 
 119.59 
 
 
 10 
 
 212.2 
 
 117.12 
 
 
 5 
 
 106.1 
 
 115.17 
 
 
 Total 
 
 2122 
 
 
 
 
 
 The Probable Error of the Average can be determined by 
 means of the formula 
 
 E:=± = (5)* 
 
 V n 
 
 whe~reE = the probable error of the average, 
 
 d = the probable deviation of an individual from the 
 
 average, 
 n = the number of observations in the series. 
 
 Substituting the values determined for the heights of girls, 
 aged 9, we have — 
 
 3.698 
 E = dz =jz 0.079 cm. 
 
 V 2122 
 The values of E are siven in Table No. 9. 
 
 * Formulas (1), (2), (3) and (5) and Table No. 6 are taken from L. 
 Stieda's admirable article : Ueber die Anwendung der Wahrscheinlichkeits- 
 rechnung in der anthropologischen Statistik. Archiv. fiir Anthropologic, 
 Bd. xiv., 1882, p. 167-182. 
 
288 
 
 Trans. Acad. Sci. of St. Louis. 
 
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Porter — The Growth of St. Louis Children. 289 
 
 The mean or average of the observations at any age in the 
 period of growth is typical of the child at that age, and a com- 
 parison of the means at different ages will reveal the law of 
 growth of the type. Again, the mean of the observations at any 
 deviation from the mean of the whole number, for example 
 the height at a deviation oi -\- d from the mean, or, if Galton's 
 method is employed, the height at any percentile grade, is the 
 type of those who stand at a certain degree of deviation from 
 the type of the whole number. Thus types of tall and short, 
 light and heavy children are secured. The types of the same 
 degree of deviation from the mean at all ages are as compar- 
 able as the type of the whole number of observations, and 
 reveal the growth of the typically tall and short, light and 
 heavy children ; but the comparison is less secure the greater 
 the deviation from the mean, for the probable error is 
 inversely as the square of the number of observations, and 
 the number of observations rapidly diminishes on either side 
 of the mean. 
 
 The methods described in this chapter have been employed 
 in the present investigation. For every entire series here 
 presented, the mean and the average, the probable deviation 
 and the probable error, and the 5, 10, 20, 25, 30, 40, 50, 60, 
 70, 75, 80, 90 and 95 percentile grades have been calcu- 
 lated. The 25 and 75 percentile grades were obtained by 
 dividing by 2 the sums of the 20 and 80, and the 70 and 80 
 percentile grades respectively. 
 
CHAPTER III. 
 
 TRUSTWORTHINESS OF THE MATERIAL; ITS LIMITATIONS. COMPARISON OP 
 MEDIAN AND AVERAGE VALUES. 
 
 The question first to be decided in the discussion of an 
 anlhropometrical series is whether the individual observations 
 are so related one to another that they constitute accidental 
 deviations from a middle value. The method of answering 
 this question by comparing the series of observations with a 
 series constructed according to the theory of probabilities has 
 already been described, and it has been stated incidentally that 
 the heights of St. Louis girls aged 8 agreed with the theoretical 
 series in their distribution. Where such an agreement exists, 
 the individual observations are to be regarded as approxima- 
 tions of a middle value which is the type of the series. It is 
 not necessary to make this comparison at more than one age, 
 or in more than one dimension, for it is known that if one 
 series in a group like that with which we have to deal shows 
 this agreement the other series will be found to do the same. 
 In the present case, additional evidence of the correspondence 
 between observation and theory could be furnished, were it 
 required, by Table No. 10, containing the probable deviation 
 (290) 
 
Porter — The Growth of St. Louis Children. 
 
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292 Trans. Acad. Sci. of St. Louis. 
 
 from the average. It is seen in this table that the probable 
 deviations are small, that is, one-half of the observations 
 deviate but little from the middle value, which is one of the 
 fundamental attributes of deviations due to accidental causes. 
 But additional evidence is hardly required, and few critics will 
 object to regarding the middle values in this investigation as 
 types of their respective series. 
 
 The objection sometimes made that the errors of observation 
 materially affect the truth of the values obtained is of little 
 weight, partly because such errors are " accidental " and com- 
 pensate each other as already explained, and partly because a 
 deviation from the middle value due to an uncompensated 
 error in measurement forms, as a rule, an inconsiderable part 
 of that greater deviation which expresses the physiological 
 difference between the individual and the type of his age and 
 class. Accidental errors of observation need not give concern 
 in measurements of great numbers of school children. Nor 
 need there be much fear of constant errors of observation, 
 provided the collection of material is made by many persons 
 and with a good number of each sort of measuring instrument. 
 If hundreds of teachers take part in the measurements, as in 
 the present investigation, a constant cause of error due to a 
 teacher's unconscious bias or personal equation on one side of 
 the middle value will very probably be compensated by the 
 bias of another teacher on the opposite side, and, similarly, 
 if a number of scales are used, the errors of those which weigh 
 too lightly are likely to be compensated by the errors of those 
 whose readings are too heavy. 
 
 The trustworthiness of this material must be encouraging to 
 those whose hold on the theory underlying these matters is 
 not very strong, because it illustrates the truth that the types 
 of physical development, and the laws of growth of the type 
 may be induced from measurements made by comparatively 
 unskilled hands and demonstrates that a system of anthropo- 
 metrical measurements may be fruitfully employed in the 
 public schools. 
 
 The use to which middle values and the deviations from 
 middle values shall be put is in part the subject of controversy, 
 and it will be well to state here the manner in which they 
 
Porter — The Groicth of St. Louis Children. 293 
 
 shall be employed in the present work. In doing so it will be 
 necessary to give a brief account of the matters concerning 
 which agreement is general as well as those which are in dispute. 
 
 It is acknowledged generally that the method of Quetelet 
 furnishes a middle value typical of the series from which 
 it was drawn, for example the middle weight of boys of 
 the same age, nationality and social condition is the typical 
 weight of boys of that age and class; and it is further 
 acknowledged that the increase in the middle value from year 
 to year expresses the law of growth of the type. It follows 
 that the middle value of those who stand at any deviation from 
 the middle value of the whole number is the type of that 
 degree of deviation from the type of the whole number and 
 that the increase in the middle value at the same degree of 
 deviation at each age in the period of growth expresses the law 
 of growth of the type at that degree of deviation. Thus the 
 curves of percentile grades printed below express the growth 
 of the typical St. Louis school-boy and girl. The type at a 
 certain deviation from the mean of an age will show the same 
 degree of deviation from the mean at any subsequent age; 
 for example a type-boy in the 75 percentile grade at age 6 
 will throughout his growth be heavier than 75 per cent, of 
 boys of his own age. Percentile curves are of course not 
 necessarily parallel. The type of the 50 per cent, who exceed 
 the middle value of the whole number has a law of growth 
 characteristic of tall boys and different from that of the type 
 of the 50 per cent, who fall below the middle value of the 
 whole number. 
 
 The application of the middle value to individuals has not 
 yet been mentioned. It is here that controversy finds its 
 hold. The relation of the individual to the type is not known. 
 It is not known whether a boy who at age 6 is heavier than 
 75 per cent, of boys at his age will at age 18 be heavier than 
 75 per cent, of boys at that age. Some anthropologists 
 believe that there is at least probability that children remain 
 in the same percentile grade throughout life, while others 
 dissent from this view. In truth the development of the 
 individual has been little studied, and it is therefore not yet 
 possible to state his probable future growth. 
 
294 Trans. Acad. Sci. of St. Louis. 
 
 This question — the relation of the "growth of the individual 
 to the growth of the type — can be determined only by the 
 individualizing method. The generalizing method deals solely 
 with units, irrespective of their individuality. If for example 
 John Smith in the 75 percentile grade and William Harrison 
 in the 60 percentile grade at age 6 exchange places at age 7, 
 the personal curve of each boy undergoes an important devia- 
 tion, but the number of units in the two grades, and conse- 
 quently the middle value in each, is unaltered. The generalizing 
 method, therefore, furnishes no data by which the future de- 
 velopment of individuals can be safely judged. The individ- 
 ualizing method, on the contrary, follows the individual from 
 year to year throughout his growth and establishes the 
 frequency and extent of his deviations from the growth of 
 the type. The lack of data collected by the individualizing 
 method is regrettable, but this gap in our knowledge does not 
 prevent the establishing of physical standards by which the 
 probability that the physique of any child is normal or abnor- 
 mal can be fixed. 
 
 The facts stated above limit the application of middle values 
 to (1) the establishing of physical standards at each age, and 
 (2) the using of these standards to determine whether the 
 physique of any child is normal: they do not, in the present 
 state of knowledge, permit prediction of future growth. 
 
 It has been much disputed whether the median value or the 
 average should be taken for the type. Many investigators 
 agree with Sir John Herschel, who declares in his celebrated 
 review of Quetelet's Lettres sur la theorie des probabilites 
 (page 23) that an average " may be convenient, to convey a 
 " ofeneral notion of the things averaged, but involves no con- 
 " ception of a natural and recognizable central magnitude all 
 " differences from which ought to be regarded as deviations 
 "from a standard. The notion of a mean, on the other 
 " hand, does imply such a conception, standing distinguished 
 "from an average by this very feature, viz.: the regular 
 " march of the groups, increasing to a maximum, and thence 
 " again diminishing. An average gives us no assurance that 
 " the future will be like the past. A mean may be reckoned 
 *' on with the most implicit confidence. All the phil- 
 
Porter — The Growth of St. Louis Children. 295 
 
 '* osophical value of statistical results depends on a due 
 *' appreciation of this distinction and acceptance of its 
 *< consequences." 
 
 Other statisticians have used the average exclusively. Out 
 of respect to this difference of opinion, both the median value 
 and the average have been employed in the present work. 
 On calculating these values for each series, it was found that 
 the difference between them was inconsiderable, showing that 
 
296 
 
 Trans. Acad. ScL of St. Louis. 
 
 TABLE No. 11. 
 Median Minus Average Values. 
 
 Dimensions. 
 
 Sex. 
 
 Unit of 
 Measure- 
 ment. 
 
 Age at Nearest Birthday, and Median Minus Average Values. 
 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 Weight 
 
 Boys. 
 
 Girls. 
 
 Kilogramme 
 
 +0.10 
 
 +0.06 
 
 -0.01 
 
 —0.01 
 
 +0.09 
 
 —0.03 
 
 +0.16 
 
 —0.04 
 
 +0.04 
 
 —0.04 
 
 +0.08 
 —0.35 
 
 —0.10 
 
 
 —0.41 
 
 Height Standing 
 
 Boys. 
 
 Girls. 
 
 Centimetre.. 
 
 +0.29 
 
 +0.43 
 
 -0.54 
 
 +0.66 
 
 +0.45 
 
 +0.49 
 
 +0.64 
 
 +0.38 
 
 +0.52 
 
 +0.44 
 
 +0.68 
 
 +0.42 
 
 +0.60 
 
 +0.41 
 
 +0.36 
 
 +0.43 
 
 Height Sitting 
 
 Boys. 
 
 Girls. 
 
 Boys. 
 
 Girls. 
 
 Centimetre.. 
 
 —0.10 
 
 +0.64 
 
 +0.47 
 
 +0.99 
 
 +0.35 
 
 +0.03 
 
 -0.40 
 
 +0.69 
 
 +0.42 
 
 +0.59 
 
 +0.13 
 
 +0.55 
 
 Span of Arms 
 
 Centimetre.. 
 
 +0.62 
 
 +0.33 
 
 +0.66 
 
 +0.75 
 
 +0.66 
 
 —0.20 
 
 +0.49 
 
 +0.65 
 
 +0.39 
 
 +0.43 
 
 +0.46 
 
 +0.22 
 
 —0.12 
 
 +0.53 
 
 Girth of Chest, 
 
 Inspiration. 
 
 Boys. 
 
 Girls. 
 
 Centimetre.. 
 
 +0.20 
 
 +0.58 
 
 +0.30 
 
 +0.28 
 
 +0.17 
 
 +0.57 
 
 +0.49 
 
 +0.56 
 
 +0.44 
 
 +0.49 
 
 +0.47 
 +0.55 
 
 +0.40 
 
 +0.48 
 
 +0.41 
 
 +0.19 
 
 Girth of Chest, 
 
 Expiration. 
 
 Boys. 
 
 Girls. 
 
 Boys. 
 
 Girls. 
 
 Centimetre. . 
 
 +0,34 
 
 +0.48 
 
 +0.24 
 
 +0.51 
 
 +0.56 
 
 +0.48 
 
 +0.37 
 
 +0.48 
 
 +0.22 
 
 +0.40 
 
 +0.40 
 
 +0.12 
 
 Strength of Squeeze, 
 Right Hand 
 
 Kilogramme 
 
 +0.21 
 
 +0.79 
 
 —0.02 
 
 +0.03 
 
 +0.21 
 
 +0.13 
 
 -0.70 
 
 —0.09 
 
 -0.19 
 
 — 0.18 
 
 -0.11 
 
 -0.06 
 
 -0.08 
 
 +0.27 
 
 -0.14 
 
 —0.07 
 
 Strength of Squeeze, 
 Left Hand 
 
 Boys. 
 
 Girls. 
 
 Kilogramme 
 
 +0.53 
 
 +0.69 
 
 —0.04 
 
 +0.54 
 
 —0.02 
 
 —0.22 
 
 -0.13 
 
 — 0.59 
 
 —0.23 
 
 +0.02 
 
 —0.29 
 
 +0.05 
 
 Length of Head 
 
 Boys. 
 
 Girls. 
 
 Millimetre.. 
 
 +0.47 
 
 +0.89 
 
 +0.38 
 +0.49 
 
 +0.82 
 + 1.23 
 
 +0.28 
 + 1.41 
 
 +0.06 
 
 +1.28 
 
 +0.49 
 
 +1.67 
 
 +0.24 
 
 +1.07 
 
 Width of Head 
 
 Boys. 
 
 Girls. ' 
 
 Millimetre.. 
 
 +0.47 
 +0.56 
 
 +0.61 
 
 +0.70 
 
 +0.33 
 
 +0.53 
 
 +0.21 
 
 +0.54 
 
 +0.52 
 
 +0.79 
 
 +0.31 
 
 +0.49 
 
 +0.38 
 
 +0.67 
 
 Root of Nose to 
 
 Point of Chin. 
 
 Boys. 
 
 Girls. 
 
 Millimetre.. 
 
 -0.52 
 
 —0.53 
 
 -0.30 
 
 —0.57 
 
 -0.20 
 
 —0.05 
 
 -0.09 
 
 —0.25 
 
 -0.33 
 
 —0.37 
 
 -0.14 
 
 —0.24 
 
 +0.20 
 
 +0.07 
 
 Width of Eace 
 
 Boys. 
 
 Girls. 
 
 Millimetre.. 
 
 +0.96 
 
 +0.68 
 
 +0.62 
 
 +0.27 
 
 +0.93 
 
 -0.18 
 
 +0.84 
 +0.79 
 
 +0.03 
 
 +0.93 
 
 +0.49 
 
 +0.47 
 
 +0.78 
 +0.63 
 
 Point of Chin. 
 
 Boys. 
 
 Girls. 
 
 Millimetre.. 
 
 +0.34 
 
 +0.39 
 
 +0.76 
 
 +0.83 
 
 +0.54 
 
 +0.41 
 
 +0.82 
 +0.32 
 
 +0.33 
 
 +0.52 
 
 +0.72 
 +0.85 
 
 +0.39 
 
 +0.66 
 
Porter — Tlie Groioth of St. Louis Children. 
 
 29' 
 
 TABLE No, 11 — Continued. 
 Median Minus Average Values. 
 
 Age at Nearest Birthday, and Median Minus Average Values. 
 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 Dimensions, 
 
 -0.36 
 
 —0.49 
 
 —0.46 
 
 +0.36 
 
 —0.73 
 
 +0.16 
 
 +0.35 
 
 +0.78 
 
 -0.07 
 
 +0.78 
 
 +0.23 
 
 —0.29 
 
 —0.36 
 
 —0.09 
 
 +0.74 
 
 +0.09 
 
 +0.08 
 
 +0.28 
 
 —0.34 
 
 
 Weight. 
 
 +0.38 
 
 —0.34 
 
 +0.28 
 +1.10 
 
 +1.00 
 
 +0.51 
 
 +0.87 
 +0.07 
 
 +1.10 
 
 +0.42 
 +0.69 
 
 +0.52 
 +0.74 
 
 Height Standing, 
 
 +0.29 
 
 +0.49 
 
 -0.13 
 
 +0.93 
 
 +0.94 
 
 +0.74 
 
 +0.94 
 
 +0.75 
 
 -0,53 
 
 +0.69 
 
 +0.82 
 
 Height Sitting, 
 
 +0.24 
 
 +0.64 
 
 +0.34 
 
 +0.98 
 
 +0.36 
 
 —0.17 
 
 +1.35 
 
 +0.80 
 
 +1.02 
 
 +0.61 
 
 +0.90 
 
 +0.41 
 
 +0.19 
 
 +0.91 
 
 +0.45 
 
 +1.33 
 
 —0.39 
 —0.64 
 
 Span of Arms. 
 
 +0.39 
 
 +0.30 
 
 +0.23 
 
 +0.43 
 
 +0.24 
 
 +0.12 
 
 +0.52 
 
 +0.17 
 
 -0.52 
 
 +0.31 
 
 +1.01 
 
 +0.57 
 
 +1.23 
 
 +0.48 
 
 +0.90 
 
 +0.80 
 
 Girth of Chest, 
 
 Inspiration. 
 
 +0.41 
 
 +0.40 
 
 +0.08 
 
 +0.48 
 
 +0.35 
 
 +0.16 
 
 +0.72 
 +0.26 
 
 +0.44 
 
 +0.45 
 
 +0.51 
 
 +0.41 
 
 +0.61 
 
 Girth of Chest, 
 
 Expiration. 
 
 -0.09 
 
 —0.62 
 
 -0.50 
 
 —0.24 
 
 —1.14 
 
 —0.18 
 
 +0.37 
 
 +0.75 
 
 +0.02 
 
 —0.16 
 
 +0.44 
 
 +0.43 
 +0.38 
 
 -0.11 
 
 
 Strength of Squeeze, 
 Right Hand. 
 
 —0.36 
 
 — 0,12 
 
 -0.50 
 
 —0.69 
 
 +0.08 
 
 +0.41 
 
 +0.54 
 
 —0.08 
 
 +0.60 
 
 —0,10 
 
 +0.48 
 
 —0.28 
 
 Strength of Squeeze, 
 Left Hand. 
 
 +0.37 
 
 +1.04 
 
 -0.69 
 
 +1.30 
 
 +0.68 
 +0.55 
 
 +0.98 
 +0.86 
 
 +1.48 
 +0,46 
 
 +0.40 
 
 +0.27 
 
 
 Length of Head. 
 
 +0.27 
 ^0.37 
 
 +0.54 
 
 +0.35 
 
 +0.78 
 +0.42 
 
 +0.37 
 
 +0.72 
 
 +0.41 
 
 +0.39 
 
 +0.34 
 
 +1.07 
 
 +1.06 
 —0.38 
 
 —0.12 
 +0.04 
 
 
 Width of Head. 
 
 +0.10 
 
 -0.21 
 
 +0.08 
 —0.15 
 
 -0.11 
 
 —0.39 
 
 +0.10 
 
 —0.61 
 
 +0.55 
 
 +0.71 
 
 —0.26 
 
 +0.53 
 
 +0.94 
 
 +0,46 
 
 +1.79 
 
 +0.75 
 
 +0.16 
 
 +0.27 
 
 —0.06 
 
 Root of Nose to 
 
 Point of Chin, 
 
 +0.19 
 
 +0.71 
 
 +0.51 
 
 +0.84 
 
 +0.71 
 
 +0.45 
 
 +0.75 
 
 +0..55 
 
 +0.20 
 
 +1.29 
 
 
 Width of Face. 
 
 +0.54 
 
 +0.80 
 
 +0.55 
 
 +0.62 
 
 +0.78 
 +0.65 
 
 -0.03 
 
 +0.90 
 
 +1.99 
 
 +0.96 
 
 1 
 —1.831 —0,09 
 
 +1.78 
 
 Hair Line to 
 
 Point of Chin. 
 
298 Trans. Acad. Sci. of St. Louis. 
 
 either may be used for the type without any error of prac- 
 tical importance, provided the series are similar to those 
 analyzed here. This point is of practical interest because 
 the labor of reckoning the average is much greater than in 
 reckoning the median value. 
 
 Bowditch, in The Growth of Ghildren, Boston, 1891, p. 
 495 e< seq., discusses the relation of median and average value. 
 "It is evident," he writes, " that the value M will tend to 
 " approximate to the average value of all the observations and 
 *' will be identical with it when the [percentile] curve S T 
 *'is symmetrically disposed on both sides of M, i. e., when 
 " the values at sixty, seventy, eighty, ninety and ninety-five 
 "per cent, exceed M by the same amount, respectively, by 
 " which the values at forty, thirty, twenty, ten and five per 
 " cent, fall short of it. If A represent the average value of 
 " all the observations, then the value of M-A will be a meas- 
 " ure of the direction and extent of the asymmetry of the 
 " curve S T,for this value will be zero when the curve is sym- 
 ^^ metrical i positive v^hen the values at the lower percentile 
 " grades fall short of M more than those at the higher grades 
 " exceed it, and negative when the reverse is the case.'' [Dr. 
 Bowditch now gives a table of median minus average height 
 and weight.] " An examination of this table or of the curves 
 " constructed from it, as given in Plate I, shows that the 
 " asymmetry of the curves of percentile grades varies very 
 " much, at different ages, both in direction and amount. The 
 " variation in the value of M-A in the curves of height is much 
 " the same as that in the curves of weight for each sex consid- 
 " ered by itself, but there is a great difference between the 
 " two sexes. This difference shows itself most distinctly 
 "between the ages of eleven and fifteen years. During this 
 " time a rise in the curves for the males coincides with a fall 
 " in those for the females, while before and after this period 
 " the curves, as a rule, rise and fall together. We must con- 
 " elude, therefore, that the rate of annual increase, both in 
 " height and weight, is different at different percentile grades, 
 " or, in other words, that large children grow differently from 
 " small ones, and moreover, that between the ages of eleven 
 " and fifteen years there is a striking difference in the mode 
 " of growth of the two sexes." 
 
Porter — The Growth of St. Louis Children. 299 
 
 Table No. 11 and the curves constructed from it (Plates II, 
 III, IV) furnish considerable material for the study of the 
 relation between median and average values. The curves of 
 median minus average heia^ht aojree with those of Dr. Bow- 
 ditch in showing (1) a difference in the rate of growth of the 
 same sex at different percentile grades, (2) an agreement in the 
 rate of growth of the sexes from age 6 to 12, inclusive,* 
 and (3) a marked difference in the rate of growth from age 12 
 to age 16, beyond which the number of observations is per- 
 haps too small for sure work. In the curves from both cities, 
 moreover, the greatest asymmetry in girls is near age 13, and 
 in boys near age 16, the culmination being a little later in St. 
 Louis children, and the least asymmetry is near age 12. 
 The asymmetry of Boston bo3'.s' curves at age 15 and girls' 
 curves at ages 16 and 17 is somewhat greater than that of the 
 St. Louis curves. It is further worthy of notice that the 
 values in the case of St. Louis boys do not become negative. 
 
 There is a general similarity also between the median minus 
 average weights of the children of the two cities, the asym- 
 metry of girls being again greatest about age 14 and of boys 
 greatest at about age 16. Dr. Bowditch's conclusions, quoted 
 above, are therefore fully confirmed. 
 
 The St. Louis curves on Plates II, III and IV should now 
 be compared with each other. The maximum asymmetry of 
 girls about 14 years and boys about 16 years old, appears in 
 weight, height, height sitting, and span of arms, while the 
 remaining curves exhibit no characteristic sexual differences 
 during the period of prepubertal acceleration. The asym- 
 metry is for the most part positive, weight, strength of 
 squeeze and height of face from root of nose to point of chin 
 being the only considerable exceptions. Sexual differences, 
 aside from those already mentioned, are unimportant, save 
 perhaps in length and width of head, in both of which the 
 asymmetry of girls is greater than that of boys from age 6 to 
 age 13, 
 
 The errors in the median minus average values of height, 
 weight and other single dimensions may be partially compen- 
 
 * It should be remembered that Dr. Bowditch's ages are recorded at last 
 birthday, while mine are recorded at nearest birthday. 
 
300 
 
 Trans. Acad. Sci. of St. Louis. 
 
 sated by adding the median minus average values of several 
 dimensions of each sex and age, without regard to plus or 
 minus sian. This has been done in Table No. 12. 
 
 TABLE No. 12. 
 Sums of Median minus Average Values. 
 
 J at Nearest 
 Birthday. 
 
 Weight, Height 
 
 Standing, Height 
 
 Sitting, Span of 
 
 Arras. 
 
 Girth of Chest at 
 Full Inspiration 
 and Expiration. 
 
 Strength of 
 Squeeze, Right 
 and Left Hand. 
 
 Head and 
 
 Face 
 Measure- 
 ments. 
 
 M 
 < 
 
 Boys, 
 
 Girls. 
 
 Boys. 
 
 Girls. 
 
 Boys. 
 
 Girls. 
 
 Boys. 
 
 Girls. 
 
 6 
 
 1.55 
 
 1.48 
 
 0.54 
 
 1.06 
 
 0.74 
 
 1.48 
 
 2.76 
 
 3.05 
 
 7 
 
 1.22 
 
 1.89 
 
 0.54 
 
 0.79 
 
 0.06 
 
 0.57 
 
 2.67 
 
 2.86 
 
 8 
 
 1.86 
 
 1.60 
 
 0.73 
 
 1.05 
 
 0.23 
 
 0.35 
 
 2.82 
 
 2.40 
 
 9 
 
 1.52 
 
 1.16 
 
 0.86 
 
 1.04 
 
 0.89 
 
 0.27 
 
 2.24 
 
 3.31 
 
 10 
 
 1.51 
 
 1.58 
 
 0.66 
 
 0.89 
 
 0.24 
 
 0.65 
 
 1.27 
 
 3.89 
 
 11 
 
 1.56 
 
 1.57 
 
 0.87 
 
 1.03 
 
 0.31 
 
 0.29 
 
 2.15 
 
 3.72 
 
 12 
 
 0.71 
 
 1.92 
 
 0.81 
 
 0.31 
 
 0.43 
 
 0.12 
 
 1.99 
 
 3.10. 
 
 13 
 
 1.27 
 
 1.96 
 
 0.80 
 
 0.70 
 
 0.45 
 
 0.74 
 
 1.47 
 
 3.13 
 
 14 
 
 1.21 
 
 3.37 
 
 0.31 
 
 0.91 
 
 1.00 
 
 0.93 
 
 2.37 
 
 3.26 
 
 16 
 
 1.51 
 
 1.89 
 
 0.76 
 
 0.29 
 
 0.60 
 
 0.72 
 
 3.06 
 
 2.46 
 
 16 
 
 3.52 
 
 2.34 
 
 1.36 
 
 0.73 
 
 1.68 
 
 0.26 
 
 2.26 
 
 3.43 
 
 17 
 
 3.19 
 
 1.52 
 
 1.62 
 
 0.67 
 
 
 0.47 
 
 4.65 
 
 2.96 
 
 18 
 
 
 
 2.42 
 
 1.77 
 
 0.93 
 
 
 
 0.77 
 
 3.40 
 
 3.29 
 
 The conclusions drawn from the curves discussed above are 
 substantiated in the main by this table. It is, however, dif- 
 ficult to believe that a sexual difference such as exists in 
 weight, height standing, height sitting and span of arms 
 will not be found also in girth of chest and the various 
 dimensions of the head. But a purely objective attitude 
 towards the material in hand does not permit speculation as 
 to what might be revealed if the material were very much 
 larger and its intrinsic laws easier to unveil. 
 
CHAPTER IV. 
 
 DANGERS OF COMPARING MEASUREMENTS OF CHILDREN IN DIFFERENT COUN- 
 TRIES. INFLUENCE OF OCCUPATION AND NATIONALITY OF PARENTS. 
 
 It has been a custom of anthropometrists to compare the 
 type-children of cities, states or provinces very different in 
 situation and character. Such comparisons may be expected 
 always to show that the laws of growth are in their main 
 features the same for all children. They cannot, however, be 
 expected to give very definite information in regard to the 
 relative size of children of different countries or districts 
 so long as the social status or environment of the children 
 is not more closely studied. The children in the public 
 schools are from all classes of society, and it has been 
 demonstrated repeatedly that the favored classes differ 
 physically from the poor. The children of the prosperous 
 have been found to be larger than the children of the poor. 
 The comparison of middle values got from two sets of schools 
 is therefore open to the objection that the composition of the 
 school population may not be the same in both sets. It would 
 for example be unsafe to say that St. Louis children are 
 larger or smaller than Copenhagen children because the type- 
 children in the St. Louis Public Schools are larger or smaller 
 than the type-children in Copenhagen, for the difference 
 observed may depend on the different composition of the 
 school population in the two cities. 
 
 Such comparisons, when rightly made, are not only of 
 great scientific interest but are almost essential to the use 
 of anthropometrical systems in education. An immense 
 saving of time would be made if it were shown that the 
 typical height, weight, etc., of children in one city of a 
 country could be adopted as the standard for the schools of 
 the entire country or even a considerable part of it. And in 
 any one city, the application of the type-values to individuals 
 would be much less liable to error if it were known how much 
 allowance should be made for the difference between the type 
 
 (301) 
 
302 
 
 Trans. Acad. ScL of St. Louis. 
 
 of a special social class and the types of a mixed school pop- 
 ulation. Every investigation of the present kind should, 
 therefore, include information concerning the social condition 
 of the children. The tax-returns .are available for this pur- 
 pose, and the occupation of parents is also of use. It was 
 not possible to inquire into tax-returns in the present re- 
 search, but some facts can be communicated regarding the 
 physical differences between the children of professional and 
 business men and those of manual tradesmen. The occupa- 
 tions included under these heads may be seen in the following 
 statement of the occupations of the fathers of 2,000 St. Louis 
 children. The names of occupations are set down as given 
 by the pupils. 
 
 PROFESSIONS. 
 
 Artist. 
 
 3 Minister. 
 
 Chemist 1 
 
 Civil Engineer 8 
 
 Dentist i 
 
 Editor 6 
 
 Electrical Engineer i 
 
 Electrician 2 
 
 Lawyer 14 
 
 Medical Student 1 
 
 Musician 6 
 
 Photographer 3 
 
 Physician 13 
 
 Teacher 9 
 
 Veterinarian 1 
 
 Total 76 
 
 MERCANTILE CLASS. 
 
 Agent 36 
 
 Banker 2 
 
 Book-keeper 40 
 
 Broker 9 
 
 Cashier 8 
 
 Clerk 3 
 
 Collector 8 
 
 Contractor 20 
 
 Dairyman 8 
 
 Drugs 10 
 
 Dealer in Butter 1 
 
 Carpets 2 
 
 Cattle 4 
 
 Cloth 4 
 
 Clothes 1 
 
 Corn 2 
 
 Coal 4 
 
 Feed and Flour 2 
 
 Fish and Oysters 3 
 
 Fruits 3 
 
 Dealer in Furniture 6 
 
 Hardware 2 
 
 Hats ... 1 
 
 Horses 1 
 
 Lime 1 
 
 Lumber 4 
 
 Marble 1 
 
 Pork 2 
 
 Produce 2 
 
 Stationery 1 
 
 Stone 1 
 
 Tobacco 5 
 
 Wall-paper 1 
 
 Foreman 24 
 
 Grocer 36 
 
 Hotel-keeper 5 
 
 Inspector, Building 2 
 
 Street 7 
 
 Not specified 1 
 
 Jeweler 7 
 
Porter — The Growth of St. Louis Children. 
 
 303 
 
 Insurance ... 4 
 
 Manager 7 
 
 Manufacturer 35 
 
 Merchant 143 
 
 Merchant Tailor 2 
 
 News-depot 1 
 
 Optician 2 
 
 Postmaster 1 
 
 President of Iron Co 1 
 
 Publisher 1 
 
 Keal Estate 7 
 
 Salesman 76 
 
 Secretary of a corporation 6 
 
 Telegrapher 1 
 
 Traveling Salesman 9 
 
 Undertaker 3 
 
 Total 579 
 
 MANUAL TRADES. 
 
 Baker 24 
 
 Barber , 23 
 
 Blacksmith 29 
 
 Book-Binder 2 
 
 Brewer 14 
 
 Bricklayer 21 
 
 Builder 9 
 
 Butcher 40 
 
 Carpenter 148 
 
 Carriage Eepairer 2 
 
 Cigar Packer 1 
 
 Cloth Sponger 1 
 
 Compositor 2 
 
 Confectioner 7 
 
 Cook 5 
 
 Cooper 37 
 
 Coppersmith 1 
 
 Cord-Wainer 1 
 
 Dairyman 1 
 
 Decorator 4 
 
 Draughtsman 5 
 
 Dressmaker 4 
 
 Dyer 2 
 
 Engineer 43 
 
 Engraver 1 
 
 Fireman 11 
 
 Eoundryman 2 
 
 Gardener 5 
 
 Gilder 1 
 
 Glass Blower 2 
 
 Iron Worker 3 
 
 Laundryman 1 
 
 Lithographer 1 
 
 Locksmith 1 
 
 Maker of : 
 
 Bags 2 
 
 Baskets 1 
 
 Belts 1 
 
 Maker of : 
 
 Boilers 7 
 
 Boxes 9 
 
 Brushes 3 
 
 Candies 3 
 
 Carriages 16 
 
 Chains 2 
 
 Chairs 2 
 
 Cigars 31 
 
 Collars 1 
 
 Cornices . 1 
 
 Harness 2 
 
 Lanterns 1 
 
 Mattresses 1 
 
 Models 1 
 
 Organs 1 
 
 Patterns 4 
 
 Shoes 47 
 
 Tobacco 3 
 
 Trunks ... I 
 
 Wagons 6 
 
 Watches 6 
 
 Machinist 55 
 
 Maltster 4 
 
 Marble Cutter 3 
 
 Mechanic 42 
 
 Miller 7 
 
 Millwright 5 
 
 Miner 1 
 
 Molder 33 
 
 Motorman 2 
 
 Packer 5 
 
 Painter 51 
 
 Paper-Hanger 8 
 
 Paver 4 
 
 Pipe-Fitter 2 
 
 Planer 1 
 
 Plasterer 10 
 
304 
 
 Trans. Acad. Sci. of St. Louis. 
 
 Plumber 13 
 
 Polisher 1 
 
 Potter 2 
 
 Printer 19 
 
 Puddler 1 
 
 Saddler 12 
 
 Selector of Tobacco 1 
 
 Shoe Varnisher 1 
 
 Slater 1 
 
 Stair Builder 4 
 
 Stone Mason 50 
 
 Tailor 56 
 
 Tanner 6 
 
 Tinner 15 
 
 Turner 6 
 
 Upholsterer 5 
 
 Varnisher 5 
 
 Waterproofer and Painter 1 
 
 Weaver 1 
 
 Whitener U 
 
 Wood- Worker 33 
 
 Total 1086 
 
 LABORERS. 
 
 Baggageman 2 
 
 Carriers, Letter 9 
 
 Carriers, Paper 6 
 
 Coal-heaver 1 
 
 Driver 3 
 
 Elevator man 1 
 
 Engine-cleaner 1 
 
 Expressman 3 
 
 Eireman 11 
 
 Gripman 6 
 
 Hostler 7 
 
 Huckster 2 
 
 Janitor 3 
 
 Laborer 31 
 
 Live-stock driver 1 
 
 Lumberman .- 1 
 
 Mill-hand 4 
 
 Oiler 2 
 
 Peddler 19 
 
 Policeman and watchman 21 
 
 Porter 4 
 
 Riverman 1 
 
 Railway-hand 12 
 
 Saloon-keeper 51 
 
 Sexton 1 
 
 Shepherd 1 
 
 Steward, Hotel 2 
 
 '* Steamer 1 
 
 " 3 
 
 Teamster 6 
 
 Waiter 1 
 
 Total 216 
 
 MISCELLANEOUS. 
 
 Captain of Steamer. 
 
 Conductor 
 
 Farmer.. 
 
 "Independent ". . .. 
 
 Pilot c. 
 
 No occupation 
 
 "Retired" 
 
 Total. 
 
 1 
 14 
 12 
 1 
 5 
 7 
 3 
 
 43 
 
 SUMMARY. 
 
 Professions 76 
 
 Mercantile classes 579 
 
 Manual trades 1086 
 
 Laborers 216 
 
 Miscellaneous 43 
 
 Total 2000 
 
Porter — The Grotvih of St. Louis Children. 
 
 305 
 
 The number of children of rich families and of very poor 
 families in the public schools is small, the larger part of the 
 pupils being from what would be called in England the lower 
 middle class, and the school population is accordingly more 
 homogeneous than would have seemed possible at the first 
 glance. 
 
 The difference in the weight of children of the professional 
 and merchant class is probably of little importance until the 
 period of prepubertal acceleration. Such at least is the 
 inference from Table No. 13, where the weights of these two 
 classes are compared. 
 
 TABLE No. 13. 
 
 A. Comparison of the Weights of the Daughters of Manual Trades- 
 men WITH THE Weights of the Daughters of Professional Men 
 AND Merchants. 
 
 Professional Men and Merchants. 
 
 Manual Tradesmen. 
 
 Age at 
 Nearest 
 
 Number of 
 Observa- 
 
 Median 
 Weight. 
 (Kilo- 
 grammes) 
 
 Median 
 Weight. 
 (Kilo- 
 grammes) 
 
 Number of 
 Observa- 
 
 Age at 
 
 Nearest 
 
 Birthday. 
 
 tions. 
 
 tions. 
 
 Birthday. 
 
 6 
 
 74 
 
 19.53 
 
 18.95 
 
 237 
 
 6 
 
 7 
 
 148 
 
 20.63 
 
 20.74 
 
 604 
 
 7 
 
 8 
 
 170 
 
 23.00 
 
 22.89 
 
 723 
 
 8 
 
 9 
 
 152 
 
 25.48 
 
 25.09 
 
 688 
 
 9 
 
 10 
 
 168 
 
 27.61 
 
 27.46 
 
 651 
 
 10 
 
 11 
 
 173 
 
 30.63 
 
 29.45 
 
 569 
 
 11 
 
 12 
 
 153 
 
 33.86 
 
 32.28 
 
 556 
 
 12 
 
 13 
 
 160 
 
 39.04 
 
 37.07 
 
 402 
 
 13 
 
 14 
 
 140 
 
 43.59 
 
 41.68 
 
 251 
 
 14 
 
 15 
 
 112 
 
 47.49 
 
 45.62 
 
 145 
 
 15 
 
 16 
 
 87 
 
 50.16 
 
 49.18 
 
 52 
 
 16 
 
 17 
 
 46 
 
 53.58 
 
 51.07 
 
 24 
 
 17 
 
 What is true of weight is in this instance probably true of 
 the physical development as a whole, and Table No. 13 would 
 seem to indicate that a wide difference in social status or 
 material prosperity may exist without much influencing the 
 growth of children up to the prepubertal acceleration. But 
 further investigation is necessary before a generalization can 
 be made. It must suffice here to state: 1. The daughters of 
 professional men and merchants are very little heavier than 
 the daughters of manual tradesmen until the period of pre- 
 
806 Trans. Acad. Sci. of St. Louis. 
 
 pubertal acceleration. 2. The weight of girls is much more 
 influenced by the material prosperity or social status of 
 parents during and immediately after the period of pre- 
 pubertal acceleration than in the earlier years of growth. 
 
 The proportion of children of the more prosperous class in 
 the public schools is not the same in all grades. In the higher 
 grades, containing the older children, the number from pros- 
 perous families is relatively larger, the children of the poor 
 having in many instances been compelled to leave school in 
 order to earn money. Some idea of the extent of this change 
 may be gained from Table No. 14, in which the per cent, of 
 daughters of professional men and merchants and daughters 
 of manual tradesmen is given at each age and school grade. 
 
Porter — The Growth of St. Louis Children. 
 
 307 
 
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308 
 
 Trans. Acad. Sci. of St. Louis. 
 
 The ratio betw^een the two is more easily grasped when the 
 difference between the classes at each age and grade is stated, 
 black type being used where the professional and merchant 
 class exceed the tradesmen's daughters and lower case type 
 where the contrary is true. 
 
 Age. 
 
 Kinder- 
 garten. 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 % 
 
 VIII. 
 
 6 
 
 7 
 
 3.9% 
 6.1 
 
 0.0 
 
 3.9% 
 
 6.8 
 15.9 
 13.7 
 
 4.0 
 
 1.6 
 0.3 
 
 % 
 0.7 
 15.7 
 2.2 
 
 13.0 
 3.5 
 3.9 
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 % 
 
 % 
 
 % 
 
 a 
 
 0.6 
 7.4 
 1.1 
 
 17.1 
 5.7 
 8.1 
 1.1 
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 8.4 
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 6.9 
 6.4 
 
 7.4 
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 5.6 
 
 0.3 
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 3.2 
 4.1 
 3.4 
 3.5 
 4.9 
 
 
 
 11 
 
 
 
 12 
 13 
 
 0.6 
 1.7 
 4.4 
 1.5 
 5.9 
 
 5.6 
 
 14 
 
 
 
 11.2 
 
 15 
 
 
 
 
 11.8 
 
 16 
 
 
 
 
 4.0 
 
 
 
 
 
 
 The number of boys withdrawn from school to earn money 
 is of course greater than the number of girls withdrawn. 
 Thus of 562 boys, aged 6, 17.8 per cent, were sons of pro- 
 fessional men or merchants and 42.9 per cent, sons of manual 
 tradesmen, while at age 14, 29.3 per cent, of 498 boys were 
 from the former class and 37 per cent, from the latter. 
 
 Age 
 at Nearest 
 Birthday. 
 
 Number of 
 Individuals. 
 
 Sons of Pro- 
 fessional Men 
 and Merchants. 
 
 Sons of 
 
 Manual 
 
 Tradesmen. 
 
 Others. 
 
 6 
 14 
 
 562 
 498 
 
 17.8% 
 29.3 
 
 42.9% 
 37.0 
 
 39.3% 
 33.7 
 
 The nationality of the children should be considered in an 
 anthropometrical inquiry. It is well known that children of 
 the same age but different nationality exhibit differences in 
 physical development. The annual report of the Superinten- 
 dent of Public Schools, issued Aug. 1, 1891, contains in Table 
 V, appendix, page XL VI, a statement " Showing the Birth- 
 place of Pupils Eegistered in Each School for the Year 
 1890-91," from which the number of pupils in the schools in 
 which the measurements were made has been taken and the 
 following percentages calculated : — 
 
Porter — The Groivtli of St. Louis Children. 
 
 309 
 
 BIRTHPXACB OF 46,870 PUPILS IN THE ST. LOUIS PUBLIC SCHOOLS. 
 
 St. Louis 79.26 % 
 
 other Parts of the United States 16.92 " 
 
 Great Britain 0.63 " 
 
 Ireland 0.19 " 
 
 German States 1.97 " 
 
 Other Foreign Countries 0.87 " 
 
 Unknown 0.16 '* 
 
 Total 100 
 
 The children of foreign birth are too few to affect the 
 results of the measurements, and the number of children born 
 in or near St. Louis is such that the middle values obtained 
 must be taken as characteristic for this community. 
 
 The children of foreign parentage are of course much more 
 numerous than those of foreign birth. The number of Ger- 
 mans is especially large. The median weights of boys and 
 girls whose parents were born in Germany are compared in 
 Tables No. 15 and 16, with children of American parentage. 
 
 TABLE No. 15.* 
 The Weights of Girls whose Parents were born in Germany com- 
 pared WITH the Weights of Girls whose Parents were born in 
 the United States.! 
 
 * The birth-place of the girls themselves is not considered in this table. 
 t A few were born in Canada. 
 
310 
 
 Trans. Acad. Sci. of St. Louis. 
 
 TABLE No. 16.* 
 
 ■The Weights of Boys whose Parents were born in Germany Com- 
 pared WITH THE Weights of Boys whose Parents were born in 
 THE United States. f 
 
 GERMAN. 
 
 AMERICAN. 
 
 Age at 
 
 Nearest 
 
 Birthday. 
 
 Number of 
 Observa- 
 tions. 
 
 Median 
 Weight. 
 (Kilo- 
 grammes) 
 
 Median 
 Weight. 
 (Kilo- 
 grammes) 
 
 Number of 
 Observa- 
 tions. 
 
 Age at 
 
 Nearest 
 
 Birthday. 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 158 
 334 
 426 
 369 
 370 
 358 
 385 
 321 
 166 
 106 
 26 
 
 20.04 
 21.93 
 23.98 
 26.64 
 28.51 
 31.21 
 33.51 
 35.92 
 39.59 
 44.68 
 52.22 
 
 19.66 
 21.67 
 23.91 
 26.08 
 28.49 
 31.26 
 33.45 
 35.96 
 40.34 
 47.25 
 52.10 
 55.14 
 
 263 
 756 
 907 
 878 
 847 
 668 
 549 
 437 
 352 
 219 
 92 
 40 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 The difference in weight is seen to be of no great impor- 
 tance. 
 
 In the absence of special investigations of the influence of 
 social condition and the nationality of parents on the growth 
 of children, it is impossible to estimate accurately to what 
 degree middle values, calculated without regard to social con- 
 dition and nationality, are affected by these factors. The 
 data presented in this chapter go to show that the middle 
 values of St. Louis children are little influenced by ponsider- 
 able differences in social condition before the period of 
 prepubertal acceleration and are not very largely influenced 
 by such differences during this period. Further, these values 
 are at no time much affected by differences in nationality of 
 parents not greater than those existing between Germans and 
 Americans. But the whole question evidently requires ex- 
 tended study of data difficult or impossible of collection by 
 private hands. 
 
 * The birth-place of the boys themselves is not considered in this table, 
 t A few were born in Canada. 
 
CHAPTER V. 
 
 PERCENTILE GRADES OF WEIGHT, HEIGHT STANDING, HEIGHT SITTING, SPAN 
 OF ARMS, GIRTH OF CHEST, LENGTH OF HEAD, WIDTH OF HEAD, HEIGHT OF 
 FACE FROM ROOT OF NOSE TO POINT OF CHIN, WIDTH OF FACE, AND HEIGHT 
 OF FACE FROM HAIR LINE TO POINT OF CHIN. 
 
 The Percentile Grades of weight, height, etc., presented in 
 Tables No. 17 to No. 28, inclusive, are represented graphically 
 in Plates V to XXIV. By their aid, the percentile rank of 
 an individual in respect of weight, span of arms or any physi- 
 cal dimension included in the tables can be easily and quickly 
 determined. Suppose, for example, the percentile rank of a 
 boy, aged 11, weighing 32 kg. was desired. A horizontal line 
 is drawn from 32 in the column of kilogrammes on the left of 
 Plate V to the curve of age 11, and a perpendicular is dropped 
 from the point of intersection to the scale of percentile 
 grades at the bottom of the plate. The perpendicular falls at 
 60 per cent. Hence the boy is heavier than 60 per cent, of 
 boys of his age and lighter than 40 per cent. 
 
 Other facts are made plain by these curves. The increase 
 at any percentile grade during one or more years is expressed 
 by the distance between the curves at that grade. Thus, in 
 Plate V, the gain in weight of the type-boy in the 15 per- 
 centile grade during the years 6 to 11 inclusive is 9.3 kg., and 
 the gain at the 85 percentile grade during the same year 13.0 
 kg. The difference in size between large and small boys of 
 the same age appears in the inclination of the curve to its 
 axis, the slope being steepest in the years of quickest growth. 
 And finally, the tendency of the greater number of individuals 
 to approximate the middle value of their group is illustrated, 
 the inclination of each curve being much less at the central 
 part than at the ends, where the giants and the dwarfs are 
 found. The principal service of such curves, however, is to 
 determine percentile rank. 
 
 (311) 
 
312 
 
 Trans. Acad. Sci. of St. Louis. 
 
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CHAPTER VI. 
 
 SEXUAL DIFFERENCES IX GROWTH. 
 
 When the curves of growth in weight, height standing, 
 height sitting, span of arms and girth of chest are drawn on 
 the same system of co-ordinates, as has been done in Plates 
 XXV to XXIX inclusive, the attention of the observer is 
 arrested by the extraordinary difference in the development 
 of girls and boys during the period of prepubertal 
 acceleration. Girls enter this time of rapid growth at age 11 
 or 12, two years earlier than boys, and during several years are 
 larger than boys of the same age. The period during which 
 girls are larger than boys does not correspond exactly with 
 the period of accelerated development, but begins and ends 
 a little later. The ages at which girls begin and cease to be 
 larger than boys are given in the following table. The ages 
 
 TABLE No. 29. 
 Ages at which Girls begin and cease to be larger than Boys. 
 
 DIMENSION. 
 
 Weight 
 
 Height standing 
 
 Height sitting 
 
 Span of arms 
 
 Girth of chest 
 
 Height of face from 
 hair line to point of 
 chin 
 
 Age at which Girls begin 
 to be larger than Boys. 
 
 Percentile Grades. 
 
 12i\-yrs. 
 HA 
 
 12A 
 
 50 
 
 
 12A3 
 
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 (1 
 
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 75 
 
 ll-i\yrs, 
 
 iiA " 
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 12 " 
 
 Age at which Girls cease 
 to be larger than Boys. 
 
 Percentile Grades. 
 
 26 
 
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 ISA 
 
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 are nearly the same for the same percentile grade in all five 
 dimensions. An examination of plates XXX to XXXVI 
 
 (324) 
 
Porter — The Growth of St. Louis Children. 
 
 325 
 
 shows that the sexual difference just noted is not present in 
 expansion of chest, or in strength of squeeze, or in 
 any head or face measurement except height of face from 
 hair-line to point of chin. Boys have therefore a larger ex- 
 pansion of the chest, greater strength of squeeze and greater 
 leno;th and width of head and height and width of face than 
 girls throughout their period of growth. 
 
 An interesting comparison can be made of the duration of 
 the period in which girls are larger than boys. It appears 
 
 Duration of the Period during which Girls are larger than Boys. 
 
 DIMENSION. 
 
 Weight 
 
 Height standing 
 Height sitting... 
 Span of arms . . . 
 Girth of chest... 
 
 Percentile Grades. 
 
 3i%yrs. 
 
 4 " 
 
 5 " 
 
 3A " 
 
 3-1% yrs. 
 
 Qli <( 
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 75 
 
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 <5i2 
 
 that the period is shortest in span of arms and is considerably 
 longer in height sitting than in any other dimension. 
 
 The age at which girls begin to be larger than boys differs 
 at different percentile grades, big girls (75 percentile grades) 
 beginning to be larger than big boys at an earlier age than 
 that at which small girls begin to exceed small boys. A 
 difference is seen also in the duration of the period in which 
 girls are larger than boys: the small girls keep their 
 superiority during a longer time than the larger girls. 
 
 Sexual differences are further displayed in Plates XXXVII 
 to XLI, inclusive, in which the percentile curves of both sexes 
 are drawn one a short distance under the other, and the points 
 at which girls begin and cease to be heavier than boys joined 
 by heavy unbroken lines. The early superiority of large 
 girls and the relative early loss of their superiority is seen in 
 all the plates. The fact that the period during which big girls 
 are larger than big boys is shorter than the period during which 
 
326 Trans. Acad. Set. of St. Louis. 
 
 little girls are larger than little boys is very clearly demon- 
 strated by Plates XXXVIII, Height Standing, XXXIX, 
 Height Sitting and XL, Span of Arms ; it can be seen also 
 in Plate XXXVII, Weight, and XLI, Girth of Chest, if the 
 ninety and the five percentile grades, in which the small 
 number of observations has probably led to error, are 
 neglected. 
 
CHAPTER VII. 
 
 THE RATE OP GROWTH. 
 
 The Absolute Annual Increase is the gain in weight or height, 
 etc., during the twelve preceding months ; thus, the absolute 
 annual increase in height at age 7 is the gain in weight during 
 the twelve months from age 6 to age 7, obtained by subtract- 
 ing the average or median weight at age 6 from that at age 7. 
 
 The absolute annual increase of height standing, weight and 
 span of arms is shown in Plate XLII and Tables No. 30, 31 
 and 32. In all three, the maximum for girls is at age 13 and 
 the maximum for boys at age 15. The same may be said of 
 the curves for height sitting, girth of chest and strength of 
 squeeze, in Plate XLIII, from Tables No. 33, 34, 44 and 45, 
 although the curves are less regular, owing to the observations 
 being more difficult than those from which the preceding plate 
 was constructed. In all six curves, the small number of ob- 
 servations at age 17 and 18 cause the median values at those 
 ages to be less reliable than at other ages. 
 
 The Relative Annual Increase is the increase for any year 
 divided by the average value at that year ; thus, the relative 
 annual increase in weight at age 7 is the difference between 
 the average weight at age 6 and age 7 divided by the average 
 weight at age 6. The relative annual increase gives a truer 
 idea of growth than the absolute annual increase, because the 
 latter value is entangled with the size of the individual meas- 
 ured. The absolute increase is commonly greater in a big 
 boy than in a small boy, and yet the rate of growth may be 
 the same. The relative annual increase is free of such errors. 
 
 The relative annual increase in strength of squeeze, weight, 
 height standing, height sitting, span of arms and girth of 
 chest is drawn in Plate XLIV. The gain in weisrht during the 
 prepubertal acceleration is extraordinary in both girls and 
 boys, as is the rapid fall immediately thereafter. The quick- 
 ness of growth in height standing of boys is slightly greater 
 
 (327) 
 
828 
 
 Trans. Acad. Sd. of St. Louis. 
 
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Porter — The Groivth of St. Louis Children. 333 
 
 during the years 6 and 7 than at any other time, and in 
 girls is nearly as great in these years as in the period of 
 acceleration. The curve of girls' height sitting is very similar 
 to that of girls' height standing. In both, the rate of growth 
 is more uniform than in weight. Indeed, the period of accel- 
 eration in the last named dimension is greater than in any of 
 the others. The relative annual increase of boys' height sit- 
 ting seems almost atypical, by reason of its sharp ascent 
 at ages 8 and 9 and its failure to sink after age 16. 
 The latter feature is perhaps due to an error in the average 
 value caused by the small number of observations at age 
 
 17. I am unable to explain the ascent at ages 9 and 
 10. The growth in span of arms is somewhat more rapid 
 at ages 7 and 8 than during the prepubertal acceleration. 
 The curve of girls' girth of chest differs from the usual 
 type in its sudden rise at age 11, the increase at that year 
 appearing slightly greater than at age 13. The boys' 
 curve, on the contrary, agrees very well with the curves of 
 weight, height, etc., except that the curve rises at age 
 
 18, where the number of observations, it may be repeated, 
 is perhaps too small for very sure work. The quickness 
 with which the strength of squeeze decreases after age 7 
 is certainly remarkable, as is the sharpness with which the 
 prepubertal acceleration is shown. 
 
 Attention will be called in chapter IX, to the importance 
 in children of the relation between height and weight, girth of 
 chest and other physical dimensions. Unusual height, it will 
 be pointed out, is commonly a disadvantage, because it entails 
 an unusual loss of energy. If such individuals have a weight 
 and girth of chest, etc., so much above the common as to com- 
 pensate their excessive height, they are likely to be able to 
 meet all demands on their strength. If they do not possess 
 this compensatory development, they will probably be unable 
 to meet any excessive demand. Thus the question of how far 
 this, compensation exists in any individual, or, more broadly 
 stated, the question what weight, girth of chest, etc., should 
 accompany any given height, becomes of the greatest in- 
 terest. This interest, it should be remarked, is unusually 
 great in the case of children, for children are taxed with the 
 
334 Trans. Acad. Sci. of St. Louis. 
 
 mechanical motion and other forms of dissipation of energy 
 making up the ordinary output of life, and, in addition, with 
 the extraordinary function of storing energy in the increase 
 of tissue which constitutes growth. 
 
 In view of these facts, Plate XLV cannot fail to be instruct- 
 ive. It shows the ratio of span of arms, height sitting, chest- 
 girth, weight, strength of squeeze with right hand, and five head 
 and face measurements to height standing. Height standing 
 is here expressed by an abscissa, and the percentage relation 
 of weight and the other dimensions are displayed in curves. 
 Of all these, span of arms most closely approximates the 
 height, the difference being less than one per cent, of the 
 latter from age 6 to 11 and scarcely more than 2 })er cent, 
 in subsequent ages. Span of arms in both sexes is therefore 
 nearly the same as height standing throughout the period of 
 observation, becoming very slightly greater than the height as 
 growth progresses. The height sitting and the girth of chest 
 run a parallel course and are, moreover, nearly equal, the 
 girth of chest being about 2 per cent, less than the height 
 sitting. They increase a little less rapidly than the height, 
 showing a decline of about 4 per cent, in thirteen years. 
 Height sitting and chest-girth are not far from half the height 
 standing. 
 
 Far different is the development of weight and strength of 
 squeeze. These increase much more rapidly than height, for 
 at age 6 the height stands to weight in the ratio of 100 to 18 
 and to strength of squeeze as 100 to 6, while at age 16 these 
 ratios are 100 to 34 and 100 to about 16, respectively. The 
 parallelism in the development of weight and strength of 
 squeeze is of much interest. The dimensions of head and 
 face increase somewhat less rapidly than the height. The 
 length of head, for example, falls from -rg-th of the height, at 
 age 6, to about iVth at age 18. 
 
CHAPTER VIII. 
 
 THE RELATION BETWEEN THE PHYSICAL DEVELOPMENT OF SCHOOL 
 CHILDREN AND THEIR CAPACITY FOR MENTAL LABOR. 
 
 Ill Vol. VI, No. 7 of the Transactions of the Academy of 
 Science of St. Louis, issued March 21, 1893, I demonstrated 
 that children who possess more than the ordinary power of 
 mental labor, as measured by their progress in their studies, 
 are heavier, taller and larger in girth of chest and in width of 
 head than their less gifted companions of the same age. A 
 more extended statement of these observations was presented 
 to the Berliner Gesellschaft fiir Anthropologic, Ethnologic 
 und Urgeschichte, July 15, 1893, and appears in Virchow's 
 Zeitschrift fiir Ethnologic under the title Untersuchungen der 
 Schulkinder in Bezug auf die physischen Grundlagen ihrer 
 geistigen Entwickelung. In these papers, the material was 
 the total number of observations irrespective of the social 
 condition of parents. An example, selected from Tables Nos. 
 2 and 4, page 165 and 167, of The Physical Basis of Pre- 
 cocity and Dullness, will illustrate the result of the 
 inquiry. Pupils aged 11 are found in Grades I, II, III, IV, 
 V and VI of the St. Louis Public Schools, as the following 
 table shows. The 59 boys of Grade I, the lowest grade, 
 
 TABLE No. 35. 
 
 Median Weight of Boys aged U distributed by School Grade. 
 
 No. of Boys Median 
 
 Grades. Weighed. Weight. 
 
 1 59 28.83 Kg. 
 
 II 311 29.74 
 
 III 664 30.92 
 
 IV 546 31.43 
 
 V 123 32,41 
 
 VI 33 33,29 
 
 weigh less than the boys of Grade II, and these, again, are 
 lighter than the boys in higher grades. 
 
 (335) 
 
336 Trans. Acad. Sci. of St. Louis. 
 
 It is a well-known fact that children of the prosperous 
 classes are better developed physically than the children of 
 the poor. It has been suggested that the children of poor 
 parents are not so successful in school work as the children 
 of the rich, and that the poor children are compelled to leave 
 school at an earlier age than the rich, and for these reasons 
 are relatively less numerous than the rich in the higher grades. 
 According to this idea, the better physical development of 
 the children of the same age in the higher grades, as illus- 
 trated above in boys aged 11, is due to the preponderance in 
 the higher grades of the well nourished children of the rich. 
 This may be, and probably is, a factor in the phenomenon, 
 but is surely only a partial influence. 
 
 For when children of the same age and as nearly as possible 
 of the same social class are weighed and the weights dis- 
 tributed by school grade, it is found that they follow the law 
 established for the whole material irrespective of social condi- 
 tion. A glance at Plate XLVI, derived from Table No. 36, 
 will convince the reader of the truth of this statement. 
 
Porter — The Growth of St. Louis Children. 
 
 337 
 
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338 
 
 Trans. Acad. Sci. of St. Louis. 
 
 Further evidence is afforded by Table No. 37, in which the 
 daughters of professional men are divided into two equal 
 groups, in the manner explained on page 177 of The Physical 
 Basis of Precocity and Dullness, one group containing the 
 fifty per cent who are found in the upper grades, the other 
 the fifty per cent found in the lower grades. It should be 
 
 TABLE No. 37. 
 
 Median Weight of the Daughters of Professional Men Distrib- 
 uted BY School Grade. 
 
 
 ■*H 
 
 ■^ an e3 
 
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 7 
 
 50 
 
 8 
 
 52.5 
 
 9 
 
 53.5 
 
 10 
 
 57.5 
 
 11 
 
 58.0 
 
 12 
 
 50 
 
 13 
 
 55.5 
 
 School Grades. 
 
 Kg., 10 I. 
 
 Kg., 97 I. 
 
 I, 69 II. 
 
 I, II, 48 III. 
 
 I, II, III, 28 IV. 
 
 I, II, III, 81 IV. 
 
 II, III, IV, 78 V, 
 
 Median 
 
 Weight. 
 
 (Kilogram's) 
 
 Median 
 
 Weight. 
 
 (Kilogram's) 
 
 20.29 
 
 20.81 
 
 22.13 
 
 23.75 
 
 24.52 
 
 25.07 
 
 27.19 
 
 27.64 
 
 28.76 
 
 31.27 
 
 33.65 
 
 34.05 
 
 38.46 
 
 39.55 
 
 School Grades. 
 
 90 I, II. 
 
 3 I, II, III. 
 
 31 II, III, IV, V. 
 
 52 III, IV, V, VI. 
 
 72 IV, V, VI, VII. 
 
 19 IV, V, VI, VII. 
 
 22 V,VI,VII,VIII. 
 
 Number of 
 Observa- 
 tions. 
 
 50 
 52.5 
 53.5 
 57.5 
 
 58.0 
 
 50 
 
 55.5 
 
 ^11 
 
 9 
 10 
 11 
 12 
 13 
 
 remarked that this method of division diminishes the cou- 
 spicuousness of the difi'erence between lower and higher 
 grades by not presenting the weights for outlying grades, but 
 for a small number of observations it is much more reliable 
 than the method of which Table No. 36 is an illustration. 
 
 The results of this study of the weights of girls from 
 the same social class distributed by school grade confirm the 
 conclusion reached in the publications cited above, namely 
 that successful pupils are larger than the unsuccessful. 
 
CHAPTER IX. 
 
 THE APPLICATION TO INDIVIDUAL SCHOOL CHILDREN OF THE MEAN VALUES 
 DERIVED FROM ANTHROPOLOGICAL MEASUREMENTS BY THE GENERALIZING 
 METHOD. 
 
 The data for the studies described in this work can be col- 
 lected either bv the " generalizing " or by the " individualiz- 
 ing " plan. In the former, a great number of measurements 
 is made but once on individuals of different ages, and the 
 measurements classified according to age. In the lattei;, the 
 same individuals are measured yearly or oftener during their 
 period of growth, and the measurements classified also by 
 age. The generalizing method, the one pursued in the present 
 investigation, is rapidly and easily carried out, whereas the 
 individualizing method demands for its execution exceptional 
 opportunities and exceptional patience, requiring not only 
 that the measurements be made and the records kept through 
 two decades, but that the number of children measured in the 
 early years of this long period be very great, lest death and 
 desertion so thin the ranks that those remaining to the end 
 shall be too few to yield trustworthy conclusions. Both 
 methods, when applied to the same material, give identical 
 results with regard to means, including those of subdivisions 
 as well as those of the whole number of observations. The 
 individualizing method does more. 
 
 The importance of the individualizing method has been much 
 emphasized, for the reason that it can give information without 
 which the laws derived from means cannot, in the present state 
 of knowledge, be applied to individuals. Before this appli- 
 cation can be made, it is necessary to know the degree of prob- 
 ability that an individual, who at a given age stands at a certain 
 deviation from the mean of any dimension will show the same 
 deviation at other ages; for example, the degree of probability 
 that a girl whose height at age 8 is 122.06 cm., and who 
 therefore deviates 3.7 cm., or +lcZ from the mean of her age 
 (118.36 cm.), will deviate to the same degree (-{-Id) from 
 
 (339) 
 
340 Trans. Acad. Sci. of St. Louis. 
 
 the mean height throughout her growth. In that case, the 
 law of growth for the type at a deviation of -\-ld from the 
 mean is her law of growth. Otherwise, she is an exception 
 and practical regulations deduced from the law for the type 
 cannot be safely made binding on her. This knowledge, as 
 has just been said, is furnished by the individualizing method, 
 while the generalizing method is of no assistance in this matter. 
 
 The application to individuals of the law of growth of the 
 mean is a subject of immediate practical interest. The con- 
 nection between theory and practical affairs is here unusually 
 short and clear. Were this application possible, the devia- 
 tions of children from the laws of normal growth could be 
 quickly recognized and largely overcome, the evil effect of 
 over study could be watched and intelligently combated, and 
 systems of education, no longer exacting of all that which 
 should be exacted only from the mean, could be rationally 
 adapted to the special needs of the exceptionally weak and 
 the exceptionally strong. 
 
 These beneficent reforms, it is at present believed, must 
 await the slow collection of data by the individualizing 
 method. If it is indeed true that the laws of growth deter- 
 mined for the mean cannot be used for the individual until 
 the individualizing method has established the probability 
 of each individual deviation remaining constant throughout 
 the period of growth, then a generation must elapse — so 
 slow is the gathering of data by this method — before the 
 necessary knowledge is in our hands. I hope to show that 
 this long waiting is unnecessary, and that the data collected 
 by the generalizing method may be used, in a way hitherto 
 unrecognized, for the making of standards by which the 
 deviation of an individual from the mean of his age may be 
 seen to be normal or abnormal. 
 
 Let the problem be clearly understood. The question is : 
 this boy or girl is above or below the mean height, or weight, 
 etc., of his or her age. How shall it be known that this 
 deviation is normal or abnormal? There has been hitherto 
 no satisfactory reply to this question. A vague and partial 
 answer is possible after two measurements separated by at 
 least a year's interval. If the deviation is the same, or very 
 
Porter — The Growth of St. Louis Children. 
 
 341 
 
 nearly the same, at both measurements, the probability is that 
 the child is growing normally. This probability is greater 
 than the general probability that a normal deviation is more 
 likely to occur than an abnormal one, but its numerical value 
 is wholly unknown. If, on the other,hand, the two deviations 
 are unequal, the probability is that the greater of them is 
 abnormal, but the numerical value is here also unknown. 
 How definitely the individualizing method could answer this 
 question is difficult of conjecture, in the present lack of data, 
 but certainly no answer whatever could be expected except 
 after two measurements separated by a year's interval, a year 
 in which the unchecked cause of an abnormal deviation might 
 inflict an irreparable damage on the organism. Such indefi- 
 nite and fragmentary knowledge can never be the basis of a 
 practical reform. Any solution of this problem which shall 
 gain general acceptance must be easy to understand and easy 
 to apply, and must give the probable degree of abnormality^ 
 of any observed deviation. These conditions are, I believes, 
 fulfilled b}' the following method. 
 
 According to the theory of probabilities, the heights of a 
 thousand individuals of the same class will arrange themselves 
 as follows: — 
 
 tween 
 
 M+4(? and U+nd 
 
 
 M+3d 
 
 « M-f4d 
 
 
 M+2d ' 
 
 ' M+3cZ 
 
 
 M+ d 
 
 ' M+2d 
 
 
 M 
 
 ' M+ d 
 
 
 M 
 
 ' M— d 
 
 
 M— d ' 
 
 M— 2d 
 
 
 M-2d 
 
 « M—Sd 
 
 
 M—3d 
 
 ' M—id 
 
 
 M—id ' 
 
 ' M — nd 
 
 3 
 
 individuals 
 
 18 
 
 
 67 
 
 
 162 
 
 
 250 
 
 
 250 
 
 
 162 
 
 
 67 
 
 
 18 
 
 
 3 
 
 
 where M = the mean and c?=the probable deviation. 
 Let these be divided into seven groups: — 
 
 I. 
 
 II. 
 
 III. 
 
 VI. 
 
 V. 
 
 IV. 
 
 VII. 
 
 All individuals betv^een 
 
 M-}-nd and 
 
 M+3d 
 
 21 
 
 M+3d " 
 
 M+2d 
 
 67 
 
 M+2d " 
 
 M+ d 
 
 162 
 
 M 
 
 Md= d 
 
 500 
 
 M— d 
 
 M— 2d 
 
 162 
 
 M—2d «' 
 
 M-3d 
 
 67 
 
 M—Sd " 
 
 M—nd 
 
 21 
 
342 Trans. Acad. Sci. of St. Louis. 
 
 The mean height, weight, girth of chest, etc., of each 
 of these groups at any age will be the type of a certain 
 deorree of deviation from the mean of the age. That is to 
 say, the weights, etc., of each group will be symmetrically 
 distributed above and below the mean weight, etc., of the 
 group in the manner already illustrated for the entire undivided 
 number of observations, i. e., the entire thousand. Each 
 group, therefore, will be characterized by a physical develop- 
 ment definitely determined by the means of height, weight 
 and other physical dimensions. These means, taken together 
 form the type or norm of the group. The individual devia- 
 tions from this norm follow the theory of probability, and 
 the degree of abnormality presented by any individual devia- 
 tion can be expressed in the terms of this theory. An exam- 
 ple will illustrate this. A boy X shows a deviation in height 
 of -\-1.5d from the mean height of his age. He falls therefore 
 in Group III. The boys in this group possess a mean weight 
 of M kilogrammes, with a probable deviation of zLd ; that 
 is, boys between d and 2d taller than the norm of their age 
 should weigh M±f^ kilogrammes. In like manner, they 
 should have a girth of chest of M:hd centimetres, and a 
 span of arms of M±tZ centimetres, and so on. If the 
 weight, etc., of the boy X coincide with the means of his 
 group (Group III) his physique is normal, the accuracy of 
 this conclusion being proportionate to the number of different 
 dimensions on which it is based. If the boy X deviate more 
 than zLld from the mean in one or more dimensions, his 
 development is abnormal, and the degree of abnormality is 
 measured by the amount of his deviation. 
 
 The necessity of choosing some one dimension as the basis 
 of such a system is self-evident. There are good reasons, 
 partly theoretical and partly practical, why height rather than 
 weight should be taken as a basis. Height is more stable, 
 less liable to irrelevant fluctuations, than weight. An excess 
 in weight can be reduced ; a child whose weight is out of pro- 
 portion to its height may be brought into proportion by suitable 
 diet and exercise ; but height, once attained, cannot be reduced, 
 nor can the growth in height be easily influenced. Practically, 
 therefore, the physical trainer must be content to bring the 
 
Porter — The Growth of St. Louis Children. 343 
 
 weight, girth of chest, strength of squeeze and other physical 
 dimensions up to the mean development which corresponds to 
 the height of the child. Experience has abundantly shown 
 that the relation of weight to height is of great importance to 
 health, life insurance companies declining to receive applicants 
 whose weight falls much below the standard weight of their 
 height. For these reasons, height should be preferred as the 
 basis of the system . 
 
 The question whether any given deviation is normal or 
 abnormal is answered by this system in two ways : in respect 
 of height, by the degree of deviation from the mean or norm 
 of the whole number of observations ; in respect of other 
 dimensions, by the degree of deviation of the weight, girth of 
 chest, etc., from the mean weight or girth of chest corre- 
 sponding to the height of the individual under examination, 
 this normal weight, etc., being determined with sufficient 
 exactness by taking the means and probable deviations of the 
 group in which the height falls. It is evident that all cases 
 included within M±c^ must be termed normal, for the chances 
 are even that any individual measurement in a series will fall 
 within M±tZ and are against its exceeding these limits, being 
 4.64 against 1 that it will fall at M±2d. 
 
 Strictly speaking, all abnormal deviations in any dimension 
 are probably unhealthful, yet an important difference exists 
 in this respect between abnormal deviations in height and 
 abnormal deviations in weight, girth of chest, etc., as related 
 to height. It cannot be doubted that abnormal height is 
 probably (using the word in its technical sense) a disadvan- 
 tage. The potential energy of the body is converted into 
 mechanical labor and heat, by far the greater expenditure 
 taking the latter form. In the adult, the total expenditure 
 in the form of heat is about 2,700 calories in 24 hours 
 (Helmholtz), of which 80.1 per cent escape in radiation, con- 
 duction and evaporation from the skin. Thus the superficies 
 of the body plays a great part in the dissipation of energy. 
 The superficies is greater, usually, in tall children than in 
 short, a difference of special importance in the young, in 
 whom metabolism is much more active than in the adult. 
 More heat is therefore lost by the abnormally tall than by 
 
344 Trans. Acad. Sci. of St. Louis. 
 
 those of normal height. There is a disadvantage also in the 
 loss by mechanical labor. Greater height entails increased 
 work on the heart and on the skeletal muscles. In short, 
 increased loss of energy goes hand in hand with increase in 
 height. Hence in the tall the necessity for a physical 
 development which shall be so much above the mean as to 
 compensate their greater loss of energy. In growing children 
 not only must there be compensation for the expenditure of 
 energy, but there must be also energy stored in the increase 
 of tissue which constitutes growth. 
 
 If the greater demands of tall children are balanced by a 
 correspondingly greater income of energy, a normal equilib- 
 rium or " health " is preserved. It should be clearly recog- 
 nized that this equilibrium is unaffected by the absolute 
 height and is dependent only on the relation between height 
 and the other physical dimensions. Consequently health is 
 as possible in tall children as in those of normal height, 
 although less probable, for the chances against a compensatory 
 development of weight and other dimensions increase very 
 rapidly with the deviation of the height from the norm. 
 The absolute height of an individual is of very secondary 
 interest from a practical point of view, because it is not nec- 
 essarily a state of ill health, whereas the development of 
 weight, girth of chest, etc., in proportion to height is of 
 supreme interest. A lack of proportion between height 
 and other physical dimensions is itself ill health. The ten- 
 dency of organisms to adopt ends to means is strong, and an 
 imperfect compensation may suffice for most demands. A 
 heart in which an hypertrophy of the left ventricle has par- 
 tially compensated an insufficiency of the mitral valve may 
 beat regularly enough for ordinary exertions, and yet fail 
 utterly when its possessor is forced suddenly to ascend a 
 height or to make any other unusual exertion. So a tall child 
 may have a sufficient income of energy to meet the demands 
 of a wisely regulated life, and sink under the burden of 
 unusual tasks. 
 
 It has been shown in the foregoing pages that the means 
 derived from anthropometrical metrical measurements by the 
 generalizing method can be used to determine whether the 
 
Porter — The Groiolh of St. Louis Children. 345 
 
 weight and other physical dimensions of an individual are 
 normal in relation to height, and it has been pointed out that 
 this normal relation constitutes health. It follows that the 
 normal amount of labor cannot be exacted without injury 
 from those in whom this equilibrium is wanting. These 
 facts must therefore be taken into account in a rational 
 school system, and it should now be made plain how this is to 
 be done. 
 
 All systems of education have for their object the largest 
 possible development of individual minds. In large schools 
 the tasks by which this development is promoted are those 
 which secure from the child of mean ability its maximum 
 mental output. In practice they are determined by examina- 
 tions. Hence the existence in every educational institution 
 of classes based on the mental output of the mean pupil, and 
 related to age only in that the output fixed as the standard of 
 any class is necessarily found more often at a certain age than 
 at other ages. Thus there exists a mean age for each class; 
 the greater number of pupils at any age is found in the same 
 class, while some have advanced beyond, and others, equally 
 old, have not yet come so far as this class. On an average, 
 those who have advanced beyond the greater number of their 
 age are precocious, that is, possess more than the mean capac- 
 ity for mental labor, while those who are less advanced are 
 dull, possessing less than the mean capacity. It has been 
 demonstrated that there is a physical basis for precocity and 
 dullness : ^ when numbers sufficiently large for statistical 
 purposes are employed, it is seen that precocious pupils are 
 of greater mean weight, height, etc., than the mean pupils 
 and that the latter are heavier and taller that the dull. The 
 mental output is therefore directly related to the physical 
 condition of the pupils. The mean height, weight, girth of 
 chest, etc., in any grade is the mean physical development 
 corresponding to the mental output of the grade. It follows 
 that those who do not possess this development cannot with- 
 out abnormal strain do the work exacted in this grade. On 
 the other hand, pupils who possess more than the mean 
 
 1 See Chapter VIII, page 335 et seq. 
 
346 Trans. Acad. Sci. of St. Louis. 
 
 physical development of their age should be capable of more 
 than the mean labor. Yet the management of this latter 
 class presents but few difficulties, whereas the former class 
 cannot be too carefully protected. 
 
 The consequences of continued overstrain in a growing boy 
 or girl are most unhappy. The curves of growth in height 
 and weight of the mean child are characteristic. The quick 
 rise to age 7 or 8, the slower ascent to age 11 in girls and 13 
 in boys, the remarkable three years of accelerated develop- 
 ment preceding puberty, and, finally, the rapid decrease in 
 the rate of growth as full development approaches express 
 the normal development of the type and, presumably, the 
 normal development of the individual. Overwork may cause 
 a temporary or a permanent deviation in these curves. It is 
 probable, though not certain, that a temporary loss consequent 
 on a slight overstrain may not lower the final outcome of the 
 development, but there can be no doubt as to the result of a 
 prolonged strain. In such a case, the probability is strong 
 that the whole subsequent curve will be turned out of its 
 course. A prolonged strain in a growing child harms for 
 life and leaves a mark which can never be effaced. The 
 danger is greatest in the periods of quickest development, 
 particularly great in the prepubertal period. It is a sufficient 
 commentary on the evils of the present educational methods 
 that during these very years the undiscriminating routine of a 
 system devised for the average pupil is most inflexibly applied 
 to weak and strong alike. 
 
 Overstrain can often be recognized both by subjective and 
 objective symptoms. Subjective symptoms, however, are 
 frequently obtained with difficulty, especially in pupils who 
 are unusually ambitious and who overstudy from choice. An 
 objective symptom must therefore be found — a symptom 
 easily demonstrated and almost never wanting. Such a 
 symptom is the failure to gain weight at the normal rate. A 
 persistent loss of weight in an adult is regarded as a matter 
 of grave concern; the persistent failure of a child to make 
 the normal gain in weight is no less grave. It is not pretended 
 that the failure to gain weight always accompanies overstrain, 
 but it is claimed that the number of exceptions is small and 
 
Porter — The Growth of St. Louis Children. 347 
 
 that frequent weighing is the most practical and on the whole 
 the most certain method of detecting the presence of influences 
 that are working injury to the development of the child. 
 The skillful breeder of cattle depends on systematic weighing 
 to inform him if his efibrts are meeting with success, but 
 children are left to grow at haphazard. 
 
 It is not enough that overstrain should be recognized by the 
 harm it has done. The child should be guarded aorainst the 
 possibility of harm. The anthropometrical system proposed 
 ofi'ers a means of doing this. It infallibly discovers 
 the children whose physical development is below the 
 standard of their age. It no less certainly indicates the 
 physical development which most often accompanies the 
 power to do the mental work of any grade. It therefore 
 divides the pupils into two bodies; those physically compe- 
 tent and those physically incompetent for a clearly defined 
 degree of mental exertion. When working with great num- 
 bers, the infallibility of this system is practically absolute and 
 theoretically almost absolute. When applied to individuals, 
 errors will certainly occur, but the number of errors will 
 according to the laws of probability be less than the number 
 of correct conclusions, and these errors cannot influence the 
 great fact that such a system is competent to call attention to 
 the children who will probably be unable to do the normal 
 work of their age without injury. Each individual case must 
 then be treated on its own merits. 
 
 The proposed system of physical examination requires: — 
 
 I. The collection of sufficiently extensive data by the gen- 
 eralizing method. 
 
 II. The determination of the means and the probable 
 deviations of height, weight, girth of chest, strength of 
 squeeze, etc., for each age. 
 
 III. The division of the individuals at each age into groups 
 in terms of the probable deviation from the mean height, as 
 illustrated above, and the calculation of the mean and prob- 
 able deviation of the weight, girth of chest, etc., of each 
 group. 
 
 IV. The determination of the mean physical development 
 of the pupils in each class or grade of the school system. 
 
348 Trans. Acad. Sci. of St. Louis. 
 
 V. The physical examination of each applicant for entrance 
 to any grade. 
 
 These data permit the enforcement of the following regula- 
 tion : That no pupil whose physical development varies more 
 than ±cZ from the weight, etc., of the mean pupil of his 
 height in a class which his mental output would otherwise 
 entitle him to enter, shall be admitted to that class, unless 
 with the approval of a medical expert, if possible a regularly 
 appointed school physician, who shall testify that the pupil's 
 strength will be equal to the strain. 
 
TABLES NO. 38 TO 51. 
 
 The tables which follow this page repeat some of the 
 more commonly used statistical values in a form which admits 
 of ready reference and comparison. Such are the average, 
 probable error of the average, probable deviation, median or 
 50 percentile grade and median minus average values. Yet 
 these tables are by no means summaries of the statistical calcu- 
 lations of the investigation, since they omit much that is given 
 in the foregoing pages. They contain, moreover, not a little 
 new matter. The relation of probable deviation to average, 
 relation of average to height standing, relative annual 
 increase of average, the 25 percentile grade, the 75 percentile 
 grade, the cranial indices and the absolute annual increase of 
 average of strength of squeeze and of measurements of the 
 head and face are here presented for the first time. 
 
 Some of this material has been already discussed in this 
 paper. Some is reserved for future discussion. One series, 
 the relation of probable deviation to average, was treated at 
 some length in ray paper on " The relation between the 
 growth of children and their deviation from the physical type 
 of their sex and age," Transactions of the Academy of Science 
 of St. Louis, Vol. VI, No. 10, pp. 233-250, November 14, 
 1893, to which the reader is referred. 
 
 Five dynamometers were used in testing the strength of 
 squeeze ; they were distinguished by the first five letters of 
 the alphabet ; A and D were graduated alike ; C and E were 
 also alike but differed from A and D, and B differed from all 
 the others. The original values obtained with these various 
 instruments are set down in Tables No. 45 and 46 ; from them 
 were made Tables No. 43 and 44, by reducing the arbitrary 
 graduation of all dynamometers to a uniform scale in kilo- 
 grammes. 
 
 (349) 
 
350 
 
 Trans. Acad. Sci. of St. Louis. 
 
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 Naturforscher. Bd. 26, 1858. 
 
 ZuBKOFFSKY : An investigation of the sanitary condition of the Military 
 Gymnasium in Polozk. Inaugural Dissertation. St. Petersburg, 1879 
 (Russian, cited by Sack). 
 
CORRIGENDA. 
 
 Page 263. Author's name omitted : W. To wnsend Porter. 
 
 288. Boys, aged 16, hair-line to point of chin should read 0.425 mm. 
 
 297. Boys, aged 10, median minus average should read — 0.07 cm. 
 
 313. Boys, aged 8, 50 percentile grade should read 119.77 cm. 
 
 313. Girls, aged 8, 50 percentile grade should read 118.74 cm. 
 
 315. Girls, aged 6, 50 percentile grade should read 107.29 cm. 
 
 315. Girls, aged 8, 50 percentile grade should read 118.33 cm. 
 
 321. Girls, aged 14, number of observations should read 997. 
 
 (370) 
 
LIST OB^ PLATES. 
 
 Plate I. The calculated and the observed distribution of the height 
 standing of 2192 St. Louis school girls, aged 8. 
 II. Median minus average values (weight, height, height 
 sitting, span of arms) . 
 
 III. Median minus average values (chest-girth and strength 
 
 of squeeze). 
 
 IV. Median minus average values (head and face measure- 
 
 ments) . 
 V. Boys' weight (percentile grades) . 
 VI. Girls' weight (percentile grades) . 
 VII. Boys' height standing (percentile grades). 
 VIII. Girls' height standing (percentile grades) . 
 IX. Boys' height sitting (percentile grades). 
 X. Girls' height sitting (percentile grades). 
 XL Boys' span of arms (percentile grades) . 
 XII. Girls' span of arms (percentile grades). 
 
 XIII. Boys' girth of chest (percentile grades) . 
 
 XIV. Girls' girth of chest (percentile grades) . 
 XV. Boys' length of head (percentile grades). 
 
 XVI. Girls' length of head (percentile grades). 
 XVII. Boys' width of head (percentile grades). 
 XVIII. Girls' width of head (percentile grades). 
 XIX. Boys' height of face from root of nose to point of chin 
 (percentile grades) . 
 XX. Girls' height of face from root of nose to point of chin 
 (percentile grades) . 
 
 XXI. Boys' width of face (percentile grades) . 
 
 XXII. Girls' width of face (percentile grades). 
 
 XXIII. Boys' height of face from hair-line to point of chin (per- 
 
 centile grades). 
 
 XXIV. Girls' height of face from hair-line to point of chin (per- 
 
 centile grades). 
 XXV. Weight, 75, 50 and 25 percentile grades. 
 XXVI. Height standing, 75, 50 and 25 percentile grades. 
 XXVII. Height sitting, 75, 50 and 25 percentile grades. 
 XXVIII. Span of arms, 75, 50 and 25 percentile grades. 
 XXIX. Girth of chest, 75, 50 and 25 percentile grades. 
 XXX. Mean expansion of chest. 
 XXXI. Mean strength of squeeze. 
 XXXII. Length of head, 75, 50 and 25 percentile grades. 
 
 XXXIII. Width of head, 75, 50 and 25 percentile grades. 
 
 XXXIV. Height of face from root of nose to point of chin, 75, 50 
 
 and 25 percentile grades. 
 
 (371) 
 
372 
 
 List of Plates. 
 
 Plate XXXV. 
 XXXVI, 
 
 xxxvir. 
 
 XXXVIII. 
 
 XXXIX. 
 
 XL. 
 
 XLI. 
 
 XLII. 
 
 XLIII. 
 
 XLIV. 
 
 XLV. 
 XLVI 
 
 Width ol face, 75, 50 and 25 percentile grades. 
 
 Heiglit of face from hair-line to point of chin, 75, 50 and 
 25 percentile grades. 
 
 Percentile grades, weight. 
 
 Percentile grades, height standing. 
 
 Percentile grades, height sitting. 
 
 Percentile grades, span of arms. 
 
 Percentile grades, girth of chest. 
 
 Absolute annual increase (height standing, weight, span 
 of arms). 
 
 Absolute annual increase (height sitting, girth of chest, 
 strength of squeeze). 
 
 Relative annual increase (strength of squeeze, weight, 
 height standing, height sitting, span of arms, chest- 
 girth). 
 
 Relation of average weight, span of arms, girth of chest, 
 etc., to average height. 
 
 The weights of daughters of manual tradesmen distrib- 
 uted by school grade. 
 
INDEX OF TABLES. 
 
 PAGE. 
 
 No. 1. The distribution of 2000 measurements of the same quantity 
 when the deviation of the individual observations from the 
 trne value of the measured quantity is due to purely accidental 
 causes 277 
 
 2. Heights of United States recruits 278 
 
 3. Observed distribution of the heights of 2192 St. Louis school 
 
 girls, aged 8 279 
 
 The calculation of the average height of St. Louis school girls, 
 aged 9 280 
 
 5. The calculation of the probable deviation (d) from the average 
 
 height (118.36 cm.) of 2193 girls, aged 8 283 
 
 6. Stieda's table for calculating the number of observations at any 
 
 distance from the mean or average within the limits : M -\- 5d 
 and M — 5d 284 
 
 7. The theoretical and the observed distribution of the heights of 
 
 2192 girls, aged 8 286 
 
 8. The percentile distribution of the heights of girls, aged 9 287 
 
 9. The probable error of the average 288 
 
 10, The probable deviation (d) from the average 291 
 
 11. Median minus average values 296, 297 
 
 12, Sums of median minus average values 300 
 
 13. A comparison of weights of the daughters of manual tradesmen 
 
 with the weights of the daughters of professional men and 
 
 merchants 305 
 
 14. The percentile distribution by school grade of the daughters of 
 merchants and professional men (i. e. favored classes) com- 
 pared with that of the daughters of manual tradesmen (hand- 
 workers) 307 
 
 15. The weights of girls whose parents were born in Germany com- 
 
 pared with the weights of girls whose parents were born in 
 the United States 309 
 
 16. The weights of boys whose parents were born in Germany com- 
 
 pared with the weights of boys whose parents were born in 
 the United States 310 
 
 17. The weight (percentile grades) 312 
 
 18. The height standing (percentile grades) 313 
 
 19. The height sitting (percentile grades) 314 
 
 20. The span of arms (percentile grades) 315 
 
 21. The girth of chest at full inspiration (percentile grades) 316 
 
 22. The girth of chest at full expiration (percentile grades) 317 
 
 23. The girth of chest midway between full inspiration and full ex- 
 
 piration (percentile grades) 318 
 
 24. The length of head (percentile grades) 319 
 
 (373) 
 
374 Index of Tables. 
 
 PAGE. 
 
 No. 25. The width of head (percentile grades) 320 
 
 26. The height of face from root of nose to point of chin (percentile 
 
 grades) 321 
 
 27. The width of face (percentile grades) 322 
 
 28. The height of face from hair-line to point of chin (percentile 
 
 grades 323 
 
 29. Ages at which girls begin and cease to be larger than boys 324 
 
 30. The absolute annual increase in height standing 328 
 
 31. The absolute annual increase in weight 329 
 
 32. The absolute annual increase in span of arms 330 
 
 33. The absolute annual increase in height sitting 331 
 
 34. The absolute annual increase in girth of chest 332 
 
 35. Median weight of boys aged 11 distributed by school grade 335 
 
 36. Median weight of the daughters of manual tradesmen distrib- 
 
 uted by school grade 337 
 
 37. Median weight of the daughters of professional men distributed 
 
 by school grade 338 
 
 38. The height standing 350 
 
 39. The weight 351 
 
 40. The height sitting 352 
 
 41. The span of arms 353 
 
 42. The girth of chest midway between inspiration and expiration . . 354 
 
 43. The strength of squeeze, right hand 355 
 
 44. The strength of squeeze, left hand 356 
 
 45. The strength of squeeze, right hand 357 
 
 46. The strength of squeeze, left hand • 358 
 
 47. The length of head 359 
 
 48. The width of head 360 
 
 49. The height of face from root of nose to point of chin 361 
 
 50. The width of face 362 
 
 51 . The height of face from hair-line to point of chin 363 
 
GENERAL INDEX. 
 
 PAGE . 
 
 Accidental influences 275 
 
 Acuteness of vision* 271 
 
 American girls' weights 309 
 
 American boys' weights 310 
 
 Annual increase — 
 
 Absolute 327, 328 to 332, Plates XLII, XLIII 
 
 Kelative 327, 333, Plate XLIV 
 
 Anthropometrical series 277 
 
 Anthropometrical system in schools 341, 347 
 
 Apparatus 269 
 
 Assistants — 
 
 Names 264 
 
 Duties 268, 269 
 
 Authorization by School Board 263 
 
 Average — 
 
 Calculation 280 
 
 Definition 280 
 
 Deviation from 291 
 
 Error of 287, 288 
 
 Of different series 281 
 
 Relation to mean 294 
 
 Bibliography 364 
 
 Birth-place of pupils 309 
 
 Bowditch on median and average 294 
 
 Chart of days 268 
 
 Chest expansion Piate XXX 
 
 Chest-girth at full expiration — 
 
 Median minus average 296, 300, Plate III 
 
 Method of measuring 271, 274 
 
 Percentile grades 311, 317 
 
 Chest-girth at full inspiration — 
 
 Median minus average 296, 300, Plate III 
 
 Method of measuring 271, 274 
 
 Percentile grades 31 1, 31S 
 
 * The acuteness of vision of St. Louis school children will be discussed in 
 a separate paper. 
 
 (375) 
 
376 General Index. 
 
 PAGE. 
 
 Chest-girth midway between full inspiration and full expiration — 
 
 Absolute annual increase 332, Plate XLIII 
 
 Median minus average 296, 354r 
 
 Percentile grades 311, 318, 354, Plates XIII, XIV, XXIX, XLI 
 
 Probable deviation 291, 354 
 
 Probable error 288, 354 
 
 Relation to height standing 334, 354, Plate XLV 
 
 Relation of probable deviation to average 354 
 
 Relative annual increase 327, 333, 354, Plate XLIV 
 
 Collection of data = 26» 
 
 Constant causes > 275 
 
 Curves all printed 264 
 
 Deafness unsuspected 273 
 
 Difference of individual from type 292 
 
 Distribution of observations — 
 
 About middle value ■ 277 
 
 According to Thoma 277 
 
 Girls' heights 279 
 
 Of 1000 individuals 341 
 
 Theoretical and observed 283, 286, Plate I 
 
 Duration of investigation 26* 
 
 Errors — 
 
 Constant 275, 292 
 
 Of observation 292 
 
 Physiological 292 
 
 Variable 275, 292 
 
 Face (see Height of face and Width of face) . 
 
 Gallon's percentile grades 286, 287 
 
 Generalizing method 263, 294, 33» 
 
 German parentage and vreight 309, 310 
 
 Girls larger than boys of same age 324, 32i 
 
 Head (see Length of head and "Width of head). 
 
 Head measurers 269 
 
 Hearing tests 272 
 
 Hearing tests impracticable 273 
 
 Height — 
 
 Abnormal height a disadvantage 333, 343 
 
 Basis of a system of standards 342 
 
 Of United States recruits 278 
 
 Height of face from hair-line to point of chin — 
 
 Absolute annual increase 363 
 
 Median minus average 296, Plate IV 
 
 Method of measuring 273 
 
 Percentile grades 311, 323, 363, Plates XXIII, XXIV, XXXVI 
 
General Index. 377 
 
 PAGE. 
 
 Height of face from hair-line to point of chin — Continued. 
 
 Probable deviation 291, 363 
 
 Probable error 288, 363 
 
 Relation of probable deviation to average 363 
 
 Relation to height standing 334, 363, Plate XLV 
 
 Relative annual increase 363 
 
 Height of face from root of nose to point of chin — 
 
 Absolute annual increase 361 
 
 Median minus average 296, Plate IV 
 
 Method of measuring 273 
 
 Percentile grades 311, 321, 361, Plates XIX, XX, XXXIV 
 
 Probable deviation 291, 361 
 
 Probable error 288, 361 
 
 Relation to probable deviation to average 361 
 
 Relation to height standing 334,361, Plate XLV 
 
 Relative annual increase 361 
 
 Height sitting — 
 
 Absolute annual increase 327, 331, Plate XLIII 
 
 Median minus average 296, 352, Plate II 
 
 Method of measuring 270 
 
 Percentile grades 311, 314, 352, Plates IX, X, XXVII, XXXIX 
 
 Probable deviation 291, 352 
 
 Probable error 288, 352 
 
 Relation of probable deviation to average 352 
 
 Relation to height standing , 334, 352, Plate XLV 
 
 Relative annual increase 327, 333, 352, Plate XLI V 
 
 Height standing — 
 
 Absolute annual increase 327, 328, Plate XLII 
 
 Distribution of, in girls aged 8 286, Plate I 
 
 Median minus average 296, 350, Plate II 
 
 Method of measuring 270 
 
 Percentile grades 311, 313, 350, Plates VII, VIII, XXVI, XXXVIII 
 
 Probable deviation 291, 350 
 
 Probable error 288, 350 
 
 Ratio to other physical measurements 334, Plate XLV 
 
 Relation of probable deviation to average 350 
 
 Relative annual increase 327, 333, 350, Plate XLIV 
 
 Herschel on means o 294 
 
 Indices — 
 
 Cranial 360 
 
 Facial 362 
 
 Individualizing method 294, 339, 340 
 
 Influences affecting measurements 275, 276 
 
 Instructions to observers 269 
 
 Length of head — 
 
 Absolute annual increase 359 
 
 Median minus average 296, Plate IV 
 
 Method of measuring 272 
 
378 General Index. 
 
 PAGE. 
 
 Length of head — Continued. 
 
 Percentile grades 311, 319, 359, Plates XV, XVI, XXXII 
 
 Probable deviation 291, 359 
 
 Probable error 288, 359 
 
 Eelation of probable deviation to average 35^ 
 
 Relation to height standing 334, 359, Plate XLV 
 
 Relative annual increase 359 
 
 Loans and gifts 264 
 
 Material of investigation — 
 
 Limitations 294 
 
 Trustworthiness 290 
 
 Manual tradesmen 303 
 
 Manual tradesmen's daughters — 
 
 Relative number 307, 308 
 
 Weights 305, 337 
 
 Mean (see Median value"). 
 
 Median value — 
 
 Advantage over average 294, 298 
 
 Application to individuals 293, 294, 339, 340 
 
 Calculation 281 
 
 Definition 279, 281 
 
 Minus average 296> 298, 299, 300, Plates II, III, IV 
 
 Uses limited 294 
 
 Mental labor and physical development 335 
 
 Method of collecting measurements 263 
 
 Middle value — 
 
 Definition 279 
 
 Uses 293 
 
 Nationality, infiuence on weight 309 
 
 Number of children measured 268 
 
 Occupation of parents 302 
 
 Overstrain 346 
 
 Percentile grades — 
 
 Calculation 286 
 
 Plates V to XLI, inclusive 
 
 Tables 312 to 323 and 350 to 363, inclusive 
 
 Uses 311 
 
 Plates, List of 371 
 
 Printed "forms " employed 265, 267, 269 
 
 Probable deviation — 
 
 Calculation 282 
 
 Definition 282 
 
 From average 291 
 
 From mean 284 
 
 Table 291 
 
 Probable error of average- 
 Calculation 287 
 
 Table •- 288 
 
General Index. 379 
 
 PAGE. 
 
 Professional men and merchants 302 
 
 Daughters' weights 305, 306, 338 
 
 Quetelet's law 278 
 
 Kate of growth 327 
 
 Schools measured 266 
 
 Sexual difEerences in growth 324 
 
 Social status influences weight 305, 310, 336, 338 
 
 Span of arms — 
 
 Absolute annual increase 327, 330, Plate XLII 
 
 Median minus average 296, Plate II 
 
 Method of measuring 270 
 
 Percentile grades 311, 315, 353, Plates XI, XII, XXVIII, XL 
 
 Probable deviation 291, 353 
 
 Probable error 288, 353 
 
 Kelation of probable deviation to average 353 
 
 Eelation to height standing 334, 353 
 
 Eelative annual increase 327, 333, 353, Plate XLIV 
 
 Squeeze (see Strength of squeeze). 
 
 Statistical methods employed 275, 279, 289 
 
 Strength of squeeze — 
 
 Absolute annual increase 327, 355, 356, Plate XLIII 
 
 Dynamometer tables 357, 358 
 
 Median minus average 296, 355, 356, Plate III 
 
 Method of measuring 271 
 
 Percentile grades 355, 356, Plate XXXI 
 
 Probable deviation 291 , 355, 356 
 
 Probable error 288, 355, 356 
 
 Relation of probable deviation to average 355, 356 
 
 Relation to height standing 334, 355, 356 
 
 Relative annual increase 327, 333, 355, 356, Plate XLIV 
 
 Successful pupils larger than unsuccessful 338 
 
 Tables, Index of 373 
 
 Types 277,289, 293, 301 
 
 Weight — 
 
 Absolute annual increase 327, 329, Plate XLII 
 
 Median minus average 296, 351, Plate II 
 
 Method of weighing 271 
 
 Percentile grades 311, 312, 351, Plates V, VI, XXV, XXXVII 
 
 Probable deviation 291, 351 
 
 Probable error 288, 351 
 
 Relation of probable deviation to average 351 
 
 Relation to height standing 334, 343, 351, Plate XLV 
 
 Relative annual increase 327, 333, 351, Plate XLIV 
 
380 General Index. 
 
 PAGE. 
 
 Width of face — 
 
 Weight of American girls 309 
 
 German girls 3§9 
 
 Manual tradesmen's daughters 338, Plate XLVI 
 
 Successful and unsuccessful pupils 336, 337 
 
 Absolute annual increase 362 
 
 Indices of width — height 362 
 
 Median minus average 296, 362, Plate IV 
 
 Method of measuring 273 
 
 Percentile grades 311, 322, 362, Plates XXI, XXII, XXXV 
 
 Probable deviation 291, 362 
 
 Probable error 289, 362 
 
 Relation of probable deviation to average 362 
 
 Relation to height standing 311, 334, 362, Plate XLV 
 
 Relative annual increase 362 
 
 Width of head — 
 
 Absolute annual increase 360 
 
 Index of width — length 360 
 
 Median minus average 296, 360, Plate IV 
 
 Method of measuring 273 
 
 Percentile grades 311, 320, 360, Plates XVII, XVIII, XXXIII 
 
 Probable deviation 291, 360 
 
 Probable error 288, 360 
 
 Relation of probable deviation to average . , 360 
 
 Relation to height standing 334, 360, Plate XLV 
 
 Relative annual increase 360 
 
 Working-plan , 265 
 
 Issued April 14, 1894. 
 
Trans, Acad. Sci.. of St.. Louis. 
 
 No. 
 
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 Vol. VI. Xo. 12. Plate I (from Table No. 7; page 286). 
 
 The calculated and the observed distribution of the height standing of 2192 
 St. Louis School Girls, aged S. 
 
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Trans. Acad. Sci. of St. Louis. 
 
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 Vol. VI. No. 12. Plate III (from Table No. 11; pages 29ii, 299). 
 
 Median Minus Average Values. 
 
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Trails. Acad. Sci. of St. Louis. 
 
 Ase: 6 7 S 9 10 11 1-2 1:; 14 15 16 17 IS 
 
 VOL. VI. No. 12. Plate IV (from Table No. 11; pages 296, 299). 
 
 Median Minus Average Values. 
 
 Unbroken Line: Boys. Broken Line : Girls. 
 
Trans. Acad. Sci. of St. Louis. 
 
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 Vol. VI. Xo. 12. Plvte VI (from Table Xo. 17; pages 311, 312) 
 Girls' Weight. 
 
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 VOL. VI. No. 12. Plate VII (from Table No. 18; pages 311, 313). 
 Boys' Height Standing. 
 
Trans. Acad. Sci. of St. Louis. 
 
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 Age: 
 
 Vol. VI. No. 12. Plate VIII (from Table >.o. IS; pages 311,313). 
 Girls' Height Standing. 
 
Trans. Acad. Sci. of /St. Louis. 
 
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 Boys' Heigbt Sitting. 
 
Trans. Acad. Sci. of St. Louis. 
 
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 VOL. VI. No. 12. Plate X (from Table No. 19; pages 311,314). 
 Girls' Height Sitting. 
 
Trans. Acad. Sci. of St. Louis- 
 
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 VOL. VI. No. 12. Plate XI (from Table No. 20; pages 311,315). 
 Boys' Span of Arms. 
 
Trcms. Acad. ScL of St. Loni- 
 
 30 40 50 60 
 
 Percentile Grades. 
 
 Vol. VI. No. 12. Plate XII rfrom Table Xo. 20; pages 311, 315). 
 Girls' Span of Arms. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Cm. 
 
 VOL. VI. No. 12. PLATE XIII (from Table No. 23; pages 311, 818). 
 Boys' Girth of Chest. 
 
Trans. Acad. Sci. of St. Louis. 
 
 11. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 Vol. VI. No. 12. Plate XIV (from Table No. 23; pages 311,318). 
 Girls' Girth of Chest. 
 
Trans. Acad. Sci. of St. Louis. 
 
 im. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 Vol. VI. No. 12. Plate XV (from Table No. 24; pages 311,319). 
 Boys' Length of Head. 
 
 Age: 
 16 
 
Trans. Acad. Sci. of St. Louis. 
 
 19S 
 
 e==ee|ee==- 
 
 Age: 
 
 ■JO 50 60 
 
 Percentile Grades. 
 
 Vor.. VI. NO. 12. Plate XVI (from Table No. 2-1; pages 311,319). 
 Girls' Length of Head. 
 
Trans. Acad. Sci. of St. Louis. 
 
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 Vol. VI. Xo. 12. Plate XVII (from Table No. 25; pages 311, 320). 
 Boys' Width of Head. 
 
Trans. Acad. Sci. of >St. Louis. 
 
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 Age: 
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 VOL VI. No. 12. Plate XVIII (from Table No. 25; pages 311,320). 
 Girls' Widtli of Head. 
 
Trans. Acad. Sci. of St. Louis. 
 
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 Percentile Grades. 
 
 70 
 
 90 
 
 Age: 
 
 VOL.-VI. No. 12. Plate XIX (from Table No. 26; pages 311,321). 
 Boys' Height of Face from Root of Nose to Point of Chin. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Mm. 
 
 12-2 
 
 110 
 
 98 
 
 94 - 
 
 
 Age: 
 16 
 
 10 20 30 40 50 60 70 SO 9 
 
 Percentile Grades. 
 
 Vol. VI. No. 12. Plate XX (from Table Xo. 26; pages 311,321). 
 Girls' Height of Face from Root of Xose to Point of Chin. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Mm. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 140 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 40 50 60 70 
 
 Percentile Grades. 
 
 Vol. VI. No. 12. Plate XXI (from Table No. 27; pages 311, 322). 
 Boys' Width of Face. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Mm. 
 
 140 
 
 136 
 
 132 
 
 121 
 
 116 
 
 112 
 
 108 
 
 
 x\ge: 
 
 20 30 
 
 •10 50 60 
 
 Percentile Grades. 
 
 90 
 
 Vol. VI. Xo. 12. Plate XXII (from Table No. 27; page 322). 
 Girls' Width of Face. 
 
Trans Acad. Sci. of St. Louis. 
 
 Im. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 190 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 16 
 
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 Percentile Grades. 
 
 Vol. VI. Xo. 1-2. Plate XXIII (from Table No. 28; pages 311, 323). 
 Boys' Height of Face from Hair-Line to Point of Chin. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Mm. 
 
 188 
 
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 Percentile Grades. 
 
 Vol. VI. No. 12. Plate XXIV (from Table No. 28; pages 311, 323). 
 Girls' Height of Face From Hair-Line to Point of Chin. 
 
Trans. Acad. Sci. of St. Louis. 
 
 A^e: 6 7 8 9 
 Kilog. 
 
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 VOL. VI. No. 12. Plate XXV (from Table No. 39; pages 324,351). 
 
 Weight. 
 
 75, 50 ami 25 Percentile Grade?. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of Si. Louis. 
 
 A-ge: 6 7 S 9 10 11 12 13 U 15 16 17 U 
 Cm. 
 
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 VOL. VI No 12. PLATE XXVI (from Table Xo. 3S; pages 324,350). 
 
 Height Standing. 
 
 75,50 and 25 Percentile Grades. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trfiris. Acad. Sci. of St. Louis. 
 
 VOL. VI. No. 1-2. Plate XXXTl (from Table No. 40: pages 324, 352;. 
 
 Height Sitting. 
 
 75, 50 and 25 Percentile Grades. 
 
 Boys: Unbroken Lines. Girls: Broken Lines 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 7 S 9 10 11 12 13 14 15 16 
 
 Cm. 
 
 175 
 
 17 IS 
 
 169 
 
 163 
 
 157 
 
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 YOL. VI. No. 12. PL.4.TE XXVIII (from Table Ko. 41; paj(cs 324,353). 
 
 Span of Arms. 
 
 75, 50 and 25 Percentile Grade?. 
 
 Bovs: Unbroken Lines. Girls: Brolien Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 
 Cm 
 
 10 11 12 13 14 15 16 17 18 
 
 70 
 
 
 
 
 
 
 
 
 
 
 
 
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 Vol. VI. Xo. 12. Plate XXIX (from Table Xo. 42; pages 324, 354). 
 
 Girth of Chest. 
 
 T.'i, 50 and 25 Percentile Grades. 
 
 Boys: Unbroken Lines. Girls: Broken Linos. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 7 S 10 11 12 13 U 15 16 17 
 
 Cm. 
 
 
 VOL. VI. No. 12. Plate XXX (from Tables No. 21,22; pages 316,317,325). 
 Mean Expansion of Chest. 
 Boys: Unbroken Lines. 
 
 Girls: Broken Lines. 
 
Trans. Acad. Sci. of SL Louis. 
 
 Age: 6 
 Kilog 
 
 10 11 12 13 14 15 16 17 
 
 26 
 
 14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 Vol. VI. No. 12. Plate 2;XXI (from Tables No. 43,44; pages 835,355,356). 
 
 Mean Strength of Squeeze. 
 
 K: Right Hand. L: Left Hand. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St Louis. 
 
 Age: 6 7 8 9 10 11 12 13 1^ 15 16 17 
 
 PC. G. 
 
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 VOL. VI. No. 1-2. Plate XXXII (from Table No. 47; pages 325,359). 
 
 Length of Head. 
 
 75, 50 and 25 Percentile Grades. 
 
 Bovs; Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 
 Mm. 
 
 9 10 11 VI 13 U 15 IB 17 
 
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 VOL. VI. Xo. 1-2. Plate XXXIII (fi-oai Table Xo. 4S; pages 325, 360j. 
 
 Width of Head. 
 
 75, 50 and 25 Percentile Grades. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: (i 7 S 9 10 11 l-> 
 
 Mm 
 
 13 U 15 J6 17 
 
 106 
 
 102 
 
 94 
 
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 Vol. VI. No. 12. Plate XXXIV (from Table No. 49; pages 325,361). 
 
 Height of Face from Root of Nose to Point of Ohin. 
 
 75, 50 and 25 Percentile Grades. 
 
 Bojs: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis 
 
 Age : 6 7 
 
 Mm 
 
 136 
 
 9 10 11 12 13 U lo 16 17 
 
 132 
 
 128 
 
 124 
 
 120 
 
 116 _ 
 
 
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 Vol. VI. No. 12. Plate XXXV (from Table No. 50; pages 325, 362). 
 
 Width of Face. 
 
 75, 50 and 25 Percentile Grades. 
 
 Boys: Unbroken Lines. 
 
 Girls: Broljen Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 '.) 10 U ]'2 13 14 15 K; Yi 
 
 176 
 
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 Vol. VI. NO, 12. Plate XXXVI (from Table No. 51; pages 325,363). 
 
 Height of Face from Hair-Line to Point of Chin. 
 
 75, 50 and 25 Percentile Grades. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 
 Kilo 
 
 7 S 9 10 11 1-2 13 -U 15 16 17 18 
 
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 Vol. VI. Xo. 12. Plate XXXVII (from Table Xo. 17; pages 312,325). 
 
 Percentile Grades. 
 
 Weight. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Ase: 6 7 8 9 10 11 12 13 14 15 16 17 18 
 
 Cm. 
 
 
 
 
 
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 Vol. VI. No. 12. Tlatb XXXVIII (from Table No. IS; pages 313,325). 
 
 Percentile Grades. 
 
 Height Standing. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 
 Cm 
 
 90 
 
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 VOL. VI. Xo. 12. Plate XXXIX (from Table No. 19; pages 314,325). 
 
 Percentile Grades. 
 
 Height Silting. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad iSci. of St. Louis. 
 
 •Age: 
 
 6 7 
 
 i 
 
 9 
 
 10 11 1 
 
 2 13 U 
 
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 Vol. VI. No. 12. Plate XL (from Table No. 20; pnges 315,325). 
 
 Percentile Grades. 
 
 Span of Arms. 
 
 Boys: Unbroken Lines. 
 
 Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 
 Cm 
 
 S 9 10 11 12 13 H 15 16 17 IS 
 
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 ir:^^^^ 
 
 r<" 
 
 
 
 
 
 
 ^_-:: 
 
 ir:::^ 
 
 — - 
 
 
 
 
 
 
 
 
 
 
 
 "^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Pc.G. 
 
 VOL. YI. Xo. 12. Plate XLI (from Table No. 23; pages 318, 325). 
 
 Percentile Grades. 
 
 Girth of Chest, 
 
 Boys: Unbroten Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 7 8 9 10 11 12 13 U 15 ](i IT IS 
 
 Cm 
 
 1. 
 
 
 
 
 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 ^■.. 
 
 
 
 
 )^ 
 
 .^ 
 
 X 
 
 
 
 
 
 
 
 ^:>— H 
 
 
 ^^ 
 
 \ 
 
 
 
 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 '^ 
 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 
 
 xige 
 Kilos 
 
 Height Standing. 
 S '.I 10 11 1-2 lo 14 15 16 IT IS 
 
 
 Weight. 
 
 Age: 
 Cr 
 
 10 11 1-2 
 
 14 15 16 IT IS 
 
 . 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 / 
 
 
 
 ^^^'^ 
 
 
 
 -;:::: 
 
 N, 
 
 / 
 
 
 
 ^ 
 
 / 
 
 4 
 
 
 
 
 
 
 X 
 
 / 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 ' 
 
 ^^ 
 
 
 
 
 
 
 
 
 
 
 
 
 \. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ...- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Span of Arms. 
 
 Vol. VI. No. 12. Plate XLII (from Tables No. 30, 31, 32; pages 327, 328, 829, 330. 
 
 Absolute Annual Increase. 
 
 Boys: Unbroken Lines. Girls: Brol^en Lines. 
 
Age: 7 
 Cm 
 
 Trans. Acad. Sci. of St. Louis. 
 
 ',) lu 11 12 13 U 15 Hi 17 IS 
 
 
 Height Sitting. 
 
 Age: 
 Cm. 
 
 9 10 11 1-2 13 U 15 16 17 IS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 .. ^--> 
 
 ^-^ 
 
 / 
 
 
 
 
 .•■ 
 
 
 
 
 
 
 
 
 _,—--- 
 
 ==^' 
 
 '•-., 
 
 / 
 
 
 
 
 
 '' 
 
 
 
 
 
 
 
 '■••. 
 
 Jvilog 
 
 Strength of Squeeze. 
 
 VOL. VI, Xo. 12. Plate XLIII (from Tables No. 33, 34, 43, 44, 45; pages 327, 331, 332, 355, 366) 
 
 Absolute Annual Increase. 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Age: 6 7 
 
 Per cent. 
 
 Vol. VI. No. 12. Plate XLIV (from Tables No. 38 to 43; pages 327, 333, 350 to 355). 
 
 Relative Annual Increase. 
 
 Boys: Unbroken Lines. Girls: Broken Lines. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Lge: 6 
 
 S 
 
 c 
 
 10 11 
 
 12 13 14 15 
 
 16 17 18 
 
 % 
 104 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,r-^^ 
 
 
 
 . - 
 
 
 
 
 «r:r:!:rt 
 
 
 - ."^ 
 
 
 
 
 ,..-•■' 
 
 
 100 
 
 
 
 
 
 
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 56 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 r^:::^ 
 
 
 
 
 
 
 
 
 
 
 
 
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 ::::;^ 
 
 K ■ 
 
 — 
 
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 .... 
 
 
 
 
 
 
 
 
 
 "^ 
 
 
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 -..., 
 
 4S 
 
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 — 
 
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 ^ 
 
 
 
 
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 z' 
 
 
 
 
 
 
 
 
 
 
 /> 
 
 " 
 
 
 
 
 
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 ^^ 
 
 ^" 
 
 
 
 
 
 
 
 
 
 
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 "^ 
 
 
 
 
 
 
 
 
 IS 
 
 
 r::^ 
 
 -^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 14 
 
 
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 ^^^^^^ 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 ^ 
 
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 6 
 
 
 ^^ 
 
 
 
 
 
 
 
 
 
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 Span of Arms. 
 Height. 
 
 Height Sitting. 
 
 Weight. 
 
 Squeeze, 
 Right Hand. 
 
 Length of Head. 
 Hair Line. 
 
 Width of Head. 
 Width of Face. 
 Heiglit of Face. 
 
 VOL. VI. No. 12. Plate XLV (from Table Xo. 38 to No. 51 ; pages 334, 350 to 363). 
 RelatioB of Average Weight, Span of Arms, Girth of Chest, etc., to Average Height. 
 
Trans. Acad. Sci. of St. Louis. 
 
 Grade: Kg. I II HI IV V VI VII 
 
 Kilos 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 ^ 
 
 
 
 
 40 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 "^ 
 
 ./* 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 \l3 
 
 38 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 /' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 — 
 
 
 / 
 
 
 
 
 3t) 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 34 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 ^- 
 
 11 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 32 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 30 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /> 
 
 
 ^ 
 
 
 
 II 
 
 
 
 
 
 
 
 
 
 y 
 
 y 
 
 ^ 
 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0(j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^y 
 
 
 
 <] 
 
 
 
 
 
 
 
 
 24 
 
 
 
 y 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 y' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2U 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Vol. VI. No. 12. Plate XLVI (from Table No. 36; pages 336, 337). 
 The Weights of Daughters of Manual Tradesmen distributed by School Grade. 
 

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