THE 
Physique of Women in Massachusetts. 
Prof. H. P. B0WD1TCH, M.D. PHYSIQUE OF WOMEN IN MASSACHUSETTS. THE PHYSIQUE OF WOMEN IN MASSACHUSETTS. 
Prof. H. P. Bowditch, M.D. 
In the eighth annual report of the State Board of Health 
of Massachusetts was printed an article entitled, “ The 
Growth of Children.” In this paper were embodied the 
results of a study of the height and weight of school chil- 
dren of Boston and vicinity, about 24,500 measurements 
having been made, chiefly upon pupils of the public schools 
of the city. Tables and curves were given, showing the 
average heights and weights of school children from live to 
eighteen years of age, of both sexes, and of parentage of 
various nationalities. In a subsequent article, two years 
later, the same data were further discussed, with a view to 
ascertaining the relative importance of race and environment 
in determining the rate of growth. 
In order to enlarge the body of statistics from which con- 
clusions could be drawn, the State Board of Health, Lunacy 
and Charity, in 1880, issued the following circular : — 
Commonwealth of Massachusetts. 
State Boakd of Health, Lunacy and Charity, 
Department of Health, State House, 
Boston, Jan. 1, 1880. 
Dear Sir: — As a contribution to the vital statistics of Massa- 
chusetts, the State Board of Health, Lunacy and Charity desires 
to suggest the importance of collecting observations upon the 
physique of the inhabitants of the State. The usefulness of such 
an investigation will be evident from a consideration of some of 
the problems upon which it will throw light. These may be briefly 
enumerated as follows : — 
1. The influence of geographical and climatic conditions on the 
growth of children and on the physique of adults. 4 
2. The number of generations necessary for the complete 
development of the influence of changed climatic conditions on 
the physique of a given race. 
3. The comparative effect of city and country life on the 
growth and development of the human race. 
4. The relation between diseases and the rate of growth. 
5. The effect of local hygienic conditions on the physique of 
children and adults. 
That the results of the inquiry may have the greatest possible 
value, it is desirable that measurements should be made upon 
individuals of all ages and of both sexes. In pursuance of this 
object, the Board will be glad to co-operate with superintendents 
of public institutions, both charitable and penal, with persons 
having facilities for making observations in factories and mills, 
with school committees, with principals of academies and colleges, 
with fatliei’S of families, and with all who are interested in this 
branch of scientific investigation. 
To secure uniformity of method, the Board will distribute gra- 
tuitously, to all who desire to assist in this research, blank cards, 
on each of which are to be recorded the statistical data relating to 
a single individual. 
If you desire to aid in this investigation, you are requested to 
state the number and sex of the persons in regard to whom you 
will be able to collect any or all of the above-mentioned statistical 
data. The Board will then gladly supply you with the necessary 
number of blank cards, and furnish you with full instructions as 
to the best method of taking and recording the measurements. 
The use of the metric system for this purpose is attended by so 
many and such decided advantages, that the Board is willing, if 
desired, to furnish certain simple forms of apparatus to facilitate 
the work. If, however, it is for any reason impossible to employ 
the metric system, measurements recorded in inches and pounds 
will be gladly received, and the conversion afterwards made at 
this office. 
The statistics collected in this way will be placed in the hands 
of Prof. II. P. Bowditcli, to whose articles on the growth of chil- 
dren in the eighth and tenth reports of the State Board of Health, 
investigators in this field of research are referred. 
In behalf of the State Board of Health, Lunacy and Charity, 
Very respectfully yours, 
Charles F. Folsom. M.D., 
Secretary. 5 
To those who expressed a willingness to aid in this investigation 
blank cards were forwarded, printed on both sides, as follows : — 
FEMALES. 
FOR A SINGLE SET OF OBSERVATIONS. 
SEE THE 
OTHER SIDE. 
Record all linear measurements at nearest centimeter; all weights at nearest kilogram, 
Name (or initials). 
Height, without shoes, 
Age, 
yrs._ 
_mos. 
girth, inspire, 
Sitting height,. 
expire, 
Weiyht, 
Finger reach, 
(in ordinary in-door' 
clothes, „ 
Nationality of 
Father, 
Mother, 
Color of Eyes, 
Birthplace, 
Color of Hair, 
Paternal Grandfather,_ 
Occupation (of husband if a married 
woman), (of parents if a minor). 
Paternal Grandmother,. 
Maternal Grandfather, 
Maternal Grandmother,_ 
Name (or initials) of observer. 
This card when filled is to be returned to Sec. of State Hoard 
of Health, Lunacy and Charity, State House, Boston, Mass. 
The Height is to be taken in an upright position, without shoes, the feet being close 
to the measuring rod. If, in the case of infants, it is necessary to measure in a recum- 
bent position, the fact should be stated. 
The Sitting Height is the vertical distance between the top of the head and the sur- 
face upon which the individual is seated. 
The Finger Reach is the distance between the tips of the middle fingers when the 
arms are extended horizontally, the breast and arms being in contact with a wall. 
The Chest Girth should be taken after a forcible inspiration and also after a forcible 
expiration, the measuring tape being passed horizontally round the chest on a level 
with the nipples, over only a single garment. This measurement is to be taken only 
on men and children. 
The Weight is to be taken in ordinary in-door costume. In the case of children less 
than ten years of age, it is to be recorded at the nearest tenth of a kilogram. 
The Color of the Eyes is to be recorded as blue, gray, brown or black. 
The Color of the Hair is to be recorded as fair, golden, red, brown, black or gray. 
If gray, record also, if possible, the original color. 
The Nationality is determined by the place of tiirth. 
The Occupation should be given so as to indicate as far as possible the degree of com- 
fort in which the Individual lives. 
See nlso article on “ Anthropometrical Methods,” tenth annual report Massachusetts State 
Hoard of Health, 1879, p. 55. 
The advantages of this card method of collecting statistics are 
fully set forth in an appendix to the second of the above-mentioned 
articles.* To the explanations there given it need only be added 
that the short vertical lines, one centimeter apart, printed at the 
* See tenth annual report of the Massachusetts State Board of Health, 1879, page 55. 6 
top of the card, are intended to aid in marking the cards 
coming from any one institution or locality, so that they 
may be distinguished, when mixed with others, in sorting 
them with reference to any particular statistical inquiry. 
The marking was effected by screwing all the cards belong- 
ing to any one institution into a vise, and scoring the tops 
of them with a hand-saw at one or more of the vertical lines. 
A record being kept of the scored lines corresponding to 
efich institution, it was always easy to identify the cards 
belonging to it. 
The Board also authorized the construction of several sets 
of weighing and measuring apparatus which were sent to the 
different institutions in turn, in order to secure uniformity 
in the method of making the observations. By these means 
measurements were obtained in the following institutions, 
public and private, during the years 1881-85 : — 
Name of Institution. 
Number of 
Observations. 
Name of Observer. 
Male. 
Female. 
Wellesley College,. 
302 
Miss E. A. Nunn. 
Mt. Holyoke Seminary, . 
- 
203 
A. A. Richardson, M.D. 
Smith College, Northampton, 
- 
92 
Lucy B. Hunt. 
Normal School, Westfield, 
11 
106 
J. G. Scott. 
Normal School, Bridgewater, 
39 
129 
A. C. Boy den. 
Normal School, Worcester, . 
- 
38 
E. H. Russell. 
Normal School, Framingham, 
- 
65 
Miss E. Hyde. 
Practice School, Framingham, 
21 
41 
Miss E. Hyde. 
Private School, Boston, . 
- 
40 
Miss Selma Wesselhoeft. 
Private School, Boston, . 
_ 
35 
Miss Ireland. 
Private School, Boston, . 
_ 
25 
Miss Gibbens. 
Reform School, Westborough, 
119 
- 
C. A. Robbins. 
Reform School, Lancaster, 
- 
70 
N. Parker Brown. 
Reform School, Lancaster, 
- 
73 
Miss Putnam. 
Farm School, Boston, 
97 
- 
F. M. Barrett. 
Conservatory of Music, Boston, 
Almshouse, Tewksbury, 
- 
127 
S. L. Tourj6e. 
37 
324 
200 
1,546 
Ur. Lathrop. 
To the intelligent co-operation of the above observers the 
success which has attended the investigation is chiefly due. 
The publication of the results of this research has been 
delayed in the hope that they might be embodied in a com- 
prehensive treatise on anthropometry in Massachusetts ; but 7 
the pressure of other duties lias thus far prevented the prep- 
aration of such a work, and there seems to he no probability 
that in the immediate future such a task can be undertaken. 
Moreover, anthropometrical investigations have, in recent 
years, been carried on under the auspices of Harvard Col- 
lege, on a larger scale and in a much more thorough manner 
than was contemplated when these data were collected. The 
development of the human ph}rsique in Massachusetts is, 
therefore, a subject the discussion of which may properly 
be postponed till the data# constantly accumulating in the 
hands of the Director of the Hemenway Gymnasium shall 
be numerous enough to enable him to draw positive con- 
clusions upon the numerous questions to which his investi- 
tion is directed. It has, therefore, been decided to present 
a few of the most obvious results derived from the study of 
the data thus far collected, and to point out some of the 
questions to the solution of which they may contribute in 
the hands of future investigators. 
It will be observed that, in the above list, the observations 
on females are much more numerous than those on males. 
This was due to a special effort to obtain statistics relating 
to the female sex, which, in most anthropometrical researches, 
has been strangely neglected, though in all questions relating 
to the growth and development of the race its importance is 
at least equal to that of the male sex. 
With the exception of the observations made at the 
Tewksbury Almshouse, which were set aside for special 
study, and have not been incorporated in any of the follow- 
ing tables, the great bulk of all the data were collected from 
individuals between the ages of seventeen and twenty-four 
years. Now, at the age of seventeen years, most girls have 
nearly completed their growth, as will be seen by a reference 
to the curves on Plate I in the above-mentioned article on 
the growth of children, in the eighth annual report of the 
State Board of Health. It therefore seemed possible, by 
means of the data at our disposal, to obtain a fairly correct 
idea of the physical type of the adult young woman of this 
community. One thousand one hundred and seven cards 
were found to contain data suitable for this determination, 
and attention was at first directed only to the record of the 8 
height, weight, sitting height and finger reach, or stretch of 
arms, as it may more properly be called. As these last two 
measurements are interesting chiefiy for the light they throw 
on the proportionate development of different parts of the 
body, their absolute values are less important than their 
relation to the total height of the individual. As a prelimi- 
nary to tabulation, therefore, the absolute values of the sit- 
ting height and stretch of arms on each card were converted 
into percentage values of the total height. The cards were 
then treated by the method described in the appendix to the 
above-mentioned supplementary article on the growth of 
children, published in the tenth annual report of the State 
Board of Health. 
Although, for the determination of the physical type of 
the adult young woman, the observations were to be used 
without regard to the age or the institution to which the 
individual belonged, yet, with a view to some future possible 
utilization of the statistics, the cards were at first sorted 
with reference to both these points. Thus the first tabula- 
tion showed, for each age and for each institution, the num- 
ber of individuals observed, at each centimeter of height, 
each kilogram of weight and each half per cent, of sitting 
height and stretch of arms. Tables 1 to 4 give the result of 
this first tabulation after the observations had been added 
together, without regard to age or the institution in which 
the observations were made. Thus Table 1 shows that, out 
of 1,107 women of seventeen years of age and upwards 
whose height was measured, one was 139, one 141, four 143 
centimeters high, and so on. From a table of this sort the 
average height is easily calculated, by multiplying each 
height in centimeters by the number of observations recorded 
at that height, adding the products together, and dividing 
the sum by the total number of observations. Average 
values for the dimensions recorded in the other tables are 
obtained in a similar manner. 9 
Table 1. 
Showing Distribution of Observations on Height of Women in 
Massachusetts (Seventeen Years Old and upward). 
Height 
In Centi- 
meters. 
Fo. of 
Observa- 
tions. 
Height 
in Centi- 
meters. 
No. of 
Observa- 
tions. 
Height 
in Centi- 
meters. 
No. of 
Observa- 
tions. 
Height 
in Centi- 
meters. 
No. of 
Observa- 
tions. 
139 
1 
149 
15 
159 
75 
169 
12 
140 
- 
150 
28 
160 
64 
170 
13 
141 
1 
151 
29 
161 
81 
171 
3 
142 
- 
152 
36 
162 
68 
172 
4 
143 
4 
153 
45 
163 
56 
173 
_ 
144 
4 
154 
59 
164 
49 
124 
5 
14.5 
2 
155 
65 
165 
56 
175 
_ 
146 
6 
156 
59 
166 
44 
176 
1 
147 
8 
157 
73 
167 
21 
177 
1 
148 
12 
158 
86 
168 
21 
Total number of observations, 1,107. Average height (without shoes) 
= 1.58.76 centimeters. 
Showing Distribution of Observations on Weight oj Women in 
Massachusetts (Seventeen Years Old and upward). 
Table 2. 
Weight 
In 
Kilograms. 
No. of 
Observa- 
tions. 
Weight 
In 
Kilograms. 
No. of 
Observa- 
tions. 
Weight 
in 
Kilograms. 
No. of 
Observa- 
tions. 
Weight 
in 
Kilograms. 
No. of 
Observa- 
tions. 
32 
1 
46 
19 
60 
60 
74 
3 
33 
- 
47 
32 
61 
52 
75 
8 
34 
- 
48 
30 
62 
39 
76 
1 
35 
1 
49 
43 
63 
29 
77 
5 
3G 
- 
50 
61 
64 
28 
78 
1 
37 
2 
51 
51 
65 
22 
79 
3 
38 
1 
52 
56 
66 
20 
80 
3 
39 
1 
53 
68 
67 
17 
81 
2 
40 
5 
54 
70 
68 
16 
32 
1 
41 
1 
55 
37 
69 
4 
83 
— 
42 
9 
56 
64 
70 
11 
84 
— 
43 
4 
57 
62 
71 
9 
85 
_ 
44 
12 
58 
42 
72 
2 
86 
3 
45 
12 
59 
74 
73 
8 
Total number of observations, 1,105. Average weight (in ordinary 
in-door costume) =56.51 kilograms. 10 
Table 3. 
Showing Distribution of Observations on Sitting Height as Per- 
centage of Total Height of Women in Massachusetts Seventeen 
Years Old and upward. 
Per cent. 
of 
Height. 
No. of 
Observa- 
tions. 
Ter cent. 
of 
Height. 
No. of 
Observa- 
tions. 
Per cent. 
of 
Height. 
No. of 
Observa- 
tions. 
Per cent. 
of 
Height. 
No. of 
Observa- 
tions. 
37.5 
1 
42.5 
49.5 
2 
55.5 
49 
38. 
- 
44. 
- 
50. 
6 
56. 
28 
38.5 
1 
44.5 
- 
50.5 
23 
56.5 
10 
39. 
1 
45. 
- 
51. 
44 
57. 
8 
39 5 
- 
45.5 
- 
51.5 
60 
57.5 
1 
40. 
1 
46. 
1 
52. 
119 
58. 
1 
40.5 
1 
46.5 
- 
52.5 
111 
58 5 
2 
41. 
- 
47. 
2 
53. 
156 
59. 
- 
41.5 
- 
47-5 
1 
53.5 
177 
59.5 
- 
42. 
- 
48. 
- 
54. 
121 
60. 
- 
42.5 
- 
48 5 
- 
54.5 
101 
60.5 
1 
43. 
49. 
4 
55. 
73 
Total number of observations, 1,106. Average sitting height —53.24 
per cent, of total height. 
Table 4. 
Showing Distribution of Observations on Stretch of Arms as Per- 
centage of Total Height of Women in Massachusetts Seventeen 
Years Old and upward. 
Per cent, of 
Height. 
No. of Obser- 
vations. 
Ter cent, of 
Height. 
No. of Obser- 
vations. 
Per cent, of 
Height. 
No. of Obser- 
vations. 
93. 
3 
98.5 
34 
104. 
24 
93.5 
5 
99. 
30 
104.5 
22 
94. 
2 
99.5 
81 
105. 
15 
94.5 
3 
100. 
182 
105.5 
13 
95. 
8 
100.5 
118 
106. 
7 
95.5 
9 
101. 
56 
106.5 
3 
96. 
14 
101.5 
56 
107. 
5 
96.5 
10 
102. 
91 
107.5 
3 
97. 
26 
102.5 
88 
108. 
- 
97.5 
47 
103. 
46 
108.5 
1 
98. 
71 
103.5 
31 
Total number of observations, 1,104. Average stretch of arms = 
100.54 per cent, of total height. 11 
It will be observed that in Table 3 five of the observations 
are widely separated from all the rest, showing that five of 
the women who were measured had a sitting height from 
37.5 to 40.5 per cent of their total height; while, with the 
exception of these five cases, the smallest percentage sitting 
height recorded was 40. This wide separation of a group 
of cases from the great mass of the observations suggests 
the influence of some abnormal cause of variation. It seems 
not improbable that in these cases some deformity (e. g., 
spinal curvature) may have produced a great diminution in 
the sitting height; but, in the absence of any precise infor- 
mation on the subject, it has been thought best to include 
them in the table. Their effect upon the average percentage 
sitting height is inconsiderable. By rejecting them, this 
value is raised to 53.3 per cent., and thus becomes identical 
with the “ median value,” as will be shown below in Table 5. 
It is evident that the arithmetical average represents but 
very imperfectly the series of observations front which it is 
calculated, since the same average value may be obtained 
from sets of observations differing very widely in their distri- 
bution. For instance, the two series of numbers 24, 25, 26, 
and 5, 25, 45, both give the average value 25. It is also evi- 
dent that tables of distribution such as those above given are 
inconvenient, on account of their not being readily compara- 
ble with similar tables in which the total number of observa- 
tions is different. 
Various devices for overcoming these difficulties have 
been suggested by statisticians ; but the scheme of “per- 
centile grades” as proposed by Francis Galton, F.R.S., 
in 1885, and fully elaborated by him in his recent work on 
“Natural Inheritance,”* is perhaps better adapted than any 
other to display the results of a statistical inquiry, and to 
facilitate a comparison between various sets of observations. 
In this scheme are given values which are surpassed or un- 
reached by various percentages of the total number of obser- 
vations. In Table 1, for instance, five per cent, of the total 
number of observations (i. e., 1,107) is 55.35. Now, in 
this table, since the heights are recorded at the nearest centi- 
* Macmillan & Company, London & New York, 1889. 12 
meter, it is evident that each successive group includes the 
observations between the half centimeter below and the half 
centimeter above the height recorded in the table. By 
adding together the numbers in the successive groups, we 
find that the sum of all the observations, at heights up to 
149.5 centimeters inclusive, is 53 ; and, by adding the next 
group of 28 observations, the sum 81 is reached. Now, 
since 55.35 is between 53 and 81, it is evident that the 
height below which five per cent, of the observations fall is 
between 149.5 and 150.5 centimeters. The exact height 
can readily be calculated by interpolation. Thus the frac- 
tion of a centimeter which is to be added to 149.5 to <rive 
the required height, is obtained by dividing 2.35 (i. e., 
55.35 — 53) by 28 (i. e., the number of observations at 150 
centimeters). This fraction is 0.08 ; and therefore 149.58 
centimeters is the height below which five per cent, and above 
which ninety-five per cent, of the observations fall. In a 
similar way,'the heights corresponding to other percentages 
can be obtained, and a table constructed which presents in 
a very compact form the result of a large series of obser- 
vations.* 
Thus, in the first, fourth, seventh and tenth lines of Table 
5 will be found the percentile distribution of the observa- 
tions contained in tables 1, 2, 3 and 4 respectively; while in 
the second, fifth, eighth, ninth, eleventh and twelfth lines are 
introduced, for purposes of comparison, the results of simi- 
lar observations made by Dr. D. A. Sargent,f director of 
the Hemenway Gymnasium, upon individuals of both sexes, 
in this community; and in the third and sixth lines are 
given the figures obtained by in his measurements 
of English women at the anthropometric laboratory in the 
international exhibition of 1884. In the lines numbered la 
to 6a the values o;iven in the first six lines in centimeters and 
kilograms are reproduced in inches and pounds, to facilitate 
comparison with tables in which the English weights and 
measures are used. 
* A geometrical method of determining the values corresponding to the various 
percentile grades is given by Francis Galton in an article on “ Anthropometric Per- 
centiles,” Nature, Vol. 31, page 223. 
* Scribner’s Magazine, Vol. 172. 
t Natural Inheritance, London, 1889, page 200. Table 5. 
No. of 
Values at the Under-mentioned Percentile Grades. 
SUBJECT OF MEASUREMENT. 
Name 
or Observer. 
Age. 
Sex. 
Observa- 
tions. 
Unit of Measurement. 
5 
Per Cent. 
to 
Per Cent. 
30 
Per Cent. 
so 
Per Cent. 
40 
Per Cent. 
50 
Per Cent. 
60 
Per Cent. 
TO 
Per Cent. 
NO 
Per Cent. 
oo 
Per Cent. 
93 
Per Cent. 
1 
Height (without shoes), .... 
Bowditch,. 
17 years and upward, 
F. 
1,107 
Centimeters, 
149.58 
151.52 
154.01 
155.78 
157.44 
158.77 
160.37 
161.82 
163.67 
165.82 
167.72 
2 
Height (without shoes), .... 
Sargent, . 
16-26 years, 
F. 
1,835 
Centimeters, 
150.1 
151.9 
153.9 
155.9 
157.5 
159.1 
160.5 
162.0 
164.1 
166.6 
168.4 
3 
Height (without shoes), .... 
Galton, 
23-51 years, 
F. 
770 
Centimeters, 
149.5 
152.2 
155.7 
157.7 
159.2 
160 7 
162.2 
164.0 
165.7 
168.7 
171.0 
4 
Weight (in ordinary in-door clothes), 
Bowditch,. 
17 years and upward, 
F. 
1,105 
Kilograms, . 
45.82 
47.85 
50.28 
52.33 
53.97 
56.07 
58.00 
59.75 
61.85 
65.82 
69.93 
5 
Weight (without clothes), 
Sargent, . 
16-26 years, 
F. 
1,901 
Kilograms, . 
42.0 
44.0 
46.3 
49.0 
50.4 
52.0 
54.0 
55.4 
58.6 
62.2 
65.8 
6 
Weight (in ordinary in-door clothes), 
Galton, 
23-26 years, 
F. 
276 
Kilograms, . 
46.3 
47.7 
49.9 
51.7 
53.6 
55.4 
58.6 
59.9 
61.7 
64.5 
67.6 
7 
Sitting height, . . \ 
Bowditch,. 
17 years and upward, 
F. 
1,106 
Percent, of height, 
50.87 
51.43 
52.05 
52.54 
52.95 
53.30 
53.61 
54.01 
54.51 
55.17 
55.70 
8 
Sitting height, < 
Sargent, . 
16-26 years, 
F. 
$ about) 
} 2,000 $ 
Percent, of height, 
50.6 
51.1 
51.6 
52.1 
52.4 
52.7 
53.1 
53.4 
53.9 
54.4 
54.9 
9 
Sitting height, 
Sargent, . 
16-26 years, 
M. 
$ about( 
) 2,000 $ 
Percent of height, 
50.2 
50.5 
51.1 
51.6 
52.0 
52.2 
52.6 
52.9 
53.3 
53.8 
54.3 
10 
Stretch of arms, 
Bowditch,. 
17 years and upward, 
F. 
1,104 
Per cent, of height, 
96.77 
97.57 
98.58 
99.68 
100.02 
100.36 
100.92 
101.83 
102.46 
103.47 
104.79 
11 
Stretch of arms, 
Sargent, . 
16-26 years, 
F. 
$ about( 
) 2,000 $ 
Per cent, of height, 
97.0 
97.9 
98.8 
99.7 
100.3 
100.8 
101.3 
101.9 
102.9 
103.8 
104.5 
12 
Stretch of arms, 
Sargent, . 
16-26 years, 
M. 
$ about( 
) 2,000 $ 
Per cent, of height, 
99.1 
100.0 
100.9 
101.7 
102.2 
102.8 
103.4 
104.0 
104.8 
106.0 
106.8 
1 a 
Values of line 1 converted into, 
Inches, . 
58.9 
59.7 
60.6 
61.3 
62.0 
62.5 
63.2 
63.7 
64.5 
65.3 
66.0 
2 a 
Values of line 2 converted into, 
Inches, . 
59.1 
59.8 
60.6 
61.4 
62.0 
62.6 
63.2 
63.8 
64.6 
65.6 
66.3 
3 a 
Values of line 3 converted into, 
Inches, . 
58.9 
59.9 
61.3 
62.1 
62.7 
63.3 
63.9 
64.6 
65.3 
66.4 
67.3 
4 a 
Values of line 4 converted into, 
Pounds, 
100.9 
105.0 
110.8 
115.3 
119.0 
123.7 
127.9 
131.7 
136.2 
145.0 
154.1 
5a 
Values of line 5 converted into, 
Pounds, 
; 92.6 
97.0 
102.0 
108.0 
111.0 
114.6 
119.0 
122.0 
129.0 
137.0 
145.0 
6 a 
Values of line 6 converted into, 
. 
Pounds, 
1 102.0 
105.0 
110.0 
114.0 
118.0 
122.0 
129.0 
132.0 
136.0 
142.0 
149.0 13 
The figures in the column headed 50 per cent, give the 
measurements which are exceeded by one half and not 
reached by the other half of the individuals measured. 
These values are termed by Galton “median values” (or 
M) and are considered by him (at least in the observations 
which he discusses) as practically the same as the arithmetical 
means or averages.* It will be observed that in Table 5 the 
median values do not differ materially from the average 
values given in tables 1, 2, 3 and 4. The median and the 
average values of the height and sitting height are almost 
identical ; while in the case of weight and stretch of arms, 
the median values fall somewhat short of the averages. 
It is evident that, when the values at the lower percentile 
grades fall short of the median value by the same amounty 
the values at the higher percentile grades exceed it (or, 
in Galton’s words, when “the curve of the scheme is sym- 
metrically disposed on either side of M”), the median and 
average values will be identical. When, however, the 
lower percentile values fall short of the median value more 
than the higher percentile values exceed it, the average will 
be less than the median value ; while a difference in the 
opposite direction will cause the average to exceed the 
median value. The difference between the median and the 
average value, or, as we may express it, the value M — A, 
becomes, therefore, a convenient indication of the direction 
and extent of the asymmetry of the curve of percentile dis- 
tribution. 
The interesting results which may be expected from an 
application of this method of discussion to the data already 
collected relating to the growth of children, will be presented 
in a future article. 
An important feature in a table of percentile distribution, 
like Table 5, is found in the facility which it affords for 
determining the rank of an individual among others of the 
same class. Suppose, for instance, that a woman belonging 
to the class whose heights are given in the first line of Table 
5, desires to know how her height compares with that of the 
other women measured. Suppose her height to be lfiO cen- 
timeters. The table shows at once that this height exceeds 
* Natural Inheritance, page 41. 14 
that of 50 per cent., but does not exceed that of 60 per 
cent., of the women measured ; and a simple sum in propor- 
tion shows that 160 centimeters corresponds to about 57.7 per 
cent. In other words, the woman in question, if ranked 
according to height, would stand about 577th in a group of 
1,000 women selected at random. 
Let us now consider what conclusions can be drawn from 
a comparison of the measurements described in this paper 
with those of other observers, as recorded in Table 5. 
It will be observed, in the first place, that the heights 
recorded in the first line are slightly inferior to the cor- 
responding measurements by Dr. Sargent, as given in line 
2 ; while the figures in line 3, given by Mr. Galton as the 
result of his measurement of English women, are somewhat 
in excess of those obtained on this side of the Atlantic. In 
explanation of these differences, it may be said that the 
American measurements, having been taken upon women as 
young as sixteen or seventeen years, probably include a cer- 
tain number who, being of slow growth, have not yet 
attained their full height; while the English measurements, 
being limited to women between twenty-three and fifty-one 
years, represent more accurately the adult height of the 
female portion of the community. It is also possible that 
we are dealing here with a difference of race, though the 
close correspondence which has been shown to exist between 
the heights of growing boys of the two nationalities does 
not support this view. 
It is, furthermore, interesting to note that the difference 
between the heights at the fifth and the ninety-fifth percentiles 
is greater for the English than for the American women ; 
being: 21.5 centimeters for the former and 18.1 centimeters 
for the latter. It will be convenient to term this difference 
the range of the heights, though it of course indicates the 
range of only nine-tenths of the whole number of observa- 
tions, the highest and lowest 5 per cent, being omitted. It 
will also be observed that the difference in height between 
the women of the two nationalities increases with tolerable 
regularity, as we ascend the series of percentile grades, 
from — 0.8 to 3.28 centimeters. 
Height. 15 
The slight excess of Dr. Sargent’s measurements over our 
own is probably to be explained by the fact that the former 
were taken in schools frequented by the children of the most 
favored classes, while the latter include a certain number of 
individuals who had not grown up in the midst of comfort- 
able surroundings. 
Weight. 
The weights given in the fourth line of Table 5 are seen 
to be considerably in excess of Dr. Sargent’s figures in 
line 5, owing to the fact that the latter represent net weights, 
while our own observations were made upon women “ in 
ordinary in-door clothing.” The excess at most of the 
grades amounts to 3.3-4.0 kilograms (8-9 pounds), — a dif- 
ference which corresponds very well to the weight of clothing 
of the older girls, as given in Table 25 of the article on the 
growth of children, already alluded to. 
A more accurate comparison may be made between our 
own observations and those of Mr. Galton (line 0), since 
the latter were also made upon individuals in ordinary 
in-door clothing. It will be observed that the range of the 
weights is greater in American than in English women, 
there being between the fifth and the ninety-fifth percentile 
grades a difference of 24.1 kilograms for the American and 
21.4 kilograms for the English women. It will be also 
noticed that at most of the percentile grades the weight 
of the American exceeds that of the English women, the 
difference being most marked in the highest percentiles. 
This observation, in connection with the one above noted 
with regard to heights, seems to show that there is little 
difference between the shortest as well as between the light- 
est women of the two nationalities; but that the tallest 
English women surpass the tallest American woman in height, 
while the heaviest American women exceed in weight the 
heaviest English women. Before this conclusion can be 
accepted as absolutely established, it will be necessary to 
determine how far the greater age of the English women has 
affected the result. In other words, we must ascertain more 
accurately than is at present possible, at what age the growth 
of women, both in height and weight, can be regarded as 
completed. 16 
Sitting Height. 
A comparison of the figures in the seventh and eighth 
lines of Table 5 shows that the ratio of the sitting height to 
the total height is somewhat greater in our measurements 
than in those of Dr. Sargent, the median value being 53.3 
per cent, in the former, and 52.7 per cent, in the latter. 
This difference is doubtless associated with the superior 
height of the women measured by Dr. Sargent, in a manner 
which will be presently explained. For purposes of com- 
parison, Dr. Sargent’s measurements of the sitting height of 
men are given in the ninth line of Table 5 ; and it is inter- 
esting to notice that they are lower than the corresponding 
measurements of women at all the percentile grades. In 
other words, women appear to be relatively longer in the 
body and shorter in the legs than men. Whether this is a 
sexual peculiarity, or whether it depends upon the fact that 
men are, as a rule, taller than women, is a question which 
can be settled only by a comparison of the percentage sitting 
height of a large number of men and women of the same 
total height.* It is a good illustration of the readiness with 
which the card method of recording statistics lends itself 
to the solution of problems which may arise subsequently to 
their collection, that the data already on hand can be made to 
contribute to the settlement of the question thus suggested. 
In the first place, in order to obtain a set of statistics as 
comparable as possible with those of Dr. Sargent, those 
observations only were selected for discussion which were 
made in schools and colleges on women of seventeen years 
of age and upwards. Ten hundred and fifty-eight cards were 
found to contain records of this sort. These cards were then 
sorted according to the height of the individuals, the measure- 
ments falling within each successive set of 5 centimeters being 
brought into a single group. The cards in each group were 
then sorted according to the percentage sitting height, as 
shown in Table 3, and the percentile distribution of the obser- 
vations in each group calculated in the manner above de- 
scribed. The results of this calculation are given in Table 3. 
* Ranke (Beitrage zur Anthropologie und Urgeschichte Bayerns VIII. 56) regards 
the relatively greater length of the body in women as a proof that the female sex 
stands embryologically on a lower level than the male. 17 
Table Showing Percentile Distribution of Observations on Patio of Sitting Height to Total Height in Women of Seventeen 
Years and upward, arranged in Groups according to Total Height. 
Height, Centi- 
meters. 
No. of 
Observa- 
tions. 
Values at Undermentioned Percentile Grades. 
5 
lO 
20 
30 
40 
so 
00 
70 
80 
oo 
95 
1 
145-149 
43 
52.29 
52.80 
53.34 
53.58 
54.05 
54.44 
54.68 
55.06 
55.49 
56.03 
56.67 
2 
150-154 
184 
51.59 
52.20 
52.79 
53.19 
53.51 
53.81 
54.09 
54.41 
54.81 
55.34 
55.81 
3 
155-159 
343 
51.29 
51.67 
52.14 
52.78 
53.13 
53.53 
53.88 
54.16 
54.65 
55.21 
55.65 
4 
160-164 
303 
50.70 
51.34 
52.03 
52.49 
52.86 
53.10 
53.34 
53.56 
53.91 
54.56 
54.99 
5 
165-169 
155 
50.52 
50.89 
51.36 
51.84 
52.10 
52.35 
52.59 
53.00 
53.49 
54.03 
54.50 
6 
170-174 
23 
47.32 
48.20 
50.45 
50.99 
51.31 
52.08 
52.43 
52.66 
53.31 
53.70 
54.17 
Table 6. 18 
An examination of this table shows that the ratio of the 
sitting height to the total height at all the percentile grades 
decreases as the total height increases. In other words, tall 
women differ from short women less in the len£th of the 
body than in the length of the legs. That this is also true 
of men, there is no reason to doubt; but whether the ratio in 
question varies with the sex as well as with the height of the 
individual, is a question to be settled by a comparison of the 
values in Table 6 with those to be obtained by a similar dis- 
cussion of Dr. Sargent’s observations on men. In his dis- 
PERCENfiLE GRADES 
FIG. I CURVES CONSTRUCTED FROM TABLE G 
cussion of the anthropometrical differences between boys 
and girls, Dr. Sargent, in the above-mentioned article, 
points out that, at the age of fifteen years, boys are superior 
to girls in height, mainly on account of the greater lenglh of 
the thigh bone. It would be of great interest to determine, 
by a further discussion of his observations in the manner 
above indicated, whether a disproportionate increase in the 
length of this portion of the body is mainly responsible for 
the differences in height between individuals of the same sex. 
The way in which the ratio of the sitting height to the 
total height varies with the total height, may perhaps be 19 
better understood from an examination of the curves in 
Fig. 1, which have been constructed from the figures in 
Table 6. The abscissas represent the successive percentile 
grades, and the ordinates the corresponding values of the 
ratio. It will be observed that the curves, which represent 
in order from above downward the values in the successive 
lines of the table, are in a general way parallel to each 
other; with the exception, however, of the lowest curve of 
all, which, being constructed from only twenty-three obser- 
vations, is, of course, much less accurate than the others. 
These curves show very clearly, that, with an increase of 
height is generally associated a relative diminution of the 
sitting height, and thus furnish a sufficient explanation of 
the fact above referred to, — that Dr. Sargent’s measure- 
ments give a lower relative sitting height than our own. 
They show also, that, when the observations are arranged in 
groups according to the value of the total height, there is in 
each group a large range in the value of the relative sitting 
height; so that a certain number of women in the tallest 
group sit relatively higher than certain other women in the 
shortest group. For instance, a relative sitting height of 
53.3 per cent, is surpassed by 20 per cent, of the women in 
the tallest group, while it is not reached by 20 per cent, of 
those in the shortest group. 
Stretcii of Arms. 
It is popularly supposed that the distance between the 
finger tips when the arms are horizontally outstretched, is 
equal to the total height. An examination of the figures in 
the tenth, eleventh and twelfth lines of Table 5 shows that 
this is much more nearly true for women than for men ; the 
median values in Dr. Sargent’s observations being 100.8 
per cent, for women, and 102.8 for men. Our own obser- 
vations give at nearly all percentile grades slightly lower 
values than those of Dr. Sargent,—a difference which it 
seems reasonable to associate with the somewhat superior 
height of the women measured by Dr. Sargent; for, as we 
have just seen, tall individuals differ from short ones more 
in the length of the legs than in that of the body, and length 
of arms is generally associated with length of legs. A dis- 20 
cussion, similar to that of the sitting height as above given, 
showing how the ratio of the arm-stretch to the height 
varies with the height, would, of course, settle the question ; 
and a further discussion of Dr. Sargent’s observations would 
also determine how far the superior ratio of the male sex is 
dependent upon a greater length of arms, and how far the 
greater breadth of the shoulders contributes to the result. 
In both sexes it will be observed there is a range of 7 or 
8 per cent, between the fifth and ninety-fifth percentile 
grades. 
It is evident that the data already on hand may be made 
to contribute to the solution of various questions connected 
with the physical development of the human race in Massa- 
chusetts ; and that, with a further increase of the body of 
statistics, light will be thrown upon a variety of anthropo- 
logical problems, especially those relating to the effect of 
race and environment on the physique of the individual. 
The systematic collection of such statistics in the public 
institutions of the State, would, in a few years, furnish data 
of inestimable value for the hygienist and the educator, as 
well as for the anthropologist and the statesman. 
In conclusion, I desire to express my thanks to Miss Mary 
P. Nichols and to Miss Lucy R. Bowditch for much valuable 
assistance in the computation of tables.