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y
A BIOMETRIC STUDY OF BASAL
METABOLISM IN MAN
BY
J. ARTHUR HARRIS and FRANCIS G. BENEDICT
Published by the Carnegie Institution op Washington
Washington, 1919
CARNEGIE INSTITUTION OF WASHINGTON
Publication No. 279
17/
H37
PRINTED BY J. B. LIPPINCOTT COMPANY
AT THE WASHINGTON SQUARE PRESS
PHILADELPHIA, V. S. A.
CONTENTS.
PAGB
Chapter I. Introductory 1
Chapter II. Methods of statistical analysis 9
Chapter III. Individuals and measurements considered 25
/ 1. Measurements considered 25
2. Data analyzed 31
3. Criteria of suitability of materials dealt with 48
4. Recapitulation 69
Chapter IV. On the interrelationship of various phj'sical and phj^siological measure-
ments 71
1. Weight and pulse-rate 72
2. Stature and pulse-rate 75
3. Pulse-rate and gaseous exchange 78
4. Pulse-rate and total heat-production 80
5. Weight and gaseous exchange 83
6. Stature and gaseous exchange 85
7. Weight and total heat-production 89
8. Stature and total heat-production 95
9. Recapitulation and discussion 105
Chapter V. Changes in metabolism with age 107
1. Historical review 107
2. Statistical constants measuring changes in metabolism with age 109
3. Comparison of changes in pulse-rate in relation to age 123
4. Recapitulation and general considerations 125
Chapter VI. A critique of the body-surface law 129
1. Historical 130
2. Physiological evidence on the body-surface law 135
3. Measin^ment of body-surface area 141
4. Inadequacy of criteria of validity of body-surface law hitherto employed 144
5. Statistical tests of relative value of the Meeh formula and of the Du Bois
height-weight chart 151
6. Correlation as a criterion of the validity of the body-siuiace law 152
7. The prediction-value of body-weight and body-surface 161
8. Further tests of the value of body-weight and body-surface for estimating
total heat-production 177
9. Prediction of heat-production from two physical characters 182
10. Prediction of heat-production from two physical characters (stature and body-
weight) and age 189
11. Comparison of body-weight and body-surface as bases of prediction in male
and female infants 193
12. Recapitulation and discussion 195
Chapter VII. A comparison of basal metabolism of normal men and women 201
/ 1. Historical 201
2. Comparison of metabolism of men and women on the basis of general constants 203
3. Comparison of metabolism of men and women by use of graduation equations. 205
4. Comparison of basal metabolism of male and female new-bom infants 219
5. Recapitulation 221
Ul
IV CONTENTS
PAQB
Chapter VIII. Standard basal metabolism constants for physiologists and clinicians. 223
1. The necessity for and the fundamental nature of standard metabolism constants 223
2. Tables of multiple prediction standard metabolism constants 228
3. Illustrations of practical applicabiUty of standard multiple prediction tables of
basal metabolism 230
Illustration A . Tests of normaUty of series of determinations 230
Illustration B. Metabolism in childhood and youth and in extreme old age. 237
Illustration C. Metabolism of individuals of aberrant physical form 243
Illustration D. Metabolism of athletes 244
Illustration E. Metabolism of vegetarians 245
Illustration F. Metabolism in disease 246
Illustration G. Rationing in periods of emergency 249
4. Recapitulation 249
5. Standard multiple prediction tables of basal metabolism for normal men and
women 251
PREFACE.
In carrying out the work underljdng this volume we have attempted
to do more than to treat the available data for the basal metaboUsm
of normal men, women and children by a method which is practically
new in its apphcation to human physiology; we have endeavored to
make this investigation a prototype of that speciaUzation in methods
and cooperation in problems which we beUeve will be characteristic
of the best scientific work of the future. We are convinced that this
cooperation of speciaUsts of widely dissimilar training is the only means
by which science can attain both the height of refinement of measure-
ment and analysis and the breadth of comparison and interpretation
which is essential to continued progress.
The measurements considered in this volume have been made
possible by the painstaking cooperation of a score or more fellow-
workers, all of whom are connected or have been associated with the
Nutrition Laboratory. How large their contribution has been will be
evident from the names of the observers in the protocols of data and
from the references to earlier publications scattered through the follow-
ing pages. The exacting clerical and arithmetical work has been carried
out at Cold Spring Harbor by the Misses Ga\an, Holmes, Lockwood,
and Peckham, who deserve the highest praise for the energy and care
which they have devoted to this task. We are indebted to Major
C. B. Davenport, Director, for permission to have this work carried
out at the Station for Experimental Evolution. Finally it is a great
pleasure to acknowledge our indebtedness to our associate, Professor
W. R. Miles, who went over the first draft of the manuscript with us
and offered many helpful suggestions, and to Mr. W. H. Leslie, in
charge of the computing division at the Nutrition Laboratory, who has
aided in correcting the proofs.
In taking up this work over two years ago, the authors fully recog-
nized that the data must be wholly rearranged and interpreted as the
statistical constants might indicate without any regard to opinions
heretofore expressed from the Laboratory. Practically all of the con-
clusions already drawn at the Nutrition Laboratory have been fully
substantiated by the statistical constants, and it is naturally a source
of satisfaction that so Uttle of the ground already held has had to be
given up as a result of a wholly independent analysis from the outside.
This original conviction has been strictly adhered to, and every
effort has been made to have the treatment physiologically sound
throughout. We have endeavored to carry the analysis of the data to
the practicable limits of the biometric formulas, at the same time pre-
serving all that is of value in the older and simpler methods of treat-
V
VI PREFACE
ment which are more familiar to physiologists. We shall appreciate
the fullest criticism by fellow physiologists, biologists, and statisticians,
but criticisms to carry weight must be based on either statistical or
physiological foundations and not merely the ex cathedra expression of
the personal opinion that the new line of attack is valueless.
We are presenting this volume, not as a finished treatment of the
subject of basal metabolism, but merely as an introduction to the many
problems which await solution by the use of the more refined methods
of analysis when more extensive data are available.
Nutrition Laboratory of the Carnegie Institution
of Washington, Boston, July 10, 1918.
CHAPTER I.
INTRODUCTORY.
The purposejof this volume is to present the results of a first attempt
to analyze the data of basal metabolism in normal men and women by
the higher statistical or biometric formulas.
N* These methods, associated primarily with the names of Sir Francis
Galton and Professor Karl Pearson, are steadily making their way in
the most varied fields of biological work. While Pearson and his
associates at the Biometric Laboratory and the Galton Laboratory for
National Eugenics, University College, London, have touched on vari-
ous problems of interest to physiologists in their studies of inheritance
and of environmental influence, the methods have, up to the present
time, been Uttle employed in the domain of human physiology'. Per-
haps the most important papers in their bearing upon the problems
with which we are here concerned are those by Bell,^ by WTiiting,^ and
by WUliams, Bell and Pearson^ on oral temperature in school children.
Valuable as such studies unquestionably are from the standpoint of
social and general biological science, statistical constants based on the
returns of the pubhc-school medical officer or of the prison surgeon can
not be considered adequate for the requirements of modem nutritional
physiologj', in which measm-ements of a high degree of accuracy and
made under carefully controlled conditions are indispensable.
Both the unfamiliarity of the biometric methods to most physiolo-
gists and the relative paucity of data on basal metaboUsm have prob-
ably been responsible for the failm^e of physiologists up to the present
time to apply the higher statistical methods in this field. While physi-
ologists have been engaged for several decades with the problem of the
exact measurement of the metabolism of man and the lower animals,
both by the direct determination of the amount of heat produced in
the calorimeter and by the indirect calculation of heat-production from
oxygen consumption and carbon-dioxide excretion, satisfactory data
have until recently been exceedingly limited.
This state of afifairs may be attributed to various causes. First of
all, satisfactory apparatus is expensive and technical requirements
exacting. The number of fully equipped laboratories and of adequately
trained workers have, therefore, been very limited. Again, there is a
personal element in all investigations based on normal human individ-
1 Bell, Biometrika, 1911, 8, p. 232.
* Whiting, Biometrika, 1915, II, p. 8.
* Williama, Bell, and Pearson, Drapers' Company Res. Mem., Stud. Nat. Det., London, 1914, 9.
1
2 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
uals which is apt to be overlooked by those whose experimentation has
been carried out on chickens, guinea pigs, or other animals or plants
on the one hand or in the cUnic on the other. In the study of normal
metaboUsm the prejudices or suspicions of the subject must be over-
come and his convenience considered. This imposes a limitation upon
the number of measurements which can be fully realized by those only
who have had to meet these difficulties. Finally, the progress of the
work has shown the necessity for continuous refinement of method.
Thus it is quite impossible to use for present pm-poses the observations
of a few years ago. In the earlier work the necessity for complete
muscular repose on the part of the subject under investigation was not
fully enough realized. Individuals in the respiration chamber were
allow^ed to move about, telephone, write, or otherwise occupy them-
selves. More recent work has indicated that such apparently trivial
matters as the difference between the sitting and the reclining position
or such slight exertion as that required to raise the hand from the side
to the mouth may have a measurable influence on heat-production.
Furthermore, it has long been known that the presence of food in the
alimentary tract affects heat-production. The stimulatory action of
food has, therefore, to be taken into account.
Thus the conditions under which the more truly basal metabolism
of the individual may be measiu-ed have been continually narrowed.
Of recent years students of human metabolism have reached a general
understanding concerning the conditions under which the heat-
production of an individual should be measured in order to obtain
values of the metabolism constant which shall be comparable from
individual to individual, and hence suitable as a standard basis of
departure for all studies of the influence of special conditions, whether
of sex, age, food, exercise or disease, upon the gaseous exchange. Deter-
minations made on the individual during complete muscular repose
and at a period 12 hours after the last meal, i.e., in the post-absorptive
condition, give what is commonly known as the basal metabolism.
Until very recently the number of measurements which fulfil the modem
high requirements was necessarily so small that it had not seemed worth
while to apply the modem methods of analysis to them.
The development of series of measurements sufficiently large to
justify the use of the more refined statistical formulas in their analysis
has been in part due to a wider realization of the great practical as well
as the purely theoretical importance of a detailed and precise knowledge
of basal metabolism. The general pubUc, as well as the handful of
nutritional specialists, is being forced these days by conditions of unpre-
cedented stress to a realization of the fact that an exact knowledge
of human nutrition is not merely fundamental in the clinic and useful
in home economics, but that it may even lie at the basis of national
survival.
INTRODUCTORY. 6
The desirability of applying the biometric formulas to the steadily
increasing volume of data on basal m^etabolism in man has more than
once suggested itseK. Thus, as early as July 1915 Professor August
Krogh, of Copenhagen, in his ever stimulating correspondence, urged
that the data accumulated by the Nutrition Laboratory were already
so extensive that the modem statistical formulas might profitably be
employed in their expression and interpretation. After the manuscript
for this volume was practically completed, a paper by Professor Armsby
and his collaborators^ appeared, gi\'ing the correlation between body-
weight and daily heat-production and body-surface area and heat-
production.
Fortunately the niunber of individuals whose basal metabolism has
been determined is now fairly large. Deahng as we have in this volume
with indiv-iduals measured at the Nutrition Laboratory, or by those
who have been associated with the Laboratory, we are able to discuss
the constants of nearly 250 adults and of about 100 infants. In the
past these have been treated ahnost exclusively by the simple method
of averages and graphic representation. But a series of metabolism
constants, like other biological measurements, show differences among
themselves. These differences must be due to either iuaccuracies of
measurement, or must represent real physiological differences between
the individuals considered. That the latter rather than the former is
true seems evident from the fact that technical errors in the making of
the measurements have in all careful work been reduced to a miTiimuni
by the frequent use of physical tests of the apparatus, by the measure-
ment of standard combustions, and by other precautionary measures
which have placed the data of gaseous metabohsm among the more
accurately controlled of the physiological measurements. That the
differences between the measurements of individuals are of the nature
of real biological difference rather than of errors of observ^ation is also
clear from the fact that such attempts as have been made to obtain a
more precise average metabolism constant by reducing the total heat-
production to calories per kilogram of bod}'- weight or to calories per
square meter of body-surface have effected a material reduction in the
amount of variation in the measures of the actually observed metabol-
ism of individuals. Notwithstanding this correction for the physical
characteristics of the individual due to the reduction of the gross heat-
production to calories per kilogram or calories per square meter of
body-surface, the variation in the metabohsm constant is not entirely
eliminated. It seems necessary, therefore, in any thoroughgoing inves-
tigation of metabolism in man, to take accoimt of the variation from
individual to individual, as well as of the general average. Further-
more, the fact that some lessening in the differences in the metabolism
* Annsbj-, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, p. 1. See also Joum. Agric
Reeearcb, 1918, 13, p. 43.
4 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
constants of a series of individuals is made by reducing them to units
of body-weight or body-surface indicates that the total metabolism of
the individual is correlated with his physical characteristics. Thus
the desirabiUty of a detailed investigation of the correlation of the
various physical and physiological measurements which have been
made suggests itself.
Such investigations of variation and correlation can be carried out
only by means of the biometric formulas. A full justification for the
application of the higher statistical methods to the data of basal
metabolism is to be found in the fact that these methods have been
successfully applied in other fields in which the observational data
exhibit comparable irregularity. During the past two decades instances
of the demonstration of law and order in processes hitherto apparently
chaotic have been rapidly multiplying, while on the other hand, long-
maintained biological theories have been shown to be groundless by
the mathematical description and analysis of series of measurements.
This fact estabhshes a strong presumption that the same condition will
be found to apply in the field of human metabolism. The presumption
has seemed to justify at least a preliminary test of the methods.
It seems desirable to outline at the start the possibilities of the
statistical formulas in their application to the problems of basal
metaboUsm.
First of all, these formulas permit a more concise and adequate
descriptive statement of the results of experimentation. The statistical
method furnishes not merely an average measure of metabolism, but
also a measure in a single constant of the deviation of the individual
determinations of metabolism from their average value. The average
value of the metabolism constant serves many useful purposes, but it
is no more truly a characteristic of the series of measurements which
have been made than their differences among themselves. Measures
of variability in metaboUsm are, therefore, quite as necessary for a
full understanding of the physiological problem as are measures of the
average values. Such constants have been determined during the
course of this work, and expressed in both absolute and relative terms.
The measures in absolute terms are particularly useful for some pur-
poses, while those in relative terms permit direct comparison of the
variabihty of metabolism constants with those of other physical and
physiological measurements in man.
Again, one of the greatest possibilities of the statistical method lies
in the determination of the degree of association or correlation of differ-
ent physical and physiological or of different physiological characters.
For example, we know that in general the total heat-production of a
tall individual is greater than that of a short individual, that the heat-
production of a heavy individual is greater than that of a light individ-
ual, and so on. But what is needed for a full and scientific analysis of
INTRODUCTORY. 5
the whole problem is some measure of the intensity of these and many
other interrelationships, expressed on such a scale that comparisons
between various characters may be easily and directly made. This end is
readily attained by the use of the modem correlation formulas.
The analysis may be pushed further. We have just said that tall
indi\'iduals produce on the average a larger number of calories than
short ones, and that hea\'y indi\'iduals set free on the average more
heat than light ones; but tall indi\iduals are on the average heavier
than short ones, and the question naturally arises whether their greater
heat-production may not be due exclusively to their greater average
weight. This problem can be solved only by correcting the correlation
between stature and heat-production for the influence of the correlation
of both statm-e and total heat-production with body-weight. A quite
similar method of analj^sis may be applied when it is desired to correct
the relationship between two variables, for example between age and
heat-production, for the influence of both of two other variables, say
statiue and body-weight.
Knowing the correlation between two variables (for example, body-
weight and total heat-production) it is possible within certain limits
of accuracy to predict the average value of one from the known magni-
tude of the other. Thus it is possible to pass at once from measures of
interdependence on the universal scale of correlation to coefficients
showing just how much on the average an associated character increases
in units of the actual scale on which it is measured for each unit's
change in the first variable. These relationships are of the greatest
practical importance, in that they enable us to determine the most
probable metabolism of an unknown subject of given statm^e, weight,
and age, and these predicted values may serve as a control in cases in
which it is desired to investigate the influence of particular conditions,
e.g. the incidence of a specific disease, on metabohsm.
Finally, one of the great advantages of the use of the statistical
method lies in the system of probable errors which are pro\'ided by
the biometric constants. Metabohsm varies from individual to indi-
vidual. If the average value of a series of determinations be employed
as a basis of argument concerning some physiological relationship, the
worker must fully recognize the fact that a repetition of the measure-
ments upon another set of individuals apparently comparable with the
first would give averages somewhat different. The probable errors
of random sampling, to be discussed in somewhat greater detail in
a special section on methods of statistical analysis, do much to
estabhsh the limits of trustworthiness of not only the arithmetical
means or averages but of all the other statistical constants. Thus
the biometric formulas make possible a far more definite conception
of the Hmits of trustworthiness of metabolism constants than has
heretofore been possible.
6 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Turning now from generalities to concrete problems, we may outline
very briefly the actual physiological problems upon which we have
touched.
First of all it may be stated that this volume contains the raw data
for age, body-weight, stature, pulse-rate, and gaseous exchange, with
the computed heat-production, in 47 men and 35 women hitherto
unpubhshed. These are laid before the reader, together with the data
for 89 male and 68 female adults and the 51 male and 43 female infants
already pubUshed from the Nutrition Laboratory. These represent a
contribution to the problem of human metabolism of experimentally
determined facts which must be taken into account even by those who
may be imwilhng to accept the results of the statistical analysis to
which all the data at our disposal have been subjected.
Turning to the results of statistical analysis, properly so called, we
note the following :
1. The more important statistical constants of the largest available
series of metabolism measurements have been determined. These
must serve as standards in metabolism work until more extensive data
are available.
2. The relationship between physical and physiological measure-
ments of the human individual has been discussed in as great detail
as possible by means of correlation constants. Specifically, we have
considered the relationship between both body-weight and stature,
representing physical measurements, and the physiological measure-
ments, pulse-rate, gaseous exchange, and total heat-production, and
determination has been made of the effect upon these correlations of
correction for other factors.
3. The degree of interdependence between various physiological
characters has also been considered. Specifically, the relationships
between pulse-rate and gaseous exchange, and between pulse-rate and
total heat-production and heat-production per unit of body-weight
and of body-surface have been determined.
The illustrations presented in the following pages should amply
demonstrate the material advances in our knowledge of physiological
processes which may be expected when the degree of interrelationship
between various physical characters and physiological activities, or
between physiological activities themselves, shall be generally measured
on a definite quantitative scale.
4. The validity of the so-called body-surface law has been tested
by means of criteria hitherto unapplied. This ' ' law ' ' has been discussed
as an empirical means of predicting the metabolism of an unknown
subject and as an expression of a true physiological interrelationship.
5. In connection with the investigation of the so-called body-
surface law, various methods of predicting the total heat-production
of an unknown subject from sex, age, stature, and body-weight have
IXTRODLXTORY. 7
been considered in detail. Standard tables have been prepared from
which the most probable metabolism of a subject, whose normal metab-
olism is unknown, may be predicted as a basis of comparison with that
measured in a pathological state. Such tables should be of great value
in the cUnical investigations which should contribute much to the
future advancement of medical science.
6. By the use of such tables, the metaboUsm of subjects of par-
ticular characteristics, or subjected to special conditions, has been
reconsidered. Specifically, the problems of the typical or atypical
character of certain series of metabolism measurements, of the differen-
tiation of the sexes with respect to metaboUc acti\'ity, of the metabohsm
of athletes as compared with non-athletic individuals, of vegetarians
as compared ^s-ith non-vegetarians, and of individuals suffering from
disease have been investigated.
In preparing this report on the results of the appUcation of the
biometric formulas to the data of basal metabolism in normal men and
women we have utihzed only the measurements made at the Nutrition
Laboratory or by those who have been associated with it. This limita-
tion has been made, not because there are not many satisfactory deter-
minations which have been made in other laboratories, but because,
all things considered, it has seemed most satisfactory to avoid invidious
comparisons by the discrimination which would have been necessary
had we gone outside the series of determinations for which responsibiUty
rests directly or indirectly upon the Nutrition Laboratory.
Finally, a few words concerning the form in which the results of
this investigation are presented: It has not seemed desirable to trans-
form a research publication into a primer of statistics, or to state results
which are necessarily mathematical in a popular and non-mathematical
form. We have, however, made every effort to express our results in
a form so clear and direct that they will be fully comprehensible to
those without special statistical training. In the case of all the more
comphcated processes we have given the formulas by which the results
were reached. This has been done to enable those who may care to do
so to check through our work from the beginning. The reader who is
interested in end results rather than in methods should pass over these
features, just as the general biologist must pass over the details of
method and the section on structural formulas in a paper by an organic
chemist, reahzing that they are essential to the technical development
of the subject. The analogy is by no means wide of the mark. The
statistical technique is of course comphcated, as are the manifold
technical refinements necessary in the experimental phases of the
measurement of metabolism in man. An adequate presentation of the
subject demands a statement of the formulas emplo^^ed quite as much
as a description of the phj'sical and chemical apparatus used in the
laboratory phases of the work. With this featm-e of the following
8 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
treatment the non-statistical reader must bear as patiently as possible.
There is no royal road to statistical analysis, and the popularization
of statistical methods is quite comparable with the problem of the
popularization of organic or physical chemistry. The demand for
simplification can, so far as those of us who have been working in
this field can now see, be attained only at a serious loss of effectiveness.
To assist the non-statistical reader as much as possible in the under-
standing of our results we have added a summary at the end of each
chapter in which we have given the results in a form as general and
non-statistical as possible. With these precautions, and with the
cooperation of those who may attempt to follow us through these
pages, we trust that a highly difficult subject has been presented with-
out important loss in the technical detail which is essential to those
who may care to pursue the subject further and in a manner compre-
hensible to the general physiologist.
Chapter II.
METHODS OF STATISTICAL ANALYSIS.
Before taking up the actual data ^-ith which we have to deal, a
brief discussion of the statistical formulas employed will be necessary
although it is not possible to give an adequate introduction to the use
of the statistical methods. These methods are compUcated and many
pitfalls abound in the field of statistical reasoning. This section may,
however, give the reader definitions of terms and a general conception
of the method of attack.
The first statistical constant to be determined for a series of meas-
urements is the arithmetic mean or average value. This is simply the
simi of all the observations divided by their number. It is already
familiar to the physiologist and need not be discussed further.
The second statistical constant with which we shall have to deal
in the treatment of these data is a measure of the deviation of the
individual measurements from their average value. Physiologists in
conamon with psychologists and other investigators have sometimes
measured the variation in their observations by obtaining and aver-
aging the differences between the individual readings and the general
average. Thus an average deviation^ or an average dispersal, of the
individual measurements about the general average for the whole
series of individuals dealt with, is obtained. This average deviation is
very useful for some purposes, but for more refined work has three
disadvantages. (1) Some of the measurements are smaller while others
are larger than the general average for the whole series of individuals
dealt with. Thus some deviations are positive while others are nega-
tive in sign. In obtaining an average value which shall furnish a
true measure of scatter both above and below the mean, it is necessary
to disregard the signs and thus to do violence to one of the laws of math-
ematical usage. (2) The significance to be attached to a deviation is
considered proportional to its actual magnitude. It may be legitimate
to regard a large deviation as both absolutely and relatively more
important than a small one. (3) The average deviation is poorly
suited for use in more comphcated statistical work.
The larger deviations can be given a proportionately greater weight
by squaring all the deviations, summing these squares, and dividmg
by the number of deviations to obtain the mean-square deviation. The
square root of this mean-square deviation is the measure of variation,
scatter, or dispersal most used by the statistician. It is called the
standard deviation, S. D. or a. There are great practical advantages
in the use of the standard deviation, in that it is particularly suited
10 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
for the more complicated calculations involved in the determination
of measures of interrelationship.
The standard deviation may be calculated by actually obtaining
the deviations of the individual measurements from the general average,
squaring these deviations, dividing by the number of observations, and
extracting the square root of the quotient . Thus if x represents the value
of an individual measurement, x the average of all the N measurements
where a^ is to be read "the standard deviation of the measurement x"
and S denotes the summation of all the squared deviations. Thus in
the case of a series of 16 athletes given in our table of data on p. 40 the
total weight is 1181.1 kilograms and the average weight 1181.1/16 =
73.8 kilograms. The sum of all the daily heat-productions is 30,025
calories and the average daily heat-production 1876.6, or in round
numbers 1877 calories. The deviation of the individual weights, w,
from the average weight, w, and of the individual heat-productions, h,
from the average heat-production, h, are given in table 1.
Table 1. — Deviations and squares of deviations of body-weight, w, and heat-production, h,
from their respective averages.
Subject.
w
(w — w)
{w—wy
h
ih-h)
(h-ly
W.A. S
C. J. D
56.3
56.7
63.5
63.5
73.9
71.2
74.0
66.0
62.4
108.9
82.2
82.1
78.9
79.0
88.5
74.0
-17.5
-17.1
-10.3
-10.3
+ 0.1
- 2.6
+ 0.2
- 7.8
-11.4
+35.1
+ 8.4
+ 8.3
+ 5.1
+ 6.2
+ 14.7
+ 0.2
306.25
292.41
106.09
106.09
0.01
6.76
0.04
60.84
129.96
1232.01
70.56
68.89
26.01
27.04
216.09
0.04
1562
1524
1677
1619
1842
1810
1908
1695
1816
2559
1978
2034
2126
1944
2017
1914
-315
-353
-200
-268
- 36
- 67
+ 31
-182
- 61
+682
+ 101
+ 157
+249
+ 67
+ 140
+ 37
99225
124609
40000
66564
1225
4489
961
33124
3721
465124
10201
24649
62001
4489
19600
1369
M. Y. B
R. D. S
H. R. W
P. D. F
C. D. R
M. A. M
W. F. M
H. W
J. H. R
D. H. W
E. G
M. H. K
W. 8
F. G.R
The standard deviations are therefore given by
2[(/i_^)2] =961351
<r,= 12.867
ah= 245.12
2l(w-wy] = 2649.09,
2[iw -w)VN = 165.5681 = a J
2[{h - h)yN = 60084.44 = (t^^
The standard deviation furnishes a measure of variation in terms
of the unit in which the variable was measured, i.e., in number of
heart-beats, in number of respirations per minute, or in number of
calories produced per 24 hours. If comparison between the variability
of characteristics measured in different working units is to be made,
it is necessary to reduce the two standard deviations to a comparable
METHODS OF STATISTICAL ANALYSIS. 11
basis by expressing them as percentages of their respective means.
Thus, if X represents heat produced per 24 hours and y represents
pulse-rate, it is quite impossible to say from a comparison of <r, and <Xy
whether pulse-rate or heat-production is the more variable character.
But if the two standard de\'iations be expressed as percentages of
their respective means,
„ _100(r, ^ _100^
X y
it is possible to determine which of the two characters is relatively
more variable.
Thus in the case of the measurements of body-weight and total
heat-production given above, the relative variabiUties are :
F.,=
100(r^ .r 100<r;k
w h
or numerically
,. 12.867X100 --.„ jr _ 245.12X100 _ ,^ ^^
^"^ 73:8:^ ^^^-^^ '' 1876.6 "^^-^^
This relative variation constant is known as the coefficient oj varia-
tion. It shows in the present case that the body-weight of the athletes
is about 4.4 per cent more variable than their daily heat-production.
We now turn to the problem of the measiu-ement of interdependence
or correlation.
Remembering that we are seeking a measure of the degree of inter-
relationship of the magnitudes of two variables, it is first necessary
to adopt a standard vnXh. which indi\-idual measures of body-weight,
body-surface, metaboUsm, pulse-rate, or other variables may be com-
pared in order to determine their place in their own series. Such a
standard is furnished by the average value of the character in the series
of individuals available. This arithmetical mean has the advantage
for metaboUsm work that it has been regularly used as a standard
value by various workers. The only difference between our use of the
mean and that of some other wTiters on metabolism is that the average
value which we employ as a standard is always the average for the
particular series of individuals under consideration, not an average for
some selected standard series. Thus, in working ^ith athletes, vege-
tarians, or all normal men the averages employed as standards are
those for athletes, vegetarians, or for all normal men, as the case may be.
Let X be the measure of any physical or physiological characteristic
of an indi\ddual, y the measure of any other physical or physiological
characteristic — for example, oxygen consumption, carbon-dioxide out-
put, or calories of heat-production, in the same indi\'idual. Then if
we designate by bars the average values of these two characteristics in
the series of individuals dealt with, ix—x), (y—y) furnish at once the
12 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
measiire of the position of an individual in the whole series of measure-
ments. Values with the negative sign indicate a position below the
average, values with a positive sign a position above the average of
the series as a whole, while the numerical value gives at once the mag-
nitude of the deviation.
Now remembering that (x—x) and (y—y) are values with signs,
it is clear that if we take the products of these deviations we shall have
positive products for all values with like signs and negative products for
the values of all deviations with unhke signs. Summing these products
with regard to sign for the whole series of individuals under investiga-
tion, the net total will be positive if the two measures x and y tend to
vary in the same direction, that is, if y tends to be above its mean value
in individuals in which x is above its mean value and y tends to lie
below its mean value in individuals in which x lies below its mean value.
For example, the table for the athletes given above shows the actual
amount of the deviation of the weight and the daily heat-production
of each individual above or below the mean weight and mean heat-
production of the whole group of athletes. The fact that two positive
or two negative signs tend to occur together shows at a glance that there
is some correlation between body-weight and total heat-production.
The products of these deviations are given in table 2.
Table 2.
-Products of deviations of body-weight and daily heat-production from
their respective means.
Subject.
(w — w)
Qi-h)
iw-w) Qi-h)
W.A. S
C.J.D
M.Y.B
R. D. S
H. R. W
-17.5
-17.1
-10.3
-10.3
+ 0.1
- 2.6
+ 0.2
- 7.8
-11.4
+35.1
+ 8.4
+ 8.3
+ 5.1
+ 6.2
+ 14.7
+ 0.2
-315
-353
-200
-258
- 35
- 67
+ 31
-182
- 61
+682
+ 101
+ 157
+249
+ 67
+ 140
+ 37
+ 5512.5
+ 6036.3
+ 2060.0
+ 2657.4
- 3.5
+ 174.2
+ 6.2
+ 1419.6
+ 695.4
+23938.2
+ 848.4
+ 1303.1
+ 1269.9
+ 348.4
+ 2058.0
+ 7.4
P. D.F
C.D.R
M. A. M
W. F. M
H. W
J. H.R
D. H. W
E. G
M.H.K
W. S
F.G. R
Sum (S)
=fc 0.0
±0.0
+48331.5
In 15 of the 16 cases the heat-production is larger than the average
heat-production when weight is larger than the average weight and
smaller than the average heat-production when weight is smaller than
the average. Summing the products with regard to sign, we have
-f 48335.0-3.5 = +48331.5,
which divided by 16 = 3020.7188.
METHODS OF STATISTICAL ANALYSIS. 13
Thus the sum of the products of the de\-iatioiis of x and y from their
respective means for the whole series of indi\iduals, di\dded by the
number of individuals considered, furnishes a mean productHie\'iation
which is a measure in absolute terms of the closeness of interdependence
of the two characters under investigation.
To obtain a measure in relative terms (that is in a form to faciUtate
comparison between unUke characters) some standard of the amoimt
of the deviation from the general means in the case of the two characters
is essential. The mean product-deviation must be expressed as a
fraction of the product of the de\'iations of the two characters in
the whole series of indi\'iduals from their respective means — that is,
of <Ts<Xy.
The measure of interdependence in relative terms is therefore
merely the ratio of the mean product-de\4ation discussed above to the
product of the two standard de^^ations in the whole series. Thus
^ _A{x-x){y-y)]/N
'xy
is the measure of interdependence sought.
For the illustration in hand, the athletes, we have nimierically,
3020.7188 3020.7188 ^ ^.^
r„ft = = =0.958
12.867X245.12 3153.9590
This is the familiar product-moment coefficient of correlation of the
statistician.
The coefficient of correlation measures the closeness of interde-
pendence between two variables on a universally comparable scale, the
range of which is unity. Thus a coefficient of 0 represents an absence
of all interdependence ^ between the two variables. A correlation
coefficient of 1 indicates perfect interdependence. Thus if there be no
correlation between x and y, the measm^ement of the x character
furnishes no information whatever concerning the magnitude of the y
character in the same individual. If, on the other hand, there be perfect
correlation — a practically unknown quantity in biological work — the
magnitude of the y character is known as soon as the x character has
been measured.
Empirically, the correlation coefficient is generally found to be
positive in sign, but it may be either positive or negative. \Mien y
becomes larger as x increases in magnitude the correlation is positive
in sign. WTien y decreases as x increases, correlation is negative in
sign. The correlation formula is so written that the sign is automatic-
ally given in the process of determining the constant.
* There are conditions under which this is not true, but for the purposes of this volume th«
statement is practically valid.
14 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In metabolism work positive correlations are numerous. For
example, the correlation between body-weight and total heat-produc-
tion in the 136 men available for this investigation is 4-0.796, or about
80 per cent of perfect interdependence. Physiologists have, of course,
known of the existence of this relationship. The statistical method
has not been necessary to demonstrate its existence. What the statis-
tical formula has done is to measure on a quantitative scale a relationship
concerning which ideas were heretofore vague and qualitative only.
The positive sign shows that total heat-production increases with
body-weight.
Age is the only character for which correlations have in this work
been found to be consistently negative in sign. The correlation between
age and total heat-production in these 136 men has been found to be
—0.306. This shows that heat-production decreases as age increases
and measures, on the universally comparable scale of unity, the close-
ness of the interrelationship between these two variables.
For purposes of comparison a measure of the interrelationship of
two variables on a universal scale is invaluable. Fortunately it is
possible, by proper statistical formulas, to pass from measures in terms
of correlation to measures of interdependence expressing in the con-
crete units of actual measurement the average change in the y character
associated with a unit variation in the x character, or vice versa.
The formulas are
(y -y) =r^y -{x-x) {x-x) =r^y ^ {y -y)
or in a somewhat different form
y = {y-r^y - x) +r^y ^x x = {x-r^y - y) +r^y - y
All the symbols in these equations are familiar to the reader from the
immediately foregoing paragraphs.
In statistical terminology such equations are called regression
equations. This term, which has an historical significance, is now well
established in the literature and we shall use it, or sometimes a perhaps
better term prediction equation, throughout this volume. In equations
like the first of the two above we speak of the regression of y on x,
which is equivalent to saying the prediction of y from x. In the case
of the second equation we speak of the regression of x on y, or of the
prediction of x from y.
Such equations are easily reduced to numerical form by the sub-
stitution of the statistical constants. For example, the correlation
between body-weight and total heat-production in a group of athletes
has been shown above to be expressed by a coefficient of r«,^ =0.958.
METHODS OF STATISTICAL ANALYSIS. 15
Expressing this relationship in terms of regression, we have (remember-
ing that (T^ = 12.867 and a„ =245.12).
ih-h) =r„. ^ {w-w) =0.958 ?^ (w-w)
or
(/i-/0 -18.250 (mj-w)
In a form somewhat more convenient for practical work, i.e., in that
of the characteristic equation, the relationship is
Noting that numerically il' = 73.8 kilograms and ^ = 1876.6 calories, we
have
h = (1876.6-0.958 ?i^ 73.8) + 0.958 ?^^ w
12.867 12.867
which gives
/i =529.7+18.3 M?
Such equations predict the average value of the y character
associated with a given grade of the x character, or the average value
of the X character associated with a given value of the y character.
For examples, the values of h predicted by the equation are the average
values of a series of indi\'iduals of given stature, body-weight, or any
other physical or physiological character used as a basis of prediction.
They represent the most probable heat-production of an indi^-idual deter-
mination providing that the distribution of variation in heat-production
is symmetrical about its mean and the relationship between the char-
acter from which prediction is made and heat-production be capable
of expression by a linear equation.
In the following pages the straight Unes due to such equations are
frequently represented on a diagram showing by the position of a dot
the value of both the x and the y character of all the individuals.
Such scatter diagrams bring out clearly the fact that the predicted
measure is an average and can be taken to represent only the most
probable value of the individual case. It is necessary, therefore, to
consider the amount of deviation which may be expected to occur
about the predicted mean.
The standard deviation of the predicted character, say h, for the
individuals of any group is
xO-A=o-A\/l-r,fc^
where x denotes stature, body-weight, age or any other character
wdth respect to which the individuals maj"^ be classified in the investi-
gation of metabohsm.
16 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The practical physiological significance of this statistically well-
known relationship seems to be rather great.
First of all, if Txh be small the error of prediction of the heat-pro-
duction, h, of a single individual from the value of x will necessarily
be large. This is not due to any inadequacy of the statistical formulas,
but is the inevitable consequence of great physiological variabiUty.
On the other hand, if there be a group of n individuals of a specified
grade of x, say Xp, the prediction of the average heat-production of the
individuals of this group can be carried out with far greater accuracy.
Thus the standard deviation of the predicted mean value K is
Vn
while the probable error is
0.67449 (r,Vl -7-,;,=^
V n
where h^ is the mean heat-production of individuals of a specific
grade, p, of character x, for example body-weight, body-surface, pulse-
rate, or any other character.
Thus it is clear that when a physical character of an individual is
known — for example, stature or body-weight — the values of metabol-
ism predicted from it will show certain deviations from the actual
values of the individual subjects, but the statistician can even predict
with fair accuracy what the amount of this deviation will be. The
failure to attain exact prediction merely illustrates the fact that physi-
ology, like biology in general, is not as yet a science in which certainty
as to the individual instance is attainable. Chapter VI will be devoted
almost entirely to the problem of the closeness of prediction of heat-
production from physical characters.
As an illustration of the importance of the preceding formulas we
may note that the probable error of the mean predicted heat-production
of 4 typhoid patients would be l/v 4 or one-half as large as the probable
error of a single individual, while the probable error_of the mean pre-
dicted heat-production of 9 subjects would be l/V^, or one-third as
large as the probable error of one observation.
To determine how closely the predicted values agree with the empir-
ical average for the group of individuals classified with respect to any
character, x, we have merely to compare the mean values actually
observed with those due to the regression equation by means of a
graph. Such diagrams, of which a number occur in the following pages,
permit one to judge by the eye the goodness of fit of the regression
equations. In some cases special mathematical tests of the closeness
of agreement of the empirical and theoretical means are given, but an
explanation of the nature of these tests is unnecessary here.
METHODS OF STATISTICAL ANALYSIS. 17
In some cases we have found it necessarj^ to use regression equations
in which the value of one variable, z, is predicted from those of two
others, z and y, or from that of three others, w, x and y. Formulas
for these will be given when used.
Throughout the following pages we shall have frequent occasion
to use partial correlation formulas. Total heat-production is correlated
with stature and with body-weight; but stature and body-weight are
also correlated, taller indi\dduals being on the average hea\der than
shorter ones. The problem now arises: May not the correlation
between stature and total heat-production be merely the resultant of
the correlation between bodj^-weight and heat-production on the one
hand and body-weight and stature on the other? To solve this problem
we have to correct the correlation between stature and total heat-
production for the influence of body-weight. Or, in statistical termin-
ology, we must determine the partial correlation between stature, s, and
heat-production, h, for constant bod^'^-weight, w. This is done by the
use of the formula
v'f'th —
Vl-r «vT^
i
xeh
Here y,r,,^ is to be read "the correlation between stature and heat for
constant body-weight." The technical expression ''for constant body-
weight" means merely "with the influence of body-weight eliminated."
If the correlation between stature and total heat-production were
merely the resultant of the correlation between weight and heat-
production and weight and stature, «,r,A should be sensibly zero. For
example, for the 136 men, using the constants as given on pages 59 and
96, we have:
r., = +0.6149
r„. = -h0.5725 l-r«.« =0.6722 vT=^ =0.8199
r„, = +0.7960 l-r„,2 = 0.3663 ■>/r^«=0.6052
0.6149 -0.5725 XO.7960 0.1592
"'''•'^~ 0.8199X0.6052 "0.4962 ~
1 _ ^r,^i = 0.8969 E^r^, = 0.6745^ 7-!!!J^ = 0.0519
V N
Thus the partial correlation between stature and heat-production
for constant body-weight is only about half the magnitude of the
uncorrected value. It is clear, therefore, that the greater heat-produc-
tion of tall indi\dduals is due largely to their greater weight. The fact
that the partial correlation has a material and statistically significant
positive value indicates that the obser^-ed relationship between stature
and metabolism is not merely the resultant of the correlations between
stature and weight and between weight and metabolism.
18 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In certain instances we have found it desirable to determine the
relationship between two variables for constant values of two other
variables. Thus awfsh is to be read "the correlation between stature, s,
and heat-production, h, for constant age, a, and body-weight, ly."
The actual formulas used in computing the partial correlation
coefficients are given in each instance.
The partial-correlation method has been of great service in this
study and will, we believe, prove to be a powerful analytical tool in
the investigation of physiological relationships in many fields.
We now turn to the subject of the probable errors of the statistical
constants.
Because of the differences which obtain between the individual
determinations of a series of metaboUsm measurements, the statistical
constants of such measurements will generally differ to some extent
from series to series. For example, the average heat-production per
square meter of body-surface per 24 hours of 72 men selected by
Gephart and DuBois from a Nutrition Laboratory publication is
926.65 calories, whereas the average heat-production of 64 other men
examined by the Nutrition Laboratory is 924.14 calories. Thus the
two series differ in heat-production per square meter of body-surface
by 2.51 calories. The standard deviations of heat-production per
square meter of the two series are 62.59 and 71.92 calories, or show a
difference of 9.33 calories. When another series of measurements is
available it will probably give averages and variabilities which differ
slightly from either of these. That this should be so is simply a
matter of common experience.
The statistician as such can do nothing whatever to eliminate the
individuality of the subjects to which these differences are primarily
due or to minimize the shght experimental errors of measurements
upon which they to some extent depend. He can, however, furnish
criteria of the trustworthiness of statistical constants based on series
of observations of known variability and number. These criteria are
the so-called probable errors, or more precisely probable errors of random
sampling. Such probable errors are entirely statistical in nature and
have nothing whatever to do with the possible errors of measurement.
They assume the technical or biological correctness of the observations
and measure merely the degree of trustworthiness of statistical con-
stants based on series of observations.
In the calculation of the probable error two factors must obviously
be taken into account. The first is the variability, the second is the
number of the measurements dealt with. If a character, either physical
or physiological, is extremely variable it is obvious that an average
based upon a given number of determinations will be less trustworthy
than one based upon a character which is very slightly variable. For
example, the addition of one very heavy individual to a series will
METHODS OF STATISTICAL ANALYSIS. 19
make an enormously greater difference in the average weight of the
series than it will in the average pulse-rate, for body-weight is a far
more variable character than pulse-rate. The trustworthiness of a
constant based on a series of measurements is inversely proportional
to the variability of the individual measurements. On the other hand
it is reasonable to assume that the precision of a statistical constant
increases as the number of observations upon which it is based becomes
larger. Thus the average metabohsm of 100 indi^'iduals is admittedly
more desirable as a basis for physiological generahzation than an aver-
age based on 10 indi\'iduals; yet the trustworthiness of the constants
is not directly proportional to the number of observations upon which
they are based, but stands in the ratio of the square roots of these
numbers. Thus the probable error of an average based on 10,000
indi\4duals would not be 100/10000 = 1/100 of that based on 100
individuals, but only VlOO/VlOOOO = 1/10. The practical conse-
quence of this relationship is that while precision increases with the
number of the obser^'ations, the increase in precision is not directly
proportional to the labor involved in the making of the measurements.
After a degree of precision which meets the practical requirements is
attained, further work may be regarded as hang beyond the limit of
diminishing returns. Of course the need of greater refinement may at
any time arise and demand the accumulation of a number of data
which for earher work would have been considered superfluous.
Details concerning the calculation of the probable errors — a term
ha\'ing an liistorical significance and not as appropriate as might be
found — which can be obtained from text books on statistical methods,
need not detain us here. A few words are in order concerning the inter-
pretation of the probable error, the value appended with a plus and
minus sign to the various statistical constants. It is in reaUty a
measiu-e of the variability of that constant which would be found if it
could be determined an infinitely large nimiber of times upon random
samples of the same number of measurements and drawn from the same
population as that upon which the constant is based. It is a measure
of this variabihty of the statistical constant about its mean so chosen
that half of the values would he inside and half of them outside the
hmits of the probable error. Thus if the mean value of a character in
an infinitely large population were 86 and the probable error for sample
of 100 were ^5, 86 =^5 would indicate that if a large series of samples
of 100 indi^^duals each were dra^wn at random from this population
half of these would show averages ranging from 81 to 91 while the
remaining 50 per cent would he below 81 and above 91.
The distribution of these means based on random samples of 100
indi\'iduals each would be an orderly one. Thus in the comparison
of two means it is possible for the statistician to estimate the chances
for (or against) their being based on identical material. Or, conversely,
20 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
it is possible to estimate from the observed differences in the constants
the chances of the materials being differentiated. This is, of course,
the practical apphcation of the principle. The physiologist desires to
know, for example, whether an observed difference between two con-
stants, one based on athletic and the other on non-athletic individuals,
indicates a real biological or physiological difference attributable to ath-
letic training, or whether it is merely of the order to be expected as the
result of random di'awing of groups of subjects of the number dealt with.
For example, the daily heat-production of 16 athletes is found
from table 16 to be 1876.56=1=41.33 calories. That of the first supple-
mentary series of 28 men is 1605.18 =*=28. 19 calories. The difference
between these two constants is 271.38=*= 50.03 calories. The difference
is 5.42 times as large as its probable error and the odds against its
being due to errors of random sampling are large.^ Thus we may
conclude that athletes are different from ordinary individuals in their
gaseous metabolism.
Again we note that in a series of 72 men selected by Gephart and
Du Bois from the Nutrition Laboratory publications the average heat-
production is 1623.46=1=14.11, whereas in another series of 64 indi-
viduals it is 1641.05 =i= 19.48. The difference is 17.59 =±=24.05. Thus
the difference is less than its probable error and can not be considered
statistically significant. In short the two groups of men may be con-
sidered to show the same average metabolism.
The practical use of the probable error is almost invariably in the
carrying out of comparisons. The investigator desires to know whether
a particular statistical constant differs either from some preconceived
or theoretical standard or from some other constant. For example,
the physiologist may wish to know whether the mean metabolism of
women differs significantly from that of men. In the case of correlation
an apparently, but not essentially, different problem presents itself.
One often desires to know whether there be any relationship at all
between two variables. He then inquires whether an empirically found
value of the correlation coefficient has a "significant" value. This
is necessary because of the fact that if correlations were based upon
small series of individuals drawn at random from an infinitely large
series in which the correlations were zero, a numerical value would in
many instances be obtained. This is true for the same reason that a
small number of determinations of basal metabolism on a group of
febrile patients would show an average value differing from that ob-
tained on a small group of normal subjects, whether there be any real
influence of fever on metabolism or not.
In such cases we wish to know whether the correlation differs
• Throughout this volume we have taken differences of 2.5 or 3 times as large as their probable
errors to be significant, always remembering that the interpretation of probable errors is difficult
when the number of observations is small.
METHODS OF STATISTICAL ANALYSIS. 21
significantly from zero, which would be found if an infinitely large
series of observations were available. For example, in table 18 we
show that the correlation between stature and pulse-rate in 121 men
is +0.0916 ±0.0608, while for 90 women it is -0.0669 ±0.0708. These
constants differ from zero by 1.51 and 0.94 times their probable errors
and consequently would not be considered to prove the existence of a
real positive correlation between stature and pulse-rate in the case of
meji as a class or of a real negative correlation in the case of women as
a class. In short, the probable error indicates that the series of deter-
minations available is too small to justify any generaUzation concerning
the numerical magnitude of the correlation between stature and mini-
mum or basal pulse-rate other than that it is exceedingly small if it
exists at all. A comparison of the coeflBcients obtained in the sub-
samples sho^Ti in table 18 justifies this view, for in the several series
available for adult males the coefficients are sometimes positive and
sometimes negative in sign.
If we turn from the relationship between stature and pulse-rate
to that between stature and total heat-production given in table 32,
Chapter lY, we note that the correlation for the total males is -f 0.6149
±0.0360, while for the total females it is -F0.2318 ±0.0629. The first
of these two constants is 17.1 while the second is 3.7 times as large as
its probable error. Thus there can be no question whatever concerning
the statistical significance of the de\'iation of these correlation coeffici-
ents from the zero which would be the average value if there were no
correlation between stature and total heat-production. We may con-
clude, therefore, that as far as the relationship between stature and
total heat-production is concerned the series of determinations available
furnish a fair basis for generalization concerning the nimaerical rela-
tionship between stature and total heat-production in men and women
at large.
This discussion of the probable error has been of the most general
nature, but it may be sufficient to dispel the confusion which seems to
exist in the minds of some between technical errors of measurement and
the probable errors of random sampling of statistical constants, and to
enable the reader unaccustomed to statistical reasoning to follow argu-
ments based on probable errors in the following pages.
Finally a few words concerning the actual routuie of calculation
are in order. The formulas for the determination of r used in explaining
this coefficient above are not the most useful for practical work. In
the calculation of the standard de\'iation it is quite unnecessary to ob-
tain the actual de\'iation in each case. If the de^'iations are not wanted
for other purposes the standard deA^iation is easily obtained from^
<r^ = Vx(x^)/N-li:{x)/N]^ = Vzix'-)/N-x^
» Harris. Am. Nat., 1910, 44, p. 693.
22 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
where 2(x) and X{x^) denote the sums of the individual measurements
and their squares.
Furthermore we may write
_i:{xy)/N-xy
r„. =
<r,(r.
where S(x?/) denotes the sum of the product of the two measures under
consideration, the bars denote their means, and the sigmas their
standard deviations.
This method is particularly suited for physiological work. The
worker has merely to sum the products of the two measures under
consideration for all the individuals dealt with, divide by the number
of individuals, subtract the product of the means of the two variables
from this mean product, and divide the remainder by the product of
the two sigmas. The standard deviations are easily obtained by sum-
ming the squares of the actual measurements, dividing by the number
of individuals, subtracting the square of the mean of the character,
and determining the square root of the remainder.
Table 3. — Calculation of moments of body-weight and daily heat-production.
Subjects.
Body-
weight
in kilos.
Body-
weight
squared.
Total
heat-
pro-
duction.
Heat-
production
squared.
Product,
weight
times total
heat.
W.A. S
C.J.D
M.Y. B
R. D. S
H. R. W
56.3
56.7
63.5
63.5
73.9
3169.69
3214.89
4032.25
4032.25
5461.21
5069.44
5476.00
4356.00
3893.76
11859.21
6756.84
6740.41
6225.21
6241.00
7832.25
5476.00
1562
1524
1677
1619
1842
1810
1908
1695
1816
2559
1978
2034
2126
1944
2017
1914
2439844
2322576
2812329
2621161
3392964
3276100
3640464
2873025
3297856
6548481
3912484
4137156
4519876
3779136
4068289
3663396
87940.6
86410.8
106489.5
102806.5
136123.8
128872.0
141192.0
111870.0
113318.4
278675.1
162591.6
166991.4
167741.4
153576.0
178504.5
141636.0
P.D.F
C.D.R
M. A. M
71.2
74.0
66.0
W. F. M
62.4
H. W
108.9
J.H.R
D.H.W
E.G
82.2
82.1
78.9
M.H.K
W. S
79.0
88.5
F.G. R
74.0
Sum (2)
. 1181.1
89836.41
30025
57305137
2264739.6
This method gives constants with the maximum degree of exact-
ness. It has the special advantage for physiological work that, after
the fundamental summations have been made for a first series of experi-
ments, subsequent determinations may be added and the correlation
on the basis of a larger N determined merely by the addition of the
summations of first and second powers and products for the new series.
Or, if one suspects that a single aberrant individual, or group of indi-
viduals, has too much weight in determining a given coefficient, the
METHODS OF STATISTICAL ANALYSIS. 23
first and second powers and the products for the specific individual, or
the sum of these values for the group of individuals, may be subtracted
from the original value of 2(x), SCx^), 2(2/), X{y^) and X{xy) and the
means, standard de^'iations, and correlation be redetermined on the
basis of the reduced A"".
This has been the method followed in the calculations of the present
study. We have used the original measm-ements as published in the
fundamental tables, pp. 38-47, without modification or grouping. This
has necessitated rather hea\y arithmetical work, since the squares
and products have been veiy^ large. The course has, however, the merit
of introducing no error not already inherent in the data.
As an illustration of method we again take the constants for body-
weight and dailj' heat-production in our smallest series, the 16 athletes.
The values required are given in table 3. These give
X{w) =1181.1
2(m;0
= 89836.41 iV = 16
i:(w)/N = w= 73.8188
= Vx{w^)/N-w^ = 12.8670
2(^1) =30025
2(/i^)
= 57305137
^ = 1876.5625
<rk
= 245.1209
i:iwh) =2264739.6
X(wh)/N
= 141546.225
and finally
141546.225
- (73.8188 X 1876.5625) _q ^.-^
12.8670X245.1209
1-r' =0.0828 ^,=0.0140
That in presenting our results we have retained more figures than
are really significant for phj'siological work is quite as clear to om^elves
as to anyone who may desire to lop ofif the constants. But we have
borne continually in mind the fact that these constants may in many
instances be required for further calculation. It has seemed desirable,
therefore, to retain a number of places sufficiently large to enable
those who care to do so to check particular phases of our work without
going back to the raw data.
Chapter III.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
In the first of the three sections into which this chapter is divided
we list up and briefly discuss the measurements (both physical and
physiological) considered in these pages.
In the second section we catalogue the series of individuals with the
results of the measiu'ements which have been made upon them. These
are the data upon which our constants are based.
In the third section we apply certain criteria adapted to determining
the suitability for the purposes of the present study of the individuals
upon whom measurements have been made.
1. MEASUREMENTS CONSIDERED.
The following are the measurements which have been considered.
The symbol in parenthesis is the one used to designate the measurement
in the statistical formulas. A brief explanation of the method employed
in making the determination is given later.
Stature («), or height, in centimeters.
Bodj'-weight (w), in kilograms.
Bodj'-sxirface, or area, in square meters, as estimated by Lissauer formula (at).
Body-surface, in square meters, as estimated by Meeh formula (ojf).
Body-surface, in square meters, as estimated by Du Bois height-weight chart (flj)).
Pulse-rate (p), in beats per minute.
Carbon-dioxide output (c). Total in cubic centimeters per minute.
Oxj-gen consumption (o). Total in cubic centimeters per minute.
Carbon-dioxide production, in cubic centimeters per minute, per kilogram of body-
weight (Ck).
Oxj-gen consumption, in cubic centimeters per minute, per kilogram of body-wei^t
(Ofc).
Body-temperature (0.
Heat-production {h). Total heat-production (indirect calorimetry) per 24 hours in
calories.
Heat-production per 24 hours per kilogram of body-weight (hk).
Heat-production per 24 hours per square meter of body-surface according to Lissauer
formula (Ax,).
Heat-production per 24 hours per square meter of body-surface estimated by Meeh
formula (Ajf).
Heat-production per 24 hours per square meter of body-s\irface estimated by Du Bois
height-weight chart {ho).
The folloTsing are the details which seem essential to an understand-
ing of the measurements utilized.
Stature. — Stature, without shoes, was measiued in adults by means
of a graduated vertical rod with an adjustable horizontal bar which
was lowered to the top of the head.
25
26 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In infants the length must be taken as comparable with the stature
of the adult. In discussing the data for infants we shall, therefore,
refer to the relationship between stature and other characters rather
than to that between length and other characteristics. This is done to
maintain uniformity in the statistical symbols.
In measuring infants the vertical rod was of course replaced by a
fixed and a movable vertical on a horizontal scale.
Body-weight. — Body-weight, in kilograms, was always taken with-
out clothing. While weight of clothing may be a negligible factor in
life-insurance examinations, or even in anthropometric investigations,
it can not be disregarded in careful physiological work. Experience
at the Nutrition Laboratory has shown that weight of clothing will
amount to about 4.0 kilograms for men and 2.5 kilograms for women.
Body-surface. — In conformity with the custom of physiologists,
heat-production has for certain purposes been expressed in calories per
square meter of body-surface per 24 hours.
The measurement of body-surface presents very great difficulties.
If the superficial area of our subjects had been measured directly a
series of determinations one-tenth as large as that here considered
could probably not have been secured. The whole question of body-
surface in relation to heat-production will be discussed in detail in
Chapter VI. For the moment it is necessary to note merely that for
infants surface was estimated by the Lissauer ^ formula
where a = area in square centimeters and ly-weight in kilograms.
When the original Nutrition Laboratory series was published ^ the
Meeh formula ^
a = 12.312-C/if;^
for adults was generally accepted. The results of later studies have
also been expressed by this formula and in addition estimated by the
Du Bois height-weight chart, ^ which is based on the linear body-surface
formula of D. and E. F. Du Bois.^
This covers sufficiently the physical measurements.
The body temperature of our own subjects has not been consid-
ered. In discussing the literature we have, sometimes, referred to
temperature, designated in our formulas by t. In such cases the reader
must consult the paper cited for details as to measurement.
The physiological determinations can best be explained by a single
general description of the apparatus and method of experimentation.
* Lissauer, Jahrb. f. Kinderheilk. 1902, N. F., 58, p. 392.
* Benedict, Emmes, Roth, and Smith. Journ. Biol. Chem., 1914, 18, p. 139.
» Meeh, Zeitschr. f. Biol., 1879,, 15, p. 425.
* Du Boia and Du Bois, Arch. Intern. Med., 1916, 17, p. 863.
» Du Boia and Du Bois, Arch. Intern. Med., 1915, 15, p. 868.
INDI^qDUALS AND MEASUREMENTS CONSIDERED. 27
Before proceeding to technical details a few words on the general
principles involved may be useful to the reader who approaches this
subject for the first time.
The calorie is the unit of measurement of energy transformation.
Theoretically the measurement of heat-production by the calorimeter
is the only correct method of measuring the amount of the katabolism.
Practically the technical difficulties of the actual measurement of the
quantity of heat produced by a U\'ing organism are so great that for
many purposes direct may be replaced by indirect calorimetry — that is,
by the calculation of heat-production from the amount of the respira-
tory exchange and the ratio of the volume of carbon dioxide exhaled
to the volume of oxygen absorbed.
The apphcation of this method depends upon the fact that the heat
set free in the combustion of a given substance may be determined
with precision in the laboratory. Thus to make possible the calculation
of the total heat-production from the measurements of the two gases
in the respiration chamber, or when possible from measures of the two
gases and of nitrogen excretion, it is necessary to ascertain only the
calorific values of unit volumes of oxygen and carbon dioxide for the
combustion of the substances which are oxidized in the human body.
The consideration of the COj/Oa ratio, or the respiratory quotient as
it is commonly designated, as well as the actual volumes of the two
gases, is necessary because of the fact that the calorific value of either
of these gases is determined by the nature of the substances oxidized.
Thus a Hter of CO2 derived from the combustion of carbohydrates
(starch) corresponds to 5.043 calories,^ a Hter of CO2 derived from fat
corresponds to 6.680 calories, and a liter of CO2 derived from protein
has an equivalent of 5.690 calories. The calorific equivalents for a
hter of oxygen are 5.043 calories for carbohydrates, 4.755 calories for
fat, and 4.600 calories for protein.
Thus the ratio of the carbon dioxide set free to the oxygen used in
the combustion of carbohydrates, fats, and protein is, within limits,
constant and specific. For the combustion of all carbohydrates, the
CO2/O2 ratio must be unity. Since the composition of the several fats
and proteins varies, the CO2/O2 ratio must also vary slightly.
There are other difficulties to be considered in the indirect deter-
mination of heat-production. The synthesis of fats from carbohydrates
greatly disturbs the CO2/O2 ratio.
The use of indirect calorimetry for work in man has, however, been
fully justified by the experimentation of Atwater and his associates ^
and shown to be applicable to short periods by Gephart and Du Bois.*
• Benedict and Tompldna, Boston Med. and Surg. Joum., 1916, 174, p. 858; average values
obtained from table 1.
» Atwater and Benedict, U. S. Dept. Agr., Office Expt. Sta., 1899, Bui. 69; 1902, Bui. 109;
1903, Bui. 136. Benedict and Milner, U. S. Dept. Agr., Office Expt. Sta., 1907, Bui. 175.
' Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 850 and p. 854.
28 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
At the present time it is generally admitted by students of metab-
olism that for the short observation periods, which are essential for
the measurement of the individual in a state of complete muscular
repose and in the post-absorptive condition, the errors of computation
of heat-production by the indirect method are actually less than those
of direct measurement in the calorimeter.®
We have expressed total heat-production in calories per 24 hours.
This has seemed to us the most desirable unit for a universal standard.
In employing this unit of time there has been no attempt to obscure
the fact that the actual measurements covered shorter periods. In
practically all cases, however, the 24-hour constant is based upon
a number of periods.
Since in indirect calorimetry the thing actually measured is the
gaseous exchange, we have worked out and discussed the chief statis-
tical constants for the measures of gas volume as well as for the total
heat-production indirectly derived from them. Anyone who may be
inclined to discredit the results as expressed in calories computed by
the formulas of indirect calorimetry may see our chief conclusions
established by the constants based on the directly measured gaseous
exchange.
In passing, it is worth while to note that the high degree of con-
sistency in our oxygen and carbon-dioxide measurements affords strong
evidence for the trustworthiness of our constants.
The coefficients of correlations between oxygen consumption and
carbon-dioxide excretion in the adults ^"^ are given in table 4.
Table 4. — Correlation between two measures of gaseotis exchange.
Series.
Men.
Original series :
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series . .
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
N
16
62
88
71
28
116
19
64
135
66
35
101
Correlation
between COt
and Oi, r^„
0.9799
0.8962
0.9488
0.9350
0.9507
0.9432
0.8738
0.9333
0.9335
0.0069
0.0169
0.0072
0.0101
±0.0123
±0.0069
±0.0366
±0.0109
±0.0075
0.8794±0.0188
0.9662 ±0.0076
0.8917±0.0137
E.
142.0
53.0
131.8
92.6
77.3
136.7
23.9
85.6
124.5
46.8
127.1
65.1
• A review of the problem of direct and indirect calorimetry is given by Krogh, The Respira-
tory Exchange of Animals and Man. Longmans, Green and Co., London, 1916, p. 9.
" Because of the technique in the measurement of oxygen consumption and carbon-dioxide
production necessarily adopted in the case of infants, we have not been able to include
the correlations for these series.
INDI^IDU.^LS AND MEASUREMENTS CONSIDERED. 29
All of the constants are of a very high order indeed. In the original
published series r =0.949 =±=0.007, while in the Gephart and Du Bois
selection r = 0.935 =±=0.010. The first two series of men {N = 116) gives
r =0.943 =«= 0.007, while the whole series (A^ = 135) gives r = 0.934 =fc 0.008.
The first and second series of women differ a Uttle more in the correla-
tions. In the first r = 0.879 =»=0.019, whereas in the second the result is
r = 0.966 ±0.008, a difference of 0.087 =±=0.021.
The high correlations justify great confidence in the technical
phases of the work. Had there been large errors in the measurement
of either oxygen consumption or carbon-dioxide production, correla-
tions of the order here tabled could hardly have been secured.
The basal metabolism of all our subjects was measured by well-
known methods.
A few determinations were made by the Tissot method" with all
of the niceties of manipulation that have been worked out by Dr. T. M.
Carpenter, of the Nutrition Laboratory stsifif.^^ The larger number of
measurements in the original Nutrition Laboratory series were made
with a universal respiration apparatus devised at the Nutrition Lab-
oratory and designated as the unit apparatus. The earUer and more
modem forms of this apparatus^^ differ somewhat in the pro\Tsion made
for expansion in the closed air-circuit. Certain of the results obtained
with the bed calorimeter^* are quite comparable with those due to the
use of the universal respiration apparatus and are included in the
original Nutrition Laboratory series.
Finally, a number were made with the clinical respiration apparatus
at the New England Deaconess Hospital, under the skillful technique
of Miss M. A. Corson, of the Laboratory staff. ^^
An elaborate series of comparisons, in which all of these various
methods have been critically tested, shows that the basal metaboHsm
determined by any one is comparable with that determined by any
other.'^
The heat-productions determined directly in the bed calorimeter
are omitted, and are replaced by those indirectly computed from the
gaseous exchange and the respiratory quotient. Thus all the values
of total heat-production are due to indirect calorimetrj^ and are exactly
comparable among themselves.
All of the apparatus employed at the Nutrition Laboratory was
made and tested there. That used at Battle Creek was built on the
ground, but was subsequently tested and approved by Roth and one
" Tissot, Joum. de physiol. et de pathol. gen., 1904, 6, p. 6S8.
" Carpenter, Carnegie Inst. Wash. Pub. No. 216, 1915. p. 61.
** For the original description see Benedict, Am. Joum. Physiol., 1909, 24, p. 345. The more
modem form is described in Deutsch. Archiv. f. klin. Med., 1912, 107, p. 156.
'* Benedict and Carpenter. Carnegie Inst. Wash. Pub. No. 123, 1910, p. 45.
" The description of this apparatus is given in detail by Benedict and Tompkins, Boston Med.
and Surg. Joum., 1916, 174, pp. 857, 898, 939.
" Carpenter, Carnegie Inst. Wash. Pub. No. 216, 1915.
30 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
of US. All of the operators acquired their technique personally in the
Nutrition Laboratory. The data are, therefore, due not merely to
uniform method and apparatus but to comparable manipulation
throughout.
The routine involved the appearance of the subjects at the Labora-
tory at about 8 a. m., in the post-absorptive condition, i.e., about 12
hours after taking their last food. They then lay down upon a couch
or bed and remained perfectly quiet, usually half an hour prior to the
first period. Absence of muscular activity during the experimental
periods was assured by the bed being provided with a graphic registering
device which indicated the slightest alteration in the change of position
of the center of gravity of the body, or by the attachment of a chest
or thigh pneumograph which registered slight muscular movement.
Experiments were usually made in several periods of 15 minutes,
with interims of 15 to 20 minutes. To secure the most representative
value possible, experiments were usually made two, and frequently
many more, days with the same subject.
The pulse was nearly always taken, and usually the oral tempera-
ture. Subjects with febrile temperature were rejected.
In selecting the periods of observation to be used, those in which
there was an absence of muscular activity were chosen. This was
assured by having the individual under observation lie on a bed, one
side of which rested on a knife edge while the other was supported by
a spiral spring. A change in the level of the bed altered the tension
of a pneumograph connected with a tambour and kymograph. The
smallest motion of any kind, even a movement so slight as to be
imperceptible to the observant trained nurse, disturbed the linearity
of the kymograph record. Thus periods of perfect muscular repose
could be selected on the basis of an instrumental record alone, without
the possibility of the personal equation of the observer playing any part.
In the respiration calorimeter, in which each experiment lasted at
least 1}/^ hours, such complete muscular repose could not be obtained
as in the shorter periods with the universal respiration apparatus. But
here the subjects fully imderstood the necessity for quiet, and while
the kymograph records naturally show somewhat greater irregularity
in the long than in the selected short periods, the subjects were remark-
ably quiet and the irregularities in the tracings are so slight as to indi-
cate negligible muscular activity.
The computation of heat-production is usually based upon the
oxygen consumption, making allowances for the slight changes in the
calorific equivalent of oxygen with varying respiratory quotients. The
calorific value of oxygen is much more nearly constant, irrespective of
the character of the katabolism, than is that of carbon dioxide, and
hence in practically all of the cases we have used the oxygen consump-
tion. In a few instances where the oxygen determinations were faulty,
INDIVIDUALS AND MEASUREMENTS CONSIDERED. 31
we have used the carbon-dioxide production. When either the oxygen
or the carbon-dioxide determination was missing, we have assumed,
when no better evidence is available, a conmaon respiratory quotient
of 0.85. In certain cases we have used quotients determined on the
day antecedent to or the day subsequent to the period on which a
constant is based. Usually the quotient of 0.85 is used.
As in these short experiments it was frequently difficult to secure
accurate collection of lu-ine, we have not attempted to compute the
calories from protein nor the non-protein respiratory quotient, but
have taken the calorific equivalent of oxygen as used by Zuntz and
Schumburg,^'^ making no special correction for the influence of the
protein metabolism upon the respiratory quotient and the calorific
equivalent of carbon dioxide and oxj'gen. In short experiments, par-
ticularly with uncertainty as to the nitrogen excretion in the urine, this
procedure is recommended by Loewy^* as giving results practically
within 1 per cent of the true value.
2. DATA ANALYZED.
The data analyzed in this volume were gathered in the course of
the various investigations which have been carried out at the Nutrition
Laboratory, or by those collaborating -vv-ith this Laboratory, during the
past several years. Two series have been pubhshed. The data are
given in full in this pubhcation and are therefore available to anj'one
who cares to go over the analytical phases of the present treatment.
The materials are the following :
A. A series of 51 male and 43 female infants investigated by Benedict
and Talbot.*' This series was chosen rather than the first series
published by Benedict and Talbot'" because, in the opinion of these
workers, the second series represents a far more homogeneous series
of materials. This will be designated as the infant series.
B. A series of measurements on 89 men and 68 women made at various
times at the Nutrition Laboratory and elsewhere by cooperating
investigators, and published-* as a basis for a comparison of basal
metabolism in men and women, athletic and non-athletic indi-
viduals, vegetarians and non-vegetarians, and so forth. This will be
designated as the original adult series to distinguish it from two sup-
plementary series of measurements of adults hitherto unpublished.
C. Determinations of basal metabolism in 28 men and 1 woman carried
out subsequently to the series described immediately above. These
data will be designated as the First Supplementary Series. (The
woman has been included with the second supplementary series.)
D. The Second Supplementary Series. This comprises 19 men and 34
women.
" Zuntz and Schumbiirg, Physiologie des Marsches, Berlin, 1901, p. 361.
'* Loewj', Oppenheimer's Handbuch der Biochemie, Jena, 1911, 4, (1), p. 281.
" Benedict and Talbot, Carnegie Inst. Wash. Pub. No. 233, 1915.
'^ Benedict and Talbot, Carnegie Inst. Wash. Pub. No. 201, 1914.
" Benedict, Emmes, Roth, and Smith, Joum. Biol. Chem., 1914, 18, p. 139.
32 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
These four series are the sources of the constants pubHshed in this
volume. From the figures given in the protocols in which these data
are brought together (pages 38 to 47) the reader who desires to do
so may verify the calculation of any of our constants. The exact
statement of the several measurements of each individual subject will
not have its primary value in the possibiUty of the verification
of the arithmetic of the present work, but in enabhng the physiologist
to criticize freely our fundamental observations or groupings of
observations.
These series form units of data upon which constants have been
based. It may seem to the reader that physiologically more satisfac-
tory results might be secured by sorting the entire number of individ-
uals in these several series into more homogeneous groups as determined
by some special structural or physiological character, for example,
according to age, stature, body-weight, body-surface, or pulse-rate.
For the sake of argument, at least, this must be admitted. Such
divisions will be made in the latter part of this volume. With regard
to the question of division of materials the following considerations
must be borne in mind.
In segregating the data for purposes of analysis, two factors must
be taken into account. The more finely the materials are sub-divided
the more uniform will the groups of observations be, provided, of
course, that the divisions are logically made. On the other hand, the
smaller the groups are made the larger will be the probable errors of
random sampling attaching to the final constants, for these probable
errors are inversely proportional to the square roots of the numbers
of observations upon which they are based.
The method of dividing the materials has been determined by
both physiological considerations and by the practical exigencies of
the work.
When the application of biometric formulas to the problem of basal
metabolism in man was taken up, the only series of data available were
the original series of adults and the infant series. These were classified
according to sex in both series.
The women of the original adult series have not been further sub-
divided for purposes of general calculation. The men, however, are
both more numerous than the women and apparently more hetero-
geneous in physiological characteristics. A number are athletes and a
number are vegetarians.
After the work which has been done on the metabohsm of athletes^^
it would seem unjustifiable to merely lump together athletes, non-
athletes, vegetarians and non-vegetarians and all other individuals of
the same sex without determining what results are to be secured when
they are treated independently. We have, therefore, segregated a
" Benedict and Smith, Journ. Biol. Chem., 1916, 20, p. 243. See also page 244 of this volume.
INDIVIDUALS AND ^MEASUREMENTS CONSIDERED. 33
group of 16 athletes and computed all the constants upon which we
have based our arguments for the mdi\'iduals of this group alone.
The smallness of the nimaber of indiWduals available necessarily
results in relatively high probable errors. The same course was also
followed for the male vegetarians, but the number of these was so
small that many purely statistical difficulties arose, and since the
metabolism of vegetarians has not been shown to differ significantly
from that of men at large,^^ we have omitted the discussion of this
group.
After the segregation of these two groups, the athletes and the
vegetarians, there remain 62 other individuals, which have been used
as the basis of another series of correlations. These are designated as
the "men of the original series other than athletes and vegetarians,"
or for convenience merely as the ''other men."
The constants are also computed for the whole series of 89 men of
the original series.
When the first supplementary series became available it was treated
as a whole in the case of men and also combined with the total men of
the first series.
The same course was followed when, before the completion of the
long routine involved in the calculations, the second supplementary
series fortunately came to hand.
To avoid all possible objections which might arise from the fact
that the indi\iduals included were selected and the groups limited by
one or the other of the authors of this report, we have felt it desirable
to work out the constants on the basis of materials grouped for purposes
quite different from the present ones by some other investigator.
IMost fortunately this has been done by such experienced workers
as Gephart and Du Bois^* who have combined their own 7 metabolism
determinations for men with 72 of the 89 published by Benedict,
Emmes, Roth, and Smith, for the purpose of obtaining an average
metaboHsm constant.
From the 89 men of our original adult series, Gephart and Du
Bois have seen fit to discard 17. While we shall discuss the validity of
their reasons for this course, we are heartily glad to have at our dis-
posal, for comparison ^-ith the groupings of subjects arranged or
limited by ourselves, those which have been approved by others whose
training and personal experience in the clinic justifies them in passing
judgment upon such matters. The elimination has been made by
Gephart and Du Bois in the following manner :
"All those over 50 years of age were arbitrarily excluded and also those
under 20 years of age."
^ Benedict and Roth. Joiim. Biol. Chem., 1915, 20, p. 231. See also page 245 of this volume.
'* Gephart and Du Bois, Arch. Intern. Med., 1915, IS, p. 858.
34 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
By this ruling the following individuals,^^ 10 in all, were withdrawn
from the series:
(87) F. P. (73) L. D. A.
(81) V. G. (77) W. W. C.
(22) E. J. W. (67) F. M. M.
(31) H. F. (3) M. H. K.
(79) C. H. H. (7) H. W.
"In order to rule out those who were distinctly over or under weight, the
subjects were all plotted in a curve, the height forming the abscissae and the
weight the ordinates. All but 9 of the subjects could be grouped between two
lines not very far apart. Of the 9, W. S., O. F. M., Prof. C, H. F., F. E. M.,
and F. A. R. were evidently much heavier in proportion to their height.
" Two of the 9, R. A. C.^ and B. N. C, were evidently very light in pro-
portion to their height. E. P. C. came just outside the hne, but so close
that he has not been excluded from the averages."
This gives "a fairly homogeneous total" of 79 individuals "where
average metabolism was 34.7 calories per square meter per hour, or
exactly the same as that of the original 89 before the addition of 7 and
the exclusion of 17."
Note that (31) H. F. is excluded on the basis of both age and ratio
of weight to height.
Thus the individuals omitted from the Nutrition Laboratory series
are 17 in number as follows:
(2) W. S. (75) R. A. C. (or R. I. C?) (73) L. D. A.
(28) O. F. M. (25) B. N. C. (77) W, W. C.
(30) Prof. C. (87) F. P. (67) F. M. M.
(31) H. F. (81) V. G. (3) M. H. K.
(17) F. E. M. (22) E. J. W. (7) H. W.
(36) F. A. R. (79) C. H. H.
This series we have designated as the Gephart and DuBois selection.
Thus Gephart and Du Bois have settled for us the question of the
specific men of the original 89 studied at the Nutrition Laboratory to
be included in the determination of a set of statistical constants; but
diflBculties arose when the first and second supplementary series of
men became available for analysis and we attempted to apply the same
criteria to them in order to obtain a larger number of subjects chosen
according to approved clinical standards.
The elimination of indi\^duals on the basis of age presented no
obstacle. Of course the distinction between a man of 20 and another
of 19 is a purely arbitrary one, but such arbitrary distinctions have
to be made, and in selecting according to standards established by
others one merely has to follow the rules which have been laid down.
For the elimination of subjects on the basis of height and weight
the case is quite different. Here too the diidsion is necessarily an arbi-
trary one, but Gephart and Du Bois have given no definite criteria by
^ The niimbers in parentheses and the initials refer to the fundamental table of data on
pages 38 to 47.
^ Evidently a misprint for R. I. C. of Benedict, Emmes, Roth, and Smith.
INDIVIDUALS AND MEASUREMENTS CONSIDERED. 35
which the individuals who are to be discarded may be distinguished
from those who are to be retained in the series. They have said merely
that "all but 9 of the subjects could be grouped between two lines not
very far apart."
Had not the authors designated by initials the men to be excluded
in this specific series of determinations it would have been impossible
for another writer to decide, without actual statistical criteria, which
should be thrown out. It is, therefore, quite out of the question to
di\'ide any other series in a comparable manner without determining
(a) what shall be the slope of the lines which cut off the outlying mem-
bers of a series on the basis of height and weight, and (6) what the
amount of separation of these lines shall be, i.e., what body-weights may
be allowed in any group of indi\iduals of the same height, or vice versa.
The selection of a criterion by which indi\iduals are to be discarded
from a series ^'^ is so important a matter (if those in presumably good
health are to be discarded from control series on the basis of phj-sical
configuration at all) that it seems worth while to go into the matter
in some detail. The indi\'iduals to be segregated are distributed in a
scatter diagram or a "correlation surface," according to the measure
of heights and weights. From this surface it is desired to cut off certain
areas, representing indi^•iduals of aberrant ratios of weight to height.
Any line of di\-ision should take into account the general averages
for both stature and body-weight. We shall, therefore, select as a
standard a line which will pass through the intersection of these two
means. This establishes one position of the line. The slope must be
ascertained. This is determined by the correlation between the two
variables. Thus the equation required is given by
or, taking the constants for the original 89 men from tables in this and
the following chapter, s = 172.449, a, = 7.8032, i^ = 64.334, a^ = 10.7302,
r„ =0.5320, and we have numerically,
tr = -61.818-1-0.732 s
This is the axis of the swarm of observ ations represented by the line
A— A in diagram 1.
In this diagram we have drawn the lines, D —D, cutting off the indi-
viduals discarded by Gephart and Du Bois as exactly as we have been
able to do from their description of their method, but in a manner to
give them the benefit of ever>' doubt concerning the position and
slope of the lines. These lines do not run parallel to the best-fitting
axis, ^ — .4, of the swarm of measiu^ments distributed with regard to
^ Obviously if subjects are to be ruled out of the class of "noirasds " available for oae aa
control subjects in comparison with pathological cases, it would be better to have them diaearded
OD the basis of logical criteria before rather than after the expenditure of time and labor ;
to the determination of their basal metabolion.
36
A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
both weight and stature. We must, therefore, conclude that the
criteria for the discarding of the individuals omitted can not be
regarded as well chosen.
Thus, while we have retained the selection made by Gephart and
Du Bois, we have done so merely because we have desired to work in
one instance with a series of individuals chosen by other workers, not
because we personally feel that there is any advantage in discarding
the individuals removed by them.
STATURE IN CENTIMETERS
Diagram 1. — Distribution of stature and weight in original series of men. Individuals
outside of the lines D-D were excluded by Gephart and Du Bois on the ground of
aberrant proportions. Logically the lines cutting off aberrant individuals, D-D,
should parallel the axis of the swarm of observations, A-A.
The course followed seems to us to ob\'iate practically every source
of criticism. If statistical constants be calculated from the smaller
groups of observations, there can be no objection to combining these
into larger groups in order to ascertain how their constants compare
with those based upon the original segregations. If, however, the
constants be determined from the massed materials only, there is
always the justification for criticism based on the lumping of quite
INDIVIDUALS AND MEASUREMENTS CONSIDERED. 37
unlike data. The determination of constants on the basis of groups of
individuals just as they became available has the advantage that the
selection of groups can not be influenced by the personal equation of
the statistician.
Later in this volume we shall make some further classification of
the data.
Since the data have been treated in individual groups as collected,
in special groups arranged by both ourselves and others, and in com-
bined series, there can be no criticism whatever as to selection of data.
The constants for the data arranged in a number of different ways have
been presented and discussed in as nearly as possible an unbiased
manner. The full original data are laid on the table for anyone who
cares to arrange them differently, to go back of our constants, or to
carry the analysis farther than we have done.
The fundamental measurements upon which all the statistical
constants in this volume are based appear in tables A to D.
Tables A and B for male and female infants require no comment.
Table D for women requires merely the note that Nos. 1 to 68 represent
the original series, No. 69 the only woman included in the first supple-
mentary series, and numbers 70 to 103 the individuals of the second
supplementary series. In all calculations indi\'idual 69 has been treated
with the second supplementary series, and to avoid confusion in dis-
cussion both have been consistently referred to as the supplementary
series.
The table for men, C, is somewhat more compUcated. Nos. 1 to 16
are the athletes, Nos. 17 to 27 the vegetarians, while Nos. 28 to 89 are
the "other males," that is the non-athletic and non-vegetarian men of
the original Nutrition Laboratory series. From this original series of
89 men Gephart and Du Bois have made a selection of 72 upon which
they have based certain calculations. The key numbers and initials
of the 17 which they have discarded are given on page 34. Nos. 90
to 117 represent the first supplementary series and Nos. 118 to 136 the
second supplementary series.
After the calculations for this volume were completed, it was dis-
covered that through a change in the key letters used to designate the
subjects, T. H. Y. and T. J. (Nos. 20 and 129) are the same individual.
Since the measurements were made at 23 and 27 years respectively,
and since body-weight and bodj^-surface-area differ slightly at these
two periods, he has been treated as a different individual in the two
series. The ages as originally submitted were 22 and 28 years. The
actual date of birth (available since the calculations were completed)
gives 23 and 27 years, as more nearly the ages at the time the observa-
tions were made. The constants have been allowed to stand as com-
puted from the values given in the table, since the change could hardly
have made a sensible difference in the end results.
38 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Table A. — Fundamental data for male infants.
No.
Age.
Obser-
vations.
Body-
weight
in
kilo-
grams.
Height
in
centi-
meters.
Body-
surface
in
square
meters,
Lissauer.
Pulse-
rate.
Heat-production per
24 hours.
Days.
Peri-
ods.
Total
calories.
Calories
per
kilo-
gram.
Calories
per
square
meter.
3
2^ days
2
2
3.63
52
0.243
97
166
46
685
5
7hrs.
1
1
3.82
52.5
0.252
112
137
36
544
6
3? days
2
3
4.32
52
0.273
116
191
44
697
8
2 days
2
3
3.48
51
0.236
117
160
45
673
10
2 days
2
3
3.45
52
0.235
116
162
48
694
15
4 days
3
3
3.64
50
0.243
122
162
44
665
18
7 days
1
2
2.84
50.5
0.207
105
108
38
519
19
IJ days
2
3
3.50
53
0.237
114
155
44
653
25
4 days
2
3
3.32
51.5
0.229
123
158
47
686
27
4 days
2
2
3.58
52
0.240
111
169
48
703
30
2 days
3
4
3.33
51
0.230
114
144
43
623
31
4 days
1
2
3.56
53.5
0.239
117
158
45
682
32
2^ days
2
3
3.42
47.5
0.234
116
140
41
604
33
6 days
2
2
3.73
52
0.248
129
153
41
617
36
21 hrs.
1
1
3.33
53
0.230
129
154
46
670
46
5 hrs.
1
2
3.83
51.5
0.252
126
152
40
603
47
5 hrs.
1
2
3.51
52
0.237
107
143
41
601
51
2 days
2
2
3.73
52.5
0.248
96
154
42
623
53
2 days
1
2
2.87
47.5
0.209
126
143
50
684
54
1§ days
1
2
3.31
50
0.229
106
129
39
563
55
16 hrs.
1
2
3.45
50
0.235
124
151
44
641
56
4 days
3
4
3.19
51.5
0.224
121
150
47
669
67
22 hrs.
2
3
3.75
54
0.249
105
153
40
611
60
4^ days
1
2
3.60
52
0.241
117
149
42
617
61
2i hrs.
1
2
3.26
49.5
0.226
121
123
38
542
62
3 days
3
3
3.30
49.5
0.228
116
134
41
588
66
14 hrs.
1
2
3.19
51
0.224
103
122
38
543
67
3 days
2
3
4.74
54
0.291
122
193
41
669
68
4 days
2
3
2.12
46
0.170
113
103
48
604
69
19 hrs.
2
3
3.44
50
0.235
110
142
42
609
70
2 days
2
2
3.56
51
0.239
109
153
43
640
71
3 days
2
2
3.96
53.5
0.258
106
172
44
667
72
2i days
2
3.29
50.5
0.228
110
157
48
687
73
7 hrs.
2
3.63
50
0.243
106
164
45
673
74
2 days
2
3.63
52
0.243
94
156
43
640
75
1^ days
2
2.65
47.5
0.198
100
132
50
664
76
13 hrs.
2
3.16
50
0.222
101
137
44
618
78
12 hrs.
2
2.48
47
0.189
101
109
44
577
80
3 hrs.
1
3.47
51.5
0.236
109
128
37
542
82
3 hrs.
1
2.74
49
0.202
101
95
35
470
83
3 hrs.
2
3.73
52
0.248
131
148
40
597
85
9 hrs.
1
3.52
52
0.238
109
144
41
605
87
3J hrs.
2
3.94
51
0.257
118
146
37
567
89
8 hrs.
1
3.24
49.5
0.226
107
124
38
549
90
2^ days
3
3.00
50
0.214
86
138
46
641
93
4 hrs.
3
3.53
50.5
0.238
127
136
39
573
94
3Jhrs.
1
3.20
50
0.224
117
136
43
607
99
2h hrs.
1
3.58
51.5
0.240
103
122
34
508
100
6ihrs.
1
4.65
54
0.287
130
186
40
648
101
5^ hrs.
1
3.88
51.5
0.254
109
126
32
496
104
3 hrs.
1
3.32
51
0.229
107
105
32
459
INDmDUALS AND MEASUREMENTS CONSIDERED.
39
Table B. — Fundamental data for female infants.
No.
Age.
Obser-
vations.
°*y'- ods.
Body-
weight
in kilo-
grams.
Height
in
centi-
meters.
Body-
surface
in
' square
' meters,
Lissauer.
Pulse-
rate.
Heat-production per
24 hours.
i
Total
calories.
Calories
per
kilo-
gram.
Calories
per
square
meter.
2, 6^ days
2
2
3.80
53
; 0.251
99
1 152
40
606
4, 2 days
2
3
3.28
46.5
0.227
105
, 139
43
612
9| 2 days
1
2
4.04
51
0.262
109
i 178
44
677
12| 5 days
2
2
4.17
52.5
0.267
112
171
41
639
13; 2 days
3
4
3.25
50
0.226
113
138
43
612
16' 2\ days
4
4
4.03
53
0.261
113
175
44
670
17 15 hrs.
1
2
3.66
52.5
0.244
118
174
48
713
20 Z\ days
1
2
3.54
52
0.239
110
153
43
638
21| 2 days
1
2
2.92
50
0.211
121
136
47
645
22 2\ days
1
2
2.72
49
0.201
114
128
47
635
26 5 days
2
3
3.46
50
0.235
113
151
44
645
29 2\ days
3
4
3.37
50
0.232
112
150
45
652
34 2 days
1
2
2.90
50.5
0.210
115
134
47
638
35 4 days
3
4
4.33
M
0.274
109
175
41
640
37j 13 hrs.
1
2
2.49
46.5
0.189
119
99
40
522
38' 1^ days
1
2
3.90
51.5
0.255
127
156
40
610
39 9 hrs.
1
1
2.95
50
0.212
105
113
38
533
40, 4i days
2
3
2.78
49.5
0.204
111
134
48
655
42| 3 days
2
4
3.95
54
0.258
il3
176
45
684
431 2da>-s
1
1
3.62
50
0.242
119
165
46
682
44 2 hrs.
1
2
3.57
51
0.240
103
136
38
567
45 1 day
2
3
2.56
46.5
0.193
110
107
43
558
48 6 days
1
2
4.52
54.5
0.282
132
188
42
667
49 4 days
1
2
2.75
47.5
0.203
114
130
47
638
50 1 day
1
1
2.75
48.5
0.203
89?
142
52
700
52 2 i days
3
4
3.54
50
0.239
114
138
39
579
58 1 day
2
4
3.01
49
0.215
111
139
46
647
59 li days
2
2
360
52
0.241
112
150
42
621
63 3 days
1
2
2.37
47.5
0.183
125
109
46
596
64| 7 hrs.
1
2
3.37
48
0.232
98
128
38
552
65' 2 days
2
3
2.63
49
0.197
116
127
48
644
79 4 hrs.
1
2
4.14
52.5
0.266
116
153
37
575
81 4 hrs.
1
1
3.29
50
0.228
114
167
51
732
84 2ihrs.
1
2
4.11
54
0.264
109
133
32
504
86 6 hrs.
1
1
3.32
51
0.229
103
120
36
524
88 9 hrs.
1
2
2.62
47.5
0.196
96
122
47
623
91 ; 13 hrs.
1
1
3.33
49.5
0.230
113
140
42
609
92 4 hrs.
1
1
3.78
51
0.250
112
157
42
628
95i 5^ hrs.
1
1
2.84
46.5
0.207
123
100
35
483
96, 3i hrs.
1
1
3.23
51.5
0.225
99
113
35
502
97; 4i his.
1
2
2.82
48
0.206
113
112
40
542
98 5 hrs.
1
3
2.86
47.5
0.208
102
98
35
471
103 2i hrs.
1
1
3.29
49
0.228
125
130
40
570
40 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
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46 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
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INDIVIDUALS AND MEASUREMENTS CONSIDERED.
47
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48 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The name of the observer in the final column of tables C and D
fixes the laboratory at which the determinations were made. The
places for the several observers are:
Carpenter, Nutrition Laboratory. Means, Nutrition Laboratory.
Cathcart, Nutrition Laboratory. Riche, Nutrition Laboratory.
Miss Corson and Miss Johnson, New Eng- Roth, Battle Creek Sanitarium.
land Deaconess Hospital, Boston. Smith, Syracuse University.
Emmes, Nutrition Laboratory. Miss Tompkins, Nutrition Laboratory.
Higgins, Nutrition Laboratory.
3. CRITERIA OF SUITABILITY OF MATERIALS DEALT WITH.
In this volume we have limited ourselves to the discussion of the
metabolism of normal infants and of normal men and women.
It is important that the conception of normal as used in its present
connection be made perfectly clear at the outset.
First of all, it means individuals in presumably good health.
Second, it is important to remember that, as we have used the term,
the normal man is not an individual of any preconceived dimension,
but a group of infants, men, or women representing the typical condi-
tion in the population.
The population at large has a certain mean, variability, and corre-
lation of the measured parts of the human beings of which it is made up.
We may, therefore, properly inquire whether the subjects studied at
the Nutrition Laboratory agree reasonably well in correlation as well
as in mean and variability with men and women as they have been
studied by anthropologists. If they do agree in the physical characters
for which a basis of comparison may be secured, within the limits of the
probable errors of the determinations, we may feel confident that we
are deaUng with ''representative," ''typical," or "normal" men and
women. If they differ too widely from the population at large, our
data can not be considered altogether free from criticism.
In the following paragraphs we shall test the suitability of our
material for the solution of problems concerning the physiology of a
species, man, by ascertaining whether the sample of subjects dealt with
is really representative of man in general in mean, variability, and
correlation. In presenting our constants we are, of coiu-se, fully aware
that these problems have been so extensively investigated by anthro-
pologists and actuaries that no material contribution to the anthropo-
logical problems can be made on the basis of the number of individuals
examined in this paper — a number which, while large from the physio-
logical standpoint, is relatively small as compared with the more
satisfactory anthropological series.
In the field of metaboUsm this course seems to have a particular
justification. Practically the chief purpose of studies of the basal
metabolism of normal subjects is to obtain a basis of comparison on
which, in connection with studies in the experimental laboratory or
INDI\^DUALS AND MEASUREMENTS CONSIDERED.
49
medical ward, conclusions may be drawn concerning the influence of
special conditions, diets, or diseases upon metabolism. If results of
the kind are to be of general value they must be universally valid and
imiversally appUcable. To be generally valid and broadly appHcable
the fundamental series should be based on indi\'iduals typical, not
merely in average but in variability and correlation, of the population
as a whole, rather than composed of individuals confonning to some
personal preconception of ''normal."
First of all we may present the actual statistical constants of the
series of data which we have analyzed, and compare them with others
based on larger numbers of indiAiduals. Otherwise our own constants
will not be discussed in great detail here, but form the basis of most
of the calculations in the following chapters.
Table 5. — Physical constants of male and female new-born infants.
Series.
.V
Average.
Standard
deviation.
Coefficient
of variation-
Male.
Weight
51
51
51
51
51
43
43
43
43
43
94
94
94
94
94
3.459 ±0.0430
112.39 ±0.9524
144.55 ±1.974
0.2350 ±0.0020
50.971 ±0.1665
3.336 ±0.0564
111.77 ±0.8705
140.37 ±2.389
0.2294 ±0.0026
50.163 ±0.2265
3.403 ±0.0350
112.11 ±0.6525
142.64 ±1.537
0.2325 ±0.0016
50.601 ±0.1408
0.4554 ±0.03(>i
lO.OS ±0.6734
20.90 ±1.396
0.0209 ±0.0014
1.763 ±0.1178
0.54S3± 0.0399
8.46 ±0.6155
23.22 ±1.689
0.02oO± 0.0018
2.202 ±0.1601
0.5036 ±0.0247
9.38 ±0.4614
22.09 ±1.0S7
0.0230 ±0.0011
2.025 ±0.0996
13.17±0.89
8.97 ±0.60
14.46 ±0.99
8.88 ±0.59
3.46 ±0.23
15.44 ±1.23
7.57 ±0.55
16.54 ±1.24
10.89 ±0.80
4.39 ±0.32
14.S0±0.74
8.37 ±0.41
15.49 ±0.78
9.88 ±0.49
4.00 ±0.20
Pulse-rate ....
Total heat
Surface
Length
Female.
Weight
Pulse-rate
Total heat
Surface
Length
Both Sexes.
Weight
Pulse-rate
Total heat
Surface
Consider first the problem of the variation and correlation in stature
and weight in the series of subjects dealt with.
In doing this we shall lay emphasis upon variability as well as upon
average dimensions. This is done because in selecting a series of meas-
urements to be considered typical of the population at large it is quite
as important that they represent the diversity of the population as
that they show the proper average values.
The physical constants for our male and female infants are given
in table 5.
For body- weight we have the following series of infants for compari-
son with our own,
Quetelet's classic series, ^^ as reduced by Pearson, ^^ gives the follow-
^Quetelet, Anthropometrie, 1871, p. 355.
» Pearson, The Chances of Death, 1897, 1. p. 307.
50 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
ing means, standard deviations, S. D., and coefficients of variation, C. V.,
for new-born male (iV=63) and female (iV=56) Belgian babies:
Mean. S. D. C. V.
Male infants 3.289 ± 0.041 0.482 ± 0.029 14.66 =*= 0.90
Female infants 3.053 ±0.048 0.538 ±0.034 17.62 =fc 1.16
Reducing the data of the Anthropometric Committee's Report
to the British Association, ^° we find for 451 boy infants and 466 girl
infants :
Mean. S. D. C. V.
Male infants 3.230=fc0.016 0.508±0.011 15.73^0.36
Female infants 3.151 ±0.015 0.480 ±0.011 15.22 ±0.35
From Stuttgart babies, 500 of each sex, Pearson deduced from
Elsasser's measurements :
Mean. S. D. C. V.
Male infants 3.233±0.013 0.439±0.009 13.57±0.29
Female infants 3.161 ±0.013 0.418±0.009 13.28±0.29
For the 1000 male and 1000 female new-bom infants measured
in the Lambeth Lying-in Hospital (London) Pearson ^^ found :
Mean. S. D. C. V.
Male infants 3.312±0.011 0.519±0.008 15.664±0.242
Female infants 3.208 ±0.010 0.466 ±0.007 14.228 ±0.219
Dr. Rood Taylor ^^ has kindly allow^ed us to use his series of
measurements of new-born infants, deposited at the Wistar Institute.
These are very heterogeneous racially. We find for his 120 boys and
122 girls:
Mean. S. D. C. V.
Male infants 3.496±0.026 0.419±.018 11.99±0.53
Female infants 3.368±0.026 0.423±.018 12.57±0.55
A comparison of our constants with those due to anthropologists
is made in table 6. Here the signs of the differences show whether the
constants for our babies are larger (-f) or smaller (— ) than those
deduced by others.
Our infants show a slightly, but only slightly, greater average body-
weight than either of the European series available for comparison.
In 5 of the 8 comparisons the difference is less than 0.2 kilogram. In
general the differences may be regarded as statistically significant in
comparison with their probable errors. Our infants are slightly but
not significantly fighter than Dr. Rood Taylor's series.
In variability, as measured in the absolute terms of the standard
deviation and in the relative terms of the coefficient of variation, our
series show an excellent agreement with those which have been pub-
lished. In 7 of the 10 comparisons our standard deviations are slightly
greater, while in 3 of the 10 comparisons they are slightly less than
"> British Association Report, 1883, p. 286.
" Pearson, Proc. Roy. Soc. Lend., 1899, 66, p. 25.
32 Taylor, Am. Journ. Physiol., 1918, 45, p. 569.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
51
those due to other observ^ers. The differences can be looked upon as
statistically trustworthy in only 2 or 3 of the comparisons. Quite
comparable results, as far as the smallness of the differences are con-
cerned, are found for the coefficients of variation. In 5 of the 10 cases
oiu* series are relatively less variable and in o cases relatively more
variable than those with wliich they are compared. The differences
are statistically insignificant except in 3 or 4 cases. Thus our babies
are slightly heavier than those measured by others except Taylor,
but agree excellently in variability, both absolute and relative.
Table 6. — Comparison of weight of Nutrition Laboratory babies with other series.
Series.
Average.
Diff.
Standard
deviation.
Diff. ^
CoeflBcient
of variation.
Diff
^diff.
British association
Boys
Girls
Lambeth hospital :
Boys
Girls
Belgian babies :
Boys
Girls
Stuttgart babies:
Boys
Girls
Dr. Taylor's series
BoyB
Giris
+0.229 ±0.046
+0.185±0.058
+0.147±0.044
+0.128 =±=0.067
+0.170 =
+0.2S3 =
= 0.059
= 0.073
+0.226=*= 0.045
+0.185 ±0.057
-0.037=1=0.050
-0.032 ±0.062
4.98
3.19
3.34
1.91
2.88
3.88
5.02
3.25
0.74
0.52
-0.053 ±0.032
+0.068 ±0.041
-0.064±0.031
+0.092 ±0.041
— 0.027±0.041
+0.010 ±0.052
+0.016±0.031
+0.130±0.041
+0.036 ±0.035
+0.125±0.044
1.66
1.65
2.06
2.24
0.66
0.19
0.52
3.17
1.03
2.84
-2.56±0.96
+ 1.22±1.28
-2.49 ±0.92
+2.22 ±1.25
-1.49±1.26
-1.18±1.36
-0.40 ±0.94
+3. 16 ±1.26
+ 1.18±1.03 1.15
+3.87±1.35 2.87
2.67
0.95
2.71
1.78
1.18
0.87
0.43
2.51
For comparison with our results for length we may reduce the
British Association data used for body-weight above. The constants
for the 451 boy and 466 girl babies are:
Mean. S. D. C. V.
Male infants 49.58±0.11 3.48±0.08 7.02±0.16
Female infants 49.07±0.10 3.25±0.07 6.62±0.15
We may also compare Pearson's constants for full-term male and
female infants (1000 each) from the Lambeth Lying-in Hospital.^^ His
results are :
Mean. S. D. C. V.
Male infants 52.08±0.07 3.38±0.05 6.50±0.10
Female infants 51. 11 ±0.06 2.99 ±0.05 5.85 ±0.09
Dr. Rood Taylor's infants give the follo^ving values for total length :
Mean. S. D. C. V.
Male infants 5M8±0.13 2.04±0.09 3.98±0.17
Female infants 50.07±0.12 2.03±0.09 4.08±0.18
Comparison with our own series is made in table 7.
The average length of our babies is shghtly greater than the British
Association series but slightly less than the Lambeth Hospital series.
"Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 25.
52 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Our boys are slightly shorter and our gu-ls a little longer than
Dr. Taylor's series, but the differences cannot be asserted to be
significant. All our variabilities, both absolute and relative, as
shown by the differences between standard deviations and coefficients
of variation in table 7, are less than the British series, indicating
that our measurements were made upon a group of infants somewhat
more uniform. Our male infants are slightly less variable and our
female infants somewhat more variable than Dr. Taylor's series.
Table 7. — Comparison of length of Nutrition Laboratory babies with other series.
Series.
Average.
Diff.
^diff.
Standard
deviation.
Diff.
^diff.
Coefficient
of variation.
Diff.
^diff.
British association:
Boys
Giris
Lambeth hospital:
Boys
Giris
Dr. Taylor's series:
Boys
Giris
+1.39 =
+ 1.09 =
= 0.20
= 0.25
-l.ll=t0.18
-0.95 =±=0.24
-0.21±0.21
+0.10=4=0.26
6.95
4.36
6.17
3.96
1.00
0.37
-1.72=4=0.14
-1.05=t0.17
-1.62 =
-0.79 =
= 0.13
= 0.17
-0.27=t0.15
+0.17=t0.18
12.29
6.18
12.46
4.65
1.83
0.93
-3.56=4=0.28
-2.23=t0.36
-3.04=t0.25
-1.46=4=0.34
-0.52=4=0.29
+0.33±0.37
12.71
6.19
12.16
4.29
1.79
0.89
The correlations between stature (length) and weight in our infants
are as follows:
For males N^51, rsw = 0.770 ^0.038
For females N=43, r,u, = 0.864 =*= 0.026
For both sexes iV=94, r,„ = 0.821 ±0.023
For comparison with those we have the constants based on 1000
male and 1000 female full-term new-born infants from the Lambeth
Lying-in Hospital by Pearson ^^. The results are:
For males iV=1000, r„. = 0.644 =*= 0.012
For females iV=1000, r„„ = 0.622 =4=0.013
Reducing the Anthropometric Committee's ^^ data, which as noted
by Pearson are somewhat heterogeneous in origin, we find:
For males N=451, r„„ = 0.665 =4= 0.018
For females iV=466, r™ = 0.539 =4= 0.022
The correlations between length and weight in Dr. Rood Taylor's
series are :
For males r„„ = 0.668 ±0.034
For females r„„ = 0.749 ±0.027
For both males and females our correlations are higher than those
found by others. The differences are :
Pearson's series. British Association. Taylor's series.
For males, +0.126±0.040 +0.105±0.042 +0.102±0.051
For females, +0.242 ±0.029 +0.325±0.034 +0.115±0.037
»* Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 25.
" British Association Report (Southport), 1883, p. 286.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
53
In most cases the differences are apparently statistically significant
in comparison with their probable errors. Thus our series of infants,
both male and female, are certainly more highly correlated in their
weight and length than the series studied by others.
Summarizing the results of this brief and superficial comparison,
it appears that while our series differ in correlation, they may never-
theless be considered to show a very satisfactory general agreement
in both mean, and variabiUty with babies studied by others. Con-
sidering the possible influence of race, age, and social status, the
agreement seems rather remarkable.
We assert, therefore, that we are dealing with the constants of
"normal" male and female infants, not merely because they are appar-
ently normal from the comparative standpoint of the obstetrician, but
because they give statistical constants in fair agreement with those
for babies studied by others.
We now turn to the constants for adults. Since these are funda-
mental to the determination of many of the relationships in subsequent
sections, we shall give them for each of the various subseries. The
constants for stature appear in table 8, those for body-weight in
table 11.
Table 8. — Statistical constants for stature in adults of Nutrition Laboratory series.
Series.
iV
Average.
Standard
deviation.
CoeflBcient
of variation.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
Other than Gephart and Du Bois selection.
16
62
89
72
28
117
19
64
All men of three series ! 136
Women.
Original series
Supplementary- series
Both series
68
35
103
177.44 ±1.57
171.S2±0.o8
172.45 ±0.56
172.75±0.56
174.61 ±1.04
172.97 ±0.50
172.95 ±0.75
173.20±0.69
172.96±0.44
161.87±0.43
162.14 ±0.57
161.96 ±0.34
9.33±1.11
6.79 ±0.41
7.80 ±0.39
6.98±0.39
8.17±0.74
7.94 ±0.35
4.83 ±0.53
8.21 ±0.49
7.59±0.31
5.29 ±0.31
4.99 ±0.40
5.19±0.24
5.26 ±0.63
3.95 ±0.24
4.53±0.23
4.04 ±0.23
4.68 ±0.42
4.59 ±0.20
2.79±0.31
4.74 ±0.28
4.39 ±0.18
3.27±0.19
3.08 ±0.25
3.20±0.15
If the criterion of the suitability of our series of indi\'iduals were
mean stature only, we should be embarrassed by the wealth of available
materials for comparison. Stature is one of the more conspicuous and
more generally interesting characteristics of races or of the populations
of different geographic di\dsions. The number of average statures
available is therefore very large. But our comparison involves not
merely the average value, but the distribution of the statures around
the average. Hence we must base our comparisons on series which
have full data for the determination of variability as well as of type.
54 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
For comparison, we have the constants for the stature of 1,000
students 18 to 25 years of age, measured in the Harvard gymnasium
and pubhshed by Castle, ^^ and for 25,878 American recruits calculated
by Pearson.^^ Turning to the English, we have Schuster's^^ values
for Oxford students aged 18 to 23 or more years, Pearson's^® and
Macdonell's^" constants for Cambridge undergraduates and for Mac-
donell's^^ Scottish students. Turning to data other than that for
students, Pearson^^ has given a series of constants drawn from his family
records and Pearson and Lee*^ have supplied those for first and second
generations of British families.
Table 9. — Statistical constants for stature in men and women in general.
Beries.
Men.
Mean.
Standard
devia-
tion.
Coeffi-
cient of
varia-
tion.
Women.
Mean.
standard
devia-
tion.
Coeffi-
cient of
varia-
tion.
American :
Harvard students
Army recruits
English :
Oxford students
Cambridge students, Pearson. . .
Cambridge students, MacDonell
Pearson's second generation ....
Pearson's family records
Pearson's parental generation . . .
New South Wales criminals. . . .
Scottish students
MacDonell's convicts
Goring's convicts
Swedes
Hessians
French
Bavarians, Pearl
Bavarians, Pearson
175.34
170.94
176.60
174.91
174.88
174.37
172.81
171.91
169.87
171.70
166.46
166.29
169.79
167.36
166.80
166.55
165.93
6.58
6.56
6.61
6.41
6.46
6.88
7.04
6.86
6.58
5.94
6.45
6.76
6.81
7.19
6.47
6.39
6.68
3.76
3.84
3.74
3.66
3.70
3.95
4.07
3.99
3.87
3.46
3.88
4.06
4.01
4.30
3.88
3.84
4.02
162.26
162.23
159.90
158.70
158.09
158.71
156.18
156.10
154.71
163.85
6.00
6.63
6.44
6.07
6.15
6.72
6.90
6.79
6.21
6.55
3.70
4.00
4.03
3.83
3.89
4.23
4.40
4.35
4.02
4.26
While it is now known that, in England at least, certain classes of
criminals are differentiated from the general population, it is interesting
to compare the constants for 3000 non-habitual male criminals^* meas-
ured at Scotland Yard and analyzed by Macdonell,^^ the constants for
3000 men studied by Goring^^ in his masterly treatment of the British
'* Castle, Heredity and Eugenics, Cambridge, 1916, p. 61.
" Pearson, The Chances of Death, 1897, 1, p. 276.
»« Schuster, Biometrika, 1911, 8, p. 49.
»» Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 26.
« Macdonell, Biometrika, 1901, 1, p. 191.
*^ Macdonell, Proc. Anat. and Anthrop. Soc. Univ. Aberdeen (fide K. Pearson, Biometrika,
1911, 8. p. 49).
« Pearson, The Chances of Death, 1897, 1, p. 294.
" Pearson and Lee, Biometrika, 1901, 2, p. 370.
** The majority of the prisoners were English and Welsh, many were Irish, and only a few
Scotch. None were foreigners. All were over 21 years of age.
« Macdonell.Biometrika, 1901, 1, p. 191.
« Goring, The English Convict., Lond., 1913, pp. 178-179.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
55
criminal, and for a large series of New South Wales criminals for which
we are indebted to Powys/^
For races other than Anglo-American we have Pearson's*^ Bavarian
and French men and women and Pearl's*^ constants for Swedes, Hes-
sians and Bavarians.
The means, standard deviations and coefficients of variation of
these various series are assembled in table 9.
Comparison of the constants for stature of our total men and total
women with these various series is facihtated by the differences in
table 10. These are taken so that a positive sign indicates higher mean
or variabiUty in the Nutrition Laboratory- series.
Table 10. — Comparison of statistical constants for stature in Nutrition Laboratory series vntk
the values for men and women in general.
Men.
Women.
Series.
Mean.
Standard
devia-
tion.
American :
Harvard students
Army recruits
English :
Oxford students
Cambridge students, Pearson . . .
Cambridge students, MacDonell
Pearson's second generation ....
Pearson's family records
Pearson's parental generation
New South Wales criminals
Scottish students
MacDonell's convicts
Goring's con\-ict3
Swedes
Hessians ,
French
Bavarians, Pearl
Bavarians, Pearson
-2.38
+2.02
-3.54
-1.95
-1.92
-1.41
-fO.15
+ 1.05
+3.09
+ 1.26
+6.50
+6.67
+3.17
+5.60
+6.16
+6.41
+7.03
Coeffi-
cient of
varia-
tion.
Mean.
+ 1.01
+0.63
+1.03
+0.55
+0.98
+0.65
+1.18
+0.73
+1.13
+0.69
+0.71
+0.44
+0.55
+0.32
+0.73
+0.40
+1.01
+0.52
+1.65
+0.93
+ 1.14
+0.51
+0.83
+0.33
+0.78
+0.38
+0.40
+0.09
+ 1.12
+0.51
+ 1.20
+0.55
+0.91
+0.37
-0.30
-0.27
+2.06
+3.26
+3.87
+3.25
+5.78
+5.86
+7.25
-1.89
Standard
de\'ia-
tion.
-0.81
-1.44
-1.25
-0.88
-0.96
1.53
■1.71
•1.60
■1.02
■1.36
Coeffi-
cient of
varia-
tion.
-0.50
-0.89
-0.83
-0.63
-0.69
-1.03
-1.20
-1.15
-0.82
-1.06
As far as average stature is concerned, our series show a superiority
practically throughout. Only the Oxford, Cambridge, and Harvard
men, Cambridge women, Pearson's filial generation measurements
for both men and women, and Pearson's Bavarian women are taller
than the subjects included in our normal series.
Now comparison of average statures involves very great difficulties.
In none of these series is there a correction for the slight premaximum
increase or the postmaximum decrease occurring in the age period
ordinarily designated as adult life. This is probably a matter of negli-
" Powys, Biometrika, 1901, 1, p. 44.
« Pearson, The Chances of Death, 1897, 1, p. 295.
" Peari, Biometrika. 1905, 4, p. 13.
56 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
gible importance. A far greater difficulty is inherent in the factor of
racial differentiation. One has only to glance at such tables as those
of Martin^^ or the discussion and maps of Ripley^ ^ to realize how great
the racial, geographical, and social factors are in determining the
average stature of a group of individuals. The fact that our normal
men and women are taller than those with which we have compared
them may be due to one or more of three factors.
a. A differentiation of the American population from the European
with respect to stature.
h. An indirect selection of the taller men and women from the gen-
eral American population due to the individuals volunteering for these
metabolism observations being a superior class.^^
c. Unconscious selection of taller individuals for metabolism meas-
urements by those who have had to choose among the subjects who
presented themselves.
Some evidence on the first of these questions is afforded by abstract-
ing from Martin's Anthropologie the average statures, as far as given
in the comparative table (p. 213-217).
Men.
Women.
French
....164.1
157.0
Bavarians
.... 165.6
Swedes
.... 170.9
American whites . . . .
....171.9
English
....172.8
159.9
Even if we increase the stature of the French and Bavarian men
by 1 cm. to correct for the age at which measurements were made for
military purposes, we note that the American white population stands
next to that of the middle classes of Great Britian in stature.
Fortunately we may take from Baxter's ^^ report the average stat-
ures of immigrants of various nationalities. As abstracted by the
Anthropometric Committee of the British Association^* they are as
follows:
Centi- Centi- Centi'
meters. meters. meters.
Norwegians 171.9 English 169.2 French 168.3
Canadians, chiefly Hungarians 169.2 Poles 168.2
French 170.3 Germans 169.1 ItaUans 167.7
Swedes 170.0 Swiss 168.7 Spaniards 166.8
Danes 169.4 Russians 168.7 Portuguese 166.3
Dutch 169.3
"• Martin, Lehrbuch der Anthropologie, 1914. See especially pp. 204-237.
»i Ripley, The Races of Europe, 1900. See especially pp. 78-102.
*^ How great the influence of social differentiation may be is well shown by a comparison of
the regression slopes for fraudulent criminals and for criminals at large, in Goring's
English Convict- It is also clear from the Swiss data for stature by occupation given
on page 90 of Ripley's Races of Europe.
* Baxter, Statistics, Medical and Anthropological, 1875.
"British Association Report (Southport), 1883, pp. 269-271. See also W. H. Holmes,
Am. Journ. Phys. Anthrop., 1918, 1, p. 84.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
57
Thus racial differentiation between European and American popu-
lation is ample to account for the observ^ed differences in our mean
statures. Our men are intermediate between the general population
and a highly selected group like Harvard University students."^
In regard to variability, our men are more variable and our women
are less variable throughout than those studied by others for purely
anthropometric purposes.
Since the average stature for Americans seems to be higher than
that of most of the European groups with which they are compared,
the absolute variability would be expected to be greater in Americans;
but the relationships noted hold whether variability be measured in
centimeters by the standard deviation or in percentages of the total
stature by the coefficient of variation.
Table 11. — Statistical constants for body weight in adults.
Series.
N
Average.
standard
de\'iation.
Coefficient
of variation.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series. . .
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women,
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
73.82*2.17
63.03*0.77
64.33*0.77
63.33*0.67
62.69*1.34
63.94*0.67
65.06*1.13
64.96*1.02
64.10*0.60
54.49*0.88
60.36*1.35
56.48*0.76
12.87*1.53
9.02*0.55
10.73*0.54
8.37*0.47
10.48*0.94
10.69*0.47
7.30*0.80
12.04*0.72
10.30*0.42
10.78*0.62
11.84*0.95
11.49*0.54
17.43*2.14
14.32*0.88
16.68*0.87
13.22*0.76
16.72*1.55
16.73*0.76
11.22*1.24
18.54*1.14
16.06*0.67
19.78*1.19
19.61*1.64
20.35*1.00
Now, admitting freely that many of these differences are statis-
tically significant, we nevertheless feel that one can hardly examine
these constants collected by various writers in anthropometric investi-
gations, with no physiological purpose whatever in view, in comparison
with our own without being impressed by the general suitability of
our materials as a basis for generalizations applicable to large popula-
tions. Our averages seem to be roughly representative of the American
population. Our men are somewhat more variable than we would like,
but our women are distinctly less variable than women in general.
It is clear, therefore, that our series of indi\dduals is characterized not
merely by an average stature comparable w^th that of men in general,
but that it exhibits (at least in the males) a variability of stature
which is (roughly speaking) typical of the population at large. This
"lack of uniformity" or ''lack of homogeneity" in the series of
" The average stature of 327 Amherst College students (of average age 21.5 years) is 172.9 cm.
Anthropometric Committee's Report Brit. Ass. Kept. (Southport), 1883, p. 260.
58 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
men and women dealt with is one of its chief merits. If laboratory
studies of basal metabolism are to have a broad application in
medical and social science they should be made upon series representa-
tive of the population at large. It is only under these conditions that
generalizations of wide usefulness can be safely made.
Our constants for body- weight, taken without clothing, in the various
series are given in table 11.
For comparison with our own series of body-weights we are fortu-
nate in having the table of weight taken without clothifig of 1,000 Harvard
men aged 18 to 25 years published by Professor Castle, ^^ that for
Oxford undergraduates, weighed with clothing but without boots,
given by Schuster,^^ the values for 1,000 Cambridge men and 160
Cambridge women given by Pearson, *^ and Pearson's ^^ reduction of
Francis Galton's series of body-weights, taken with ordinary indoor
clothing, for British men (A'' = 520) and women (iV = 276). Goring
has given a most valuable series from British prisons, ^° measured in
shirt and trousers only. For Germans (Bavarians) Pearson ^^ has
determined constants for the 535 men and 340 women measured by
Bischoff.
The results, uncorrected for weight of clothing, are as follows :
Mean. S. D. C. V.
Castle's Harvard men 65.66 7.84 11.94
Schuster's Oxford men 68.91 7.45 10.80
Pearson's Cambridge men 69.30 7.51 1083
Pearson's Cambridge women 56.97 6.36 11.17
Galton's British men 64.86 4.54 10.37
Galton's British women 55.34 4.60 13.37
Goring's convicts 64.45 7.80 12.09
Pearson's Bavarian men 50.17 10.38 20.67
Pearson's Bavarian women 41.92 10.51 25.07
Unfortunately the number of series of body-weight measurements
available for comparison is small. Furthermore body-weight is a
much more variable character than stature. One must, therefore,
expect greater actual differences between series of observations made
at different times and places. How large the differences may be is
shown by the great discrepancy between the British and the Bavarians.
Our data show constants of roughly the same order of magnitude as
those available for comparison.
In turning to the problem of the closeness of correlation in the
stature and weight of the subjects examined as a criterion of their
"normality" as compared with men at large, it will be important to
'• Caatle, Heredity and Eugenica, Cambridge, 1916, p. 61.
" Schuster, Biometrika, 1911, 8, p. 49.
» Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 26.
»' Pearson, The Chances of Death, 1 : 305, 1897. Constants slightly erroneous.
•0 Goring, The English Convict, 1913, pp. 178-179.
•' Pearson, The Chances of Death, 1 : 305, 1897. We can ofifer no explanation for the
great variation in the German series.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
59
remember that in selecting our series for comparison we must choose
those of adult age in order to eliminate the influence of growth. Some
of the best studies on the correlation between stature and weight — for
example, those of Boas ^^ and of Boas and Wissler ^^ on Toronto and
Worcester children, as well as the more recent investigation of Elder-
ton ^ on the stature and weight of Glasgow school children, carried
somewhat farther by Isserlis,®^ are therefore not available for our
present purposes.
The correlations between stature and weight in our adults are given
in table 12.
Table 12. — Correlation between weight and stature and partial correlation between weight and
stature for constant age in the several series.
Series.
N
Correlation
Partial correla-
tion
r
a'wt
aTrcM
Er
Difference
Men.
Origiiial series:
Athletes
16
62
89
72
28
117
19
64
136
68
35
103
0.6943 ±0.0873
0.4010*0.0719
0.5320*0.0513
0.6654*0.0443
0.7461*0.0565
0.5712*0.0420
0.6031*0.0984
0.5149*0.0620
0.5725*0.0389
0.2191*0.0779
0.5386*0.0809
0.3257*0.0594
7.95
5.58
10.37
15.02
13.21
13.60
6.13
8.31
14.72
2.81
6.66
5.48
0.6361*0.1004
0.3999*0.0720
0.5376*0.0508
0.6773*0.0431
0.7468*0.0564
0.5783*0.0415
0.5960*0.0998
0.5362*0.0601
0.5772*0.0386
0.2205*0.0778
0.4969*0.0859
0.2995*0.0605
6.34
5.55
10.58
15.71
13.24
13.93
5.97
8.92
14.95
2.83
6.78
4.95
+0.0582
+0.0011
-0.0056
-0.0119
-0.0007
-0.0071
+0.0071
-0.0213
-0.0047
-0.0014
+0.0417
+0.0262
Others
Whole series
Gephart and Du Boia
selection
First supplementary
series
Original and first sup-
plementary series. . . .
Second supplementary
series
Other than Gephart and
Du Bois selection
All men of three series. .
Women.
Original series
Supplementary series. . .
Both series
The partial correlations in which the influence of age is eliminated
have been computed from the formula
n' «ea "^
' tea ' ate* n
Vl-r„jVl-j
and placed beside the others for comparison.
It is to be noted that correction for the influence of age has modified
the values of the constants very httle indeed. They have sometimes
been shghtly raised and sometimes sUghtly lowered by correction for
this factor. Age differences in the series can not, therefore, account
for any of the observ'ed differences in correlation.
K Boas, Kept. U. S. Comm. Educ, 1896-97. p. 1541.
o Boas and Wissler, Kept. U. S. Comm. Educ, 1904, p. 26.
« Elderton. Biometrika, 1914, 10. p. 288.
« Isserlis, Biometrika, 1916, 11, p. 50.
60 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The results in table 12 seem very reasonable and consistent with
one exception. The original published series of women seems abnorm-
ally low in comparison with the second series and with men. The
relationships for the original series and the supplementary series are
shown in diagrams 2 and 3.
The straight lines in these diagrams represent the equations:
For original series w= — 17.83+0.45 s
For supplementary series w= —146.68+1.28*
Clearly the rate of increase in weight per centimeter of length is
much greater in the supplementary series.
STATURE IN CENTIMETERS
Diagram 2. — Relationship between stature and weight in original series of women.
See text for discussion of four aberrant individuals in upper part of field.
In the original series one notes four individuals towards the upper
part of the field who are very heavy in relation to their stature. These
are Miss O. A., Dr. M. D., Miss H. H., and Miss H. D. If these be
removed the variabiUty in body-weight is greatly reduced, i.e., from
10.78 to 6.87. The correlation is raised from r = 0.219 to r = 0.340,
but this constant is still considerably lower than that in the supple-
mentary series. 1^
Apparently the observations are fairly well grouped aroimd the
straight Hnes and we must simply admit that, in gathering small
samples of data, two groups were secured which differed sensibly in
the degree of correlation of their bodily characters.
INDIVIDUALS AND MEASUREMENTS CONSIDERED.
61
The relationship between stature and body-weight in the total
male (iV = 136) and the total female (iV = 103) series may now be
represented in a different way.
The straight-line equation connecting weight and stature in the
total series are :
For men iv= - 70.303 +0.777s
For women w= - 60.332 +0.721s
These are represented on the same scale for the two sexes on dia-
gram 4. The ''mean body-weight" has been calculated for each grade
of stature. With less than 150 individuals available for each sex the
"averages" sometimes represent a single individual merely and are
extremely irregular. The straight line serves fairly well to smooth them.
STATURE IN CENTl^'E:TERS
Diagram 3. — Relationship between stature and body weight in supplementary serie^of
women. See diagram 2 and text.
The diagram brings out clearly a point noted above, namely the
unfortunate narrowness in the range of variation of stature in our
series of women.
For comparison we have several series of data. First of all may
be mentioned Castle 's*^*^ 1000 Harvard men — gynmasiimi records with-
out clothing — which give:
r = 0.704 ±0.015
Pearson,^^ working with measurements of 1000 male and 160 female
Cambridge students, found :
For men r = 0.486 ±0.016
For women r =0.721 ±0.026
'•Castle, Heredity and Eugenics, Cambridge, 1916, p. 61.
•T Pearson, Proc. Roy. Soc. Lond., 1899, 66, p. 26.
62 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
For Oxford men, E. Schuster ^^ found the following correlations
between height and weight, the latter unfortunately taken with the
clothing except the boots:
Age 18, A" = 129,
Age 19, AT = 330,
Age 20, AT = 209,
Age 21, AT = 137,
Age 22, A^= 95,
r = 0.50 ±0.04
r = 0.63 ±0.02
r = 0.68 ±0.03
r = 0.76 ±0.02
r = 0.72 ±0.03
General average. . . 0.66
For stature and body-weight in 2502 British convicts, weighed in
trousers and shirt only, Goring®^ finds:
r«„ =0.555=^0.009
Again for height and weight in 500 male criminals examined by
Goring, the correlations deduced by Whiting ^° are:
For stature and weight rx»= 0.580 ±0.020
For stature and weight with age constant arj«,= 0.583 ±0.020
I4S 153 IS8 163 IS8 173 178 133
193 193
STATURE IN CENTIMETERS
Diagram 4. — Variation in mean body-weight of men and women with stature.
Our correlations for men are, roughly speaking, of the same order
of .magnitude as those which have been published by others. Unfortu-
nately, only Pearson's small series of women, but slightly larger than
our own, is available for comparison. The agreement here is not good.
Only further work on the relationship between stature and body-weight
in women will answer the question of the degree of correlation to be
expected between these two physical characters.
•* Schuster, Biometrika, 1911, 8, p. 51.
" Goring, The English Convict, Lond., 1913, p. 389.
™ Whiting, Biometrika, 1915, 11, p. 8.
INDI\aDUALS AND MEASUREMENTS CONSIDERED.
63
The materials for adults may be tested for normality, in the
general sense in which we have used the term here, in two other
ways.
Age and stature, in adult Hfe, should not be sensibly correlated
except as a result of post-maximum shrinkage. Our data cover a
portion of the age of pre-maximum increase and of post-maximum
decrease as well as the age of maximum stature. Our correlations are
given in table 13. Some of the constants are positive while some are
negative. In only the athletes are the coefficients as much as 2.5 times
as large as their probable errors. WTien N is small the ordinary stand-
ards of trustworthiness can no longer be maintained. Taking the
results as a whole, we have no reason to conclude that in the age range
covered by our data there is any great change in stature with age.
Table 13. — Corrdaiion between age and stature and age and weight and •partial correlation
between age and weight for constant stature.
Series.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary
series
Second supplementary series
Other than Gephart and Du Bois
selection
All men of three series
Women.
Original series
Supplementarj' series
Both series
N
Correlation
between age
and stature
16
62
89
72
28
117
19
64
136
68
35
103
-0.4346=
+0.0687 =
-0.1651 =
+0.0283 =
+0.0641 =
-0.1230 =
-0.1594 =
-0.1972 =
-0.1154 =
+0.0921 =
+0.2395 =
+0.1462 =
= 0.1368
= 0.0853
= 0.0696
= 0.0794
= 0.1269
= 0.0614
= 0.1508
= 0.0810
= 0.0571
= 0.0811
= 0.1075
= 0.0650
E,
3.18
0.81
2.37
0.36
0.51
2.00
1.06
2.43
2.02
1.14
2.23
2.25
Correlation
between age
and weight
^r„
Partial
correlation
-0.3763=*= 0.1447
+0.3037=^0.0778
— 0.0106=^0.0715
-0.1476=^0.0778
+0.1565 =»=0.1243
2.60
3.90
0.15
1.90
1.26
+0.0209=^0.0623 0.34
-0.1185=t0.1526; 0.78
+0.0515=fc0.0841
+0.0067=*= 0.0578
-0.0050=*= 0.0818
+0.4422 =fc 0.0917
+0.2867 =*=0.0610
0.61
0.12
0.06
4.82
4.70
-0.1150 =*=0.1664
+0.3022=*= 0.0778
+0.0925=^0.0709
-0.2230=1=0.0755
+0.1636 =«=0.1241
+0.1120 =
-0.0284 =
+0.1820=
+0.0893 =
= 0.0616
= 0.1546
=0.0815
=0.0574
- 0.0259 =fc 0.0817
+0.3828 =fc 0.0973
+0.2557=1=0.0621
0.69
3.88
1.30
2.95
1.32
1.82
0.18
2.23
1.56
0.32
3.93
4.12
For comparison with our own constants we have those for 500
criminals examined by Goring. The correlations deduced by Whiting^*
are:
For age and stature ras= +0.023 =*= 0.030
For age and stature with weight constant »r«= —0.070=*= 0.030
General observ^ation suggests that individuals tend to gain in weight
with increasing age,'^ even after the normal period of growth has
passed. In support of such general observation may be cited the
" Whiting, Biometrika, 1915, 11, p. S.
" It seems quite possible that the correlation between weight and heat-production may be
somewhat disturbed by the correlation of weight with age. It is, therefore, necessary to
investigate such relationships as this in detail.
64 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
constants obtained by Whiting ^^ for age and weight in 500 criminals
examined by Goring. The correlations deduced are:
For age and weight raw= +0.136±0.030
For age and weight with stature constant jraa,= +0.151 ±0.030
These constants indicate a sUght increase in weight with increasing
age.
Our own materials show the correlations given in table 13. Since
the problem of any actual gain in weight after the completion of growth
involves a consideration of the stature of the individuals, the correla-
tions for age and weight have been corrected for the influence of
stature by the use of the formula
„ 'aw ' aa' sw
a' aw
Vl-r,„2Vl-5
. 2
aw
Among the men only the correlation for the 62 "other men" of the
original series can be looked upon as statistically significant.
The partial correlations between age and weight for constant stat-
ure are positive in all the larger series of men, excepting only the
Gephart and Du Bois selection,^* and indicate a slight tendency for
increase in body-weight with age in men.
The women of the first series show practically no correlation be-
tween age and body-weight. Correction for the possible influence of
stature does not materially alter the relationship. The supplementary
series, however, shows material and statistically significant positive
correlation, indicating decided increase of weight with age. The corre-
lation is not so large, but nevertheless apparently statistically signifi-
cant, for the total available women. The values of the gross correla-
tions are but slightly reduced when correction is made for the influence
of stature by the use of the partial correlation formula. The constants
for the second series of women and for the entire series of women seem
to suggest that women have a greater tendency than men to increase
in weight with age. The apparent contradiction between the results
of the first and of the supplementary series is perhaps due to differences
in age. The individuals of the second series are on the average about
13 years older than those of the first. Thus the average age in the first
series is 26.7 years, whereas that of the second series is 39.9 years, and
that of all the women is 31.1 years. The first series shows a standard
deviation of only 9.9 years around the average age of 26.7 years,
whereas the second series shows a standard deviation of 16.0 years
around the average age of 39.9 years, and the whole series shows a
variation of 13.8 years around the average of 31.1 years.
"Whiting, Biometrika. 1915, 11, p. 8.
'* The negative correlation and the negative partial correlation for constant stature found
in the Gephart and Du Bois selection are perhaps due to the arbitrarj' removal of
individuals which do not conform to a preconceived standard.
INDIVIDUALS AND IVEEASUREMENTS CONSIDERED.
65
Higher correlation between age and weight in a group of women
averaging 40 years in age than in a group averaging 27 j'ears of age
is in accord TN-ith the rather general beUef that after the climacteric
women tend to gain in weight.
The variation constants for body-surface measured by the Du Bois
height-weight chart appear in table 14.
Table 14. — Statistical constants for body-surface in aduUs as estimated by Du Bois
height-weight chart
Series.
N
Average.
Standard
deviation.
Coefficient
of variation.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Boia selection ....
First supplementary series
Original and first supplementary series
Second supplementary series
Other than Gephart and Du Bois selec-
tion
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
1.904±0.0326
1.742 ±0.01 13
1.760 ±0.01 14
1.753 ±0.0108
1.759 ±0.0228
1.760±0.0102
1.775 ±0.0168
1.773±0.0149
1.762 ±0.0091
1.566 ±0.01 13
1.637±0.0180
1.590 ±0.0099
0.1933 ±0.0230
0.1315±0.0080
0.1593 ±0.0081
0.1360±0.0076
0.1785±0.0161
0.1631 ±0.0072
0.1089±0.0119
0.1765±0.0105
0.1567±0.0064
0.1378±0.0080
0.1577±0.0127
0.1485±0.0070
10.15== 1.22
7.55 ±0.46
9.05±0.46
7.76 ±0.44
10.15±0.92
9.26±0.41
6.14±0.67
9.96±0.60
8.S9±0.37
8.80 ±0.51
9.63 ±0.78
9.34±0.44
For this character we have no comparable data from other sources.
The constants are, therefore, of primary importance in their relation
to the further calculation necessary for the discussion of subsequent
sections. The average body-surface is about 1.8 square meters in men
and about 1 .6 square meters in women. The variabihty of the super-
ficial area of the body is about 9 per cent of this amount in both sexes.
The coefficients of variation occupy an intermediate position between
those for stature and those for body-weight, as showm in the final
columns of tables 8 and 11, in ever\' series.
The constants for pulse-rate are set forth in table 15. The only
comparable data of which we are aware are those of Korosy and Goring
for conscripts and con^^cted men. For pulse-rate in 500 convicts
examined by Goring the constants determined bj^ "Wliiting "^ and the
difference from our own for men are :
Mean.
S.D.
C.V.
2
Our
whole series.
61.26±0.41
6.73±0.29
10.99 ±0.48
Whiting's
whole series.
74. 22 ±0.25
11.06±0.17
14.89 ±0.24
Difference
between i and S.
12.96±0.48
4.33 ±0.34
3. 90 ±0.54
Whiting's
weak-minded.
77.62±0.58
11.85±0.41
15.27±0.54
6
Difference
between i and S.
16.36±0.71
5.12±0.50
4.28±0.72
These values are far larger than ours, in mean, absolute variabihty,
and relative variability. This is clearly due to the facts (a) that they
Whiting, Biometrika, 1915, 11, pp. 1-37.
66 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
are made upon a series of individuals from which physically and men-
tally abnormal men were not excluded, and (b) that the rates were taken
with the convict sitting in his cell, writing, reading, or doing nothing
about 15 minutes after early dinner instead of 12 hours after the last
meal and in a state of complete muscular repose.
Table 15. — Statistical constants for pulse-rate in adults.
Series.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series . . . .
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
iV
16
62
88
71
28
116
60
121
68
22
90
Average.
62.00 ±1.01
60.81 ±0.54
60.92 ±0.47
61.27±0.51
62.54±0.87
61.31±0.41
61. 26 ±0.68
61.26 ±0.41
69.12 ±0.67
67.27±1.18
68.67±0.59
Standard
deviation.
6.98±0.71
6.29 ±0.38
6.48 ±0.33
6.43 ±0.36
6.81 ±0.61
6.60 ±0.29
7.14±0.48
6.73 ±0.29
8.18±0,47
8.20 ±0.83
8.25±0.41
Coefficient
of variation.
9.64±1.16
10.34±0.63
10.64 ±0.55
10.49 ±0.60
10.89±0.99
10.77 ±0.48
11.65 ±0.80
10.99 ±0.48
11. 83 ±0.69
12.19±1.26
12.01 ±0.61
Korosy's data for conscripts ^® are physiologically more nearly com-
parable with our own. They were taken on a group from which all
individuals not having a perfectly healthy heart had been excluded.
The countings were made in the early morning soon after the men
were wakened and while they were still in a position of rest. The
constants deduced by BelF^ are compared with our own as follows:
Kdrosy'a series. Our series. Difference.
Mean 64.21 ±2.71 61.26±0.41 2.95±2.74
S. D 8.49±0.36 6.73±0.29 1.76±0.46
C. V 13.22 ±0.40 10.99 ±0.48 2.23 ±0.62
These results are in much closer agreement with our own than the
determinations on convicts; but means, absolute variabihties, and
relative variabilities are larger than in our series.
Since pulse-rate is a physiological measure well known to be affected
by other physiological factors, we take these facts to indicate that our
records for pulse-rate — and in consequence those for metabolism as
well, for both were measured simultaneously — have been determined
under conditions which introduced the minimum external influence.
Turning to a more detailed examination of our own constants, we
note that the women have a more rapid and more variable pulse than
the men. The averages are :
■» Korosy, Deutsch. Archiv. f. klin. Med., 1910, p. 267.
" Bell, Biometrika, 1911, 8, p. 232.
INDI\aDUALS AND MEASUREMENTS CONSIDERED.
67
For original
Nutrition Laboratory teriet.
For 89 men 60.92±0.47
For 68 women 69.12=*= 0.67
For all men N = 12l
For all women N= 90
+8.20=*=0.82
For all
available data.
61.26^0.41
68.67=^0.59
+7.41=^0.72
In both comparisons the women show from 7 to 8 beats per minute
more than the men, and these differences are about 10 times as large
as the probable errors of their determination. The sexual differentiation
thus indicated has been noted by other writers. Thus Leonard Hill/®
in an article on "The mechanism of the circulation of the blood" says :
"The pulse frequency is greater in women than in men, but this difference
almost disappears if men and women of equal stature are compared."
Langendorff, in his article on the circulation of the blood/* states
that the pulse of adult men resting in bed is about 60, while standing
it is 70 to 75 per minute, and that in women it is somewhat higher.
Professor Robert Tigerstedt ^ states that in all ages, from 2 years on,
the pulse-rate of the woman is higher than that of the man. The
smaller size of the woman plays a role, but even if indi\'iduals of the
same stature are compared the difference is persistent though smaller.
We now turn to the constants for total heat-production.
Table 16. — Statistical constants for total heat-production per 24 hours in adults.
Series.
N
Average.
Standard
deviation.
CoeflBcient
of variation.
Men.
Original series:
Athletes
Othere
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second eupplementarj* series
Other than Gephart and Du Bois
selection
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
1876.56 ±41. 33
1607.97 ±12.20
1638.36=*= 14.64
1623.46 ±14.11
1605.18±28.19
1630.42 ±13.05
1639.84 ±26.77
245. 13 ±29.23
142.38± 8.62
204.82 ±10.36
177.55 ± 9.98
221. 14± 19.93
209.32 ± 9.23
172.99 ±18.93
1641.05 =
1631.74=
= 19.48
11.84
231.04 =
204.66 =
= 13.77
= 8.37
1354.69 ±12.25
1338.51 ±18.78
1349.19± 10.31
149.74 ± 8.66
164.72 ±13.28
155.18± 7.29
13.06 ±1.58
8.85±0.54
12.50±0.64
10.94±0.62
13.78±1.27
12.84±0.58
10.55±1.17
14.08±0.86
12.54 ±0.52
11.05±0.65
12.31 ±1.01
11. 50 ±0.55
The means, standard delations and coefficients of variation for
total heat-production in calories per 24 hours are given in table 16.
The entries in this table, representing as the}' do the constants for the
most extensive series of data available on basal metabolism in men
and women, have a great deal of interest. The first column shows
™ Hill, Schafer's Text-Book of Physiologj', London and New York, 1900, 2, p. 101.
™ Langendorflf, Zuntz and Loewy's Lehrbuch der Phvsiologie des Menschen, Leipzig, 1913,
2, Aufl., p. 373.
**" Tigerstedt, Lehrbuch der Physiologie des Menschen, Leipzig, 1913, 7, Aufl., 1, p. 282.
68 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
that the average basal metabolism of normal men is measured by a
daily heat-production of about 1600 to 1650 calories. All the series,
even those in which the number of individuals is very small, are reason-
ably consistent except for the athletes, which show an unusually high
metabolism. Women show an average daily heat-production, when in
complete muscular repose and in the post-absorptive state, of about 300
calories per day less than men. The average daily basal heat-production
of new-born infants is, as shown in table 5, about 140 to 145 calories.
This is about 10 per cent of that of adult women. In examining
these values one must, however, remember that they are uncorrected
for the influence of stature, body-weight, or age, all of which have
important rdles as proximate factors in the determination of the basal
daily heat-production of the individual.
The second column shows the great variability in basal heat-
production from individual to individual. The variabilities range
from 142 to 245 calories for men and from 150 to 165 calories for women.
For the larger series 140 to 230 calories for men and 150 to 160 calories
for women maybe taken as the variabiUties expressed in round numbers.
It is evident that with such large variations in the daily basal metabol-
ism of the normal individual the prediction of the heat-production of
an individual subject will always have a high probable error — that is,
a limited trustworthiness. In infants the standard deviations are
about 21 to 23 calories per day (table 5) .
In speaking of standard deviations of 140 to 230 calories for adults
and of 21 to 23 calories for infants as large, one must not forget that
these are for organisms giving daily average heat-productions of 1300
to 1650 calories for the adult and of 140 to 145 calories per day for the
infantile state. If the standard deviations be expressed as percentages
of the average daily heat-production we have the constants in the
third column of table 5 for the infants and table 16 for the adults.
To gain a definite idea of the relative variability of basal metabolism
as compared with other more familiar physical magnitudes and physio-
logical activities, it seems worth while to examine these constants in
some detail.
First of all we note that the values range from 8.85 to 14.08 per cent
for men and from 11.05 to 12.31 for the women, with constants for
the whole series of data for the two sexes of 12.54 =±=0.52 for the men
and 11.50 =±=0.55 for women. These values can not, with due regard to
their probable errors, be asserted to differ significantly.
In the infants the coefficients of variation are somewhat higher,
being 14.46 for the boy babies, 16.54 for the girl babies, and 15.49 for
infants irrespective of sex. The difference between the two sexes is
2.08 =±=1.59, which is statistically insignificant and hence can not be
regarded as indicative of a real physiological difference in variability
of heat production between the sexes.
INDIVIDUALS AND MEASUREMENTS CONSIDERED. 69
Comparing with other characters dealt with in this volume, we note
that the metabolism of a group of individuals is from 2 to 3 times as
variable as their stature, (table 8), but is not in any instance as vari-
able as their body- weight (table 11). The relative variability of total
heat-production is also, roughly speaking, from 20 to 25 per cent
greater than body-surface area as measured by the Meeh formula
(table 50) . This point is of particular interest because of the fact that
if heat-production were proportional to body-surface area, as maintained
by many, the variability of these two measures should be the same.
To a full consideration of this matter we shall return in Chapter VI.
These values are by no means as large as those which have been
found for the variation of weight of internal organs in man. For
example. Greenwood's^^ series shows coefficients of variation for the
weight of the spleen of 38.2 and 50.6 per cent in normal and hospital
populations. The same author finds a coefficient of variation of from
22.2 to 32.4 for the weight of the heart in hospital series and 17.7 in
normal series. For the weight of the kidneys the coefficients are 21.1
to 24.6 for hospital and 16.8 for normal subjects. For the weights of
the liver the constant is 20.8 to 21.1 for hospital series and 14.8 for
healthy series.
Comparison of the relative variabihty of total heat-production
with that of another physiological measurement, pulse-rate, shows that
the two are roughly of the same order of magnitude. In the whole
series of men total heat-production shows a variation of 12.54 =±=0.52
as compared with 10.99 =±=0.48 for pulse-rate, a difference of +1-55
=*=0.71. In the whole series of women the comparable values are
11.50 =±=0.55 for heat-production and 12.01 =±=0.61 for pulse-rate, a
difference of —0.51 =±=0.82. Thus the two differences for total series
are opposite in sign, and neither can be looked upon as statistically
significant in comparison with its probable error. Unfortunately
pulse-rate is not available for all the individuals but this can hardly
affect the correctness of the conclusion.
These comparisons with characters the variabihty of which is more
familiar to the general biologist and physiologist, will perhaps indicate
the relative magnitude of variation in total heat-production. The
individual constants will be extensively used in the analysis of the
various problems in the following chapters.
4. RECAPITULATION.
This chapter has had a threefold purpose.
A. To describe the measurements dealt "wdth and to give the
symbols by which they are designated in the subsequent discussion.
B. To give protocols of the actual measurements analyzed in
subsequent sections. These comprise 51 male and 43 female infants
" Greenwood, Biometrika, 1904, 3, p. 45; Greenwood and Brown, loc cit., 1913, 9, p. 481.
70 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
and 136 men and 103 women. Of the adult records, those for 47 men
and 35 women are pubHshed here for the first time.
C. To test the normaUty of our series of data, upon which physio-
logical generalizations are to be based.
In considering this problem we have emphasized a conception of
normality which differs somewhat from that heretofore maintained
by other students of metabolism.
1. Realizing that practically the greatest importance of a knowl-
edge of the basal metabolism of the normal individual is for the calcu-
lation of the 24 hours' requirement of the healthy individual and for
the establishment of control values to be used as a basis for conclusions
concerning the influence of special conditions or the incidence of specific
diseases on metabolism, we have made it a condition of inclusion in
our series that the individual be in presumably good health.
2. Since the populations which must be considered in rationing
problems are made up of physically varied individuals, it is essential
that any generalization which shall be applicable to these populations
be grounded on series of individuals showing like range of physical
dimensions. Since individuals in the hospital ward do not conform
to any individual physiologists conception of "the normal man," but
represent the entire range of physical dimensions and proportions, the
non-pathological controls which are to be used as a basis of comparison
should show a comparable range of physical dimensions and proportions.
3. Since some of the theoretical physiological problems to be con-
sidered have to do with the relationship between variations in physical
characteristics and physiological activities, it is essential that the sub-
jects investigated show average dimensions and variability and
correlation of dimensions typical of men and women as a class.
Thus, when we speak of a series of normal individuals we do not
mean a group of men similar to the figures in the Laocoon or a group
of women conforming to the Venus of Milo, but those who are in pre-
sumably good health and otherwise are typical of men or women of
the same race as the anthropologist knows them. With such a concep-
tion of normality it is impossible to discard individuals merely because
they are too heavy in proportion to their stature or too tall in propor-
tion to their weight.
On the other hand, it is of course quite as unallowable to form
standard series containing disproportionate numbers of very fat or
very lean individuals, as it is to discard both of these extremes and
include only those of average proportions.
The "normality" of such series must be judged by comparison of
their statistical constants with those of men and women at large.
Such criteria have been apphed to the data discussed in this volmne.
This conception of normality must, we believe, be generally ac-
cepted if investigations of human metabolism are to yield the results
of the greatest theoietical interest and practical importance.
Chapter IV.
ON THE INTERRELATIONSHIP OF VARIOUS PHYSICAL AND
PHYSIOLOGICAL MEASUREMENTS.
Our knowledge, in quantitative terms, of the degree of interrela-
tionship of the various phj'sical characteristics of man is now very
extensive indeed. Relatively httle is kno^-n of the closeness of inter-
dependence of physical magnitudes and physiological acti\'ities in
series of individuals; yet it seems clear that this subject should
receive careful quantitative treatment. Again, it seems to us self-
evident that the determination of true quantitative measures of the
degree of interdependence of the various physiological activities should
make possible material advances in our knowledge of these functions.
This position will be justified whatever the outcome of actual
investigations. If it be shown that various physiological measurements
are correlated with physical characteristics, such relationships must
form part and parcel of our sj'stem of knowledge concerning human
morphology and physiolog3^ If, on the other hand, it be found that
between certain of the phj^sical and physiological measurements there
is no sensible relationship, it will be clear that the physical character-
istics need not be considered in the selection of individuals which
may be regarded as comparable for use in studies of such physio-
logical activities as have been shown to be uncorrelated with physical
characteristics.
Again, if various physiological activities be showTi to be correlated,
a knowledge of the intimacy of the interdependence of a great variety
of physiological functions will contribute materially to our compre-
hension of the human body as a coordinated w^hole. Since oiu* general
experience of comparative and experimental physiology is such as to
render it rather difficult to conceive of an entire lack of interdependence
between the great majority of the physiological activities of the organ-
ism, those which show minimum intensities of relationships vnW be of
particular interest.
In this chapter we shall discuss the correlation between the two
physical characteristics available, stature and bodj^-weight and various
physiological measurements pertinent to metabolism investigations.
Another physical characteristic is body-surface area, but since this is
to receiv^e special attention in a subsequent chapter, it will be left out
of account here.
We shall, first of all, deal with the relationship between stature and
weight on one hand and pulse-rate on the other. We shall then con-
71
72 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
sider measures of the degree of interdependence of pulse-rate and
gaseous exchange and total heat-production. With these data at our
disposal, we shall proceed to a consideration of the relationship between
physical characters and metabolism.
Since the physical characteristics, stature and weight, have been
shown to be correlated, it is sometimes necessary in discussing the
relationship between either of these and physiological characters to
anticipate results to be given in detail later.
1. WEIGHT AND PULSE-RATE.
In the series of normal infants we find the correlation between
weight and pulse-rate, r^p, and the test of significance furnished by the
ratio of the constant to its probable error, r/E^ :
For males i\r=51, r,„/ = 0.3114 ±0.0853, r/Er = 3.65
For females iV = 43, ra,/> = 0.1570 ±0.1003, r/Er = 1.5Q
Difference 0.1544±0.1317
For both iV =94, r«,/ = 0.2289 ± 0.0659, r/Er = 3.47
The coefficient for females is only about 1.5 times as large as its
probable error, and so can not be considered to prove that there is any
correlation whatever between pulse-rate and body-weight.
The value for boys is numerically larger than that for girls, but in
comparison with its probable error the difference between the constants
for the two sexes is not statistically significant.
The constant for the male babies and that for male and female
babies suggest a real interdependence between weight and pulse-rate,
but the number of individuals is, statistically speaking, so small that
caution must be used in asserting that in male infants as a class there
is any relationship between pulse-rate and body-weight.
Even if one be inclined to accept these correlations as indicating a
real physiological relationship between body-weight and pulse-rate,
he must remember that it can not be asserted, without further analysis,
that there is a direct biological nexus between body-weight as such
and pulse-rate. Body-weight is correlated with stature, and it is quite
possible that the observed correlation between body-weight and
pulse-rate is in part at least the resultant of correlations between
stature (length) and body-weight and between stature (length) and
pulse-rate.
Furthermore, one must remember that all these variables may
change with age, and that in any detailed investigation covering the
whole period of fife such age changes must be fully taken into
account.
Consider first of all the correction to the correlation between
weight and pulse-rate to be made for stature. The partial correlation
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS,
73
I
between weight and pulse-rate for constant stature is required. Thus
_ 'wp 'los'tp
\/l-r„.2\/l-r.p2
gives the desired constants. In the infants the results are:
For males ^r^/=0.3073 ±0.0855
For females ^raa>=0.1442 ±0.1007
For both :rr,j.=0.2167 ±0.0663
Correction for stature has sHghtly but not materially reduced the corre-
lation between body-weight and pulse-rate. The partial correlations
for the males and for the males and females are about 3.6 times as large
as their probable errors and may be statistically significant.
The correlations between body-weight, iv, and pulse-rate, p, for the
several adult series and the partial correlations between body-weight
and pulse-rate for constant stature appear in table 17.
Table 17. — Correlation between weight and pulse-rate and partial correlation between
weight and pulse-rate with stature constant and with age constant.
Series.
N
Correlation
between weight
and pulse-rate
Er
Partial correla-
tion between
weight and
ptilse-rate
s^icp
J^wp
E
Partial correla-
tion between
weight and
pulse-rate
E r
a' wp
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary
series
Other than Gephart and Du Bois
selection
All men of three series
Women.
Original series
Supplementary series
Both series
I 28
116
I 50
121
-1-0.1579=
-0.1634 =
-1-0.0055 =
-0.1458 =
-1-0.0786 =
= 0.1644
= 0.0834
= 0.0719
= 0.0783
= 0.1267
0.96
1.96
0.08
1.86
0.62
H-0.0162± 0.0626 0.26
-1-0.1884 =
-f 0.0365 =
= 0.0920 2.05
= 0.0612 0.60
■0.2942 ±0.0747 1 3.94
-0.0872 ±0.1427, 0.61
-0.2483 ±0.0667: 3.72
-0.3548 ±0.1474
-0.0881 ±0.0850
-0.0402 ±0.0719
-0.0611 ±0.0797
-|-0.0957±0.1263
-0.0303 ±0.0626
-1-0.0198 ±0.0954
-0.0207 ±0.0613
■0.2835 ±0.0752
■0.1077±0.1421
■0.2398 ±0.0670
2.41
1.04
0.56
0.77
0.76
0.48
0.21
0.34
3.77
0.76
3.58
-h0.0673± 0.1679
-0.1904 ±0.0826
-1-0.0055±0.0719
-0.1608 ±0.0780
4-0.0894 ±0.0126
-1-0.0200 ±0.0626
-1-0.2121 ±0.0949
-1-0.0430 ±0.0612
0.40
2.31
0.08
2.06
7.10
0.32
2.23
0.70
-0.2971 ±0.0746 3.98
-0.1423±0.1409: 1.01
- 0.2359 ± 0.0671' 3.52
The constants are both low and irregular, sometimes negative and
sometimes positive in sign. They indicate practically no relationship
between body-weight and pulse-rate in men, but suggest a slight nega-
tive relationship in women, i.e., that slower pulse is associated with
greater body-weight. With regard to their probable errors the corre-
lations are practically without exception statistically insignificant in
magnitude. Only the original series of women and (through its influ-
ence) the total series of women show a correlation over 3 times as large
as its probable error.
74 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
If the influence of stature upon the correlation between body-weight
and pulse-rate be eliminated by determining the partial correlation
between body-weight and pulse-rate for constant stature, the results
are practically unchanged. The partial correlations, like the correla-
^
■80
.
•
■75
•
• •
•
•
■10
,
• • •
III
•
• • • •
•
1-
•
«
•
•
<
■Sf
****** •
^
^ ^
■f,o -
• • • • •• •
•
liJ
•• •• •
J
* "^
"'•'•• *" • •
*
•
)
•
•
Q.
■SS
■so
■4S
•
• • •
• •
• • •
•
•
•
3S
40
4S
SO
SS 60 6S 10
IS
80
55
90
95
100
105 no
BODY WEIGHT IN KILOGRAMS
Diagram 5. — Distribution of individual men with resp)ect to body-weight and
pulse-rate. Note the lack of relationship as shown by wide scatter of individual
measurements and slight slope of the line. Compare diagrams 6 and 7.
BOOV \A/E1GHT IN KILOGRAMS
Diagram 6. — Relationship between body-weight and pulse-rate in women.
Compare diagrams 5 and 7.
tions, are low and irregular in magnitude. Only the original and the
total series of women may be considered possibly significant in compari-
son with their probable errors.
Correcting for the possible influence of age by evaluating
T =
' tnn ' ntn ' n
Vl-r 2 Vl-3
PHYSICAL AND PHYSIOLOGICAL IktEASUREilEXTS. 75
we find the values given in comparison with the gross correlations in the
final column of table 17.
Correction for age has not materially changed the values.
The most interesting point about these results is the persistently
negative values for the women. We shall note that women seem to
differ from men in several correlations to be considered later.
The distribution of the indi\4dual observations for the grand total
male (A'' = 121) and grand total female (iY = 90) series is shown in the
two scatter diagrams 5 and 6. The straight lines are given by the
equations :
Men, p= 59.7782 +0.0232 u; Women, p= 78.5659 -0.1775 m;
The shghtness of the slope of the lines and the wide scatter of the dots
about the theoretical mean values show cleai'ly the insignificance of
the relationship between body-weight and pulse-rate in our series.
2. STATURE AND PULSE-RATE.
In the series of infants the correlation between stature (length) and
pulse-rate is:
For males N=5l r,p = 0.1529=»=0.0922 r/Er = lM
For females iV^=43 r,p = 0.0981=^0. 1019 r/^r = 0.96
I>ifference 0.0548 =*= 0.1374
For both iNr=94 r^ =0.1294 ±0.0684 r/£r=1.89
The value for the males is higher, but in comparison with its prob-
able error certainly not significantly higher, than that for the females.
Neither of the constants taken alone can be considered to differ sig-
nificantly from zero. That all three are positive in sign suggests that
there may be some sUght positive relationship between stature and
pulse-rate in infants.
But pulse-rate is more closely correlated in infants with body-
weight. Thus comparing the correlations of stature and weight we
have the f ollo^sdng values :
For ttature For w«ight and DiferencM in
and piU$«-rat«. puUe-raU. correlation.
Males 0.15-29 ±0.0922 0.3114±0.0853 0.1585±0.1256
Females 0.0931*0.1019 0.1o70±0.1003 0.0589±0.1430
Diflference 0.0548 =»= 0.1374 0.1544*0.1317
For both 0.1294*0.0884 0.2289*0.0659 0.0995*0.0950
For both males and females the correlation between weight and
pulse-rate is higher (but in comparison with its probable error not
significantly higher) than that between length and pulse-rate.
Since stature and weight are closely correlated, i.e., in infants
For males r^= 0.7703* 0.0384
For females r^ = 0.8&42 *0.0260
For both r_= 0.8209* 0.0227
76 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
it is necessary to ascertain the influence of the correlation between
weight and pulse-rate upon that between stature and pulse-rate.
Determining the correlation between stature and pulse-rate for
constant weight by the partial correlation formula
y/l—r ^Vl— r *
* •*• ' IV) ^ ^ ' wp
we have :
Tsfi ivTsp luTsp Tsf
In males 0.1529*0.0922 -0.1436 ±0.0925 -0.2965 ±0.1306
In females 0.0981±0.1019 -0.0756 ±0.1023 -0.1737 ±0.1444
In both sexes 0.1294 ±0.0684 -0.1053 ±0.0688 -0.2347 ±0.0973
Thus correction for weight has reversed the sign of the correlation
between stature and pulse-rate in infants. The partial correlations
are negative in sign, but neither can be considered statistically signifi-
cant in comparison with its probable error.
We now turn to the data for adults. These appear in the first
column of constants of table 18.
Table 18. — Correlation between stature and pulse-rate and partial correlation between
stature and pulse-rate with weight constant and with age constant.
Series.
N
Correlation be-
tween stature
and pulse-rate
^r.
Partial correla-
tion between
stature and
pulse-rate
w^sp
E
Partial correla-
tion between
stature and
pulse-rate
a^tp
E r
«P
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary
series
Other than Gephart and Du Bois
selection
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
88
71
28
116
50
121
-f0.5376±0.1199
-0.2108 ±0.0818
-1-0.0728 ±0.0715
-0.1498±0.0783
-|-0.0200±0.1274
-1-0.0710 ±0.0623
4-0.3339 ±0.0848
-f-0.0916±0.0608
-0.0844 ±0.0812
-0.0014±0.1438
-0.0669 ±0.0708
4.48
2.58
1.02
1.91
0.16
1.14
3.94
1.51
1.04
0.01
0.94
-f-0.6021 ±0.1075
-0.1607 ±0.0834
-1-0.0829 ±0.0714
-0.0703 ±0.0796
-0.0583±0.1270
-f0.0754± 0.0623
-f0.2814± 0.0878
-f0.0S65± 0.0609
-0.0214±0.0817
-f 0.0635 ±0.1432
-1-0.0107 ±0.0071
6.60
1.93
1.16
0.88
0.46
1.21
3.21
1.42
0.26
0.44
1.51
-1-0.4883 ±0.1284
-0.2157±0.0817
-1-0.0486±0.0717
-0.1502 ±0.0782
-1-0.0240 ±0.1274
-f-0.0550± 0.0624
-1-0.3102 ±0.0862
-1-0.0772 ±0.0612
-0.0738 ±0.0813
-0.0455 ±0.1435
-0.0542 ±0.0709
3.80
2.64
0.68
1.92
0.19
0.88
3.60
1.27
0.91
0.32
0.76
The values are partly negative and partly positive in sign. They
vary widely in magnitude. For the athletes the constant is positive
and of medium magnitude, but the 62 other men give a negative corre-
lation of the order r = —0.2. As a result, the correlation for the whole
series is, in comparison with its probable error, sensibly zero. The
same is true for the first supplementary series of men and for the whole
series of men (121 in number) for which records of both stature and
pulse-rate are available. For all three of these larger series the corre-
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
77
lation is, however, positive in sign, indicating that taller indi^^duals
have a more rapid pulse. If, however, one turns to the Gephart and
Du Bois selection of male subjects he finds a negative correlation of
the order r= —0.15, thus indicating that the taller men have a less
rapid pulse. This is also the relationship suggested by the constants
for the women, who give a consistently negative but statistically
insignificant correlation.
Inspection of the means obtained without grouping the values for
stature — as given in diagram 7 for the total available men (iV = 121)
and for the total available women (A' = 90) — shows (a) how widely
scattered the average pulse-rates for any given stature are, and (6)
TS
%
hh f.
t r; «
. •
■70
■+ * • ' •
» ' » ** • , *
*'
n^iT^T"
/~~^ritr^^i^
, I r -
"
■€$
JlMJ^
." • ■• *
-
—
■SO
_JL.MeNj:^
^r^nfiVV
<Ta^^^^
i ':.■
1 i «
ss
'.;
■50
i!
4S
i
»8
IS3 /rs
/« /£8 173
na t83 les
m
iZi
S"'-~-^'<h: \u cE^iTI^^ETE=<s
Diagram 7. — Variation of mean basal pulse-rate with stature in men and women. Note
extreme irregularity of means and different slojjes of the straight lines in the two sexes.
Compare diagrams 5 and 6 for bodj'-weight and pulse-rate.
how shght is the change in average pulse-rate associated with differ-
ences in stature. The straight lines in the diagrams are due to the
equations :
For men iV^=121 p=47.7179+0.0783 •
For women iV^= 90 p= 86.0430 -0.1073*
If the relationship between stature and pulse-rate be corrected for
the correlation of weight with stature, we find the partial correlations
between stature and pulse for constant weight, like the uncorrected
correlations, are low in magnitude and irregular with regard to sign.
The exception is the athletes, but these are too few in number to justify
attaching much significance to the probable errors of the constants.
Tlie partial correlations between stature and pulse-rate for constant
age are given by
r =
T — r T
' »v ' as ' a
Vl-r » Vl-j
The results obtained by appljong this formula appear in the final
column of table 18.
78 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Correction for age has not materially changed the values of the
constants.
Summarizing the results of these various calculations we note that
in male and female infants and in our male adults taken as a class there
is a suggestion of positive correlation between stature and pulse-rate,
i.e., of an increase of pulse-rate with stature. In the adults this is,
however, largely due to the athletes and the vegetarians in the original
series. The Gephart and Du Bois selection of males and the female
series suggest a negative relationship between stature and pulse-rate.
Thus the results for infants and adults, if either are really biologically
significant, indicate a different relationship at the two ages.
As far as the available data justify conclusions concerning the
problem, they seem to indicate that there is only a very slight, if any,
interdependence between stature and minimum. or basal pulse-rate in
man.
3. PULSE-RATE AND GASEOUS EXCHANGE.
Since it is well known that pulse-rate and gaseous exchange are
closely related in the individual, it seems desirable to determine
whether in a series of individuals at complete muscular repose and in
the post-absorptive state a correlation between pulse-rate and gaseous
exchange and between pulse-rate and total heat-production will be
found to exist.
Table 19. — Correlation between pulse-rate and gaseous exchange.
Series.
N
Correlation be-
tween pulse-rate
and carbon-dioxide
Correlation be-
tween pulse-rate
and oxygen
Difference
^po ^pc
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series . . . .
Other than Gephart and Du Bois selection
All men of three series
Women,
Original series
Supplementary series
Both series
15
62
87
70
28
115
50
120
66
22
-1-0.2981 =
-1-0.0306 =
-1-0.1416 =
-f0.0691 =
-h0.1387=
-f0.1482 =
-f 0.2384 =
-1-0.1539 =
-0.0734 =
4-0.4811 =
-t-0.0497 =
= 0.1587
= 0.0856
= 0.0709
= 0.0802
= 0.1250
= 0.0615
= 0.0900
= 0.0601
= 0.0826
= 0.1105
= 0.0717
16
62
88
71
28
116
50
121
-1-0.2963=*= 0.1538
-1-0.0718 =t 0.0852
-f0.2045 =1=0.0689
-1-0.1 197 =4=0.0787
-1-0.2085 =t 0.1219
-1-0.1976=1=0.0602
-hO.2788 =4=0.0880
-f-0.2012=fc 0.0588
-i-0.0318=fc 0.0817
4-0.3656 ±0.1246
-1-0.1331=^0.0698
-0.0018 =
-1-0.0412 =
4-0.0629 =
-t-b.0506 =
4-0.0698 =
4-0.0494 =
4-0.0404 =
4-0.0473 =
= 0.2210
= 0.1208
= 0.0989
= 0.1126
= 0.1746
= 0.0861
= 0.1259
= 0.0841
4-0.1052 =fc 0.1 162
- 0. 1 155 =fc 0.1665
4- 0.0834=*= 0.0100
Table 19 gives the correlations between pulse-rate and oxygen con-
sumption and pulse-rate and carbon-dioxide production, and the differ-
ences in these correlations, for the various series with which we have
worked. The results are reasonably consistent in indicating a low but
significant positive correlation between pulse-rate and oxygen con-
sumption and pulse-rate and carbon-dioxide excretion, larger gaseous
exchange being associated with more rapid pulse-rate.
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
79
In the original series of women we find a slight negative correlation
between pulse-rate and gaseous exchange, the women with the slower
pulse showing the higher carbon-dioxide excretion. For oxygen con-
sumption the correlation is sensibly zero. The second series shows a
substantial positive correlation. The slight negative relationship
between pulse-rate and carbon-dioxide excretion in the original series
of women naturally pulls down the positive correlation in the supple-
mentary series, so that a resultant low positive correlation is obtained
in the total series of women.
The correlation between pulse-rate and oxygen consumption is more
intimate than that between pulse-rate and carbon-dioxide excretion.
If we determine the partial correlation between pulse-rate and
gaseous exchange for constant body-weight by the formulas
D' Ofl
T — r
Vl-r„p'Vl-;
r =
' tirf" • trn ' ii
Vl-r^p'Vl-i
we find the results set forth in table 20.
Table 20. — Comparison of partial correlations between pulse-rate and gaseous exchange for
constant body-weight tcith gross correlations between pulse-rate and gaseous exchange.
Series.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection . . . .
First supplementary series
Original and first supplementary
series
Other than Gephart and Du Bois
selection
All men of three series
Women.
Original series ,
Supplementary series ,
Both series
N
15
62
87
70
28
115
50
120
Partial correla-
tion between
pulse-rate and
carbon-dioxide
Differ-
ence
-1-0.5640=
-f-0.1540=
-F0.1835 =
-1-0.2931 =
4-0.1278 =
= 0.1188
= 0.0836
= 0.0699
= 0.0737
= 0.1254
-1-0.2207=*= 0.0598
+0.1488=
-1-0.2027=
= 0.0933
= 0.0590
66 4-0.2242=*= 0.0788
22 -1-0.6485 ±0.0833
88 -1-0.2006=*= 0.0690
4.75
1.84
2.63
3.98
1.02
3.69
1.60
3.44
2.84
7.79
2.91
N
Partial correla-
tion between
pulse-rate and
oxj-gen
uTpo
4-0.2659, 16|4-0.5205=*=0.1229
4-0.1234, 62'4-0.2261=*= 0.0813
4-0.04191 884-0.3342^0.0639
4-0.2240 71 1 4-0.3802 =t 0.0685
-0.0109 28 4-0.2865 ±0.1 170
4-0.0725 116
4-0.3207 ±0.0562
-0.0896| 50 4-0.2244=*= 0.0906
4-0.0488 121 i 4-0.2938=*= 0.0560
4-0.2976
4-0.1674
4-0.1509
68 4- 0.4002 ±0.0687
22 14-0.5420 ±0.1016
90; 4-0.3781 ±0.0609
E
4.24
2.78
5.23
5.55
2.45
5.71
2.48
5.25
5.83
5.34
6.21
Differ-
ence
4-0.2242
4-0.1543
4-0.1297
-F-0.2605
4-0.0780
4-0.1231
-0.0544
4-0.0926
4-0.3684
-H0.1764
4-0.2460
In general, correction for body-weight has increased the intensity
of relationship between pulse-rate and gaseous exchange. This indi-
cates that the relationship is a real physiological one, and not merely
the incidental resultant of the correlation of both pulse-rate and
gaseous exchange with body-mass. The partial correlations for the
two series of women are now in agreement as far as signs are con-
cerned. These relationships will be analyzed more minutely on the
basis of total calories produced.
80
A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
4. PULSE-RATE AND TOTAL HEAT-PRODUCTION.
Table 21 gives the coefificieiits for pulse-rate and total heat-produc-
tion and for pulse-rate and total heat-production per kilogram of
body-weight.
The correlations for pulse-rate and total heat are all positive in
sign but numerically low and extremely variable in magnitude. In the
latter regard they are in full agreement with the constants for pulse-
rate and gaseous exchange, as is to be expected from the method of
computing the heat-production from gaseous exchange.
Table 21. — Comparison of correlations between pulse-rate and gross heat-production and
betiveen pulse-rate and heat-production per kilogram of body-weight.
Series.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First stipplementary series
Original and first supplementary series
OtherthanGephart and DuBoia selection
All men of three series
Women.
Original series
Supplementary series
Both series
N
16
62
88
71
28
116
60
121
68
22
90
Pulse-rate and
total heat
0.3041 ±0
0.0650 ±0.
0.1986±0
0.1103±0
0.1964±0,
0.1887=fc0.
0.2721 ±0,
0.1928±0.
1530
0853
0691
0791
1226
0604
0883
0590
0.0155 ±0.0818
0.3923±0.1217
0.1224 ±0.0700
'^ph
^ph
1.99
0.76
2.87
1.39
1.60
3.12
3.08
3.27
0.19
3.22
1.75
Pulse-rate and
heat per kilo-
gram of body-
weight
0.2783 ±0.
0.2947 ±0.
0.2722 ±0.
0.4048 ±0,
0.2179±0.
0.2583 ±0.
0.0613 ±0.
0.2285 ±0.
1556
0782
0666
0669
1214
0584
0950
0581
0.4621 ±0.0643
0.3317 ±0.1280
0.4240 ±0.0583
""ph^
Er
V^i
1.79
3.77
4.09
6.05
1.79
4.42
0.65
3.93
7.19
2.59
7.27
Difference
Diff.
^diff.
-0.0258±0.2182
0.12
-1-0.2297 ±0.1157
1.99
+0.0736± 0.0960
0.77
-1-0.2945±0.1036
2.84
-H0.0215±0.1725
0.12
-j-0.0696± 0.0840
0.83
-0.2108±0.1297
1.63
-f- 0.0357 ±0.0828
0.43
-|-0.4466±0.1040
4.29
-0.0606 ±0.1 760
0.34
-f-0.3016± 0.0910
3.31
Before deciding that physiologically there is a very slight correla-
tion between pulse-rate and gaseous exchange or pulse-rate and total
heat-production one must remember that the measures of gas volume
are to a considerable degree dependent upon the absolute size of the
individuals upon which they are based. To determine more exactly
the true physiological interdependence between pulse-rate and total
heat-production, some correction for the absolute size of the organism
must, therefore, be made. This may be done in either of two ways :
First, one may correct for size directly in the case of each individual
by reducing gross heat-production to calories per kilogram or calories
per square meter of body-surface.
Second, one may work with final constants merely by determining
the partial correlation between pulse-rate and total heat-production
for constant stature, constant body-weight, or constant stature and
body-weight.
With the exception of the small series of athletes and the group
other than the Gephart and Du Bois selection among the men and the
supplementary series of women, all of the values are raised when the
influence of extreme variation in body-size is to some extent elimin-
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
81
ated by expressing heat-production in calories per kilogram of body-
weight. The magnitude of the difference between the correlations for
pulse and total heat and pulse and heat per kilogram of body-weight
is not large. In no series of men excepting the Gephart and Du Bois
selection can the difference be looked upon as statistically significant
in comparison with its probable error. Nevertheless the consistency
of the results from the larger series certainly indicates that correction
for the influence of body-mass upon total heat-production has increased
somewhat the closeness of interdependence between the rate of heart-
beat and metabolism. In the women the original series and the total
series show significantly larger positive correlations between pulse-rate
and heat per kilogram than between pulse-rate and total heat-produc-
tion. This is not, however, true of the supplementary series.
Table 22. — Comparison of correlation between pulse-rate and total heat-production and between
pulse-rate and heat-production per square meter of body-surface.
Series.
N
Pulse-rate and
heat per square
meter by Meeh
formula
^phji
Difference
Diff.
Ediff.
Pulse-rate and
heat per square
meter by
Du Bois
height-weight
chart
rphj)
Difference
Diff.
Ediff.
0.43
2.17
1.51
2.73
0.56
1.44
0.88
1.11
3.24
0.85
3.04
E,.
Men.
Original series:
Athletes
others
Whole series . .
Gephart and
Du Bois se-
lection
First supplemen-
tary series. . . .
Original and first
supplementary
series
16
62
88
71
28
116
50
121
68
22
90
0.5779*0.1123
0.2847 ±0.0787
0.2820*0.0662
0.3835*0.0683
0.2836*0.1172
0.2754*0.0579
0.1981*0.0916
0.2522*0.0574
0.4712*0.0636
0.4705*0.1120
0.4522*0.0566
5.15
3.62
4.26
5.61
2.42
4.76
2.16
4.39
7.41
4.20
7.99
-1-0.2738*0.1223
-1-0.2197*0.1160
-f0.0834* 0.0957
-1-0.2732*0.1045
-f0.0872* 0.1696
-H0.0867* 0.0836
-0.0740*0.1272
-1-0.0594*0.0823
-1-0.4557*0.1036
-1-0.0782*0.1654
-hO.3298* 0.0900
2.24
1.89
0.87
2.61
0.51
1.04
0.58
0.72
4.39
0.47
3.66
0.2083*0.1613
0.3140*0.0772
0.3408*0.0636
0.3949*0.0676
0.2905*0.1167
0.3082*0.0567
0.1590*0.0930
0.2837*0.0564
0.3663*0.0708
0.5283*0.1037
0.4020*0.0596
1.29
4.07
5.36
5.84
2.49
5.44
1.71
5.03
5.17
5.09
6.74
-0.0958*0.2223
-H0.2490*0.1150
-f-0.1422* 0.0939
-1-0.2846*0.1041
-1-0.0941*0.1693
-fO.l 195* 0.0828
-0.1131*0.1282
+0.0909*0.0816
-h0.3508* 0.1082
-f0.1360*0.1599
-}-0.2796* 0.0919
Other than Gep-
hart and Du
Bois selection . .
All men of three
series
Women.
Original series. . .
Supplementary
series
Both series
Table 22 gives comparisons of the correlations between pulse-rate
and total heat-production as given in table 21 and pulse-rate and heat-
production per square meter of body-surface by the two surface-area
formulas used in this memoir.
The same type of relationship as that seen in the comparison of the
correlations for pulse-rate and gross heat-production and pulse-rate
and relative heat-production on a weight basis is apparent.
82 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The correlations between pulse-rate and calories per square meter
of body-surface by both methods of measurement are higher than the
correlations between pulse-rate and gross heat-production in every
series except the athletes and the individuals other than the Gephart
and Du Bois selection as estimated by the Du Bois height-weight chart
and the individuals other than the Gephart and Du Bois selection as
estimated by the Meeh formula. The differences in these anomalous
series are smaller than their probable errors.
Since it has been shown in the preceding discussion that correction
for body-size increases the intensity of the correlation between pulse-
rate and heat-production, it is worth while to inquire which method of
correction brings about the maximum intensity of interrelationship in
these two physiological measurements.
Table 23. — Comparison of correlations between pulse-rate and heat-production for body-size by
various methods.
Series.
N
Difference
Difference
Difference
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection. . .
First supplementary series
Orig'al and first supplementary series
Other than Gephart and Du Bois
sel action
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
88
71
28
116
50
121
+0.2996=*= 0.1919
-0.0100=^0.1109
+0.0098 =t 0.0939
-0.0213 ±0.0956
+0.0657=^0.1687
+0.0171=4=0.0822
+0.1369=*= 0.1320
+0.0237 ±0.0817
+0.0091 ±0.0904
+0.1388±0.1701
+0.0282 =t 0.0813
-0.0700=*= 0.2241
+0.0193=4=0.1099
+0.0686 ±0.0921
-0.0099 ±0.0951
+0.0726± 0.1684
+0.0499 ±0.0814
+0.0977 ±0.1329
+0.0552 ±0.0810
-0.0958 ±0.0956
+0.1966± 0.1647
-0.0220 ±0.0834
+0.3696 ±0.1965
-0.0293±0.1102
-0.0588±0.0918
-0.0114±0.0961
-0.0069 ±0.1654
-0.0328 ±0.0810
+0.0392±0.1305
-0.0315 ±0.0806
+0.1049 ±0.0952
-0.0578±0.1526
+0.0502 ±0.0822
This step involves (a) the comparison of the influence of correction
for the two measures of surface with that of the influence of correction
for body-weight and (6) the comparison of the two measures of surface-
area themselves. The results are shown in table 23. These are very
consistent throughout, although because of the smallness of several
of the series the probable errors of the differences are very high.
With few exceptions it appears that the correlation between pulse-
rate and heat-production per square meter of body-surface, whether
measured by the Meeh formula or by the Du Bois height-weight
chart, is higher than that between pulse-rate and heat per kilogram
of body-weight. Again, a comparison of the correlation between
pulse-rate and heat per square meter of body-surface by the two
methods of measurement, suggests that the correlation with body-
surface as measured by the Du Bois height-weight chart gives
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
83
numerically higher constants than those obtained by the use of the
Meeh formula.
These results have an obvious bearing upon the so-called Rubner's
or body-surface law, to be discussed in detail in Chapter VI.
5. WEIGHT AND GASEOUS EXCHANGE.
The correlation coefficients for body-weight and oxj-gen consimip-
tion and for body-weight and carbon-dioxide excretion appear in table
24. For both gases the correlations are for the most part of a rather
high order of magnitude and, with certain exceptions to be discussed
in a moment, of a high degree of consistency.
Table 24. — Correlations between hody-weight and gaseous exchange.
SOIM.
N
Correlation
between body-
weight and
carbon-dioxide
N
Correlation
between body-
weight and
oxj-gen
E,
Difference
Diff.
Ediff.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection . . .
First supplementary series
Original and first supplementary
series
Second supplementary series
Other than Gephart and Du Bois
selection
All men of three series
Women.
Original series
Supplementary series
Both series
0.9354^0.0218
0.5741*0.0574
0.7736 =fc 0.0289
0.7670*0.0329
0.8066*0.0445
42.91 16 0.9595*0.0134
10.00 62 0.6255*0.0521
116 0.7812*0.0244
19 0.5042*0.1154
64 0.7537*0.0364
1350.7575*0.0247
66
35
101
0.7332*0.0384
0.4251*0.0934
0.6266*0.0408
26.77
23.31
18.13
32.02
4.37
20.71
30.67
19.09
4.55
15.36
89
72
28
117
19
0.8007*0.0257
0.7828*0.0308
71.60 -f0.0241 ±0.0256' 0.94
12.0li-{-0.0ol4* 0.0775 0.66
31.16' -1-0.0271*0.0387 0.70
25.42'-|-0.015S*0.0451 0.35
0.8719*0.0306 28.491 -|- 0.0653* 0.0540 1.21
0.8179*0.0206
0.5778*0.1031
64 0.8040*0.0298
136 0.7955*0.0212
6810.7508*0.0357
3510.4583*0.0901
10310.5950*0.0429
39.70' -1-0.0367=
5.60!-f0.0736=
= 0.0319
= 0.1547
26.98, -1-0.0503 * 0.0470
37.52; -1-0.0380* 0.0325
21.03-1-0.0176*0.0524 0.34
5.09 -f0.0332* 0.1298 0.26
13.87-0.0316*0.0592! 0.53
1.15
0.48
1.07
1.17
Generally speaking, the correlations for both weight and oxygen
consumption and weight and carbon-dioxide production are of the order
r = 0.75 in men — that is to say of three-quarters of perfect inter-
dependence. This is also true in the original series of women. The
second series, of only 35 women, shows a much lower degree of inter-
dependence, with the result that the total women show a correlation
of the order r = 0.60.
Among the men the small second supplementary series shows the
lowest relationship, measured by a coeflBcient of about the same order
as those found in the women.
We shall consider the relative values of the correlations between
physical characters and oxygen consumption and carbon-dioxide pro-
duction, and the relative magnitudes of the correlations for weight
and gaseous exchange and stature and gaseous axchange after the
I
84
A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
relationship between stature and gaseous exchange has been dis-
cussed in section 6.
The characteristic equations showing the change in gas volume
with a variation of 1 kilogram of body-weight are given in table 25
Table 25. — Straight-line regression equations showing relationship of gaseous exchange to
body-weight
Series.
A^
Regression of CO2
on body-weight.
N
Regression of Oj
on body-weight.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series. . .
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
15
62
88
71
28
116
19
64
135
66
35
101
C = 59.40+2.
C =125.10+1.
C = 71.88+1.
C = 60.55+2.
C = 74.02+1,
C = 71.73+1.
C =104.32+1
C = 81.23+1,
C = 73.98+1.
33 TF
05 TT
93 TF
IITF
84 TF
92 TF
47 TF
78 TF
89 TF
C = 87.19+1,30 TF
C =123.99+0.62 TF
C =101.93 + 1.02 TF
16
62
89
72
28
117
19
64
136
35
103
= 77.63+2.56 TF
=138.91 + 1.46 TF
= 95.82+2.16 TF
= 83.44+2.36 TF
= 59.74+2.73 TF
= 87.30+2.29 TF
=103.99+2.00 TF
= 90.41+2.23 TF
= 88.48+2.27 TF
=1 14.31 + 1. 49 TF
=134.12+0.95 TF
=128.05+1.17 TT
BODY WEIGHT IN KILOGRAMS
Diagram 8. — Relationship between body-weight and oxygen consumption by women.
and represented graphically in diagrams 8 and 9. The results show that
in the women the increase in oxygen consumption ranges from 0.95
to 1.49 c.c. for each kilogram of weight, whereas in the series of men
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
85
the increase varies from 1.46 to 2.73 c.c. for each kilogram of weight.
The increase in the volume of CO2 with increase in body-weight is in
everj^ instance less than the increase in the volume of O2 with body-
weight. Thus, in the women CO2 production increases 0.62 c.c. per
kilogram of weight in the supplementary' series and 1.30 c.c. per kilo-
gram of weight in the original series. In the larger series of men the
increase in CO2 output per kilogram of body weight ranges from 1.05
to 2.11 c.c. For the total series oxygen consumption increases about
1.17 c.c. in women and 2.27 c.c. in men for each kilogram of bodj^-
weight. Carbon-dioxide excretion increases about 1.02 c.c. in the
BODY WEIGHT
Diagram 9. — Relationship between body-weight and oxj'gen consumption by men.
women and 1.89 c.c. in the men. This result would be expected from
the fact that the respiratory quotient is practically always less than
unity.
The significance of the differences in the exchange of the two gases
will be discussed below. The difference between the two sexes will be
treated on the basis of total heat-production in Chapter VII.
6. STATURE AND GASEOUS EXCHANGE.
The correlations between stature and gaseous exchange appear in
table 26. The coefficients for the relationship between stature and
both oxj'gen consumption and carbon-dioxide production in men are
of medium or moderately high value and, considering the relatively
few indi\iduals (in the statistical, not the physiological, sense), are
remarkably consistent throughout.
I
86 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The most conspicuous feature of this table is the low value of the
correlations for the women as compared with the men. Expressing
these results in terms of regression we have the straight-line equations
in table 27. The second constant in these equations shows that in
Table 26. — Comparison of correlations oj oxygen consumption and of carbon-dioxide excretion
with stature.
Series.
Men.
Original seiies:
Athletes
Others
Whole series
Gephart and Du Bois selection . . .
First supplementary series
Original and first supplementary
series
Second supplementary series
Other than Gephart and DuBois
selection
All men of three series
Women.
Original series
Supplementary series
Both series
N
15
62
88
71
28
116
19
64
135
66
35
101
Correlation
between
stature and
carbon-
dioxide
0.7677 ±0.0715
0.3830 ±0.0730
0.6013 ±0.0459
0.5699 ±0.0540
0.7179 ±0.0618
0.6065 ±0.0396
0.4102 ±0.1287
0.6019=
0.5882 =
= 0.0538
= 0.0380
0.2416 ±0.0782
0.2937 ±0.1042
0.2575 ±0.0627
10.74
6.25
13.10
10.55
11.62
15.32
3.19
11.19
15.48
3.09
2.82
4.11
N
16
62
89
72
28
117
19
64
136
68
35
103
Correlation
between
stature and
oxygen
0.7798 ±0.0661
0.4287± 0.0699
0.6063 ±0.0452
0.5974 ±0.0511
0.6972 ±0.0655
0.6190± 0.0385
0.5840 ±0.1020
0.6271 ±0.0512
0.6140 ±0.0360
0.1918±0.0788
0.3182±0.1025
0.2331 ±0.0628
E,
Difference
r — r
11.80 +0.0121 ±0.0974
6.13+0.0457±0.1011
13.41 +0.0050 ±0.0644
11.69 +0.0275 ±0.0743
10.64 -0.0207 ±0.0901
16.08
5.73
12.25
17.06
2.43
3.10
3.71
+0.0125 ±0.0552
+0.1738±0.1639
+0.0262 ±0.0743
+0.0258 ±0.0523
-0.0498± 0.1110
+0.0245±0.1460
-0.0244 ±0.0887
Diff.
Editr.
0.12
0.45
0.08
0.37
0.23
0.23
1.06
0.34
0.49
0.46
0.17
0.28
Table 27. — Equations showing variation of gaseous exchange with stature.
Series.
Regression of CO2
on stature.
N
Regression of O2
on stature.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series .
Second supplementary series
Other than Gephart and DuBois selection
All men of three series
Women.
Original series
Supplementary series
Both series
15
62
88
71
28
116
19
64
135
66
35
101
=-219.65+2.565
=+ 31.69+0.93S
=-160.51 + 2.075
=-136.80+1.915
=-177.44+2.105
=-155.98+2.035
=-113.11 + 1.815
=-164.04+2.085
= -152.74+2.015
=+ 13.78+0.895
=- 4.10+1.025
=+ 7.60+0.945
16
62
89
72
28
117
19
64
136
68
35
103
=-242.65+2.875
=+ 2.33+1.335
=-163.32+2.255
=-140.18+2.165
=-258.58+2.805
=-170.27+2.345
=-293.91+3.055
=-206.60+i2.555
=-177.27+2.385
O =+ 69.99+0.775
0 =- 62.07+1.565
0 =+ 29.93+1.015
women oxygen consumption increases from about 0.75 to 1.50 c.c. for
each centimeter of stature, whereas in men the values are 2 to 3 c.c.
for each centimeter of stature. Comparable but somewhat lower
values are found for CO2 excretion.
Diagram 10 shows the mean oxygen consumption of men and
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
87
women of different statures. Comparable values for carbon-dioxide
elimination are represented in diagram 11. The straight lines are
given by the equations for total men and women in table 27.
Because of the relatively small numbers of indi\'iduals for statistical
work, the medium value of the correlation between stature and gaseous
exchange, and the wide variation in stature and gas volume, the
means show great irregularity. The straight line probably represents
the four sets of averages as well as any other single curve of a
higher order. At least it does not seem worth while at the present
time to try any other equation until further materials are available.
■360
•
3*0
3Z0
300
%
^
230
• ^^^
^--''^
■260
■2*0
>-^ ; \ > *
■220
■700
■ISO ^
<*
« ;
b-'
v." v'
1*8
/}?
ISS
1^0 mi iss
m
nS 180 '?» '5?
192
I9S
J
STATURE IN CENTIMETERS
Diagram 10. — Mean oxj-gen consumption by men and women of various statures.
In this and the preceding sections we have shown that oxj'gen
consumption and carbon-dioxide excretion are correlated with both
body-weight and stature and have discussed the degree of the relation-
ship. We now have to inquire whether the correlations between physi-
cal characters and gaseous exchange differ consistently in the case of
the two gases. It might at first appear that these two values should
be identical, but that the correlations between the physical characters
and gaseous exchange would not necessarily be identical for the two
gases is shown by the fact that the correlation between the two meas-
ures of gaseous exchange, while necessarily verj' high indeed, is not
perfect. This point is brought out by the discussion of the correlation
between oxygen consumption and carbon-dioxide production in
Chapter III.
88 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Turning to the question of the relative magnitude of the correlation
between physical measurements and oxygen consumption and physical
measurements and carbon-dioxide excretion, we may refer to the differ-
ences between the correlations for weight and the two gases as given
in table 24 and for stature and the two gases as set forth in table 26.
The correlation for weight and gaseous exchange shows that, with
an insignificant exception in the case of the total women, the relation-
ship between body-weight and the amount of oxygen consumed is
higher than that between body-weight and the quantity of carbon-
dioxide eliminated. The same is true, with three exceptions only, in
the lower correlations between stature and gaseous exchange.
ISZ .'S6 leo f£4- 168 172 176 180 184- 188 ISZ 196
STATURE IN CENTIMETERS
Diagram 11. — Mean carbon-dioxide production by men and women of various statures.
The differences in correlations between body-weight and stature
and the two gases are of a low order of magnitude, and because of the
small number of individuals available can not be considered statistically
significant for the individual series; but taking the data as a whole,
there can be scarcely a doubt that the correlations between physical
characters and oxygen consumption are significantly higher than those
for physical characters and carbon-dioxide excretion.
In view of the fact that the total volume of oxygen consumed is
not excreted as carbon dioxide, one might perhaps have expected the
lower correlation between physical characters and gaseous exchange
to be found for the gas which, considered alone, gives the minimum
measure of the katabolic transformations occurring in the body. The
same relationship has been shown to hold in the correlation between the
volume of the two gases and pulse-rate discussed on page 78.
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
89
The second point of interest pertains to the problem of the relative
magnitude of the correlations for weight and gaseous exchange and
stature and gaseous exchange.
The differences between the correlations for stature and oxygen
consumption and carbon-dioxide excretion, and body-weight and oxy-
gen consumption and carbon-dioxide excretion are shown in table 28.
With one single and numerically insignificant exception in the case of
oxygen, the correlation between weight and gaseous exchange is higher
than that between statiu-e and gaseous exchange. A number of the
differences are large enough in comparison with their probable errors
to be looked upon as statistically significant.
Table 28. — Comparison of correlations between weight and gaseous exchange and stature and
gaseoris exchange.
Series.
A'
Difference
Diff.
E
diff.
N
Difference
Diff.
'diff.
Men.
Original series :
Athletes
Others
Whole series
Gephart and Du Bois selection. . .
First supplementary series
Orig'al and first supplementary series
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
+0.
+0,
+0.
+0.
+0.
+0.
-0.
+0
1797 ±0.
196S=fcO.
1944 ±0.
lSo4±0.
1747 ±0.
1989 ±0.
0061±0.
1815^0.
0674
0872
0520
0597
0723
0437
1449
0418
+0.5590 ±0.0865
+0.1401±0.1364
+0.3619=^0.0761
2.67
2.26
3.74
3.11
2 42
4.55
0.04
4.34
6.46
1.03
4.76
15 +0.1677=
62 +0.1911 =
88+0.1723 =
+0.1971 =
+0.0887 =
+0.1747 =
+0.0940=
+0.1693 =
71
28
116
19
135
= 0.0747
= 0.0929
= 0.0542
= 0.0632
= 0.0762
= 0.0465
= 0.1729
= 0.0453
2.24
2.06
3.18
3.12
1.16
3.76
0.54
3.74
66+0.4916±0.0S71 5.64
351+0.1314*0.0140 9.39
101 +0.3691 =fc 0.0748: 4.93
Body-mass is, therefore, a more important factor in determining
(in the statistical but not necessarily in the causal sense) gaseous
exchange than is stature.
7. WEIGHT AND TOTAL HEAT-PRODUCTION.
That large individuals should produce absolutely more calories
than small ones would seem a natural a priori assumption. Our prob-
lem at this moment is to determine how intimate is the relationship
between body-mass and heat-production. Examining, first of all, the
results for the series of infants we find :
For males A^ = 51
For females A" =43
r^A =0.7520 =tO.(Mll
r-u A = 0.8081=^=0.0357
rE.= 18.30
r/£r= 22.64
Difference 0.0561 =fc0.0544
Disregarding sex and treating boy and girl babies together, we have
r«* =0.7833 ±0.0269 r/Er = 29,12
90 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
These results are larger than those for stature (length) and total
heat, which are 0.1329=^0.0712 smaller for males, 0.0655=^0.0583
smaller for females, and 0.0985=*= 0.0457 smaller for male and female
babies considered together.
The change in actual heat-production in calories per 24 hours for a
variation of a kilogram in body-weight is shown by the regression
equations, which are :
For males A =25.16 +34.52 tr
For females A =26.18+34.23 w
The results are in remarkably close agreement. In both male and
female babies a difference of 100 grams in weight between two subjects
would mean a probable difference of 3.4 calories in their daily
heat-production. The results are represented graphically in diagram
-190
f ^
■180
/ / ^"^
no
^)/j
■160
/-,,
X/'
m
/^
~^-v'
■MO
^■^^y
w
.»--_
^
^^^<.'-^'
■ao
y^
"'"--o-'
•■--•- MALE INFANTS
•— «- FEMALE INFANTS
^y
--'
^-'
229
2G4-
299
334
369
4.04 433 47*
BODY WEIGHT
Diagram 12. — Mean total daily heat-production by male and female infants of
various body-weights.
12. The lines for the boy and girl babies lie very close together indeed.
While the observed means show considerable irregularity, this is appar-
ently attributable to the (statistically) small number of observations
available, and a straight line seems to serve quite as well as a curve
of a higher order to smooth the results.
Turn now to the available data for the adults. The correlations
between body-weight and heat and the partial correlations between
body-weight and heat-production for constant stature are set forth in
table 29.
Considering first the actual correlations between body-weight and
total heat-production, it is clear that the relationships are very high.
For men they are of the order r = 0.80 in the larger series, although the
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
91
smaller subdi\'isions show fluctuations from r = 0.58 for the 19 men of
the second supplementary series to r = 0.96 for the 16 athletes of the
original series.
For women the results are somewhat lower. For the original series
the correlation is r = 0.76, a value in good accord with that for men,
but the constant for the supplementary series is only r=0.45, a con-
stant lower than the minimum relationship found in the several group-
ings of men. The low value in this supplementary series has the effect
of reducing the measure of interdependence based on the original
female series when the two are combined, with the resultant correlation
of r =0.61 for the 103 women.
Table 29. — Comparison of correlation between weight and total heat-production and partial
correlation between weight and total heat-production with stature constant.
Series.
AT
Correlation
between weight
and heat-
production
'^wh
Partial corre-
lation between
weight and heat-
production
s^tch
J^wh
Difference
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Oiiginal and first supplementary series. . .
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
0.9577 ±0,
0.6251 ±0.
0.8012 ±0.
0.7879 ="=0.
0.8664 ±0.
0.8175±0.
0.5758 ±0,
0.8022 =tO.
0.7960 ±0.
0139
0522
0256
0301
0318
0207
1034
0301
0212
0.7575 =t 0.0349
0.4536=1=0.0906
0.6092=1=0.0418
68.90
11.98
31.30
26.18
27.25
39.49
5.57
26.65
37.55
21.71
5.01
14.57
0.9259
0.5481
0.7105
0.6526
0.7196
0.7192
0.3609
0.7177
0.6867
=4=0.0240
=±=0.0599
=±=0.0354
=fc 0.0456
±0.0614
=fc 0.0301
±0.1346
=±=0.0409
=1=0.0306
0.7472=1=0.0361
0.3556 ±0.0996
0.5803 ±0.0441
38.58
9.15
20.07
14.31
11.72
23.89
2.68
17.55
22.44
20.70
3.57
13.16
-0.0318
-0.0770
-0.0907
-0.1353
-0.1468
-0.0983
-0.2149
-0.0845
-0.1093
-0.0103
-0.0980
-0.0289
The nature of the relationship between body-weight and total heat-
production is cleariy brought out by diagram 13, which gives the aver-
age heat-productions for each weight grade for both men and women
(total series) and the theoretical heat-productions due to the straight-
line equations,
For total men N^ISQ
For total women iV=103
;»= 617.493 +15.824 u>
A = 884.5276-}- 8.227 to
Thus heat-production increases 15.8 calories for each kilogram of
body-weight in the men and 8.2 calories for each kilogram of body-
weight in the women.
The averages for the women are very irregular and apparently not
well represented by a straight-hne equation. The agreement of the
empirical and the theoretical means in the case of the men is excellent
for the groups containing a considerable number of subjects, i.e., for
those from 45 to 77 kilograms in weight.
92 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
We now turn to the partial correlations between weight and heat
for constant stature. When we say we determine the correlation
between body-weight and total heat-production for constant stature
we mean that we determine from the whole material at our disposal,
by the use of appropriate formulas, the correlation which would be
found (within the limits of the probable errors of random sampling)
if it were possible to sort our materials into groups of individuals of
approximately like stature without so reducing the number of individ-
uals in the groups as to render untrustworthy the correlation between
weight and total heat-production.
The physical relationships involved in such determinations should
be borne clearly in mind. If we determine the correlation between
weight and total heat-production in individuals of constant height it
is clear that the heavier individuals must be the "heavier set," plumper
or fatter individuals.
BODY WEIGHT IN KILOGRAMS
Diagram 13. — Mean total daily heat-productions of adults, varying in body-weight.
Obtaining the partial correlations for weight and total heat per
24 hours for constant stature by
„ 'wh ^ 'W8 'sh
s'wh
we find the following values for infants :
For males 0.7520 ± 0.041 1 0.5493 =*= 0.0660
For females 0.8081 =*= 0.0357 0.4937 ± 0.0778
For both 0.7833±0.0269 0.5313=*= 0.0499
Correction for stature has very considerably reduced the correlation
between body-weight and total heat-production. In the case of boy
babies there is a reduction of 0.2027 or about 27 per cent, in the case
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 93
of the girl babies a reduction of 0.3144 or about 39 per cent, while if
sex be disregarded the reduction is 0.2520 or about 32 per cent. The
results indicate, however, that the correlation is primarily due to body-
mass rather than to hody-len^h.
The partial correlations for men and women are laid beside the gross
correlations in table 29.
We note that without exception the correction for stature has
reduced the correlation between weight and total heat-production.
The amount of reduction is not, however, large. For the various series
it is as follows :
Pereentagt
Men: Reduction.
Original series, A'^=89 ^ 11-3
Gephart and Du Bois selection, -V=72 17.2
First supplementary series, A''=28 16.9
Original and first supplementary series, N=\V7 12.0
Total men, 2V^ = 136 13.7
Women:
Original series, .V = 68 1.4
Supplementary series, A' =35 21.6
Total women, iV = 103 4.7
The results which are based upon moderately large series of men
are fairly regular. The smaller groups, of course, give much more
variable percentages. The two series of women differ very greatly.
The whole series of women seems to show a much smaller reduction
in the correlation between weight and heat as a result of the correction
for stature than do the total men. When more data are available, the
detailed investigation of this point will be well worth while.
We now turn to the corrections for age in the adults. The results
due to the formula
Vl-r.*'Vl-r,.«
are laid beside the gross correlations in table 30. The results in this
table are very striking. The partial correlations are, with the insig-
nificant exception of the small series of athletes, larger than the original
correlations uncorrected for age. Thus age heterogeneity has a meas-
urable disturbing influence on the relationship between body-weight
and total heat-production. When this influence is removed the close-
ness of correlation is increased.
Correcting for the influence of both age and stature, we have the
partial correlations between weight and heat-production given by the
formula
- r^hi^ —rgg*) — r^tr^aA— r^.fr,;,4-ra^(rau.rM+roA^,M>)
att'wk : —
V (1 -r«*-r«,2-r„„2+2r„r„„0 V (1 -r«--r^»-r„i2_j_2r„r^r J
94 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
These can be best Understood if they are laid beside (1) the gross
correlations between weight and heat, r^,h, beside (2) the correlations
for weight and heat for constant stature and (3) the correlations be-
tween weight and heat for constant age. This is done in table 31.
Table 30. — Comparison of correlations between weight and heat-production and between
weight and heat-production for constant age.
Series.
Correlation
between weight
and heat-
production
Partial correla-
tion between
weight and
heat-production
a''wh
Difference
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series . .
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
0.9577=
0.6251=
0.8012=
0.7879 =
0.8664=
0.8175=
0.5758 =
0.8022 =
0.7960=
= 0.0139
= 0.0522
= 0.0256
= 0.0301
= 0.0318
= 0.0207
= 0.1034
= 0.0301
= 0.0212
0.9544 =
0.7032 =
6.8524=
0.7983 =
0.8955=
0.8624=
0.6009 =
0.8583=
0.8384=
= 0.0150
= 0.0433
= 0.0196
= 0.0288
= 0.0252
= 0.0160
= 0.0989
= 0.0222
= 0.0172
0.7575=4=0.0349
0.4536=^0.0906
0.6092=*= 0.0418
0.7776 ±0.0323
0.6040 =t= 0.0724
0.7117=^0.0328
-0.0033
+0.0781
+0.0512
+0.0104
+0.0291
+0.0449
+0.0251
+0.0561
+0.0424
+0.0201
+0.1504
+0.1025
We note that in all cases correction for age and stature has decreased
the values of the correlations between weight and heat-production in
men but increased the constants measuring the relationship in women.
Thus correction for two of the disturbing factors in the relationship
between weight and heat-production has tended to bring the results
obtained for the two sexes into closer agreement. For the total series
the differences between the gross and the partial correlations are :
Gross Partial
wh. as wh.
Men 0.7960±0.0212 0.7510±0.0252
Women 0.6092±0.0418 0.6866±0.0351
Difference 0.1868 =t 0.0469 0.0644 =*= 0.0432
Thus the difference between men and women is 3 times as large
before correction for the influence of stature and age has been made
as it is after the influence of these two variables has been eliminated.
The difference between the gross correlations in the two sexes is prob-
ably significant in comparison with its probable error. The difference
between the correlations corrected for the influence of age and stature
is probably not statistically significant.
Comparing the partial correlations for both age and stature constant
with those for stature only and age only constant, we note that the
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
95
differences between them are not large. The addition of the correction
for age to that for stature has not greatly influenced the measure of
the degree of interdependence between weight and heat.
Table 31. — Comparison of gross correlation between weight and total fieat-production and
partial correlations between weight and heat-production for constant stature, constant age,
and constant stature and age.
.
Gross corre-
lation for
weight and
heat-
production
Correlation
Correlation
Correlation
corrected for
corrected for
corrected for
Series.
N
the influence
the influence
both stature
of stature
of age
and age
'■wfc
TirA
a^wh
as^ich
Men.
Original series:
Gephart and Du Bois selection .
72
0.7879*0.0301
0.6526 ±0.0456
0.7983 ±0.0288
0.6385 ±0.0471
Other than Gephart £ind Du Bois
selection
64
0.8022 ±0.0301
0.7177 ±0.0409
0.8583 ±0.0222
0.7942 ±0.0311
All men of three series
136
0.7960 ±0.0212
0.6867 ±0.0306
0.8384 ±0.0172
0.7510 ±0.0252
Women.
Original series
68
35
0.7575 ±0.0349
0.4536 ±0.0906
0.7472 ±0.0361
0.3556 ±0.0996
0.7776 ±0.0323
0.6040± 0.0724
0.7674 ±0.0336
0.5197± 0.0832
Supplementary series
Both series
103
0.6092 ±0.0418
0.5803 ±0.0441
0.7117±0.0328
0.6866 ±0.0351
8. STATURE AND TOTAL HEAT-PRODUCTION.
In infants the correlation between stature (length) and total heat
produced is fairly high. The results are :
Formales Ar = 51 r,A =0.6191 ±0.0582 r/Er = n.22
For females N=i3 r,h =0.7426 ±0.0461 r/£:r = 16.11
Difference 0.123o±0.0719
Both constants are unquestionably significant. That for females
is somewhat higher than that for males. In comparison with its
probable error the difference can not, however, be considered signifi-
cant. Disregarding sex the correlation for the 94 babies is :
r,H =0.6848 ±0.0369 r/E, = 18.56
Expressing these results in terms of actual change in total heat-
production with differences in stature we have the following equations
For males h = - 229.58 -f-7.34«
For females A = -252.55 +7.83 «
which are represented graphically in diagram 14.
The excellent agreement of the results for the two sexes is shown
by the close paralleUsm of the two lines. While the observed means
are very irregular because of the limited number of indi\4duals, these
straight lines serve fairly well to represent them, and until further
data are available it is not worth w^hile to try equations other than the
linear.
96 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
For the various adult series the correlations between stature and
total heat appear in table 32.
The constants for adults are positive throughout, indicating greater
total heat-production by taller individuals.
•-- .= MALE INFANTS
o— o- FEMALE INFANTS
STATURE IN CENTIMETERS
Diagram 14. — Mean total daily heat-production of infants classified according to stature.
In the men the correlations are of the order r = 0.60. Because of
the smallness of the groups of individuals — and possibly also for
biological reasons — the constants for the subseries fluctuate between
Table 32. — Comparison of correlation between stature and total heat-production with
me correlation between weight and total heat-production.
Series.
N
Correlation
between stature
and heat-
production
♦■.A
Correlation
between weight
and heat-
production
Difference
DifF.
Ediff.
i Men.
Original series:
Athletes
16
62
89
72
28
117
19
64
136
68
35
103
0.7861 =fc 0.0644
0.4261=1=0.0701
0.6098=1=0.0449
0.5966=1=0.0512
0.7071=1=0.0637
0.6218=1=0.0382
0.5589=^0.1064
0.6290 ='=0.0510
0.6149=1=0.0360
0.1913=1=0.0788
0.3139^0.1028
0.2318 ±0.0629
0.9577=1=0.0139
0.6251 =t 0.0522
0.8012=1=0.0256
0.7879=^0.0301
0.8664=1=0.0318
0.8175=*= 0.0207
0.5758=^0.1034
0.8022=1=0.0301
0.7960=1=0.0212
0.7575=*= 0.0349
0.4536=1=0.0906
0.6092=1=0.0418
+0.1716=*=0.0659
+0.1990=1=0.0874
+0.1914=1=0.0517
+0.1913=1=0.0594
+0.1593=*= 0.0712
+0.1957 =±=0.0434
+0.0169=1=0.1077
+0.1732=^0.0592
+0.1811=1=0.0418
+0.5662=1=0.0862
+0.1397=1=0.1370
+0.3774=1=0.0755
2.60
2.28
3.70
3.22
2.24
4.51
0.16
2.93
4.33
6.57
1.02
4.99
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
Other than Gephart and Du Bois selection. .
All men of three series
Women.
Original series
Supplementary series
Both series
r = 0.43 for the 62 non-athletic and non-vegetarian individuals of the
original series, and r=0.79 for the 16 athletes. For the larger series,
the values are in very good agreement indeed, considering them in
comparison with their probable errors.
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
97
The women show correlations which differ remarkably from those
found in the men. The original series is characterized by a correlation
of only r = 0.19, the supplementary series by a correlation of only
r = 0.31, and the total series by a correlation of r = 0.23.
Comparing the total available materials for adult men and women,
we find the following correlations and their difference:
For 136 men r,^ * 0.6149 =»= 0.0360
For 103 women r,^ =0.2318 ±0.0629
Difference 0.3831 *0.0725
The difference is over 5 times as large as its probable error and
certainly suggests a significant difference in the correlation between
STATURE IN CENTIMETERS
DiAOBAK 15. — Distribution of total daily heat-productions of men of various statures.
stature and total heat-production in men and women. Against the
conclusion that this is a real sexual differentiation, may be possibly
urged the fact (demonstrated immediately above) that in the infants
the correlations are of about the same magnitude, the constant for
girl babies being, as a matter of fact, sUghtly greater than that for
boy babies.
98 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The results for the relationship between stature and total heat in
the two sexes may be conveniently compared in diagram 15 for men
and 16 for women. The straight-line equations are:
For men A = -1237.637+16.589*
For women h'= 226.585+ 6.931 «
Thus heat-production increases about 16.6 calories per day in men
and 6.9 calories per day in women for each variation of 1 cm. in stature.
The constant term fixes the position of these lines when represented
graphically. The averages represented in diagram 17 show that the
heat-productions for men are regularly higher than those for women of
the same stature. There is a strong suggestion of non-linearity in the
case of the averages for men, but the numbers of individuals in the
classes, especially the very tall and the very short individuals, is so
small that detailed mathematical analysis seems unprofitable at present.
■1785
• •
z
0
■/ess
m
•
1-
• •
•
V
«
n
■IS8S
D
• •
• •
Q.
■I48S
• • • . •
>-
<
•
** ^.s-'
--^
111
I38S
•
• • •
-^-^
.
I
•
•
, • •
>
-I
<
■1285
•
• * •
•
O
^
•
■lies
•
• •
J
<
.
•
H
•
H
■1085
■385
•
iSO
IS5
/60 165
170
175
180
STATURE IN CENTIMETERS
Diagram 16. — Distribution of total daily heat-productions of women of various statures.
We have now to consider the problem of the relative magnitude of
the correlations for body-weight and total heat-production and stature
and total heat-production. Total heat is correlated with weight some-
what more closely than with stature in both males and females. The
differences for infants are :
Stature and Weight and Difference in
total heat. total heal. correlation.
= 0.0582 0.7520=^0.0411 0.1329=^0.0712
= 0.0461 0.8081=^0.0357 0.0655 ±0.0583
Males 0.6191
Females 0.7426
Difference 0.1235^0.0719
Both sexes 0.6848=^0.0369
0.0561=^0.0544
0.7833^0.0269
0.0985=^0.0457
On the basis of the present data for infants the differences in the
correlations can not be considered statistically significant.
The more extensive data for adults also consistently show higher
correlations between weight and total heat than between stature and
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
99
total heat. The actual differences and their probable errors appear in
table 32. The correlations are consistent throughout in indicating a
more intimate relation between body-weight and total heat-production
than between stature and total heat-production. Notwithstanding the
(statistically) few indi\'iduals considered, a number of the differences
may be looked upon as individually significant in comparison with
their probable errors.
169
STATURE IN CENTIMETERS
Diagram 17. — Mean daily heat-production of normal men and women of various statures.
The differences in correlation vary considerably from series to
series, ranging from 0.017=1=0.108 in the 19 men of the second sup-
plementary series to 0.566=*= 0.086 in the original women. We note,
however, that the probable error is so high in the case of the second
supplementary series of men that it can not really be asserted to differ
significant!}^ from the other groups of men. The larger groups of men
show a difference of the order r^k—^sh = 0.19. In the women the differ-
ences are much larger because of the very low correlations between
stature and total heat-production.
In the preceding section we considered the influence of age on the
correlation between body-weight and total heat-production. It now
100 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
seems desirable to eliminate the possible influence of age upon the
correlations between stature and total heat-production by using the
partial correlation formula
J^$h =
^.*—''.o^aA
Vl-rJ y/l-r,H^
With such low correlations as those which have been demonstrated
between age and stature in Chapter III, the correction due to the
correlation between age and stature will be small.
Table 33. — Correlation between stature and total heat-production and partial correlation
between stature and total heat-production vnth age constant.
Series.
N
Correlation
between stature
and heat
Partial
correlation be-
tween stature
and heat
oTsh
a^th
^a^ah
Differ-
ence
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
Other than Gephart and Du Bois selection . .
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
0.7861 ±0.
0.4261 ±0.
0.6098 =*=0.
0.5966 ±0.
0.7071 ±0
0.6218±0,
0.5590 =«=0,
0.6290 ±0,
0.6149±0
0644
0701
0449
0512
0637
0383
1064
0510
0360
0.1913±0.0788
0.3139=*=0.1028
0.2318=t0.0629
12.21
6.08
13.58
11.65
11.10
16.24
5.25
12.33
17.08
2.43
3.05
3.69
0.7324±0,
0.4397*0.
0.5977 ±0,
0.6542 ±0.
0.7175 ±0,
0.6175±0.
0.5608 ±0.
0.6093 ±0.
0.6129 ±0.
0782
0691
0460
0455
0618
0386
1061
0530
0361
0.2196 ±0.0778
0.3737 ±0.0981
0.2700 ±0.0616
9.37
6.36
12.99
14.38
11.61
16.00
5.29
11.49
16.98
2.82
3.81
4.38
-0.0537
+0.0136
-0.0121
+0.0576
+0.0104
-0.0043
+0.0018
-0.0197
-0.0020
+0.0283
+0.0598
+0.0382
The results are laid beside the gross correlations in table 33. In
the larger series of data the differences between the gross correlations
and the partial correlations are in no case as large as their probable
errors. The disturbing influence of age upon the correlation between
stature and total heat-production is, therefore, insignificant.
Since stature and body-weight are known to be correlated charac-
ters (see Chapter III), it is clear that the correlation between stature
and total heat-production might be merely the resultant of the corre-
lation between weight and heat-production and weight and stature.
The fact that the correlation between stature and total heat-production
is consistently lower than that between weight and total heat-produc-
tion would, superficially considered, seem to support this view.
To test the question critically we must have recourse to the partial
correlation coefiicient between stature and heat-production for constant
body-weight. Inserting the values of the correlation coefficients for
stature and heat, weight and heat, and stature and weight in the
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS.
101
partial correlation formula for stature and total heat for constant weight,
.»•,* =
we find for the infants :
Vl-r^»\/l-r,,«
For males 0.6191 ±0.0582
For females 0.7426 ±0.0461
0.0949*0.0936
0.1492*0.1006
If sex be disregarded, we have :
r.fc =0.6848 =^0.0369 „r.;^ =0.1178 ±0.0686
In comparison with their probable errors the partial correlations
are sensibly 0. All three are, however, positive in sign. Correction
for body-weight has almost but apparently not entirely wiped out the
relationship between stature and total heat-production.
For adults the results of the gross correlations and the partial cor-
relations have been presented in table 34.
Table 34. — Correlation between stature and total hetU-prodiiction and partial correlation
between stature and total heat-production with weight constant.
Series.
N
Correlatioa
between stature
and total
heat-produetioQ
'.A
^*
Partial corre-
lation between
stature and total
haat-production
v^th
E
w^ah
Differ-
ence
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection. . .
First supplementary series
Original and first supplementary series
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
136
68
35
103
0.7861*0
0.4261*0
0.6098*0
0.5966*0
0.7071*0
0.6218*0
0.5589*0
0.6149*0
0644
0701
0449
0512
0637
0382
1064
.0360
0.1913*0.0788
0.3139*0.1028
0.2318*0.0629
12.21
6.08
13.58
11.65
11.10
16.28
5.25
17.08
2.43
3.05
3.69
0.5851*0
0.2453*0
0.3623*0
0.1573*0
0.1827*0
0.3275*0
0.3246*0
0.3207*0
1109
0805
0621
0775
1232
.0557
.1384
0519
0.0397*0.0817
0.0927*0.1130
0.0445*0.0663
5.28
3.05
5.83
2.03
1.48
5.88
2.35
6.18
0.49
0.82
0.67
-0.2010
-0.1808
-0.2476
-0.4393
-0.5244
-0.2943
-0.2343
-0.2942
-0.1516
-0.2212
-0.1873
It is clear that in every series the correlation between stature and
total heat-production is reduced when correction is made for body
weight. The partial correlation between stature and heat for constant
weight is not on the average zero. Instead, we have fairly substantial
positive values throughout. Some of the constants taken individually
may very reasonably be considered significant in comparison with their
probable errors. The actual magnitude is of the order ^r,^ = 0.30 in the
larger series of men, although the first supplementary series gives only
^,r,;,=0.18 and the Gephart and Du Bois selection gives ^r,;,=0.16.
The women seem to differ from the men and to agree with the infants
102 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
in indicating that correction for weight has practically, but not entirely,
eliminated the correlation between stature and heat-production.
As a result of the analysis in this and the preceding section, we have
shown that the correlation between weight and total heat-production
is appreciably lowered when the factor of stature is eliminated by the
use of the partial correlation coefficient and that the correlation be-
tween stature and metabolism is considerably reduced when the factor
of body-weight is eliminated in a similar manner; but in neither case
does the correlation disappear. Thus there is a relationship between
weight and metabolism which is independent of stature, also a relation-
ship between stature and metabolism which is independent of weight.
These partial, residual, or net correlations, however one cares to desig-
nate them, are of a positive character. In other words, if a group of
individuals of identical weight be examined the taller individuals will
be found to have the higher metabolism. If a group of individuals of
the same stature be examined, the heavier individuals will be found to
have the greater metabolism.
It is evident that our partial correlations have a direct bearing on
the problem of the metabolism of fat and lean individuals, a subject
which has received considerable discussion in the literature of basal
metabolism. If individuals of the same body-weight be classified
according to stature, the taller individuals will necessarily be thinner
than the shorter ones. The partial correlations show that in a given
weight class the taller individuals have the greater gaseous exchange.
In a group of individuals of identical weight, slenderness or spareness
of build can result only from reduction in weight of bone, muscle, or fat.
Reduction in fat mass seems the most probable source of an increase
of stature without alteration in weight. We conclude, therefore,
that the leaner individuals are those showing the higher metabolism.
The partial or residual correlation is not in this case large.
In turning to the data which show that within a group of individuals
of the same stature the heavier individuals show the higher heat-
production, the reader may believe he sees a contradiction to the con-
clusion that the leaner individuals are those showing the higher
metabolism. But such does not, on closer analysis, seem to be the case.
In a group of individuals of the same stature, differences in body-weight
may be due to fat, which in the main is inert in its direct contribution
to metabolism, or they may be due to differences in the mass of mus-
cular and other active tissues. Thus there is no incompatibility what-
ever in the statements that within a group of individuals of the same
weight the taller have the greater metabolism, whereas in a group of
the same stature the thicker individuals show the greater metabolism.
The recent investigation of Armsby and Fries, ^ in which they
demonstrated a disproportionately high heat-production in a fat as
' Armsby and Fries, Journ. Agr. Res., 1918, 11, p. 451.
PHYSICAL AXD PHYSIOLOGICAL MEASUREMENTS. 103
compared with a lean period in a steer does not seem to invalidate the
conclusion that human individuals who are relatively tall for their
weight have a higher metabohsm than shorter ones. In the case of
the fattening experiment reported by Amisby and Fries the experi-
mentally induced changes in the nutritional level of the animal were
brought about with relatively great rapidity. Concomitant with the
fattening there was an increase of 36 per cent in the basal katabohsm,
just as in the case of a man undergoing a 31-day fast at the Nutrition
Laboratory there was a 28 per cent decrease in the basal katabolism.^
Without further CAddence one would not be warranted in assuming that
like differences would necessarily be found between different individuals
of relatively permanent lean and fat physical constitution.
More recent investigations have sho'vsTi that the basal metabolism
of the human subject is profoimdly affected by sudden modifications
of the nutritional level, particularly those which are accompanied by
rapid reduction in body-weight. If the food-intake be reduced below
the maintenance level it is plain that with constant basal requirements
there must be draft upon previously stored body-reserves.
Experiments with human subjects along this line demand a high
degree of personal integrity and veracity on the part of the subjects.
Such requirements were fulfilled by two squads of 12 men each from
the International Y. j\I. C. A. College at Springfield, IMassachusetts.^
The first squad was kept for a period of 4 months upon a much re-
stricted diet \\ath an energy content of approximately one-half to two-
thirds of the caloric requirements prior to the test. During the first
few weeks there was a pronounced decrease in body-weight. After the
body-weight had fallen on the average 12 per cent, an increase in the
diet was made to prevent further loss in weight. Measurements of
the groups as a whole in the large respiration chamber at the Nutrition
Laboratory in which the 12 men slept every alternate Saturday night
gave the basal metabolism during deep sleep.
The normal demand of the men prior to the reduction in diet
ranged from 3200 to 3600 net calories. After a decrease of 12 per cent
in weight only 1950 calories were required to maintain this weight.
The heat output as measured by indirect calorimetry and on the
basis of calories per kilogram of body-weight and calories per square
meter of body-surface was essentially 18 per cent lower than at the
beginning of the study. Throughout the period of loss in weight and
for some time following there was a marked loss of nitrogen. In round
numbers these men lost approximately 150 grams of nitrogen. The
nitrogen output per day at the maintenance diet of 1950 net calories
* Benedict, Carnegie Inst. Waah. Pub. Xo. 203, 1915. Also Am. J. Phyaioi., 1916, 41, p. 292.
'Benedict; Proc. Amer. Phil. Soc, 1918, 57, p. 479. Also Benedict and Roth, Proc. Nat.
Acad. Sci., 1918, 4, p. 149. Also Benedict, Roth, Miles, and Smith, Carnegie Inst.
Wash. Pub. 280. (In press).
104 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
was about 10.5 as compared with 14 grams in a control group with
unrestricted diet.
This lowering of the metabolism accompanying the assumption of
a thinner build is apparently opposed to the conclusions drawn above,
according to which thinner individuals show a higher metabolism.
Apparently, however, we have here, as in the fattening experiments of
Armsby and Fries and in the prolonged fast of 31 days, to do with the
special factor of rapid experimentally induced changes in the nutritional
level of the organism, and not with the relatively permanent differences
between fat and lean individuals.
Determining the partial correlation between stature and total heat-
production in calories per day for constant body-weight and constant
age by the formula
efth
'thy.'- 'aw J 'as' ah 'w»'iDhi''aw\>aa'wh'i'ah'wi)
and comparing the results with the gross correlations, r,^ and the corre-
lation corrected for weight, „r,ji, and for age, o*".*, we have the results
in table 35.
Table 35. — Comparison of gross correlation between stature and total heat-production and
partial correlations between stature and heat-production for constant weight, for constant
age, and for constant age arid weight.
Series.
N
Gross correla-
tion between
stature and
heat-
production
Correlation
corrected for
influence of
weight
w^sh
Correlation
corrected for
influence of
age
Correlation
corrected for
both age and
weight
aw'''sh
Men.
Original series:
Gephart and Du Bois selection
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
72
64
136
68
35
103
0.5966 ±0.0512
0.6290 ±0.0510
0.6149 ±0.0360
0.1913 ±0.0788
0.3139 ±0.1028
0.2318± 0.0629
0.1573 ± 0.0775 0.6542 ± 0.0455
0.4220 ± 0.0693 0.6093 ± 0.0530
0.3207 ± 0.0519j0.6129 ± 0.0361
0.0397±0.08170.2196±0.0778
0.0927 ±0.1 130 0.3737 ±0.0981
0.0445 ± 0.0663 0.2700 ±0.0616
0.2561 ±0.0743
0.3442 ±0.0743
0.2899 ±0.0530
0.0784 ±0.0813
0.1064±0.1127
0.0850 ±0.0660
The correlations for stature and heat-production are positive
throughout, even after correction has been made for both age and
weight. This fully substantiates the conclusion drawn above concern-
ing the existence of an independent physiological relationship between
stature and heat-production. The partial correlations for both age and
weight constant are in some cases higher and in some cases lower than
those in which weight only is corrected for. This shows the relatively
small influence of age on the correlation between stature and heat-
production. This influence is small, not because there is no relationship
PHYSICAL AND PHYSIOLOGICAL MEASUREMENTS. 105
between age and metabolism, but because in adults there is little rela-
tionship between age and stature.
9. RECAPITULATION AND DISCUSSION.
1. Oiu" series of data show practically no relationship between basal
or minimum pulse-rate and body-weight in adults. In new-bom infants
there may be a slight positive correlation, more rapid pulse being asso-
ciated with greater body-weight, but further investigation is necessary
before final conclusions can be drawn.
2. As far as our data show, there is practically no relationship
between stature and pulse-rate in man.*
3. There is a low but significant positive correlation between
minimum pulse-rate and gaseous exchange in men, larger gaseous
exchange being associated with more rapid pulse-rate. The series of
women available show as yet inexpUcable inconsistencies in these
relationships. The correlation between pulse-rate and oxygen con-
simiption is more intimate than that between pulse-rate and carbon-
dioxide excretion. Physiologists have long been familiar with the
correlation between pulse-rate and metaboUsm in the same individual,
that is with the intra-indi^^dual correlation between the rate of the
heart-beat and the amount of the katabohsm. Here, however, we are
dealing with the problem of the relationship between the minimum
pulse-rates of a series of individuals and their basal metabolism con-
stants— that is, with inter-individual correlation.
4. The inter-individual correlations between pulse-rate and gross
heat-production are positive throughout, but low and variable in mag-
nitude. WTien correction for body-size is made by expressing heat
production in calories per kilogram of body-weight or in calories per
gquare meter of body-surface, the magnitude of the correlations is
materially raised. This indicates that the relationship is one of real
physiological significance. The most intimate correlations are obtained
when correction for body-size is made by expressing heat-production
in calories per square meter of body-surface. This result has an obvious
bearing on the so-called body-surface law, to be discussed in ChapterVI.
5. There is a high positive correlation between body-weight and
gaseous exchange. The correlations are of the order r=0.75 for men
and r = 0.60 for women. Expressed in actual gaseous exchange, this
degree of correlation means that in men oxygen consumption increase
about 2.27 and carbon-dioxide excretion increases about 1.89 c.c. per
minute for an increase of 1 kilogram of body-weight. For women the
values are about 1.17 c.c. Oo and 1.02 c.c. CO2 per kilogram of weight.
These are the values for the grand total series. Those for the several
sub-series differ considerably among themselves.
* Conclusioiis 1 and 2 miist be understood to be limited to our own data for minimum or baaal
pulae-rates. They may not be strictly valid for Bubjects under other conditions. This question
may be treated by one of u« later.
106 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
6. There is a substantial correlation between stature and gaseous
exchange. The correlations for men are of the order r=0.60, while
for women they are of the order r = 0.30. In terms of actual gas volume
these coefficients show that oxygen consumption increases about 1 c.c.
for each increase of 1 cm. in stature in the women, whereas in the men
the increase is between 2 and 3 c.c. Comparable, but somewhat lower
values are found for carbon-dioxide excretion.
7. The correlations between both stature and body-weight on the
one hand and oxygen consumption on the other are higher than those
between these two physical characters and carbon-dioxide excretion.
Since the total volume of oxygen consumed is not excreted as carbon
dioxide this result should have been expected.
8. Comparison of the correlations between body- weight and gase-
ous exchange and those between stature and gaseous exchange shows
that the correlation between weight and gaseous exchange is higher
than that between stature and gaseous exchange. Thus body-mass is a
more important factor than is stature in determining (in the statistical
but not necessarily in the causal sense) gaseous exchange.
9. The correlations between body-weight and total heat-production
are high. Thus coefficients of the order r = 0.75 to r =0.80 have been
found for male and female new-born infants, of the order r = 0.80 in
men and r = 0.60 in women. In terms of actual heat productions these
correlations, taken in connection with the means and standard devia-
tions, show that in the new-born infants a difference of 100 grams in
body-weight impUes a difference of about 3.4 calories in daily heat-
production. In the adults a difference of one kilogram in body-weight
is followed by an average difference of 8.2 calories in heat-production
in women and 15.8 calories in men.
10. There is a significant positive correlation between stature
(body-length) and total heat-production in both new-born infants and
adults. The correlations are consistently lower than those for weight
and total heat-production.
11. Since tall individuals are on the average heavy individuals, and
since heavy individuals are on the average tall individuals, it has been
necessary to inquire to what extent the correlation^ between total heat-
production and stature is merely the statistical resultant of the correla-
tions between weight and heat and stature and weight, and to inquire
to what extent the correlation between weight and heat-production is
merely the resultant of the correlation between stature and heat-
production and between weight and stature. In proceeding in this
way we have been treating the data in a purely objective manner,
basing our treatment on no physiological theory concerning the relative
importance of stature or weight in determining basal metabolism. Our
results show that both stature and body-weight have independent sig-
nificance in determining the basal metabolism of the normal individual.
Chapter V.
CHANGES IN METABOLISM WITH AGE.
The significance of a knowledge of the relationship of metabolism
to age is twofold.
First, the change of normal basal metabolism with age is in and
for itself a problem of prime physiological importance.
Second, metabolism determinations in the hospital ward have Uttle
value as a basis for medical theory or practice except as the constants
are interpreted in comparison with those for normal controls. It is
important, therefore, that in selecting controls for comparison with
pathological cases the influence of the age factor in both health and
disease should be fully known.
Our treatment in this place differs from that accorded the problem
by earher writers in that we have actually determined statistical con-
stants measuring the rate of change in metabolism with age during the
period of adult, or practically adult, life.
Ultimately it will be necessary to imdertake an examination of
the change of physical and physiological characters other than direct
or indirect heat measiu'ements as a first step towards a closer coordi-
nation of investigation in human metabolism and the results of general
biological research. Such coordination should be to the advantage
of both the special field of human nutrition and the broader field of
general biological theory.
In this place we shall merely present, and statistically discuss, the
available data for human basal metabolism in relation to age. A com-
parative examination of age changes in other physical and physiological
characters must be reserved for the future.
I. HISTORICAL REVIEW.
It was of course inevitable that the problem of the dependence of
metabohsm on age should be considered in a general comparative way
as soon as determinations of the basal metabolism of infants, youths,
and adults began to be made.
While the observations of Andral and Gavarret * can not be taken
as basal, we have determined the correlation between age and CO2
production per hour in the men 17 t o 102 years of age and in the women
^ Andral and Gavarret, Ann. de chim. et phys., 1843, 8, 3 s6r., p. 129.
107
108 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
19 to 82 years of age, using the constants as tabled by Sond^n and
Tigerstedt.2
We find:
For men iV^=29 r„, = -0.629 ±0.076
For women AT = 17 r„^ = -0.058 ±0.163
Both coefficients are negative, suggesting a decrease in gaseous ex-
change with age; that for men is large.
Most unfortunately statures and weights of these individuals are
not given. It is not possible, therefore, to correct for these factors
which are later shown to have a large disturbing influence on the meas-
ure of the relationship between age and metabolism. In view of this
fact, and that the constants for the individual subjects may show a
considerable variation due to their not being truly basal, and further
that the number of individuals is small, better agreement with the
results presented for our own series of subjects could perhaps not have
been expected.
The classic work of Sond^n and Tigerstedt themselves,^ while dis-
cussing in a most exhaustive way many of the fundamental questions
of metabolism, is based on observations made before the precautions
necessary for basal determinations were understood.
Magnus-Levy and Falk,* in 1899, concluded that the basal metab-
olism is low in infancy, high in childhood, and low after the onset of
old age. They considered it essentially constant during the period of
adult life.
We have determined the correlations between age and calories per
24 hours, computed from the data of Magnus-Levy and Falk. We find :
Correlation
'^ah
In men, iV = 10 -0.238±0.201
In men and old men, iV = 15 -0.481 ±0.134
In women, Ar = 14 -0.576±0.120
In women and old women, iV = 17 —0.569 ±0.111
Thus in both the men and women studied by Magnus-Levy and
Falk heat-production is shown to decrease with age.
We may, of course, further investigate the relationship between
age and heat-production in the series of Magnus-Levy and Falk by
determining the partial correlation between age and heat-production
for constant body-weight. The results are as follows :
Partial
Correlation
w ah
For men -0.147 ±0.209
For men and old men -0.712 ±0.086
For women -0.210±0.172
For women and old women —0.727 ±0.077
2 Sond6n and Tigerstedt, Skand. Arch. f. Physiol., 1895, 6, pp. 6&-56.
' Sonddn and Tigerstedt, loc. cit.
* MagnuB-Levy and Falk, Arch. f. Anat. u. Phye., Physiol. Abt., 1899, Suppl. p. 361.
CHANGES IN METABOLISM WITH AGE. 109
Again the probable errors are high because of the small numbers of
indi\-iduals studied. But one can hardly examine the results as a whole
without reaching the conviction that ;Magnus-Le\'y and Falk were in
error in concluding that metabohsm remains essentially constant dur-
ing adult life. ^Metabolism decreases throughout adult life, and this
decrease is shown by the statistical analysis of their own data to be as
evident after correction for the influence of body-size has been made
as before.
Carbon-dioxide production in boys of 10 to 18 years of age has been
investigated bj^ Olin,* although not under strictly basal conditions.
One of the objects of the investigations which have been under
way on human basal metabolism at the Nutrition Laboratory for a
number of years has been the determination of the changes which take
place in metabohsm throughout the entire period of life. It was the
intention to base this investigation upon a number of subjects suffi-
ciently large to eUminate the influence of indi\'idual variations at dif-
ferent ages, and thus to obtain a smoothed curve of basal metabolism
of both male and female indi\aduals throughout the entire period of
life. Before this program was complete Du Bois ' combined the
extensive data already pubhshed from the Nutrition Laboratory with
fragmentary data from other sources and attempted to draw a curve
of human basal metabohsm for the entire period of life.
In our opinion the time is not yet ripe for an imdertaking of such
magnitude. WTiile data are still being accumulated for this purpose,
and while the results based on 136 men and 103 women are subject to
revision as more extensive materials for the earlier and later periods
of life are obtained, it seems desirable to analyze in a preliminary way
the age changes in the subjects considered in this volume. Certain
difficulties in the way of combining different series of measurements to
secure a picture of the metabohc acti\'ity of the human subjects from
birth to death will be indicated in Chapter VIII (p. 243).
2. STATISTICAL CONSTANTS MEASURING CHANGES IN METABOLISM
WITH AGE.
The range of a^es of the indi\4duals in each class, and the statistical
constants of age in years, in the several groups of subjects appear in
table 36.
The constants showing the correlation between age and total heat-
production in calories per 24 hours are given in table 37. Without
exception the values of r^^h are negative in sign, thus indicating that in
* Olin, Finska lak.-sallsk. handl., Helsingfors, 1915, 57, p. 1434. At the time of going to
press the GermaQ report of this research, announced for appearance in the Skandi-
navisches Archiv fur Physiologie, is not available and hence analysis of the data is
unfortunately now impossible.
« Du Bois, Am. Joum. Med. Sci., 1918, 102, p. 781. Also Med. Bull. Cornell Univ., 1917, 6,
pt. 2, p. 33.
110 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
groups of individuals of the age-range here under consideration total
heat-production decreases with increasing age.
Nine of the 12 values are over 3 times as large as their probable
errors. They are, however, extremely irregular in magnitude, ranging
from — 0.092 =t 0.126 in the first supplementary series of men (iV=28)
Table 36. — Statistical constants of age in adults.
Series.
N
Age
range.
16
19-29
62
16-63
89
16-63
72
20-43
28
19-45
117
16-63
19
18-62
64
16-63
136
16-63
68
15-74
35
18-73
103
15-74
Average.
standard
deviation.
CoeflBcient
of variation.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
22.06 ±0.45
26.08 ±0.64
26. 15 ±0.56
25.74 ±0.44
25.64±0.71
26.03 ±0.46
32.11 ±2.09
28.16±0.94
26.88 ±0.51
26.66±0.81
39.86 ±1.82
31.15±0.92
2.66 ±0.32
7.51 ±0.45
7.86 ±0.40
5.57 ±0.31
5.56 ±0.50
7.38 ±0.33
13.53 ±1.48
11.20±0.67
8.77 ±0.36
9.88 ±0.57
15.97±1.29
13.79 ±0.65
12.04±1.46
28.78 ±1.88
30.07±1.97
21.63±1.27
21. 67 ±2.04
28.36±1.35
42.15±5.37
39.77 ±2.72
32.63 ±1.47
37.04±2.42
40.07±3.71
44.27 ±2.46
Table 37. — Correlation between age and total heat-production and partial correlation between age
and heat-prodxiction for constant stature and for constant body-weight.
Series.
N
Gross correlation
between age
and heat-
production
^ah
Correlation
corrected for
influence of
weight
w^ah
w^ah
Correlation
corrected for
influence of
stature
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
Other than Gephart and Du Bois selec
tion
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
-0.4664±0.1319
-0.1292 ±0.0842
-0.3529 ±0.0626
-0.3716 ±0.0685
-0.0917±0.1264
-0.2954 ±0.0569
-0.5007 ±0.1 159
-0.3003 ±0.0767
-0.3062 ±0.0524
-0.2322 ±0.0774
-0.1796±0.1103
-0.2034 ±0.0637
3.54
1.53
5.64
5.42
0.73
5.19
4.32
3.92
5.84
3.00
1.63
3.19
-0.3977 ±0.1420
-0.4290 ±0.0699
-0.5756 ±0.0478
-0.4192 ±0.0655
-0.4609 ±0.1004
-0.5428 ±0.0440
-0.5328 ±0.1 108
-0.5728 ±0.0566
-0.5147 ±0.0425
-0.3499 ±0.0718
-0.4755 ±0.0882
-0.4976 ±0.0500
2.80
6.14
12.04
6.40
4.59
12.34
4.81
10.12
12.11
4.87
5.39
9.95
•0.2240 ±0.1602
■0.1 756 ±0.0830
■0.3227 ±0.0641
■0.4842 ±0.0609
■0.1942 ±0.1227
-0.2817 ±0.0574
■0.6029±0.1156
-0.2313=
-0.3003=
= 0.0798
= 0.0526
■0.2556 ±0.0764
-0.2764±0.1053
■0.2465 ±0.0624
1.40
2.12
5.03
7.95
1.58
4.91
4.35
2.90
5.71
3.35
2.62
3.95
to —0.501 ±0.116 in the second supplementary series {N = 19). While
the probable errors of these constants are relatively very high because
of the small numbers of individuals available, this need not be taken
as the final explanation of the highly irregular values. Both stature
and body-weight vary greatly in human individuals, and, as pointed
out on page 63, this variation in the adult is largely independent of
CHANGES IN METABOLISM WITH AGE.
Ill
age. But while age and body-weight and age and stature are very
httle correlated m adult Ufe, stature and weight, especially the latter,
are closely correlated with metabohsm. Thus uregularities of stature
or body-weight would tend to dilute the correlation between age and
total heat-production.
The reader who has followed the lines of reasoning employed in
preceding sections of this volume will at once suggest that there are
two ways in which the influence of these disturbing factors can be
eliminated. First, we may determine the partial correlation coefficients
between age and total heat-production for constant stature and for
constant body-weight. Second, we may make the corrections for the
influence of body-weight or of both body-weight and stature by ex-
pressing metabohsm in terms of calories per kilogram or calories per
square meter of surface and subsequently correlate these heat-produc-
tions per standard unit with age. We have carried out the analysis
by both methods.
Table 38.— Correlation between age and heat-prodvuiion per kilogram of hody-weight and
comparison tvith corrdaiion between age and total heat-production.
Series.
N
Correlation
between age
and total
heat-production
'•oA
•"oA
Correlation
between age and
heat-production
per kilogram
rahk
rahj^
''ah,
rah/i ~rah
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series. . . .
Second supplementary series
Other than Gephart and Du Bois selection
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
64
136
68
35
103
- 0.4664 ±0.
-0.1292 =t=0.
- 0.3529 ±0.
-0.3716=fc0.
-0.0917±0.
-0.2954=fc0.
- 0.5007 ±0.
- 0.3003 ±0.
- 0.3062 ±0.
1319
0842
0626
0685
1264
0569
1159
0767
0524
-0.2322 ±0.0774
-0.1796±0.1103
-0.2034 ±0.0637
3.54
1.53
5.64
5.42
0.73
5.19
4.32
3.92
5.84
3.00
1.63
3.19
-}-0.0439±0.
- 0.4633 ±0.
-0.4208±0,
- 0.2626 ±0.
- 0.4629 ±0.
- 0.4275 ±0.
- 0.3885 ±0,
-0.4791 ±0
- 0.4078 ±0.
1683
0673
0588
0740
1002
0510
1314
0650
0482
0.26
6.88
7.16
3.55
4.62
8.38
2.96
7.37
8.46
-0.1510±0.0799 1.89
-0.6533 ±0.0653 j 10.00
-0.4931 ±0.0503 i 9.80
-1-0.5103
-0.3341
-0.0679
-fO.1090
-0.3712
-0.1321
-f0.1122
-0.1788
-0.1016
-1-0.0812
-0.4737
-0.2897
The partial correlations between age and heat for constant body-
weight,
'ah ^'aw'tch
T„h —
vc' ah
Vl-rJ Vl-rJ
and the partial correlations between age and heat for constant stature,
'ah 'as'sh
J ah —
Vl-rJ Vl^,'
are laid beside the gross correlations in table 37. The correlation
between age and heat-production per kilogram of body-weight is com-
112 A BIOMETKIC STUDY OF BASAL METABOLISM IN MAN.
pared with the gross correlation in table 38. The same comparison for
heat-production per unit of body-surface is made in table 39.
The partial correlations for age and total heat-production for con-
stant stature in table 37 show about the same irregularities as the
gross correlations. The constants are sometimes lower and sometimes
higher than the original coefficients. This failure of correction for
stature to make a large difference in the correlations between age and
heat-production is to be expected because of the relative laxness of
the correlation between stature and heat-production, as demonstrated
on page 96.
Table 39. — Correlation between age and heat-production per square meter of body-surface and
comparison with correlation between age and total heat-production.
Series.
N
Surface estimated,
Meeh formula.
Surface estimated,
Du Bois height-weight
chart.
Difference
Difference
''^^M
^rahM
rahj^
^raho
Men.
Original series:
Athletes
16
62
89
72
28
117
19
64
136
68
36
103
-0.4637 ±0.1339
-0.4817 ±0.0658
-0.6622 ±0.0489
-0.4124 ±0.0660
-0.4402 ±0.1028
-0.6401 ±0.0442
-0.4966±0.1166
-0.5778±0.0562
-0.6111 ±0.0427
-0.2745 ±0.0756
-0.6255 ±0.0694
-0.5437 ±0.0468
3.39
7.32
11.50
6.26
4.28
12.22
4.26
10.28
11.97
3.63
9.01
11.62
-0.4203 ±0.1388
-0.4243 ±0.0702
-0.5263 ±0.0518
-0.4672 ±0.0621
-0.3498±0.1119
-0.4819 ±0.0479
-0.6203±0.1128
-0.4986 ±0.0634
-0.4698±0.0461
-0.3547 ±0.0715
-0.5637 ±0.0779
-0.5238 ±0.0482
3.03
6.04
10.14
7.62
3.13
10.06
4.61
7.86
10.42
4.96
7.24
10.87
-1-0.0127 ±0.1879
-0.3525 ±0.1068
-0.2093 ±0.0794
-0.0408 ±0.0949
-0.3486 ±0.1628
-0.2447 ±0.0721
-t-0.0041± 0.1643
-0.2776 ±0.0949
-0.2049 ±0.0678
-0.0423 ±0.1082
-0.4469 ±0.1304
-0.3403 ±0.0787
-1-0.0461 ±0.1916
-0.2951 ±0.1095
-0.1 724 ±0.0812
-0.0966 ±0.0922
-0.2581 ±0.1688
-0.1866±0.0742
-0.0196±0.1619
-0.1983 ±0.0996
-0.1 636 ±0.0693
-0.1225±0.1054
-0.3843 ±0.1349
-0.3204 ±0.0800
Others
Whole series
Gephart and Du Bois
selection
First supplementary
series
Original and first sup-
plementary series
Second supplementary
series
Other than Gephart and
Du Bois selection
All men of three eeries . .
Women.
Supplementary series . . .
Both series
The case is quite different with the partial correlations for age and
metabolism for constant weight. With one single exception, in which
the difference is small, the constants for the relationship between age
and heat corrected for the influence of body-weight are numerically
larger than the uncorrected values. A careful study of these values
shows how greatly correction for body-weight has smoothed the series
of constants for the relationship between age and metabolism. They
range from —0.350 to —0.576 when the two sexes are considered to-
gether, but when the probable errors are taken into account the con-
stants can hardly be asserted to differ significantly among themselves.
The larger series indicate the medium correlation of —0.5 between age
and heat-production for constant weight.
CHANGES IN METABOLISM WITH AGE. 113
Turning now to the correlations between age and heat-production
per unit of body-weight and body-surface, we may compare the corre-
lations between age and total heat-production with those between age
and relative heat-production, i. e., heat-production per kilogram of
weight or per square meter of body-surface, in tables 38 and 39.
From table 38, in which the correlations between age and total
heat-production are compared with those between age and heat per
kilogram of body-weight, we note that in all cases except the athletes^
heat per kilogram of weight is negatively correlated with age — that is
relative heat-production as well as total heat-production decreases with
age. In the larger series of men, with the exception of the Gephart and
Du Bois selection and the second supplementary series, the correlation
between age and relative heat-production is numerically larger than
that between age and gross heat-production. This is also true in
the supplementary series and in the grand total series of women.
Thus variations in the size of the individuals as measured by weight
tend to disturb to some extent the correlations between age and heat-
production.
Turning now to the correction for differences in size resulting from
the expression of heat-production in calories per square meter of body-
surface we have the results set forth in table 39. Without exception
the 24 correlations are negative in sign. With three exceptions only^ the
correlations between age and heat-production per square meter of body-
surface are of a more strongly negative order than the correlations
between age and total heat-production.
In determining the relationship between age and total heat-
production, correction for the influence of both body-weight and
stature may be made by the use of the partial correlation formula for
two variables constant
aw' ah '
V(l -rj" -r^„2 ^j.j +2r,^r,^r„„) V(l -r,J-r^k^-r,^^-\-2r,^r,^r^^)
Comparing the values of ^Tah with the gross correlations, r^h, and
the partial correlations for stature and weight, ^r^^ and ^r^A, we have
the results in table 40.
Correction for both stature and weight has not given constants
very different from those in which the correlation is corrected for weight
only.
Correction for both stature and weight has rendered the correla-
tions between age and heat-production in the two sexes much more
^ There are only 16 athletes. The age range is only 19-29 years, and the correlation is amnH
in actual magnitude and only about one-fourth of its probable error.
•All of these exceptions are trivial in magnitude and only a fraction of their probable errors.
114 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
alike. Thus the differences between the correlations and partial
correlations for the two sexes are :
Corrdation. Partial correlation.
Tah
Men -0.3062 ±0.0524
Women -0.2034 ±0.0637
sw^ah
-0.4995 ±0.0434
-0.5016 ±0.0497
0.1028 ±0.0825 0.0021 ±0.0660
The fact that correction for stature and body-weight has made the
constants sensibly identical gives us great confidence in the reahty of
the physiological law connecting age change and metabolism.
Table 40. — Comparison of gross correlation between age and heat-production and partial
correlation between age and heat-production for constant stature, constant weight,
and constant stature and weight.
Series.
N
Gross correla-
tion between
age and
heat-production
Correlation'
corrected for
influence of
stature
t^ah
Correlation
corrected for
influence of
weight
w^ah
Correlation
corrected for
influence of
stature and
weight
sw^ah
Men.
Original series :
Gephart and Du Bois selection. .
Other than Gephart and Du Bois
selection
72
64
136
68
35
103
-0.3716±0.0685
-0.3003 ±0.0767
-0.3062 ±0.0524
-0.2322 ±0.0774
-0.1796 ±0.1 103
-0.2034 ±0.0637
-0.4842 ±0.0609
-0.2313±0.0798
-0.3003 ±0.0526
-0.2556 ±0.0764
-0.2764 ±0.1053
-0.2465 ±0.0624
-0.4192 ±0.0655
-0.5728 ±0.0566
-0.5147 ±0.0425
-0.3499 ±0.0718
-0.4755 ±0.0882
-0.4976 ±0.0500
-0.4585 ±0.0628
-0.5285 ±0.0608
-0.4995 ±0.0434
-0.3556 ±0.0714
-0.4778 ±0.0880
-0.5016 ±0.0497
All men of three series
Women.
Original series
Supplementary series
Both series
Having considered the intensity of the interrelationship of age and
total heat-production as measured on a universal standard scale, we
may now consider the actual amount of change in metabolism which
takes place with increase in age. This can best be done by expressing
the relationship in the form of regression equations. In these predic-
tion equations a=age in years, /i = total heat per 24 hours, h^. = heat-
production per 24 hours in calories per kilogram, and hr, = heat-produc-
tion per 24 hours in calories per square meter of body-surface by the
Du Bois height-weight chart. Inserting the proper values in the linear
equations given on page 14 of Chapter II, we have the following values :
Men, original series, athletes, iV = 16
ft =2825.88-43.03 a ft;^ =25.071 -f-0.025 a
Men, original series, others, N=62
ft = 1671.89 -2.45 a
ft. =30.219-0.169 a
Men, original series, whole series, A'^=89
ft = 1878.72 -9.19 o ftj;. =29.241 -0.134 a
Men, original series, Gephart and Du Bois selection, N =12
ft = 1928.41 -11.85 a ft;(.= 28.322- 0.098 o
Men, first supplementary series, iV=28
ft = 1698.79 -3.65 a ftj^ =30.111 -0.167 a
ftc = 1119.61-6.17a
ftc = 1019.08-3.630
fti5 = 1045.07 -4.38 a
fti, = 1061.81-5.25 0
ft/, = 1013.81 -4.04 a
CHANGES IN JklETABOLISM WLTH AGE.
115
Men, original and first supplementary series, iV = 117
A = 1848.47 -8.38 a A;t =29.366—0.139 a
Men, second supplementary series, jV = 19
A = 1845.34 -6.40 a
;!i.= 27.588 -0.070 a
Men, other than Gephart and Du Bois selection, A' = 64
A = 1815.48 -6.20 a
Men, of three series, X = 136
/i = 1823.80-7.15 a
Women, original series, N = 68
A = 1448.54 -3.52 a
A. =28.862 -0.116 a
A* =28.703 -0.112 a
At =26.580 -0.046 a
Women, supplementary series. A' =35
;i = 1412.33 -1.85 a
Women, both series, A' = 103
^ = 1420.47-2.290
A. =28.590 -0.147 a
Ai =28.308-0.124 a
^c = 1037.51 -4.29 a
Ac = 1016.38 -2.89 a
Ajt, = 1014.29 -3.20 a
Ad = 1022.17 -3.60 a
Ac = 927.58 -2.33 a
Ac =948.70 -3.22 a
Ac = 942.25 -2.96 o
These equations fail to give the comparative \'iew of the relationship
between age and total heat and age and heat per unit of body-size that
is afforded by the correlation coefficients. They give information of a
very different and very essential sort concerning the relationship
between age and heat-production.
DiAGBAM 18. — Daily heat-production of women classified according to age.
The variable term of the equations for the regression of total heat
on age shows that in the larger series of men the daily heat-production
of an indi\-idual decreases by an average amount of 2.45 to 11.85 calories
per 24 hours for each j'ear of life. Naturally 7.15 calories, based on
the whole series, must be taken as the most probable value. With the
women the decrease in heat-production per 24 hours is 1.85 calories
in the 35 supplementary^ women, 3.52 calories in the 68 women in the
original series, and 2.29 calories in the whole (103) series. Naturally
the latter value must be taken as the standard imtil further data are
available.
Diagrams 18 and 19 show the distribution of the indi\ddual meas-
urements with reference to the straight-line equations.
116 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The regressions of heat per kilogram on age show that there is an
average yearly decrease of from 0.098 to 0.169 calorie per kilogram per
24 hours in heat-production in the larger series of men and from 0.046
to 0.124 calorie per 24 hours in the larger series of women.
Absolute values are of course much larger in the case of body-
surface because the number of square meters of area is much smaller
than the niunber of kilograms of weight. The constants show an
Diagram 19. — Daily heat-production of men classified according to age.
annual decrease of from 3.20 to 5.25 calories per square meter per 24
hours in the larger series of men and from 2.33 to 2.96 calories per
square meter per 24 hours in the larger series of women.
In the foregoing discussion the influence of the factor of body-size
has been to some extent minimized by expressing the decrease in
heat-production in calories per kilogram of body- weight and in calories
per square meter of body-surface as estimated by the Du Bois height-
weight chart.
It is quite possible to correct for the influence of both stature and
weight in a different way. We have already used the partial correla-
CHANGES IN METABOLISM WITH AGE.
117
tion coefficients between age and heat-production for constant stature,
j-^h, and between age and heat-production for constant body-weight,
^Tah, and finally the partial correlation between age and heat-production
for both stature and weight constant, i.e., ^j-ah-
These express the interrelationships between age and heat produc-
tion, correction being made for stature, for weight, and for stature and
weight, on a relative scale. To obtain the actual smoothed change in
metaboHsm per year with correction for the influence of stature and
weight we have merely to determine the partial regressions, p, i.e.,
$Pah, wPah, twPah.
The needful regression slopes in calories per 24 hoiu^ are given by :
/5 . = T '
tfi ah w' ah
vh<^o
tPah = t^ah
th<^a
where the partial correlations are already knoTvn (table 40) and the
partial standard de\4ations are given by :
as (Th = a, Vl-r„A» Vl -,r,, ^ = a, Vl -r.* » Vl-.r^,^
ck<^a
= <r„ Vl -r„J Vl-,„r„.^ = a^ Vl -r„x ^ Vl^
ah
■kTa
The results for the larger series are set forth in table 41. Here the
second coluron gives the decrease in heat-production per year in the
Table 41. — Regression and -partial regression of heat-production on age.
Series.
N
Pak
^«A
tpPah
72
-11.85
-12.40
-8.32
64
- 6.20
- 3.78
-7.07
136
- 7.15
- 5.57
-7.27
68
- 3.52
- 3.82
-3.46
35
- 1.85
- 2.79
-4.87
103
- 2.29
- 2.73
-4.64
vtrak
Men.
Gephart and Du Boia selection
Other than Gephart and Du Boia selection
Grand total
Women.
Original series
Supplementary series
Grand total
-9.13
-6.12
-6.75
-3.53
-4.87
-4.68
several series. These are merely repeated from the list of equations
on page 114. The three following columns give the smoothed annual
decrements in heat-production corrected for the influence of stature,
of weight, and of stature and weight. The entries in the two final
columns are certainly much more uniform than those in the first two.
Correction for body-weight and for stature and weight have greatly
reduced the irregularities which are evident in the gross regressions
or in the regressions corrected for stature only.
118 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The reader personally unacquainted with the difficulties in the
measurement of human metabolism may consider these results numer-
ically very discordant. We have purposely set down the full series of
equations to bring out this range of differences. To us — considering
the great difficulties of measurement, the wide individuality of the
subjects in physique, diet, and life-history, and the (statistically) small
number of individuals considered — the results seem remarkably con-
sistent. There are differences, to be sure, but so there are in the first
determination of any chemical, physical, or astronomical constants.
As the number of determinations increases it will be possible to give
the statistical constants measuring the influence of age upon metabol-
ism in men and women as a class with ever increasing precision.
Table 42.-
—AUeraiion oj metabolism with age.
Men.
Women.
Mean
Mean
Mean
Mean
Mean
Mean
Age.
total
heat
heat
total
heat
heat
N
heat-
per
per
N
heat-
per
per
produc-
kilo-
square
produc-
kilo-
square
tion.
gram.
meter.
tion.
gram.
meter.
15-19 =17
11
1753
26.95
968.4
12
1371
26.51
894.8
20-24 =22
59
1676
26.10
946.2
35
1371
25.16
870.6
25-29 =27
33
1590
25.90
919.6
20
1335
25.83
868.5
30-34 =32
15
1624
26.59
913.1
4
1404
24.26
881.3
35-39 =37
7
1620
23.00
857.0
9
1322
24.32
828.3
40-44 =42
5
1511
24.58
867.8
6
1427
21.35
809.7
46-49 =47
1
1365
22.20
771.0
1
1608
26.80
975.0
50-64 =52
6
1269
21.12
772.2
65-59 =57
2
1373
24.70
864.0
4
1290
19.20
741.3
60-64 =62
3
1641
21.47
836.0
3
1238
22.20
768.3
65-69 =67
1
1150
20.60
723.0
70-74 =72
2
1253
21.10
768.0
The theoretical significance of these results will be discussed in
the final section of this chapter. From the standpoint of practical
application it is important to determine whether or not in the age
range of adult Ufe covered by our data, changes in metabolism with
age can be sufficiently well represented by the slope of a straight line.
If so, correction for age in clinical calorimetry will be a relatively
simple problem.
Straight-line equations for a number of the series have been given
on pages 114-115. These are based on observations ungrouped with
respect to age. For purposes of graphical representation it has seemed
desirable to class the individuals in quinquennial groups. Table 42
shows the method of grouping, the number of individuals, and the aver-
age heat-production in total calories, in calories per kilogram of body-
weight, and in calories per square meter of body-surface by the Du Bois
height-weight chart for 24-hour periods.
CHANGES IN METABOLISM WITH AGE.
119
A comparison of the empirical means and the straight-line equations
is made in diagrams 20 to 22. The empirical means are very irregular
because of the small number of indi\'iduals in the higher age groups,
resulting not merely from the fact that a diWsion of 103 and 136 indi-
viduals into several groups must give small subclasses, but from the
fact that the great majority of metabohsm observations have been
made on indi\iduals between 20 and 35 years of age.
Notwithstanding this irregularity of the means, these diagrams
seem to justify the following generahzations.
\
..^
1600
\
\
^
J
iSOO
aHv
/
■!i>3
^
/\
V----S2!;ai\
L
■IJOO
l>^
\^
--,
.^
■1200
\
\/
/
n zi
Z7
iZ
r ~2 i" -.1 f
€2
V
72
Diagram 20. — Mean total daily heat-production of men and women
classified according to age.
(1) There is far better agreement between the empirical and the
theoretical means when heat-production is expressed in calories per
square meter of body-surface than when given in terms of gross heat-
production.
(2) From the graphs alone it is impossible to decide whether the
expression of metabolism in calories per kilogram of body-weight has
resulted in an improvement in the agreement of the empirical and
smoothed means over that which is found when heat-production is
recorded in total calories per 2-i-hour j)eriods.
(3) The regression lines for men and women lie much closer together
and are more nearly parallel when heat-production is expressed in
relative terms, i.e., m calories per kilogram or calories per square meter,
than when given in terms of gross heat-production.
120 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
(4) Considering both sexes and the three Unes for each, it is im-
possible to assert, on the grounds of inspection merely, that a curve of
a higher order would be more suitable than a straight line for smoothing
the means.
:^
>^
S^
A
■2S
v<
x^
^
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■20
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31
42
4-7
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S7 $2 67
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Diagram 21. — Mean daily heat-production per kilogram of body-weight
of men and women classified according to age.
(5) In all three relationships the line graduating the means for the
men lies above that for the women. In general this is also true of the
empirical means. ^ ^
We note that (1) is merely another expression for results already
demonstrated by the correlation coefficients, namely that the relation-
DiAGRAM 22. — Mean daily heat-production per square meter of
body-surface of men and women classified according to age.
ship between age and heat-production is more intimate if correction be
made for the irregularities of body-size.
Result (2) will be tested by statistical methods below. Results
(3) and (5) are expressions of the sexual differentiation in adults which
will be reserved for treatment in detail in Chapter VII.
CHANGES IN METABOLISM WITH AGE. 121
We shall now turn to a more detailed consideration of (4). To test
more critically the linearity of the regression of total heat-production
on age we may have recourse to the calculation of the correlation
ratio® and the application of Blakeman's test for linearitj^ of regression.
To secure correlation ratios which shall be of value we must group
with regard to age. Table 42 shows the age grouping adopted, the
number of individuals, and the mean heat-productions in the total
men and women.
For age and total heat-production as deduced from this table the
correlation coefficient, r^h, and correlation ratio, r^h, are :
Correlation Corrdation
coefficient, r. ratio, ij.
Men -0.3017*0.0526 0.3575*0.0504
Women -0.1946 *0.0639 0.3458 *0.0585
The correlation coefficients for the two sexes differ so greatly that
one would be inclined at first to suspect arithmetical error, but the
value for the women ungrouped with respect to age as recorded on
page 111 is essentially identical with this constant, i.e., —0.2034=*=
0.0637 as compared with -0.1946 =*=0.0639.
The correlation ratios are in much closer agreement than the corre-
lation coefficients. With regard to their probable errors the correlation
ratios do not differ. The difference between the correlations for men
and women is 0.1071 =*= 0.0827, a value which, while large in comparison
with the constants upon which it is based, by no means represents a
certainly trustworthy difference.
Applying Blakeman's criterion
1 1
c/^,= ---V>72-
Xi 2 "' l-t-(l->7^)'-(l-r«)«
where Xi is the value of 0.6744898/\/iv from Miss Gibson's tables/®
we find:
For men C/^^=l-72
For women ^/B^=2.33
Applying the same methods to the problem of the interrelationship
between age and total heat-production per kilogram of body weight we
have for r . and >? . :
Correlation Correlation
coefficient, r. ratio, rj.
For men -0.3840*0.0493 0.4414*0.0466
For women -0.4962 * 0.0501 0.5695 * 0.0449
The correlation coefficients and the correlation ratios are numer-
ically higher in both sexes. The correlations are but slightly more
» Blakeman, Biometrika, 1906, 4, p. 332.
"Gibson, Biometrika, 1906, 4, p. 385. Also in Pearson's Tables for Statisticians and bio-
metricians, Cambridge, 19i4.
122 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
consistent than thoSe for age and gross heat-production. The differ-
ence between the two sexes is only 0.1122 =±=0.0703, and is therefore
insignificant in comparison with its probable error. The difference
between the two correlation ratios is 0.1281 =t 0.0647, or approximately
twice its probable error and of questionable biological significance.
Applying Blakeman's criterion we find :
For men !i/E^=lM
For women C/^f =223
On the basis of the usual criterion, regression can not be asserted
to be non-linear in either sex.
Turning now to the measures of heat-production corrected for
body-size by reduction to calories per square meter of body-surface
by the Du Bois height-weight chart, we have for rah and yiah :
Correlation Correlation
coefficient, r. ratio, t;.
For men -0.4584 ±0.0457 0.5008 ±0.0433
For women -0.5149 ±0.0489 0.5824 ±0.0439
Difference 0.0565 ±0.0669 0.0816 ±0.0617
Again the differences between the constants for men and women
can not be considered to differ significantly. Blakeman's criterion gives
For men C/^f = 1-80 For women C/^; = 2.16
The results can not be considered to show that regression is non-
linear. The calculation of the correlation ratios and the interpretation
of the results of Blakeman's test on a series of only 136 and 103 indi-
viduals presents some difficulties. We have not applied the corrections
to the correlation ratio suggested by Pearson and "Student," never-
theless we feel justified in concluding from the results of Blakeman's
test and from the graphical test of the Hnearity of regression that
throughout the age range involved the change in metabolism with age
can be satisfactorily represented by a straight line. When larger series
of data are available the use of regression coefficients of a higher order
may be justified.
A discussion of the practical application of correction for age is
reserved for Chapters VII and VIII. Before leaving the subject of
the change of metabolism with age, it seems desirable to compare the
heat-production per square meter of body surface by the Du Bois
height-weight chart given by our equations for total men (N = 136)
and for total women (N = 103) with the ''normal standards " for various
ages calculated by Aub and Du Bois ^^ from their age curve and that
given by Lusk.^^
''Aub and Du Boia, Arch Intern. Med., 1917, 19, p. 831. Also Cornell, Univ. Med. Bull.,
1918, 7, No. 3, 19th paper, p. 9.
" Lusk, Science of Nutrition, Philadelphia, 3 ed., 1917, p. 129.
CHANGES IN METABOLISM WITH AGE
123
The results in terms of calories per square meter per 24 hours
appear in table 43.
Without exception the values of daily heat-production as given by
Aub and Du Bois are higher, and sometimes verj' materially higher,
than those indicated by our equations showing the regression of heat-
production per square meter of body-surface by the height-weight
chart on age.
3. COMPARISON OF CHANGES IN PULSE-RATE IN RELATION TO AGE.
We now turn to a comparison of the changes in another physiological
character. It seems desirable in this connection to consider the pos-
sible relationship between age and pulse-rate.
Table 43. —Comparison of Avb and Du Bois standard normal unth daily metabolism Qiven
by regression eqriation.
Age in
years.
Men.
Women.
Aub and
Du Bois
normal
stand-
ard.
Metab-
olism as
given by
equa-
tion.
Differ-
ence.
Aub and
Du Bois
normal
stand-
ard.
Metab-
olism as
given by
equa-
tion.
Differ-
ence.
14-16 (15)
16-18 (17)
18-20 (19)
21-30 (25.5)
31-40 (35.5)
41-50 (45.5)
51-60 (55.5)
61-70 (65.5)
71-80(75.5)
1104
1032
984
948
948
924
900
876
852
968
961
954
930
894
858
822
786
750
+ 136
+ 71
+ 30
+ 18
+ 54
+ 66
+ 78
+ 90
+ 102
1032
960
912
888
876
864
840
816
792
898
892
886
867
837
808
778
748
719
+ 134
+ 68
+ 26
+ 21
+ 39
+ 56
+ 62
+ 68
+ 73
Our data for adults give the correlations between age and pulse-rate
shown in table 44. The partial correlations, given by
«'*ap
f — f f-
Vl-r ' Vl
,r =■
r — r r
' ap ' aw' rrp
Vl-r^J Vl-1
are laid beside the gross values.
All the correlations are numerically low. Taken individually no
one of the series would be regarded as certainly significant in compari-
son with its probable error by any careful statistician. Considering
the series as a whole and noting that 9 out of the 11 constants are
negative in sign, we consider that there is a reasonable probabihty
that pulse-rate decreases with age. This probability is increased when
correction is made for the possible influence of weight and height. The
partial correlations, ^.rap, .r^p, are the same in sign as the original
correlations.
Since correction for the two most conspicuous physical characters
of the indi\'idual have left the relationship between age and pulse-rate
124 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
practically unchanged, there can be little doubt that there is a slight
but definite relationship between these two variables in the range of
age covered by our data for adults. Pulse-rate decreases slightly with
advancing years. This decrease is not directly due to any change in
stature or weight.
As far as we are aware the only correlations available from the
literature are those provided by Whiting. ^^
Table 44. — Correlation between age and pulse-rate and partial correlation between age and
pulse-rate for constant stature and constant body-weight.
Series.
N
Correlation
between age and
pulse-rate
Partial correla-
tion between age
and pulse-rate
E
Partial correla'
tion between age
and pulse-rate
r
» ap
t'ap
a ap
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection ....
First supplementary series
Original and first supplementary series
Other than Gephart and Du Bois se-
lection
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
88
71
28
116
50
121
-0.2597 ±0.1573
-F0.0581=i= 0.0583
-0.1405=1=0.0705
-0.0963 ±0.0793
-0.0609*0.1270
-0.1252±0.0616
-0.1947 ±0.0918
-0.1483 ±0.0600
-0.1250±0.0805
-f0.1084±0.1421
-0.0855 ±0.0706
1.65
0.68
1.99
1.21
0.48
2.03
2.12
2.47
1.55
0.76
1.21
-0.2189±0.1605
+0.1146±0.0845
-0.1405 ±0.0705
-0.1180±0.0789
-0.0743 ±0.1268
-0.1257±0.0616
-0.2177 ±0.0909
-0.1500±0.0599
-0.1323±0.0804
+0.1566±0.1403
-0.0313±0.0710
1.36
1.36
1.99
1.50
0.59
2.04
2.39
2.50
1.65
1.12
0.44
-0.0343 =
-f- 0.0744 =
-0.1297 =
-0.0969 =
-0.0623 =
-0.1170 =
-0.1461 =
-0.1400 =
= 0.1684
= 0.0852
= 0.0707
= 0.0793
= 0.1270
= 0.0618
= 0.0934
= 0.0601
-0.1338 ±0.0803
-(-0.1177±0.1418
-0.0760 ±0.0707
0.20
0.87
1.83
1.22
0.49
1.89
1.56
2.33
1.67
0.83
1.07
For age and pulse-rate in 500 criminals examined by Goring the
correlations deduced by Whiting are :
For age and pulse r„p = -|-0.121 ±0.022
For age and pulse with temperature constant ti^ap = +0.174 ±0.022
For age and pulse with respiration constant r'>'ap = +0.117 ±0.022
For age and pulse with stature constant s^ap = +0.124 ±0.022
For age and pulse with weight constant w^ap = +0.107 ±0.022
For age and pulse with both weight and stature constant „s^ap = +0.097 ±0.022
These values, both the gross correlation between age and pulse-rate
and the correlation corrected for various other physical and physio-
logical characters, are low but consistently positive throughout. Thus
they indicate that pulse-rate increases with age instead of decreasing
as in our series. This contradictory result may possibly be due to the
essentially different conditions under which the rates were measured.
Our determinations were made with the subject lying down and at
complete muscular repose in the post-absorptive state; they, therefore,
probably represent the minimum or basal pulse-rate for individuals in
their state of nutrition. Goring's countings were made with the patient
sitting in his cell after early dinner, either idle, reading, or writing. The
'^ Whiting, Biometrika, 1915, 11, pp. 8-19.
CHANGES IN IklETABOLISM WITH AGE. 125
average pulse-rate found by Whiting for these data was 74.22, which
is 12.96 beats or 21.2 per cent higher than our average for men. Pos-
sibly pulse-rate in older indi\iduals is more susceptible to increase
due to physiological or physical activity than it is in younger. If so,
this difference in the conditions under which the rates were measured,
may be sufficient to account for the differences in the correlations.
4. RECAPITULATION AND GENERAL CONSIDERATIONS.
In this chapter we have considered the relationship between age
and basal metabolism in adult men and women. The significance of
such an investigation is twofold. From the theoretical side the mor-
phological and physiological changes which accompany the aging of the
individual constitutes one of those groups of fundamental problems
which has always attracted the interest of biologists and of the medical
profession. Any contribution of actual fact is a valuable addition to
the vast Uterature. From the practical standpoint, a knowledge of
the quantitative relations between age and basal metabohsm is essen-
tial for the establishment of standard controls to be used in applied
calorimetry.
The results of the present study show that throughout the whole
range of what we commonly designate as adult fife the heat-production
of the individual decreases. The correlation between age and heat-
production is therefore negative in sign, lower daily heat-production
being associated with greater age. The gross correlations are of the
order —0.31 for men and —0.20 for women.
Daily heat-production has been shown in the foregoing chapter to
be correlated with both stature and body-weight. Since in adult fife
these vary for the most part independently of age, it is evident that if
the correlation between age and metabohsm be due to definite and
progressive physiological changes in the tissues of the organism with
increasing age, the measure of the correlation between age and metab-
olism will be lowered by the disturbing influence of these factors.
Correcting for the influence of stature makes relatively Httle differ-
ence in the intensity of the correlation between age and metabolism.
Correction for the influence of body-size by expressing heat-production
in calories per kilogram of body-weight raises the numerical value of
the correlation coefficient for age and heat-production from —0.31 to
—0.41 in the total series of men and from —0.20 to —0.49 in the total
series of women. If correction be made for body-size by expressing
heat-production in calories per square meter of body-surface as esti-
mated by the Du Bois height-weight chart, the correlation is increased
(in the negative direction) from —0.31 to —0.47 for the men and from
-0.20 to -0.52 for the women.
Comparable results are obtained by correcting the correlations
between age and heat-production for the influence of physical dimen-
126 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
sions by the use of partial correlation formulas. If the partial correla-
tion between age and metabolism for constant stature and body-weight
be compared with the gross or uncorrected correlations, it will be found
that the numerical values of the interdependence of the two variables
has been raised from —0.31 to —0.50 for the men and from —0.20 to
—0.50 for the women.
These statistical results indicate in the clearest way the existence
of fundamental changes in the tissues and their physiological activities
with age. This evidence inheres not merely in the fact that the intens-
ity of the interrelationship is increased when correction is made for the
disturbing influence of body mass in both of the sexes, but that when
these corrections are made the results for the two sexes are rendered
very nearly identical.
Expressing the relationships between age and metabolism in terms
of the actual decrease in daily heat-production per year, we note that
this amounts to about 7.15 calories in men and 2.29 calories in women.
Of course men and women differ greatly both in stature and weight
and in daily heat-production. The decrease in heat-production per
kilogram of body-weight is more nearly identical in the two sexes, i.e.,
0.112 calorie in men and 0.124 calorie in women. The decrease in
calories per square meter of body-surface area, as estimated by the
Du Bois height-weight chart, is 3.60 calories per 24 hours per year in
men and 2.96 calories per 24 hours per year in women.
The problem of the regression of heat-production (either gross
heat-production or heat per kilogram of body-weight or per square
meter of body-surface) on age is one of both great theoretical interest
and practical importance. It is of great physiological interest to deter-
mine the rate at which metabolism decreases with advancing years,
to ascertain whether this changes at some period of life, and (if so) how
these rates of change or periods of change correspond with other physio-
logical periods. Certainly this phase of the problem of growth, age,
and death should take rank with the others which have been investi-
gated. The quantitative statement of the laws governing the change
in metabohsm with age is the first logical step in the analysis of this
problem.
From the practical standpoint, determination of these laws is
essential for the calculation of standard control values to be used as a
basis of comparison in physiological and pathological research.
Tests of the rate of change throughout the age-range of adult life
indicate that it is essentially uniform, so that, as far as the data at
present are adequate to show, it can be expressed as well by the slope
of a straight line as by a curve of a higher order.
The data for the lower and higher age-groups are still inadequate,
and the exact Umits of appUcability of a straight line for the expression
of changes in metabohsm with age must remain a problem for future
consideration.
I
CHANGES IN METABOLISM "V^^TH AGE. 127
Practically the linear nature of the change of metabolism with age
is of great importance in connection with the establishment of standard
control series to be used in appUed calorimetry — a subject to be fully
discussed in Chapter VIII.
For the purposes of throwing some hght on the general problem of
senescence, we have brought together for comparison such quantita-
tive data as are available on the changes of another physiological
character with age.
Pulse-rate in our own data shows a slight decrease with increasing
age. The amoimt of change is so small that its nature has not been
investigated.
Referring to the problem of senescence, rejuvenescence, and death
in man and other higher animals, Child ^^ says :
"As regards the relation between senescence, death, and rejuvenescence,
the higher animals and man differ from the lower organisms in the limitation
of the capacity for regression and rejuvenescence mider the usual conditions.
Senescence is therefore more continuous than in the lower forms^^ and results in
death, which is the final stage of progressive development. These character-
istics of man and the higher animals are connected with the evolutionary
increase in the physiological stability of the protoplasmic substratum and the
higher degree of indi%dduation which results from it."
Now, without passing any judgment on the vahdity of Child's
extension to the higher vertebrates of his remarkable experimental
results with planarians and other lower forms, we may point out that
our owTi quantitative results fully substantiate his conclusion concern-
ing the greater continuity of senescence in the higher forms. In man,
changes in metaboHsm after physical maturity are not merely contin-
uous, they are uniform in amount, so that they can be reasonably well
represented by the slope of a straight Hne.
^* Child, Senescence and Rejuvenescence, Chicago, 1915, p. 399.
'* Italics ours.
CHAPTER VI.
A CRITIQUE OF THE BODY-SURFACE LAW.
The simple relation between the volume and the surface-area of
comparable soUds has always appealed to biologists. Absorption,
secretion, or excretion, whether of water, of aqueous solutions, or of
gases, are surface phenomena. Gills, lungs, glands, or other organs
which are highly speciaUzed for these fimctions in the higher organisms
are primarily characterized by great siu-face exposure. Thus the well-
being of the organism as a whole in many ways depends upon the
ratio of the surface-area to the mass of many of its tissues.
Again, except when great changes in the proportion of parts are
concomitant with increase in size, it is e%4dent that growth must
decrease the ratio of external surface-area to body-mass. Inphylogeny
the same relationship obtains as in ontogeny. In organisms of gen-
erally similar physical conformity, the larger species must expose a
relatively smaller surface. It is therefore natiu-al that one should
find the two-thirds power relationship considered in various general
writings on body-size. A whale in the Arctic exposes relatively far
less siurface to the surroimding water than a flying-fish in the tropics.
An auk in the Arctic exposes relatively far less smface for the
loss of heat than a humming-bird in the tropics. Biologists have not
failed to grasp the possible significance of such facts for geographical
distribution.
Turning to an entirely different phase of the general discussion,
we may refer to the investigations of Dreyer, Ray, and Walker,^ in
which they considered blood-voliune, area of the cross-section of the
trachea, and area of the cross-section of the aorta in various animals
and birds in relation to this principle.
Surface rather than volume has been suggested as an important
factor in muscular work. In the problem of the phj'siolog^' of excretion
it has been stated that the volume of urine is not proportional to the
weight of the kidney but to the internal surface. Snell and Wamecke
have attempted to arrange vertebrates in series according to relative
brain-weight, brain-surface, and intelUgence. Perhaps the most ex-
treme apphcation of the principle in biological theorj^ is that in Miihl-
mann's theory of old age, which depends upon the change in the relation
of sm^ace and volume with increasing size.^
' Dreyer and Ray, Phil. Trans., 1909-1910, 201, ser. B, p. 133. Drejer, Ray, and Walker,
Proc. Roy. Soc, 1912-1913, 86, ser. B, pp. 39 and 56.
* See bibliography and extensive discussions of Muhlmann's writings by Minot, The Problem
of Age, Growth, and Death, 1908, and by Child, Senescence and Rejuvenescence, 1916.
129
130 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Given an inert body at a temperature higher than its medium, the
rate of loss of heat will be determined to a large degree by the nature
and extent of its surface-area and the difference in temperature of the
body and its medium. For three-quarters of a century, or more,
various physiologists have urged that the heat-production in different
individuals and species of animals is proportional to their surface-area.
Our purpose in this chapter is threefold : {a) To outline briefly the
history of the so-called body-surface law. (6) To discuss certain phys-
iological evidences bearing upon the question of its validity, (c)
Finally, to test it by the application of biometric formulas to the series
of data available for this investigation.
1. HISTORICAL.
While discussions of the so-called "body-surface law" generally
begin with the work of Rubner,^ and while it is frequently referred
to as "Rubner's Law" the conception of surface and volume relation-
ships in the balance between thermolysis and thermogenesis seems to
have been quite prevalent at least among French writers, at a much
earlier date. Thus Robiquet and Thillaye, in reporting on a memoir
submitted to the Academy of Medicine of Paris * by Sarrus and Ra-
meaux, refer to the arguments of the authors as based upon "une prop-
osition de g^om^trie incontestable, une loi physique g^n^ralement
admise et quelques faits physiologiques plus ou moins bien con-
states." These they state as follows:
"Voici done les bases sur lesquelles s'appuie le travail dont il s'agit.
"1" Entre deux poly^dres semblables, les volumes sont comme les cubes,
et les surfaces comme les carr^s des cot^s homologues.
"2° Toute chose 6tant 4gale d'ailleurs, des corps de m^me nature perdent
k chaque instant des quantit^s de chaleur qui sont proportionnelles k I'^tendue
de leur surface libre.
"3° Dans les animaux de meme esp^ce, consid^r^s k I'^tat normal et places
dans des conditions identiques, les quantit^s de chaleur d^velopp^e dans un
temps donn^ sont proportionnelles aux quantit^s d'oxygene absorb^ par I'acte
de la respiration, ou bien encore sont proportionnelles au volume d'air inspird
pendant la meme dur^e; en admettant toutefois que I'air introduit dans les
poumons k chaque inspiration abandonne toujours la m^me proportion de
son oxygene.
"Si actuellement nous admettons que la temperature des animaux est
constante, c'est reconnaitre que chez eux il y a une parfaite ^galite entre la
chaleur qu'ils produisent et celle qu'ils ^mettent. Or, comme la deperdition
est proportionnelle k I'^tendue des surfaces libres et que celles-ci sont comme le
carre des cotes homologues, il faut ndcessairement que les quantit^s d'oxygene
absorb^, ou, ce qui est I'^quivalent, que la chaleur produite d'une part et
perdue de I'autre soit comme le carre des dimensions correspondantes des
animaux que Ton compare, condition indispensable et qui pent 6tre remplie
de plusieurs manieres."
» Rubner, Zeitschr. f. Biol., 1883, 19, p. 535.
* Robiquet and Thillaye, Bull. Acad. roy. de m6d., Paris, 1839, 3, p. 1094.
A CRITIQUE OF THE BODY-SURFACE LAW. 131
The memoir by Rameaux and Sarrus was never published in full
by the Academie de Medecine, but abstracts had appeared earlier in
Comptes Rendus ^ and through a letter to Quetelet in the Bulletins de
r Academie Rayale de Bruxelles,^ and the final memoir was read by
Rameaux before the Belgian Academy in 1857 and pubUshed in 1858/
In none of these pubUcations is the proposition that heat-production
is proportional to body-surface emphasized as a new conception. In
his volume of 1889 Richet,^ in referring to one of his tables, calls
attention to "la demonstration physiologique de ce fait bien connu que
la production de calorique est fonction de la surface et non du poids."
Ten years after the appearance of Rameaux's preliminary papers
Bergmann ® attempted to explain the relatively higher food demands
of small as compared with those of larger animals of the same species
by the generahzation that the heat-production of a body is proportional
to its surface. Bergmann's work was entirely comparative and theo-
retical. WTiile Rameaux in his final memoir brought together and
analj'zed considerable series of data for pulse-rate, respiration-rate,
and lung-capacity, the first experimental evidence seems to have been
that presented by Miintz ^° who in discussing the maintenance food
requirement for horses as investigated in a series of experiments made
in 1879 gives a clear statement of the conception of the relationship
between body-surface and metabohsm. Although his experiments
contribute nothing of importance to the general problem, his concep-
tion is of sufiicient importance, historically at least, to be quoted
infuU:
"II nous semble, des a present, que la quantite d'aliments necessaire k
I'animal pour s'entretenir sans travailler doit se trouver plutot en rapport
avec la surface qu'avec le poids de son corps. Toutes choses egales d'ailleurs,
on peut admettre que la quantite de chaleur enlevee au corps est proportion-
nelle a sa surface. Une notable partie de Taliment est certainement consom-
mee pour I'entretien de la chaleur vitale qui tend constamment k se perdre,
par rayonnement ou par conductibilite. dans le milieu ambiant. Une autre
cause de refroidissement est I'evaporation cutanee qui est fonction de la surface
du corps, si elle ne lui est pas proportionnelle. L'^vaporation produite par
les organes respiratoires peut ^galement etre regardee comme ayant un rapport
avec la surface bien plus qu'avec le poids. Nous sommes done, par ces con-
siderations, autoris^s a admettre I'influence preponderante de la surface du
corps sur la quotit6 de la ration d'entretien.
» Sarrus and Rameaux, Compt. rend. Acad, sci., Paris, 1838, 6, p. 338; loc. cit., 1839, 9, p. 275.
* Rameaux, Bull. Acad. roy. d. sci. de Bruxelles, 1839. 6, (2), p. 121.
^ Rameairx. M6m. couron. Acad. roy. d. sci. (etc.) de Belg., Brux., 1858, 39, 64 pp.
* Richet, La chaleur animale, Paris, 1889, p. 222.
* Bergmann and Leuckart, Anatomisch-physiologische Ubersicht des Thierreichs, Stutt-
gart, 1852, see especially p. 272. Also Bergmann, Ueber die Verhaltnisse der Warme-
dkonomie der Thiere zu ihrer Grosse, Gottingen, 1848. An earlier paper in MiiL'ers'
Archiv, 1845, p. 300 is also cited.
*" Miintz, in an article entitled "Recherches sur ralimentation et s\ir la production du
travail," in Annales de I'lnstitut National Agronomique, Paris, 1880, 3, pp. 23-61.
This quotation is from p. 59. According to a statement on p. 25. " Les experiences de la
3"' s6rie ont dur6 du 12 Septembre 1879 au 7 Fevrier 1 880, c*e8t-4-dire pendant 148 jours.' •
132 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
"Plus tard nous apporterons k I'appui les experiences que nous faisons
dans cette direction et qui sont rendues possibles grace au concours de
M. Lavalard et de M. Poret, grace aussia I'obligeant empressement avec
lequel MM. Geoffroy Saint-Hilaire et Menard ont mis k notre disposition les
precieuses ressources du Jardin d'acclimatation."
The first experimental data which requires consideration in relation
to modern work was published almost simultaneously by Rubner ^^
and Richet ^^ both of whom maintained that the heat lost from living
organisms is essentially constant per unit of body-surface. Because
of his unusual technique the work of Rubner has rightfully been ac-
corded the greater weight by physiologists, and the "body-surface law"
is generally referred to as "Rubner's law." It has unquestionably
been one of the most stimulating ideas in nutritional physiology.
While this constancy of heat-production per unit of body-surface
area is the dominant note in Rubner's papers, in several instances he
writes as if a causal relationship between body-surface and heat-pro-
duction was by no means thoroughly established. Richet, too, lays
stress upon many factors, such as nature of integument and external
temperature.
After the appearance of Rubner's paper the hypothesis of a simple
mathematical relationship between body-surface and total metabolism
became naturally the subject of much discussion. Magnus-Levy and
Falk ^^ referred to Rubner's dictum as the most important recent
contribution in the study of the gaseous metabolism. The range in
the animal kingdom over which this supposed law has been assumed to
extend is astonishing. It has been extensively applied to variations in
the heat-productions of the same species. The computations of
E. yoit ^* attempt to show that animals ranging in size from a 2-kilo-
gram fowl to a 441-kilogram horse have essentially the same heat-
production per square meter of body-surface, namely, 970 calories per
24 hours. Armsby and his collaborators,^^ referring to a series of con-
stants for man, cattle, horses and swine say :
"They show a rather striking degree of uniformity and tend to confirm
the conclusions of E. Voit that the basal katabolism of different species of
animals is substantially proportional to their body-surface."
An illustration of the extremes to which strict adherence to the
body-surface law may lead is afforded by Putter's contention ^^ that
the ''active" surface, i.e., the cell surfaces of the various organs of the
body, should be taken into account. Putter maintaining that the energy
" Rubner, Zeitachr. f. Biol., 1883, 19, p. 535.
^^ Richet, La chaleur animale, Paris, 18S9. Hia earlier writings, some of which appeared
at about the same time as Rubner's paper, are here summarized.
" Magnus-Levy and Falk, Arch. f. Anat. u. Physiol., Physiol. Abt., Supp., 1899, p. 314.
^* Voit. Zeitschr. f. Biol., 1901, 41, p. 120.
'* Armsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, pp. 3-4. See also Journ. Agric.
Research, 1918, 13, pp. 49-55.
'« Putter, Zeitschr. f. allg. Phys., 1911, 12, p. 125.
A CRITIQUE OF THE BODY-SURFACE LAW. 133
consumption is proportional not to the body-surface but to the area
of the lung-surface.
A careful study of the large mass of literature on metabolism subse-
quent to 1883 will show that there has been at no time a fixed inter-
pretation of the relationship between body-surface and heat-production.
Even the most ardent advocates of the body-surface law have at times
called attention to noticeable abnormalities. But attempts were made
to explain these discrepancies by the nature of the integument, the
density of the fur and hair coverings, and variations in the amount of
body-surface exposed . ' ~
To attempt to re\aew in any detail the extensive discussions of the
earlier writers would be a useless task.
Unfortunately many modern authors are not so conservative in
their expressions as to the cause of this relationship between body-
surface and heat-production as were earlier students. The attitude
maintained in more recent times may be illustrated by the following
quotations. In his deservedly oft-cited contribution on respiration in
Schaefer's Physiology, Pembrey says : ^^
"Now, small mammals and birds have a temperature equal to or even
higher than that of large animals of the same classes; and, on account of the
relatively greater surface which ihey expose for the loss of heat, they must
have a relatively far greater production of heat than the large animals, for
there is generally no marked difference in the protective coat of fur or feathers."
WTiile Minot ^^ does not explicitly state that heat-loss and heat-
generation are determined by body-surface, his comparison and dis-
cussions would seem to have this impUcation.
The range of apphcability over which Rubner himself would con-
sider the surface law valid is i>erhaps indicated by a quotation from a
paper of 1908,^^ in which he discusses the metabolism of various
mammals after birth. Referring to the values used, he says:
"Wenn es auch nicht immer Neugeborene waren, die der Stoffwechsel-
untersuchung unterzogen sind, so wissen wir auf Grund des von mir erwiesenen
Oberflachengesetzes, dass bei den Saugern ihr Stoffwechsel nicht des Masse,
aber genau der Oberflache proportional verlauft. Man kann daher die
gewiinschten Grossen des Energieverbrauchs fiir jede beliebige Kleinheit der
Thiere, also auch fiir die Neugeborenen, durch Rechnung finden."
Lef^\Te specifically states that the application of the law of Newton
to li^^ng animals is illusory,^^ but in his discussion of the production
of heat per unit of surface the following statement appears : ^"
^^ For example, we frequently find in the text of the earlier writers such statements aa the
following: " Wiirmeabgebende Flache und Hautflache sind zwei sehr verschiedene
Dinge." Rubner, Beitrage zur Ernahrung im Knabenalter mit besonderer Beriicksicht-
igung der Fettaucht, Berlin, 1902, p. 40.
'* Pembrey, Schaefer's Text-Book of Physiology, London, 1898, 1, p. 720.
'» Minot, The Problem of Age, Growth, and Death, New York, 1908, pp. 18-20.
^ Rubner, Sitzungsb. d. Kgl. Preuss. Akad. d. Wissensch., phys.-math. Kl., 1908, p. 36.
-' Lefevre, Chaleur Animale et Bioenergetique, Paris, 1911, p. 379.
^ Lefevre, loc. cit., p. 500.
134 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
"La production chez I'hom^otherme est en equation avec la perte calori-
que. Or, k pouvoir ^missif 6gal, la deperdition est ^videmment proportion-
nelle a la surface rayonnante. La production calorique (c'est-£-dire, chez
I'organisme en dquilibre et au repos, le besoin d'energie) est done proportion-
nelle a I'etendue de la surface totale du corps."
Furthermore, Professor H. P. Armsby, whose more recent conclu-
sions have been noted above, states : ^^
"The results which we have been considering show that in general the
emission constant, i.e., the rate of heat emission per unit of surface, is sub-
stantially the same in small and large animals and that the greater loss of
heat in the former case is met by an increased production. In this aspect the
effect is simply an extension of the influence of falling temperature, the in-
creased demand for heat being met by an increased supply, so that the extent
of surface appears as the determining factor of the amount of metabolism."
Moulton, who (on the basis of a series of graphs) has given a detailed
discussion of the interrelationship between body-surface, body- weight,
blood-volume, nitrogen-content of body, etc., in cattle in various con-
ditions, says : ^^
"A better conception of the basal needs of animals for food can be obtained
from a comparison of the relative surface areas of the animals. Since Rubner
and Richet presented evidence to show that the heat production of living
animals was proportional to the body surface, this has been a much used unit
of reference."
In other current (1915) literature we find such statements as the
following :^^
" 'Rubner's law,' to quote from Lusk, is that 'the metabolism is propor-
tional to the superficial area of an animal. In other words, the metabolism
varies as the amount of heat loss at the surface, and its variance in accordance
with this law is necessary for the maintenance of a constant temperature.' "
In a popular text-book on nutrition ^^ we also find :
"Since the body loses heat in proportion to the extension of its surface
it is not strange that this is the determining factor for the metabolism."
Du Bois, in his Harvey lecture ^'' of November 27, 1915, said:
"Rubner demonstrated many years ago that the metabolism is propor-
tional to the surface-area of the body and that for each square meter of skin
large men, small men, dogs, horses, and mice have about the same heat pro-
^ Armsby, The Principles of Animal Nutrition, New York, 1906, 2d ed., p. 365. Professor
Armsby, in a recent personal communication states that this phraseology does not
exactly express his belief: " The true state of the case is, as I conceive it, that the body
does not produce heat to any considerable extent to keep itself warm but is kept warm
because it produces heat. In other words, heat production is substantially not an end
but an incident of metabolism."
" Moulton, Journ. Biol. Chem., 1916, 24, p. 303.
^ Means, Journ. Med. Research, 1915, 32, p. 139.
*« stiles. Nutritional Physiology, Philadelphia, 1915, 2d ed., p. 200.
" Du Bois, Am. Journ. Med. Sci., 1916, 151, p. 781. Also Studies Dept. Physiol., Cornell
Univ. Med. Bull.. 1917, 6, No. 3, Part II. Also The Harvey Lectures, 1915-1916, p. 106.
I
A CRITIQUE OF THE BODY-SURFACE LAW. 135
duction. Just why this should be we do not know. It reminds us at once of
Newton's law that the cooling of bodies is proportional to their surface-area,
but the metabolism does not follow this law when the external temperature
is raised or lowered."
The foregoing re^'iew, while fragmentary, may give a general idea
of the attitude of physiologists toward the problem of bodj-surface
area in relation to metabohsm. One essential distinction has not
always been clearly drawn by those who have written on the so-called
body-sm-face law. One may inquire whether the law holds for the
different species of animals which vary greatly in size, or he may
inquire whether it is vaUd when appUed to individuals differing in size
within the same species. In brief the inter-specific and the intra-specific
apphcabiUty of the so-called law present two different problems. It
is quite conceivable that it might be very appUcable intra-specifically
but not inter-specifically or vice versa.
In this volume we shall limit ourselves chiefly to the question of
intra-specific appUcabihty.
2. PHYSIOLOGICAL EVIDENCE ON THE BODY-SURFACE LAW.
Direct physiological e\'idence of an experimental nature of two
sorts are available. The first is that afforded by determinations of
metabohsm in similar organisms subjected to different external tem-
perature. The second is that afforded by measures of metabohsm
secm-ed on indi\'iduals of like body-surface but in different physio-
logical state.
The physical basis of the body-surface law has often been stated
to be Newton's "law of cooling." Some of the earher physiological
writers seem to have fully understood the nature of Newton's law, but
in recent j-ears a confused and inadequate conception of this law has
estabhshed itself in physiological literature. Physiologists have stated
the physical law as they would hke it to be rather than as it really is.
For example the inmaediately foregoing quotation from one of the
Harvey lectures ^* is quite t>T)ical of the conception of Newton's law
which has been held by physiologists, including the workers at the
Nutrition Laboratory.
But Newton's law is not primarily a surface law at all, but a law
of the rate of cooUng, now known to have only a limited apphcabihty
even in the simpler cases of controlled physical experimentation. Heat
is lost by cooling bodies by convection, conduction, and radiation. The
relative importance of these three methods depends upon the nature
of the surface and the nature of the surrounding medium. In the
majority of cases of transference of heat all these modes are simultane-
ously operative in a greater or less degree, and the combined effect is
generally of great complexity. The different modes of transference
* The Harvey Lectures, 1915-1916, p. 106.
136 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
are subject to widely different laws, and the difficulty of disentangling
their effects and subjecting them to calculation is often one of the most
serious obstacles in the experimental investigation of heat under the
controlled conditions of the physical laboratory.
If one assumes the apphcability of Newton's law to living organisms
it is evident that it might under special conditions reduce to a surface
law. Thus in 1898 Richet ^^ wrote:
"Supposons, en effet, qu'il s'agisse d'un corps inerte; sa radiation sera,
conform6ment k la loi de Newton, 6gale k la difference des deux temperatures,
multipli^e par sa surface S (t — t') . En supposant t — t' constant, ou peu vari-
able, il s'ensuit que la radiation calorique est proportionnelle k la surface. Or
j'ai pu prouver que les chiffres calorimetriques experimentalement obtenus
sont tels que I'unite de surface d^gage toujours k peu pr^s la meme quantity
de calories."
In modern discussions of the body-surface law the question of the
nature of the integument is generally ignored. Yet in the earlier writ-
ings the nature of the surface received detailed consideration.
This subject is discussed in detail by Richet,^° who not merely
treats it from the comparative side but records experiments with
animals in normal condition, with shaved animals, and with those
whose fur had been smoothed down by a coating of oil or varnish. He
even gives the results of experiments with animals having white, gray,
and black coats, and claims differences in their heat loss.^^
Since Newton's law is really a law of the rate of coohng due to
differences in temperature, it should be evident that its validity when
applied to organisms could be tested only by having all basal-metab-
olism determinations made under comparable conditions of internal
and external temperature. Certainly this can not be assumed of the
series of determinations on diverse organisms which are brought
together for comparison in substantiation of the body-surface law.
Among the earlier physiologists who had not yet lost sight of the
true significance of Newton's law, studies of metabolism at varying
temperatures were seriously considered. When the influence of en-
vironmental temperature was studied, difficulties were immediately
encountered. In discussing the fact that certain animals show abnor-
mal relationships between the environmental temperature and their
body temperature, d'Arsonval^^ introduces the following significant
sentence :
Cela tient evidemment k ce que la surface rayonnante physiologique de
I'animal n'est pas constante comme sa surface physique. Aux basses tempera-
tures, le phenom^ne se complique d'une constriction vasculaire peripherique,
qui restreint considerablement le pouvoir rayonnant de I'animal k ^galite de
^* Richet, Dictionnaire de Physiologie, Paris, 1898, 3, p. 130.
'" Richet, La Chaleur Animale, Paris, 1889; see especially Chapter XI.
" Richet, loc. cit., p. 237.
3' d'Arsonval, Mem. Soc. de Biol., 1884, 8 ser., 1, p. 723.
A CRITIQUE OF THE BODY-SURFACE LAW. 137
surface physique. Cela montre que la connaissance de la surface g^ometrique
d'un animal est insuffisante pour qu'on en puisse d^duire la perte par rayonne-
ment: ii faut encore tenir compte de I'^tat de la circulation p^riph^rique.
In 1888 V. Hoesslin ^^ pointed out that while in warm-blooded
animals variations in the external temperature are followed by varia-
tions in metabolism, the change in heat-production is not proportional
to the change in external temperature. Thus heat-loss is not deter-
mined solely by difference in body-temperature and air-temperature,
i.e., by differences in potential, v. Hoesshn considers this a valid
refutation of Rubner's theory.
Richet, in his volume of 1889,^* treated the problem of metabolism
under varying external temperature. The reader interested in detaOs
may refer to this work or to a more recent discussion of the problem.^*
We now turn to the question of the influence of internal condition
on metabolism in its relation to the problem of the vaUdity of the body-
surface law. We shall here consider the problem as to whether, when
body-surface remains practically constant but other conditions vary, the
heat-production per square meter of body-surface area is a constant.^®
Against this line of argument is to be urged the fact that in an
early consideration of the body-surface law Rubner insisted upon
uniformity of physiological state.^^ TMiile in more recent writings the
constancy or equaUty in the nutritional level has from time to time
been emphasized as a prerequisite for the appUcabUity of the law of
surface-area, this has by no means been generally considered, and current
practice has tended to accept the universaHty of this law irrespective
of whether the individual is poorlj^ or well nourished.
As early as 1888 v. Hoesshn ^^ pointed out that a dog (studied in
the respiration chamber by Pettenkofer and Voit) required 1600 calories
per day for maintenance of body-weight. On the sixth day of inanition
it used only 1190 and on the tenth day only 940 calories. Body- weight
decreased from 33 to 30 kg. If the body-surface law holds, the heat-
production of the two periods should stand in the ratio ^^33^ : '^30^ or
10.288 : 9.655, or there should be a decrease in heat-production of
100(v/33^-V^30"0 «,^
— ^^ = — — ^ =0.15 per cent.
^33*
As a matter of fact there is a decrease of 41.25 per cent.
^ V. Hoesslin, Arch. f. Anat. u. Phya., Phys. Abt., 1888, pp. 327-328.
" Richet, La Chaleur Animale, Paris, 1889; especially Chapter XI.
" Richet, Chaleur, in Dictionnaire de Physiologie, 1898, 3, p. 138.
** Here only published materials are taken into account. An extensive series of under-
nutrition experiments made on a group of 25 men was carried out through the winter of 1917-1918
by the Nutrition Laboratory. The problem of the relation of nutritional state to metabolism is
considered in detail in the report of these experiments. See Benedict, Miles, Roth, and Smith,
Human vitality and efficiency under prolonged restricted diet, Carnegie Inst. Wash. Pub.
No. 280. (In press.)
" Rubner, Archiv. f. Hyg., 1908, 66, p. 89.
38 V. Hoesslin, Arch. f. Anat. u. Phys., Phys. Abt., 1S8S, p. 331.
138 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN".
A discrepancy in Von Hoesslin's reasoning should be pointed out
here, in that the value of 1600 calories was that found during feeding
aiid thereby unquestionably included the stimulating effect of the
meat. Consequently the true basal value would be somewhat lower
and the decrease on the tenth day is undoubtedly somewhat less
than 41.5 per cent, but in any event probably of much greater
magnitude than the 6.15 per cent computed on the ratio of the body
surfaces.
Again, v. Hoesslin points out that Rubner's own dogs show the
same decrease in metabolism with inanition. Rubner introduced a
table to show "dass sich der Stoffwechsel bei Hunger fast gar nicht
andert." Yet this table shows a decrease in the metabolism in absolute
terms of 33 per cent, in relation to body-weight of 20 per cent, and in
relation to body-surface of 25 per cent.
In an experiment upon a dog which was confined to the laboratory
for several months and which did not lose weight,^^ the metabolism
decreased very considerably (19 per cent). When the dog was again
allowed country life, her metabolism returned to essentially its original
value, but the body- weight was unchanged. Here evidently is con-
stancy in body-surface area, but variation in heat-production per
square meter.
Information with regard to the metabolism of human individuals
who are well or poorly nourished is, for the most part, obtained by
observations on different subjects. But during prolonged fasting we
may observe in the same person changes in the plane of nutrition
fully comparable to those roughly characterized as poorly or well
nourished. It is thus seen that during prolonged fasting simulta-
neous measurements of the body-surface and the basal metabolism
of the subject have an unusual value. A 31-day fasting experiment
made in the Nutrition Laboratory has a particular interest in this
connection.*"
A study of the relationships of body-weight, body-surface, and
basal metabolism during fasting is all the more important when it is
remembered that it is commonly believed that the fasting animal
rapidly adjusts itself to the minimum metabolism. The results of
earher experiments on the dog, the cock, and the guinea pig *^ indicate
that per kilogram of body-weight the fasting metabolism is constant.
With the fasting man the metabolism per kilogram of body-weight was
not constant. Furthermore, calculation of the metabolism per square
meter of body-surface on the basis of the Meeh formula — the only one
available at the time of the experiment — indicated a large loss in heat-
production during the progress of the fast. Realizing the desirability
»» Lusk, Journ. Biol. Chem., 1915. 20, p. 565,
*o Benedict, Carnegie Inst. Wash. Pub. No. 203, 1915.
*'ArmBby, The Principles of Animal Nutrition, New York, 1906, 2d ed., p. 346.
A CRITIQUE OF THE BODY-SURFACE LAW. 139
of checking the results, a photographic method *^ of measuring surface-
area was developed and the values of heat-production per square
meter of body-surface*^ were recomputed.
The subject took no food and only about 900 c.c. of distilled water
per day for 31 days.** The heat-production during the night was
measured directly with the bed-calorimeter for each of the 31 nights.*''
As the fast progressed there was a very noticeable decrease in heat-
production from night to night. This would naturally be expected
since weight decreased from about 60 kg. to about 47.5 kg. But the
metaboUsm when computed on the basis of body-weight showed a
decided loss as the fast progressed. There w^as also a loss in metabohsm
per square meter of body-surface. This is shown by the data in table
45, which gives the body-weight, the body-smiace as computed by
the Meeh formula*^ and from the measm-ements of the anatomical
photographs, and the heat-production per square meter of body-surface
per 24 hours as based upon the observations with the bed-calorimeter
during the night.
Disregarding the last food day prior to the fast, the heat-production
per square meter per 24 hours as given in the last colunm of the table
ranges from 927 calories on the third day to 664 calories on the twenty-
first day of the fast, representing a decrease of 28 per cent in the heat-
production per square meter of body-surface. Thereafter a distinct
tendency for the heat-production to increase was apparent.
In the absence of any marked change in body-temperature the diffi-
culty of considering the loss of heat from the surface of the body as
the determining factor in the metabolism of this fasting man is very
« Benedict, Am. Journ. Physiol., 1916, 41, p. 275.
« Benedict, loc. cit, p. 292.
** The fasting man remained (so far as ocular evidence ia concerned) for the most part physio-
logically normal during the progress of the fast. Strength tests made with the hand dynamometer
showed practically no change with the right hand and but a slight decrease with the left hand,
although there was an almost immediate evidence of fatigue in the first two or three days of the
fast. While there was naturally a certain amount of weakness obser\'able in the last few days,
the subject, after ha\-ing been without food for 31 days, spoke extemporaneously before a body
of physicians for approximately three-quarters of an hour, standing during the whole period and
vigorously gesticulating. Later in the day he sang and danced. It is thus clear that we have
here to do not with a fasting man who is in the last stage of emaciation and in a moribund condition
but with an individual who, judged from ocular e\-idence, would appear not at all unlike the norm-
ally emaciated tyi>e of individual. Furthermore, the body-temperature did not materially alter.
His average body-temperature in the bed-calorimeter experiment on the night of the last day of
the fast was but 0.3° C. below that of the night of the second day, a difference which indicates no
marked disturbance of the body-temperatvire. While the pulse-rate was distinctly lower at the
end of the period than at the beginning, it will be seen that the subject underwent the 31-day
fast without great loss of muscular strength or material alteration of body-temperature.
** It was likewise computed indirectly from the carbon-dioxide excretion and oxygen con-
sumption during the same period. Reference must be made to the original publication for the
methods of calculation and for a discussion of the heat-production per kilogram of body-weight,
in which an attempt was made to reduce the observation of each night to a common standard.
** It will be seen from the figures that, using as a standard the body-surface values obtained
with the photographic method, the body-surface as computed from the ^Ieeh formula is invariably
too large and consequently the heat-production per square meter computed from this measure
of the body-surface is too small.
140 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
great. Had the body-temperature fallen materially the explanation
of the decrease in heat-production could easily be made on the basis
of difference in temperature potential. No such explanation is, how-
ever, at hand. Fully confirmatory results in experiments on a squad
of 12 men, maintained for a long period on a much reduced diet have
been briefly stated in Chapter IV, p. 103.
Table 45. — Heat produced by fasting subject during experiments in bed calorimeter at night.
Date.
Day
of
fast.
Body-
weight
without
clothing.
Body-surface.
Heat produced
per square meter
per 24 hours.
By
Meeh
formula.
Com-
puted
from
photo-
graphic
measure-
Meeh
formula.
Photo-
graphic
method.
ments.
1912
kilos.
sq. meters
sq. meters
caht.
cala.
Apr. 13-14
60.87
1.91
*1.71
858
958
14-15
1st
59.86
1.88
1.70
817
904
15-16
2d
68.91
1.86
1.68
830
918
16-17
3d
68.01
1.84
*1.66
836
927
17-18
4th
57.22
1.83
1.66
827
912
18-19
6th
56.53
1.81
1.66
764
833
19-20
6th
56.01
1.80
1.65
774
845
20-21
7th
65.60
1.79
1.65
760
825
21-22
8th
55.18
1.78
1.65
790
852
22-23
9th
54.74
1.77
1.65
720
772
23-24
10th
54.25
1.77
*1.65
726
778
24-25
nth
63.94
1.76
1.64
715
767
25-26
12th
63.64
1.75
1.64
712
760
26-27
13th
53.48
1.75
1.63
709
761
27-28
14th
53.22
1.74
1.62
698
749
28-29
15th
52.92
1.74
1.62
649
698
29-30
16th
52.40
1.73
1.61
639
687
Apr
30-May 1
17th
51.91
1.71
*1.60
642
686
May 1- 2
18th
51.67
1.71
1.60
653
698
2- 3
19th
51.21
1.70
1.60
676
719
3- 4
20th
50.97
1.69
1.60
666
704
4- 5
21st
50.60
1.69
1.59
625
664
5- 6
22d
50.22
1.68
1.59
653
690
&- 7
23d
60.00
1.67
1.59
655
688
7- 8
24th
49.70
1.67
*1.59
651
684
8- 9
25th
49.40
1.66
1.58
637
670
9-10
26th
49.10
1.65
1.57
695
731
10-11
27th
48.78
1.64
1.57
673
703
11-12
28th
48.52
1.64
1.56
676
711
12-13
29th
48.19
1.63
1.55
691
726
13-14
30th
47.79
1.62
1.54
698
734
1
14-15
31st
47.47
1.61
*1.63
701
737
* Body surface for days on which photographs were obtained, i.e., April 13,
16, 23, 30, and May 7 and 14. Other values obtained by interpolation.
Turning from the results of prolonged starvation experiments on
man to those obtained by Armsby and Fries '*^ for a fattening experi-
ment on a steer, we note that they observed an increase of 36 per cent
*' Armsby and Fries, Journ. Agric. Research, 1918, 11, p. 461.
A CRITIQUE OF THE BODY-SURFACE LAW. 141
in the basal katabolism ** in the fattened state. This they attribute
in part to the greater body-weight to be supported in standing, but
they point out that the increase in heat-production vnth. fattening is
more rapid than the increase in body-weight or in body-surface as
estimated by the Meeh formula. "Apparently the accumulation of
fat tended in some way to stimulate the general metaboUsm."
3. MEASUREMENT OF BODY-SURFACE AREA.
When one thinks of a physical or biological "law" he naturally
assumes that the measurements upon which it is grounded are adequate
in number and reliability to justify fully the formulation of the general-
ization under consideration.
Du Bois and Du Bois *^ freely admit that the whole question of the
validity of Rubner's Law "rests on the accuracy of the determinations
of the basal metabolism and of the surface-area." They also point
out that "The methods of determining the metabolism have been
greatly improved, leaving the surface-area the doubtful factor." It
seems worth while, therefore, to sunamarize briefly the actual measure-
ments of body-surface area upon which the comparisons underlying
the body-surface law rest.
In much of the work which has been done on the inter-specific
appUcability of the "law" the measures of body-surface can hardly
be dignified as approximations. Richet ^° compared the surfaces of
his rabbits on the assumption that they were spheres. Certain investi-
gators have used the constant term for the horse in estimating the
body-surface of swine by the Meeh formula. Finally Putter ^^ has ap-
parently used the same formula for mammals ranging in form from
the camel to the walrus !
Even when we turn to so intensively studied an organism as man,
we find that, to quote the Du Boises again, "the number of formulae for
surface-area determination is large, the nmnber of individuals whose
area has been measured is small."
Du Bois and Du Bois give a fist and brief discussion of at least the
chief of the various formulas which have been proposed. In view of
the fact that most of these have received practically no attention from
physiologists, it seems unnecessary to discuss them here where we are
concerned primarily with the question of the adequacy of the actual
measurements upon which formulas have been based.
Meeh ^^ in 1879 pubhshed the results of his painstaking measure-
ments of 6 adults and 10 children, using a variety of methods.
** Basal katabolism in ruminants must be determined under conditions in some regards
essentially different from those obtaining in investigations on man and the camivora.
For the details the special literature of animal metabolism must be considered.
" Du Bois and Du Bois, Arch. Intern. Med., 1915, IS, p. 868.
**• Richet, La chaleur animale, Paris, 1889, p. 222.
«'- Putter, Zeitschr. f. Allg. Biol., 1911. 12, p. 201,
*- Meeh, Zeitschr. f. Biol., 1879, 15. pp. 425-i5S.
142 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Fubini and Ronchi ^^ measured one man, marking out the anatomi-
cal regions of the body and determining the areas geometrically.
Bouchard ^^ measured five adults.
Lissauer ^^ measured 12 dead babies, only one of which he con-
sidered a normal child, by covering the body with silk paper and then
measuring the area of the paper geometrically or with a planimeter.
Sytscheff ^^ measured 10 infants under one year of age but com-
puted no constants.
Du Bois and Du Bois ^^ measured the surface-area of 5 individuals
with great care.
Table 46. — "Constant" term of Meeh formula as determined by direct measurement.
Subject.
Observer.
Age
in
years.
Height
in
centi-
meters.
Weight,
in
kilos.
Meas-
ured
body-
surface,
sq. cm.
Constant
for
Meeh
formula.
Benny L
D. B. and D. B.. .
Meeh
36.
13.1
15.7
36.
45.
17.7
26.2
21.
22.
66.
32.
36.
110.3
137.5
152.'
158.
160.
169.
170.
162.
164.3
178.
172.
179.2
171.
149.7
24.20
28.30
31.80
35.38
50.00
50.00
51.75
55.75
59.50
61.60
62.25
64.00
64.08
65.50
74.05
76.50
78.25
88.60
93.00
140.00
8473
11883
12737
14988
17415
16067
18158
19206
18695
18930
19204
16720
18375
20172
19000
19484
22435
21925
18592
24966
10.13
12.80
12.69
13.17
12.96
11.84
12.96
13.16
12.27
12.13
12.01
10.45
11.49
12.48
10.55
10.81
12.26
11.03
9.06
9.26
Hagenlocher
Very thin woman.
Korner
Bouchard
Schneck
Meeh
Adult man
Nagel
Fobini and Ronchi
Fr. Brotheck
Naser
Meeh
Meeh
Bouchard
Meeh
Normal man
Fr. Haug
Morris S
D. B. andD. B....
D. B. andD. B....
Meeh
R.H.H
Forstbauer
E. F. D. B
Normal woman . . .
Kehrer
D. B. and D. B.. .
Bouchard
Meeh
Large man
Mrs. Mc. K
Very fat man
Bouchard
D. B. and D. B.. .
Bouchard
In the development of a graphic method of determining body-
surface area,^* 20 individuals w^ere photographed in different selected
positions and the areas of the prints were determined by means of the
planimeter.
Du Bois and Du Bois ^^ give a table which we reproduce in a some-
what modified form herewith, table 46, showing that actual surface-
area measurements have been made on a total of 20 adult individuals.
" Fubini and Ronchi, Moleschott's Untersuchungen z. Naturlehre, 1881, 12.
" Bouchard, Trait6 de pathologic gfenerale, Paris, 1900, 3, p. 200, 384.
65 Lissauer, Jahrb. f. KinderheUk, N.F., 1903, 58, p. 392.
** Sytscheff, Measurement of volume and surface of children of varying ages. Diss., St. Peters-
burg, 1902. (From the Clinic of Children's Diseases of Professor Gundobin). See also
Gundobin, Die Besonderheiten des Kindesalters, Berlin, 1912, pp. 53-54 (section on body
surface of children ; quotes Sytscheff and gives table of Sytscheff 's measurements on p. 54
^'' Du Bois and Du Bois, op. cit.
5« Benedict, Am. Journ. Physiol., 1916, 41, p. 275.
*• Du Bois and Du Bois, loc. cit., p. 871.
A CRITIQUE OF THE BODY-SURFACE LAW.
143
Table 47. — Constants of
Lissauer's babies.
To what extent do these measurements justify the formulas which
have been based upon them?
The constant term of both the Meeh and the Lissauer formula is
given bj'
where a' is the directly measured body-surface area.
Meeh's observations gave constants entered in the final column of
table 46.®° Those for Lissauer's group of 12 babies ®^ are given in
table 47.
Now the "constants," both those for adults whose surface-area
was measured by Meeh, Fubini and Ronchi, Bouchard, and Du Bois
and Du Bois, and those for infants whose
surface-area was measm-ed by Lissauer, show
great differences among themselves. Thus
in the adult series we find the actually de-
termined "constant" terms ranging from
9.06 to 13.17. Yet Meeh in his original pub-
Ucation retained six or seven significant figures
in recording his constants, notwithstanding
the fact that constants obtained when both
sides of the body were actually measured
differed from those in which one side only
was measured in the third or fourth signifi-
cant figure in every case. In Lissauer's in-
fants the "constants" range from 8.92 to
12.40. This great discrepancy was fully recognized by Lissauer who,
emphasizing the great variation in the individual determinations,
chose 10.3 as that most free from criticism.
If we determine the standard de\'iation and the coefficients of varia-
tion of these "constant" terms we have the following results:
For 20 adults, measured by Meeh and others:
Jk = 11.676 (r* = 1.2400 7;^ = 10.62
For 12 infants measured by Lissauer:
k = 10.398 a, = 0.7834 7» = 7.53
The coefficients of variation express the results in the most easily
comprehensible form. We see that there is a variation of 10.6 per cent
in the adults and of 7.5 per cent in the infants. In other words
•" In 5 cases the constants recomputed by ourselves do not agree exactly with those given by
Meeh. We have, however, used the values given by him.
" These are the constants given by Lissauer. Their calculation has not been rechecked.^The
first column (K*) givest he constant determined from the weight just before or after death.
The second {K) gives the constant calculated from the baby's maximum weight.
Child.
K*
K
No. 1
10.985
2
10.278
9.881
3
9.921
4
10.387
5
8.922
6
10.926
10.245
7
10.284
9.245
8
12.402
10.732
g
10.130
9.530
10
9.953
9.377
11
(10.287)
(8.472)
12
10.30
144 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
the variability about (that is above and below) the mean value is
10.6 and 7.6 per cent of this mean value in adults and infants
respectively.
What is the real significance of this result? It shows that physiolo-
gists have been regarding as a constant a figure which when actually
determined shows a variability about two or three times that of stature
in man ! Surely no careful observer would consider the statures of the
men he passed on the street identical. Yet physiologists have been
using a selected value from series two or three times as variable and
dignifying it as a "constant."
While the present discussion is limited to the problem of the validity
of the surface law in man, it is not without interest to note that Moul-
ton, in his investigation of the surface area of cattle/^ has found a
wide variation in the value of k. The formulas which he proposes
to use differ according to the fatness of the animals.
Determining the statistical constants of the values of k entered
in table 5 of Trowbridge, Moulton and Haigh, we have :
^=9.097 (T* =0.8915 7^ = 9.80
Again we find a variation in the values of the ''constant" which is
relatively large, that is about 10 per cent of the average value. The
futility of using a "constant" which is so little constant as this k is
fully admitted by Trowbridge, Moulton and Haigh when they use
different values for animals in different conditions.
Thus the Meeh method is no more satisfactory in its application
to animal than to human calorimetry.
Fortunately conditions in work on human metabolism have been
much improved by the studies of Du Bois and Du Bois, resulting in
the development of the linear formula and of the height-weight chart
which has been used throughout this chapter and which is destined to
replace entirely the Meeh formula. Computations based upon the
latter have, however, been given along with those based on the height-
weight chart in many of the tables of the following discussion, since
historically the theories considered date from the time when the Meeh
formula was the only one available.
4. INADEQUACY OF CRITERIA OF VALIDITY OF BODY-SURFACE
LAW HITHERTO EMPLOYED.
There has been in the past and prevails at present great diversity
of opinion concerning the validity and range of applicability of the
surface law. These differences of opinion are founded in part on tradi-
tion. In so far as they rest upon study of the available facts concerning
8» Trowbridge, Moulton, and Haigh, Univ. Mo. Agric. Expt. Sta., Research Bull. No. 18, 1916,
p. 14. Moulton, Journ. Biol. Chem., 1916, 24, pp. 303-307.
A CRITIQUE OF THE BODY-SURFACE LAW. 145
the measured metabolism of individuals of known or estimated body-
surface, the situation seems to be about the following.
Series of measurements of basal metabolism have been made and
expressed in calories per indi\'idual, per kilogram of body-weight, and
per square meter of body-surface for definite periods of time. The
number of calories produced by indi\dduals varies greatly. WTien
reduced to a standard of calories per square meter of body surface, the
heat-production varies much less ^adely than when the original meas-
urements are left entirely uncorrected for the size of the indi\'idual
experimented with.
Workers of one group look at such series of values and seeing the
great increase in uniformity of results which has been secured by the
correction for body-surface exclaim, "The heat production of an indi-
vidual per unit of body-surface is a physiological constant." Workers
of another group, however, see the differences which still obtain be-
tween the measurements based upon a nmnber of indi\'iduals and reply,
"Certainly, with differences of such magnitude, no one can speak of
calories per square meter of body-surface as a physiological constant."
Thus the two groups are apparently in a state of controversial
dead-lock which can not be broken by the willingness of one or the
other, or of both, parties to look at the other side of the shield, for
both groups are already examining the same surface. One group sees
in it regularity, the other irregularity. ^Tiat constitutes regularity
as contrasted with irregularity is a matter of personal opinion and must
always remain so imtil some quantitative criterion is adopted.
The expression of the amount of heat produced in terms of number
of calories per square meter of body-surface is, in its final analysis,
merely an attempt to correct for the most significant proximate factors
in the determination of heat-production. Since bodj^-surface has the
weight of tradition in its favor, it is perhaps naturally assumed to be
the most significant factor. But suppose that body-surface is not the
most significant variable physiologically? Certainly, it should not
then be used as the corrective term.
The first step in determining the most potent physiological factor
underlying heat-production would seem to be the actual measurement
of the intensity of relationship between the various body measurements
that may reasonably be suggested as influencing metabolism and total
heat-production. We shall then be in a position to consider what
measurement of this kind, or what combination of measurements, is
most suitable for use as a corrective term to be applied to gross values
of basal metabolism obtained from series of human indi^dduals.
As far as we are aware, the most quantitative test®^ which has ever
" After this manuscript was nearly completed a paper by Armsby and his associates, in which
correlations for body-weight and heat-production and body-surface and heat-production were
given for the original Nutrition Laboratory series, appeared. Armsby, Fries, and Braman, Proc.
Nat. Acad. Sci.. 1918,4, pp. 3-4. See also Joum. Agr. Res., 1918, 13, pp. 49-55.
146 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
been applied toward the solution of the problem of the relative value
of body-weight and of body-surface as a means of correcting for differ-
ences in the total metabolism due to differences in the size of the indi-
vidual has been the simple determination of the average percentage
deviation from the mean value for the whole series of individuals of
the measures of heat-production per kilogram of body-weight and per
square meter of body-surface.
Thus Gephart and Du Bois ^^ give the values shown in table 48
for the percentage deviation of calories per kilogram per hour from
the mean number of calories per kilogram per hour and of calories per
square meter of body-surface per hour from the mean of calories per
square meter of surface per hour.
Table 48. — Comparison of percentage variation of heat-production per kilogram
of body-weight and per square meter of body-surface.
Subject.
Calories
per
kilogram
per
hour.
Calories
per
meter
per
hour.
Percentage variation
from average.
Calories
per
kilogram.
Calories
per
sq. meter.
F.G.B
G. L
1.01
1.00
0.95
1.00
0.92
0.96
1.00
1.18
1.11
1.10
1.21
1.13
35.8
34.8
32.4
34.1
30.9
31.7
32.8
37.9
35.1
34.2
36.7
33.8
- 4
- 5
- 9
- 5
-12
- 8
- 5
+ 14
+ 6
+ 5
+ 16
+ 8
+ 5
+ 2
- 5
0
-10
- 7
- 4
+ 11
+ 3
0
+ 7
- 1
F. A. R
E. F. D. B....
John L
J. J.C
J. R
R. H. H
L. C. M
F. C. G
Louis M
T. M. C
Average
1.05
34.2
±8.1
±4.6
The average of the percentage deviations of the individual measures
of heat production in terms of calories per kilogram of body-weight
from the general mean of this measure is clearly higher than the average
of the percentage deviations of the measures in units of calories per
square meter of body-surface from the mean of all of the measures by
this method.
The means given by Gephart and Du Bois stand in the ratio of
8.1 to 4.6.
If instead of using average deviations without regard to sign, as
Gephart and Du Bois have done, we compute the standard deviations
and coefficients of variation of the number of calories per kilogram of
body-weight and per square meter of body-surface, we find the following
values.
" Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 852.
A CRITIQUE OF THE BODY-SURFACE LAW.
147
For calories per kilogram per hour : a = 0.0908 F = 8.67
For calories per square meter per hour : <r = 1.962 V = 5.74
The results confirm those obtained by the average deviation in
indicating greater variabihty in measures of heat-production per unit
of weight.
The same point may be brought out in a somewhat different and
not altogether satisfactory manner by comparing the coefiicients of
variation for number of calories per kilogram of body-weight with the
coefi&cients of variation for calories per square meter of body-surface
in our various adult series. This is done in table 49.^^
Table 49. — Comparison of coefficients of variation of heat-production expressed
in various units.
Series.
N
CoefiScient
of variation
of heat per
kilogram of
body-weight
CoefiScient
of variation
of heat per
square meter,
Meeh
Coefficient
of variation
of heat per
square meter,
height-
formula. I weight chart.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
136
68
35
103
5.99
10.60
9.73
8.07
7.79
9.30
9.64
9.36
11.90
15.84
14.14
3.92
7.75
7.48
6.68
6.40
7.25
8.53
7.44
8.21
12.27
10.29
3.97
6.95
8.25
6.75
7.04
7.10
8.13
8.05
7.51
11.13
9.17
On first consideration these results would seem to fully justify the
assertion that among groups of men of varying weight metabolism is
proportional to surface-area according to Rubner's law and is not
proportional to body- weight. Extreme caution must, however, be
exercised in the physiological interpretation of such a relationship.
The fact that the measures in terms of calories per square meter of
surface show a smaller percentage of variation from their average
value than do measures in terms of calories per kilogram of body-weight
does not necessarily have any relationship whatsoever to physiological
constants or to causal physiological relationships.
Consider this question somewhat more minutely. A series of meas-
urements of total heat-production, h, in n individuals are made. These
are hi, hi, hi, ... . /j„. The body-surfaces Si, Sa, Ss, . . . . 5„ and the
•* This method of analysis has the disadvantage that coefficients of variation are calculated
from ratios of heat-production to body-weight and to body-surface. Thus an index of an index
is used.
148 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
body-weights Wi, w^jWz, . ... w^ for each individual are available;
the following ratios are determined :
h.
h
h^
K
hr
h
hs
Wi
W2
> • •
W3
Wn
Si
S2
S3
Clearly enough the variability of the ratios will be determined not
merely by the variability of the values of h but by the variability of
the values of w and s as well. If the relationship between w and s
be such that one of them is necessarily more variable than the other,
the ratio in which the more variable measure is employed must of
necessity be more variable also.
Now this is precisely the condition which obtains in the relationship
between body-weight and body-surface. In computing body-surface
by the Meeh formula, the deviation of tjhe surface-area of an individual
from its mean bears only the ratio of ^w'^ to the deviation of the weight
from the average weight of the series.
Table 50. — Comparison of coefficients of variation for body-weight and two measures
of body-surface.
Series.
N
Coefficient
of variation
for body-
weight.
Coefficient
of variation
for body-
surface by
Meeh
formula.
Coefficient
of variation
for body-
surface by
height-weight
chart.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
Both series
16
62
89
72
28
117
19
136
68
35
103
17.43
14.32
16.68
13.22
16.72
16.73
11.22
18.06
19.78
19.61
20.35
11.44
9.43
10.92
8.74
11.40
11.03
7.43
10.60
12.76
12.97
13.24
10.15
7.55
9.05
7.76
10.15
9.26
6.14
8.80
9.63
9.34
Thus a lower variability of surface-area as compared with body-
weight is an arithmetical necessity. Conversely, a higher variability
of the ratio of total heat to body-weight {i.e., of the measures of heat-
production in terms of calories per kilogram) is a statistical consequence
of the use of the Meeh formula or of direct measurement of body-
surface in individuals reasonably similar in physical configuration.
It is presumably a necessary consequence of the use of the body-surfaces
given by the Du Bois height-weight chart also.
How great may be the differences in the variability of the physical
measurements themselves is readily seen by expressing the variabilities
of body-weght and surface-area in relative terms as in table 50.
A CRITIQUE OF THE BODY-SURFACE LAW. 149
Here comparison is made of the coefficients of variation,
y _100(r, y _10Q(T,
w s
where o- denotes the standard deviations and the bars indicate the
means, for body-weight and body-surface as measured by the two
methods. Without exception the measures of body-surface show a
lower percentage of variation than do the measures of body-weight.
It is inevitable that the greater variability of body- weight — a purely
mathematical phenomenon, not physiological — should influence any
ratios into which body-weight enters. It is quite possible that the
difference in the variabiUty of calories per kilogram and in calories
per square meter of body-surface due to this factor may be so great
as to invahdate any judgment concerning the physiological significance
of ratios to body-weight or body-surface based on inspection and per-
sonal judgment merely.^*
Objections essentially similar to the above may be raised against
one of the earhest series of calorimetric experiments, those of Richet, ^^
who, working with rabbits of weights ranging from about 200 to nearly
4,000 grams, concluded "La perte de chaleur est fonction de la sur-
face." Richet arranged his animals according to weight and calculated
the average heat-production per kilogram for the ascending weight
classes. The constants in this table lead to the "Resultat des plus
int^ressants et des plus nets, puisqu'il nous montre combien, avec
I'augmentation de volume, diminue la production de chaleur par kilo-
gramme du poids de ranimal." He also arranges the same animals
according to weight and determines the loss of heat per unit of surface
on the assumption that the areas of the animals bore to each other the
relationship of surfaces of spheres of comparable weights. From these
figures he concludes "On voit quelle ressemblance il y a entre ces
chiffres, tres proches les uns des autres."
But close examination shows that the heat-production per unit of
body-surface decreases with the increasing weight of the animals,
though apparently at a far lower rate than in the case of that per
kilogram of weight. Without more detailed information and closer
analysis it is impossible to say to what extent the greater decrease (when
heat-production is expressed in calories per kilogram) is due to the
fact that the volume of a solid is necessarily more variable than its
surface.
There is a statistical difficulty in classifying animals by weight
and computing the average heat per unit of weight for each weight
** The logical fallacy of deciding between weight and surface as a basis of reference has appar-
ently been overlooked by even so keen an analyst as Moulton (Journ. Biol. Chem., 1916, 24, p.
320) , who says : " On this basis the smallest variations are shown in the heat-consumption per unit
of body-surface and the greatest variations in the heat-consumption per unit of body-wei^t."
" Richet, La chaleur animale, Paris, 1889; see pp. 219-221.
150 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
group.®® Suppose, for purposes of argument, that the Nutrition Labora-
tory tenet that metaboHsm is proportional to the active protoplasmic
mass, stimulus being considered constant, is vahd. Let mi, m^, rriz
.... m„ be the active protoplasmic masses of a series of individual
animals of weights Wi, W2, Wz, . . . . w^ and heat-productions in total
calories per unit of time hi, h^., hz, . . . . hn respectively. Then
hi _hz _hz
mi nh rriz
or the ratio of the total heat-production to the active protoplasmic mass
(the unknown and undoubtedly highly complex and variable stimuli
being taken as the same in all cases) is a constant.
But practically m is never known, and the ratio which has been
used is
hi hi hz h^
Wi W2
Wz
Wr,
The observed fact that this ratio is not a constant has been the ground
for the rejection of weight as a basis for expressing heat-production
and in part the reason for the adoption of body-surface as a standard
for this purpose.
Table 51. — Correlation between body-weight and heat-production per kilogram of body-weight.
Series.
Men.
Original series
Gephart and Du Bois selection
First supplementary series ....
Second supplementary series. .
All men of three series
Women.
Original series
Supplementary series
Both series
N
89
72
28
19
136
68
35
103
'^wh.
-0.6284 ±0.0433
-0.5552 ±0.0550
-0.6143±0.0794
-0.4977 ±0.1 164
-0.6076 ±0.0365
-0.7742 ±0.0328
-0.7684 ±0.0467
-0.7852 ±0.0255
'^wh,
14.51
10.09
7.74
4.28
16.65
23.60
16.45
30.79
Now Wi =Wi+a:i, W2 =m2-\-X2, . . . . , where x denotes the amount
of non-active substances which can not contribute to the total metab-
olism. The ratios - will be influenced by m and x to an extent pro-
w
portional to their respective values. Since in the later stages of growth
of the vertebrate organism there is a continuous increase in the amount
•* In passing, it may be noted that there is another objection to these data. The diflFerences
in size are in part due to differences in age. Statements in regard to this factor are not explicit
in all cases. The smaller animals were those which produced the most heat, both per unit of weight
and per unit of surface. But the smaller animals are probably on the whole younger animals and,
as pointed out in the chapter on age, there is (in man at least) a decline in the rate of metabolism
during the later periods of growth.
A CRITIQUE OF THE BODY-SURFACE LAW. 151
of the inert tissue, and since the increase in weight subsequent to
maturity is largelj' dependent upon the deposition of fat, it is quite
clear that in a series of indi%'iduals of the same species the metaboUsm
per kilogram of body-weight should decrease as the bodj'-weight
increases. !Metabohsm as measured in units of body- weight decreases
as bodj'-weight increases. That metabolism as measured in units
of body-surface decreases at a lower rate is perhaps attributable merely
to the fact that the values of x^ increases less rapidly than x.
This type of relationship has long been familiar to statisticians.
If we correlate between x and y/x we get a negative relationship which
has been designated as a spurious correlation between indices.^^ The
relationship may be easily demonstrated on our own data. In table 51
we have given the correlation between body-weight and heat-produc-
tion in calories per kilogram of body-weight for certain of our series.
The coej65cients are negative and of a rather large size throughout.
5. STATISTICAL TESTS OF RELATIVE VALUE OF THE MEEH FORMULA
AND OF THE DU BOIS HEIGHT-WEIGHT CHART.
From table 50 the reader may have noted that without exception
the Du Bois height-weight chart gives a lower percentage variability
for body-surface than does the Meeh formula. This point brings up
the question of the relative value of these two measures of body-surface.
Quite incidentally to carrj'ing out the calculations for this chapter,
we have been able to secure certain statistical tests of the relative value
of the Meeh formula and of the Du Bois height-weight chart; it there-
fore seems desirable to insert these data in this place, after which we
shall retiUTi to the discussion of our main problem of the vaUdity of
the bodj^-surface law as applied to human indi\'iduals.
There are two distinct sources of error in the ^leeh formula. First,
the vaUdity of the use of Vw?* as a measure of the surface-area of differ-
ent bodies rests on the two assumptions (a) that the two bodies have
the same specific gra\'ity, and (b) that they are comparable in form.
Neither of these assumptions can be considered strictly vaHd when
apphed to men and women of different weights. The specific gra^^ty
of a ver>' fat indix-idual is certainly sensibly different from that of a
lean one. The relative proportions of length of trunk and of leg differ
according to the stature of the indi\idual.^° Finally a study of profile
photographs of very fat and very lean indi^-iduals should suffice to
con\'ince any one that as far as form is concerned the two extremes
can not be regarded as "comparable soUds." Secondly, the constant
factor of the ^Meeh formula is determined empirically. It carries with
it, therefore, both the errors of measurement and the probable errors
of random sampling attaching to any direct measurements of variable
•» Pearson, Proc. Roj-. Soc. Lond., 1897, 60, p. 492.
" Harris, unpublished constants.
152 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
quantities. The extent of error due to this source has been indicated
on page 144 above.
We agree with the fundamental correctness of the statement of
Du Bois and Du Bois ^^ that *'In any discussion as to whether metab-
oHsm is proportional to body-weight or to surface-area it is essential
to apply a method of measuring the surface which does not depend
entirely on weight."
A comparison of the correlation between body-weight and body-
surface as determined by the two formulas will throw some further
light upon the value of the two methods of estimating body-surface.
Table 52. — Comparison of relations between weight and body-surface by the Meeh formula
with the correlations between weight and body-surface by the Du Bois height-weight chart.
Series.
N
Correlation
between
weight and
body-6urface
by Meeh
formula.
Correlation
between
weight and
body-surface
by height-
weight chart
Differences
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series . .
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
Both series
16 0.9993 =
62 0.9996 =
890.9986 =
720.9996 =
280.9957 =
1170.9988 =
19!o.9994 =
13610.9988 =
= 0.0002
0.0001
0.0002
: 0.0001
= 0.0011
= 0.0001
= 0.0002
= 0.0001
0.9629 =±=0.
0.9275 ±0.
0.9466 ±0,
0.9577 =tO,
0.9618=t0,
0 9495=4=0
0.9632=^0
0.9505 =fcO,
0123
0120
0074
0066
0095
0061
0112
0056
- 0.0364 =fcO.
-0.0721 =tO,
-0.0520=fc0.
-0.0419=fc0,
- 0.0339 =tO.
- 0.0493 =i=0.
- 0.0362 =tO.
- 0.0483 ±0.
0123
0120
0074
0066
0096
0061
0112
0056
68;0.9982=fc0.0003 0.9578=^0.0067
35 0.9992 =fc 0.0002:0.9792 =i= 0.0047
103 0.9989 ='=0.0001!0.9683 =±=0.0041
-0.0404 ±0.0067
- 0.0200 =t 0.0047
-0.0306 ±0.0041
From the constants in table 52, it appears that the correlations
between body-weight and body-surface as determined by both methods
are large, but that in each group of individuals the correlation between
body-weight and body-surface as determined from the Du Bois height-
weight chart is lower than that between body-weight and body-surface
as determined by the Meeh formula. This must be taken as evidence
for the greater value of the Du Bois height-weight chart, since it shows
that the body-surface is less a function of body-weight than in the case
of the Meeh formula.
6. CORRELATION AS A CRITERION OF THE VALIDITY OF THE
BODY-SURFACE LAW.
Since it is clear that a mere comparison by inspection of the sets
of constants for metabolism measured in calories per kilogram of body-
" Du Bois and Du Bois, Arch. Intern. Med., 1915, 15, p. 880.
A CRITIQUE OF THE BODY-SURFACE LAW. 153
weight and in calories per square meter of body-surface, or even
simpler tests of the relative variability of the two sets of measures, are
quite inadequate as criteria for selecting the best method of correcting
for the size of the indi\'idual, a detailed treatment of this question is
in order.
In the past the physiologist has been seeking to determine whether
metabolism is proportional to body-weight or to surface-area. The
difficulty has lain in the fact that body-weight and body-surface area
are correlated characters. If indi\'iduals varied in weight only, and not
in physical configuration, body-surface would be given at once by
kX-^w^. This is, indeed, the basis of the Lissauer and the Meeh
formulas. Thus if heat-production be in any degree correlated with
one of these physical measurements, it must be in some degree corre-
lated with the other. The degree of correlation between metabolism
and either of the physical measurements due to its correlation with the
other will depend upon the intensity of the correlation between the
two physical measiu-ements.
Thus the problem of the physiologist is not so simple as has been
suggested when it is said that he must determine "whether metabolism
is proportional to bodj'-weight or to surface-area." What he has to
do is to determine whether it is more nearly proportional to body-surface
or to body- weight.
The difficulty in doing this has not been due solely to the fact that
large series of actual measurements of body-surface and metabolism
have not been available, but also to the fact that the physiologist has
had no means of comparing directly the degree of interdependence of
body-weight measm-es and metabolism and body-surface measures and
metabolism. Results expressed in calories per kilogram of body-weight
are unquestionably better than those expressed in calories per indi-
\4dual irrespective of size for standard periods of time. Results
expressed in calories per square meter of body-sm-face are also more
nearly comparable from indi\ndual to indi\idual than those expressed
merely in number of calories per individual for the same standard
periods of time. The fundamental question is : Are results expressed
in calories per square meter of body-surface so constant from indi\'idual
to indi\'idual as to justify the statement that heat-production per
square meter of body-surface is a constant? Or, in other words, to
justify the statement that it is a physiological law that organisms have
a heat-production proportional to their bodj-surface?
Now the closeness of agreement of a series of figures which shall
be demanded to justify their designation as representing a constant
must depend, in the last analysis, upon the judgment of the workers in
a particular field. Specifically, in the case of metaboHsm investigations,
physiologists, not physical chemists or astronomers, must decide how
great a variation in the number of calories per square meter of surface
154 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
may be regarded as due to uncontrollable experimental error and hence
not be considered as invalidating the generalization that heat-produc-
tion per square meter of body-surface is a constant.
While only the physiologist can determine the amount of variation
allowable in the measures of heat-production per kilogram of body-
weight or per square meter of body-surface, the statistician may furnish
certain criteria of value in formulating the decisions. While the statis-
tician as such can not pass judgment upon the question of the degree
of consistency in a set of constants which must be demanded if they
are to be regarded as the expression of a biological law, he can furnish
absolute criteria of the degree of consistency. What is really needed,
first of all, is a measure of the closeness of interdependence of the total
calories of heat produced by an individual, under the selected standard
conditions for measuring basal metabolism, and the other character-
istics of the individual with which metabolism may be reasonably
assumed to be bound up.
Table 53. — Comparison of correlation between body-weight and total heat-production ivith
the correlations between body-surface by the two formulas and total heat-production.
Series.
N
Weight and
total heat per
24 hours
rwh
Surface by
Meeh formula
and total heat
Difiference
Surface by
height-weight
chart and
total heat
Difference
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois
selection
First supplementary series
Original and first supple-
mentary series
Second supplementary
series
All men of three series. . .
Women.
Original series
Supplementary series ....
Both series
16
62
89
72
28
117
19
136
68
35
103
0.9577 ±0.0139 0.9551 ±0.0148
0.6251±0.0522 0.6311±0.0515
0.8012 ±0.0256 0.7997 ±0.0257
7879 ±0.0301
8664 ±0.0318
0.8175±0.0207
5758 ±0.1034
7960±0.0212
0.7575 ±0.0348
0.4536 ±0.0906
0.6092 ±0.0418
-0.0026 ±0.0203
-1-0.0060 ±0.0733
0.9671 ±0.0109
0.6632 ±0.0479
-0.0015 ±0.0363 0.8303 ±0.0222
0.7896 ±0.0299
0.8747 ±0.0299
0.8196 ±0.0205
0.5772±0.1032
0.7980±0.0210
0.7612 ±0.0344
0.4698 ±0.0888
0.6170±0.0412
-i-0.0017± 0.0424
-1-0.0083 ±0.0436
-1-0.0021 ±0.0291
4-0.0014 ±0.1460
-H0.0020± 0.0298
-1-0.0037 ±0.0489
-1-0.0162 ±0.1269
-f0.0078± 0.0587
0.7862 ±0.0304
0.8636 ±0.0324
0.8383 ±0.0185
0.6274 ±0.0938
0.8196±0.0190
0.7438 ±0.0365
0.4789 ±0.0878
0.6111±0.0416
-f-0.0094± 0.0177
-f-0.0271± 0.0707
4-0.0291 ±0.0339
-0.0017 ±0.0428
-0.0028 ±0.0454
-1-0.0208 ±0.0278
+0.0516±0.1396
-l-0.0236± 0.0285
-0.0137 ±0.0504
-|-0.0253±0.1262
+0.0019±0.0590
We now turn to a consideration of the problem of the selection of a
suitable measure of the degree of interdependence between the physical
character and metabolism. Following the discussion in the preceding
chapter, we shall first consider the coefficient of correlation.^^
If the direct measures of metabolism are far more closely correlated
with body-surface than with any other phj^sical measurements, it seems
''^ After the manuscript for this volume was practically completed a paper by Armsby, Fries,
and Braman (Proc. Nat. Acad. Sci., 1918, 4, p. 1 ; Journ. Agric. Research, 1918, 13, p. 43) appeared
in which the method of correlation here employed was used.
A CRITIQUE OF THE BODY-SURFACE LAW.
155
clear that body-surface is the best single factor for predicting basal
metabolism. If heat-production shows approximately the same corre-
lation with body-weight as with bodj'-surface,, the conclusion must be
drawn that the two are of practically equal significance for estimating
basal metaboUsm. If the correlation between body-surface and the
measure of metaboUsm be actually smaller than that for other physical
characters, it must be relegated to a minor place as a means of predict-
ing metabolism.
BODY WEIGHT
DiAGBAM 23. — Relationship between body-weight and daily heat-production by men.
The constants are arranged for a comparison of the correlations
between weight and heat-production and surface and heat-production
in table 53. The first problem which we have to consider on the basis
of these constants is that of the existence of a physiological law. That
total heat-production is related to body-weight and to body-surface is
clearly shown by the constants. We doubt, however, whether such a
quantitative law is what physiologists in general have had in mind
when they have stated that heat-production is proportional to body-
surface but not proportional to bodj'-weight. Our constants show that
156 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
it is in some degree proportional to both body-surface and to body-
weight and they furnish a measure of this closeness of agreement on a
universally applicable scale of —1 to +1. They further show that the
BODY WEIGHT IN KILOGRAMS
Diagram 24. — ^Relationship between body-weight and total heat-production by women.
interrelationship is in no case a perfect one. We are not, therefore,
dealing with a law in the sense that the term is used in the exact
sciences.
Knowing the number of seconds which a body has been falling
towards the earth, we can state its
velocity at this moment or at any
future moment of time. Knowing
the volume of a gas at temperature
t and pressure p, we can state its
volume at temperature V and press-
ure p'. These theoretical laws hold
in the individual instance with as
high a degree of precision as can be
demonstrated by the most exact ex-
perimental method. Such is not
the case in human metabolism. In-
stead of having a perfect correlation
between body -weight and total
heat-production, as we should if
________ heat-production were proportional
body-surface of women as estimated by to body-weight, we have only about
the Du Bois height-weight chart. gQ ^^^ ^^^^ ^j perfect Correlation.
The true significance of these correlations may be best understood
by looking at them in a quite different way. If heat-production were
actually proportional to body-weight, or to body-surface, we should
/.30 uo /SO 1.60 no l.i
BODY SURFACE
Diagram 25. — Relationship between
heat -production and square
total
meters of
A CRITIQUE OF THE BODY-SURFACE LAW.
157
find a correlation of unity. For any given weight (or surface) there
would then be only one possible heat-production. But as a matter of
fact the coefficient of correlation, here being less than unity, shows that
for any given body-weight or body-surface a variety of heat constants
may be secured. How widely the heat-productions of individuals of
sensibly identical body-weight may vary is well shown by diagram 23
for men and diagram 24 for women, in which each dot represents on
I
Diagram 26. — ^Relationship between total heat-production and square meters of
body-surface of men as estimated by the Du Bois height-weight chart.
the scale at the left the heat-production of an indi\'idual whose weight
is given by the lower scale." That body-surface is not much better
than body-weight as a basis for prediction is evident from the wide
scatter of the heat-productions for indi\'iduals of like superficial area
in diagrams 25 and 26.
Now it is quite possible to determine from the correlation coefficient
approximately the amount of variation which will be found on the
average \sdthin the different weight or body-surface classes. This
" The straight lines in these diagrams are drawn from the equations in Chapter IV, p.
91.
158 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
variability of the subgroups defined by a given grade of weight or body-
surface is given by
(^K
(^h\ l-r„./,2
<^ha^<^hVl-rah'
where (Xh is the standard deviation of heat-production in individuals
at large and <Th,„ and <Tf^ the standard deviation of heat-production in
groups of individuals of the same weight or surface. The results for
the major series are summarized in table 54.
Table 54. — Percentage of the total variation in heat-production which remains after individuals
are classified according to body-weight and body-surface by two formulas.
Series.
Men.
Original series
Gephart and Du Bois selection
Original and first supplementary
series
All men of three series
Women.
Original series
Supplementary series
Both series
Classified by
body-weight.
Correla-
tion
0.801
0.787
0.817
0.796
0.757
0.453
0.609
Percent-
age vari-
ability.
59.84
61.58
57.59
60.5.3
65.28
89.12
79.30
Classified by
Meeh formula.
Correla-
tion
0.799
0.789
0.819
0.798
0.761
0.469
0.617
Percent-
age vari-
ability.
60.04
61.36
57.29
60.27
64.85
88.80
78.70
Classified by
height-weight chart.
Correla-
tion
0.830
0.786
0.838
0.819
0.743
0.478
0.611
Percent-
age vari-
ability.
55.73
61.79
54.52
57.29
66.84
87.79
79.15
The entries in the body of this table show the relative amount of
variation in metabolism which remains after individuals are sorted
into groups according to body-weight or body-surface by the two
formulas.^* To facilitate comparison merely, the variabilities (standard
deviations) of the subgroups of like weight or surface-area have been
expressed as percentages of the standard deviation of heat-production
in all individuals irrespective of body-weight or body-surface. A
cursory inspection of the body of the table shows that the metabolism
measurements for any given grade of body-weight or body-surface
in the male series exhibit (roughly speaking) 55 or 60 per cent as much
variation as measurements made on individuals irrespective of these
characters, while in the female series they show from 65 to 90 per cent
of the population variability.
We now turn to a consideration of the actual magnitudes of the
correlations for body-weight and heat-production, r^,/,, and body-
surface area and heat-production, Vah, as given in table 53.
Since body-surface is the character upon which such great emphasis
has been laid as a standard in metabolism studies for the past quarter
''* These are the theoretical values derived from the formulas just discussed. It is useless to
compare them with the values computed directly when the number of individuals is su
small as it is here.
A CRITIQUE OF THE BODY-SURFACE LAW. 159
of a century and more, it is important to make the comparisons between
the results of different correlations in such a way as to show whether
the surface area gives larger {i.e., closer) correlations with total heat-
production or other measures of metaboUsm than the other measures
tested, or whether it gives sensibly the same or smaller values.
Our differences have, therefore, been taken (correlation for body-
surface and measure of metabolism) less (correlation for other physical
character and measure of metabohsm). Thus, when the constant
measuring the correlation for body-surface and a given measure of
basal metabolism is larger than another constant with which it is
compared, the difference is given the positive sign.
In men the correlation between body-surface by the Meeh formula
and total heat per 24 hours is shghtly higher in all but 2 cases (but
in no case significantly higher) than that between body-weight and
total heat-production. In women the correlation between surface as
estimated by the Meeh formula and total heat is in all 3 series
shghtly but not significantly higher than that between body-weight
and total heat-production.
Taking these constants as they stand they indicate, therefore, that
body-weight gives practically as good a basis of prediction for heat-
production as does body-surface by the Meeh formula. To this point
we shall return later.
When the Du Bois height-weight chart is used the differences are
not so regular. In 8 cases the chart measiu'es of body-surface give
the higher correlation, whereas in 3 cases the weight gives the higher
correlation. Thus apparently surface as estimated by the Du Bois
height-weight chart furnishes a better corrective measure than weight.
Since the differences between r^,^ and r„h are in no case significant in
comparison with their probable errors, one can not assert on the basis
of the individual series that there is an actually significant physiological
difference in the relationships between these two physical measure-
ments and metabohsm. The fact that the majority of the series indi-
cate closer correlation of body-surface and total heat-production is
evidence in favor of its closer correlation with total metabolism.
After the constants in table 53 were computed, Armsby, Fries, and
Braman ^^ published correlations for body-weight and total heat-
production and body-surface as estimated by the Meeh formula and
total heat-production for the constants published by Benedict, Emmes,
Roth, and Smith ^^ and by iMeans.^^ They find:
For 98 men 0.7263=^0.0320 0.7747=*= 0.0272
For 75 women 0.7759 ±0.0310 0.7447 ±0.0347
" Armsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, p. 3; Journ. Agric. Research,
1918. 13, pp. 50-51.
« Benedict, Emmes, Roth, and Smith, Joum. Biol. Chem., 1914, 18, p. 139.
" Means, Journ. Biol. Chem., 1915, 21, p. 263.
160 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
From these results they conclude that the constants "fail to show
any greater correlation with the body-surface as computed by the
Meeh formula than with the body- weight."
Notwithstanding this clear evidence against the body-surface law
as applied to the individuals of the same species, Armsby, Fries, and
Braman conclude ^® that their assemblage of data for man, cattle,
hogs, and horses "tend to confirm the conclusions of E. Voit, that the
basal katabolism of different species of animals is substantially pro-
portional to their body surface."
Total heat which is used as the final expression of basal metabolism
may be either directly or indirectly determined. In the case of indirect
calorimetry it is calculated from the total amounts of CO2 or O2, taking
into account the calorific value of the gas which varies with the respira-
tory quotient, i.e., the ratio CO2/O2.
Table 65. — Comparison of correlation between body-weight and oxygen-consumption with the
correlations between body-surface by the two formulas and oxygen-consumption.
Series.
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and first supplementary series
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
Both series
N
IC
62
89
72
28
117
19
136
35
103
Surface by
Meeh formula
and oxygen
consumption
0.9574 ±0,
0.6312±0,
0.7997±0.
0.7845 ±0.
0.8777 ±0,
0.8207 ±0,
0.5771 ±0,
0.7978 ±0.
0141
0515
0258
0306
0293
0204
1032
0210
0.7534 ±0.0354
0.4741 ±0.0884
0.6019 ±0.0424
Difference
-0.0021 ±0.0195
+0.0057 ±0.0733
-0.0010 ±0.0364
+0.0016 ±0.0434
+0.0058 ±0.0424
+0.002S±0.0290
-0.0008±0.1459
+0.0023 ±0.0298
+0.0026 ±0.0503
+0.0158±0.1262
+0.0069 ±0.0608
Surface by
Du Bois
height-weight
chart and
oxygen con-
sumption
0.9661
0.6647
0.8294 ±
0.7838 ±
0.8632 ±
0.8386 ±
0.6369
0.8196
0.0112
0.0478
0.0223
0.0306
0.0325
0.0185
0.0919
0.0190
0.7355 ±0.0375
0.4836 ±0.0873
0.5972 ±0.0428
Difference
+0.
+0
+0,
+0.
-0,
+0,
+0,
+0,
0066 ±0,
0392 ±0,
0287 ±0.
0009 ±0.
0087 ±0,
0207 ±0,
0590 ±0
0241 ±0.
0175
0707
0340
0434
0446
0277
1381
0285
-0.0153±0.0518
+0.0253 ±0.1256
+0.0022 ±0.0608
We turn, therefore, to a consideration of the correlations between
body-weight and oxygen consumption and carbon-dioxide production
in comparison with those for the two measures of body-surface and
oxygen consumption and carbon-dioxide production. The results are
given for oxygen consumption in table 55 and for carbon-dioxide
output in table 56. The value of r^,,, and r^^c are taken from table 24.
While the differences in the correlations are very small a great
majority are positive in sign, i.e., they indicate that the correlations
for surface-area and metabolism are higher than those for weight and
metabolism. Thus these results seem to indicate that body-surface
^* Armsby, Fries, and Braman, Proc. Nat. Acad. Sci., 1918, 4, p. 3-4.
A CRITIQUE OF THE BODY-SURFACE LAW.
161
gives a slightly better criterion of total heat-production than does
body-weight.
We shall now approach the problem from a somewhat different
angle.
7. THE PREDICTION- VALUE OF BODY- WEIGHT AND BODY-SURFACE.
WTien the physiologist asserts that heat-production is proportional
to body-surface he states that knowing the body-surface of an indi-
vidual we also know his basal metabolism. Of course there are tacitly
assumed reservations. Pathological factors, the differentiation due to
sex, and a number of other as yet intangible influences are supposed
to be neglected. Nevertheless it must be admitted that if the assertion
that heat-production is proportional to body-surface is of any practical
significance, it is tantamount to the assertion that knowing the body-
surface of the individual we have the best possible index of his basal
metabolism.
Table 56. — Comparison of the correlation between body-weight and carbon-dioxide production
with correlations between body-surface by the two formulas and carbon-dioxide production.
Series.
N
Surface by
Meeh formula
and carbon-
dioxide pro-
duction
Difference
Surface by
Du Boia
height-weight
chart and
carbon-dioxide
production
ra^c
Difference
Men.
Original series:
Athletes
Others
Whole series
Gephart and Du Bois selection
First supplementary series
Original and 6rst supplementary series.
Second supplementary series
All men of three series
Women.
Original series
Supplementary series
Both series
15
62
88
71
28
116
19
135
66
35
101
0.9295=4=0.0236
0.5807 ±0.0570
0.7703*0.0292
0.7687=*= 0.0327
0.8187=1=0.0420
0.7808=1=0.0244
0.5128=1=0.1140
0.7582=*= 0.024
0.7392 =fc 0.0376
0.4427 ±0.0917
0.6366 ±0.0399
-0.0059=1=0
-1-0.0066 ±0
- 0.0033 ±0
-f-0.0017±0
-1-0.0121 ±0
- 0.0003 ±0
-1-0.0086 ±0
-1-0.0007 ±0
0321
0809
0410
0464
0612
0345
1622
0349
-f 0.0060 =
-f-0.0176 =
= 0.0537
= 0.1309
0.9378=1=0,
0.6047±0
0.8043 ±0.
0.7589 ±0
0.8283 ±0,
0.8024 =fc0.
0.5240 ±0
0.7884±0
0144
0543
0254
0339
0400
0223
1123
0229
0.7386=
0.4503 =
-1-0.0024 =
4-0.0306 =
4-0.0307 =
-0.0081 =
4-0.0217 =
4-0.0213=
4-0.0198=
4-0.0309 =
4-0.0100 ± 0.0571 0.6357 =
= 0.0377 4-0.0054 =
= 0.090914-0.0252 =
= 0.039914-0.0091 =
= 0.0260
= 0.0790
= 0.0384
= 0.0472
= 0.0598
= 0.0331
= 0.1610
= 0.0337
= 0.0538
= 0.1303
= 0.0571
We shall start out from the assumption that the best measure of
the heat-production of an indi\'idual is that which gives the best
prediction for an unknown series. Concretely, suppose that we predict
the total heat-production of a series of individual men under standard
conditions by three different methods. Surely it seems reasonable to
regard the method which predicts the metaholism of the individuals most
exactly as the best measure. Other-^-ise the whole contention for normal
control series for use in pathological research or in other fields of prac-
tical nutrition work is stultified.
We shall, therefore, predict the daily heat-production of a series
162 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
of individuals of given weight, of given body-surface as approximated
by the Meeh formula, and of given body-surface as estimated by the
Du Bois height-weight chart, and shall determine which of these meas-
ures actually permits the closest prediction in the case of subjects whose
metabolism is unknown so far as the development of the prediction
formulas is concerned. The arithmetical routine is illustrated in tables
57-59, to be discussed below.
To avoid all criticism concerning the selection of measurements to
be used as the fundamental series, we shall take those for the 72 indi-
viduals chosen by Gephart and Du Bois, and designated in this volume
as the Gephart and Du Bois selection. From equations based upon
this series we shall compute the total heat-production which should be
found in individuals of three other series and compare the results of
predicting these values by three different methods with the metabolism
constants actually found.
The individuals used for the test series are in no case included
in the series upon which the prediction formulas are based. The
grouping of the individuals has been determined by factors which are
entirely beyond our present control. The groups were selected before
the prediction equations were calculated, and no change has been made
subsequently.
The following groups have been used, (a) The 17 men rejected
by Gephart and Du Bois from the 89 published by Benedict, Emmes,
Roth, and Smith. (6) The first supplementary series of 28 men.
(c) The second supplementary series of 19 men.
Thus it is possible to test the results of prediction in three separate
series of men and (upon the combination of these series) on a general
series of 64 individuals. Now all students of metabolism might not
agree fully with Gephart and Du Bois in their selection of the 72 indi-
viduals as a basis for metabolism constants. It seems worth while,
therefore, to base prediction formulas on a quite different series and
to compare the predicted values of the metabolism of the 72 individuals
of the Gephart and Du Bois selection with their actually determined
heat-production. Such a procedure has not merely the merit of furn-
ishing a more stringent criterion of the value of the various methods
of calculating check series, but has the advantage of emphasizing in a
clear-cut manner the fact that data are still inadequate for the most
advantageous selection of control values for use in clinical calorimetry.
The most natural procedure is, of course, to base prediction form-
ulas on the 64 individuals not included in the Gephart and DuBois
selection and to test the results secured by these formulas against the
observed values for the individuals of the Gephart and Du Bois
selection.
These series of comparisons cover only men. Turning to women,
it has seemed desirable to predict the results for the supplementary
A CRITIQUE OF THE BODY-SURFACE LAW. 163
series of 35 from the original series of 68 women, and in turn to predict
the heat -production of the original series from constants or equations
based on the supplementary series. Thus a very comprehensive
test of the validity of the different methods of forming check series is
secured.
Two methods of calculating the metabolism of an indi\'idual whose
actual heat-production is unkno\NTi suggest themselves.
First, one may merely multiply the body-weight or body-surface
of the subject by the average heat-production per unit of weight or
per unit of surface in the standard series. This has been the method
hitherto employed in the calculation of the control values to be used
in chnical calorimetry.
Second, one may use a mathematical prediction equation based on
the standard series. So far as we are aware, this method has not
hitherto been employed in studies on basal metaboUsm.
WTiile the second method seems the more logical of the two, we
shall give the results of both.
"WTien prediction of the heat-production of an indi\'idual is made
by either of the methods a value is obtained which may be identical
with the actually determined constant, but which in general deviates
somewhat from it. De\4ation may, therefore, be either positive or
negative in sign. We shall, in consequence, have to consider whether
the predictions made by a given method are on the whole too large or
too small. Since we are in this case testing methods of prediction
against actual observation, we have taken the differences (calculated
heat-production) less (actually determined heat-production). Thus
when a given prediction method gives results which are on the average
too high, the mean de\'iation (with regard to sign) of the calculated
from the actual heat-production wiU have the positive sign. TMien it
is too low, it will have the negative sign. Dividing the sum of the
deviations unth regard to sign by the total number of indi\'iduals in
the series in hand we have a measure of the average de\'iation in the
direction of too high or too low prediction.
But the question as to whether a given prediction method gives on
the whole too high or too low values is not the only one to be answered.
One wishes to know the extent of deviations both above and below
the observed value in the case of each of the methods used. One
measure of such de^dation is obtained by ignoring the signs and simply
regarding a difference between obser^-ed and predicted values as an
error of a given magnitude. Dividing the sum of these errors for the
whole series by the number of indi\'iduals in the series, we have, in
terms of average deviation without regard to sign, a measure of the rela-
tive precision of the different m.ethods of prediction employed. This
method has two disadvantages. First, it does violence to sound mathe-
matical usage with regard to signs. Second, it gives the deviations
164 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
weight proportional to their magnitudes. But one may consider that
very great deviations should be given proportionally more weight in
testing different prediction methods than very slight deviations.
The magnitudes of the deviations may be logically weighted and the
transgression against the law of signs avoided by squaring the devia-
tions before they are summed. The square root of the mean of these
summed squares will then furnish a logical measure of the deviation
of the calculated from the observed productions. For the sake of
completeness in the investigation of a problem which has the contro-
versial status of the "body-surface law" we shall use both of these
methods.
The deviations of the predicted from the actually determined heat-
production is expressed in two different ways in the accompanying
tables: (1) The differences are expressed in the absolute terms of
calories per 24 hours. (2) The differences are reduced to a relative
basis by expressing them as a percentage of the mean heat-production
in calories per 24 hours of the specific group of individuals dealt with.
We now turn to the actual data.
The average heat-productions for the 72 individuals of the Gephart
and Du Bois selection and for the 64 other individuals for the three
units of body-measurements adopted are as follows :
Heat-production per kilogram of body-weight:
72 of Gephart and Du Bois selection 25.7944 ±0.1655 calories.
64 others 25.5875 ±0.2292 calories.
Difference 0.2069 ±0.2827 calories.
Heat-production per square meter of body-surface by Meeh formula:
72 of Gephart and Du Bois selection 831.639 ± 4.413 calories.
64 others 828.203 ± 5.742 calories.
Difference 3.436± 7.242 calories.
Heat-production per square meter of body-svu-face by Du Bois height-weight chart :
72 of Gephart and Du Bois selection 926.653 ± 4.975 calories.
64 others 924.141 ± 6.063 calories.
Difference 2.512 ± 7.843 calories.
While the results for the two sets of individuals are not exactly
identical, as shown by the differences, the probable errors of these
differences show that the two groups of men can not be considered to
differ significantly. Thus, while the constants of these two series will
not give exactly identical results if used for the calculation of control
values as a basis of comparison in applied calorimetry, the differences
between them are so small that they can not be asserted to have any
physiological significance.
The results for the two series of women are:
Heat-production per kilogram of body-weight:
68 Original women 25.3500 ±0.2467 calories.
35 Supplementary women 22.7229 ±0.4103 calories.
Difference 2.6271 ±0.4788 calories.
A CRITIQUE OF THE BODY-SURFACE LAW.
165
Heat-production per square meter of body-siuface by Meeh formula:
68 Original women 772.397 =t 5.184 calories.
35 Supplementary women 715.057 =*= 10.004 calories.
Difference 57.340='= 11.267 calories.
Heat-production per square meter of body-surface by Du Bois height -weight chart:
68 Original women 865.324 =*= 5.317 calories.
35 Supplementary' women 820.257 =*= 10.410 calories.
Difference 45.067 =t 11.690 calories.
The agreement of the means for the two series of women is not as
good as that for the two series of men. Possibly this is partly due to
the fact that the larger female series has only about as many indi\iduals
as the smaller male series, while the smaller female series comprises
only about half as many individuals as the smaller of the two male
series. WTiatever the cause of the difference in the two female series,
the consequence must necessarily be a larger error of prediction than in
the case of males.
Table 57. — Comparison of actual heat-production and heat-production calculated (a) from the
mean heat per kilogram of body-weight and (6) from the equation for the regression
of total heat on body-weight in the Gephart and Du Bois selection.
Individual.
„ . Measured Calculated from
;°g;i heat- 1 -ean.
Calculated from
equation.
^^**°^|production. „
1 Heat. Dmerence.
Heat.
Difiference.
H. F
82.1 1615 2118
+503 1 1937
+486 1 1952
+266 . 2044
+322
+297
+ 27
+ 172
- 59
-174
+ 104
+ 120
-173
-123
- 20
-176
+243
-202
-159
+ 65
- 99
Prof. C
w. s
83.0 , 1655 1 2141
88.5 1 .2017 i 2283
85.8 1827 2213
79.0 ' 1944 2038
108.9 2559 2809
74.4 1704 1919
75.0 ! 1698 1935
56.8 ; 1687 1465
56.3 1629 ! 1452
57.1 ! 1.539 ! 1473
59.7 1739 i 1540
50.0 : 1158 i 1290
49.3 I 1591 1 1272
54.3 ; 1632 ' 1401
55.1 1421 1421
50.6 1 1510 1305
O. F. M
M.H.K
H. W
F. A. R
F. E. M
R. I. C
W. W. C
L. D. A
F. M. M
E. J. W
F. P
+386
+ 94
+250
+215
+237
-222
-177
- 66
-199
+ 132
—319
-231
= 000
-205
1999
1885
2385
1808
1S18
1514
1506
1519
1563
1401
1389
1473
1486
1411
V.G
C.H. H
B. N. C
Multiplying body-weight and body-surface by the two formulas
by these values, we obtain the predicted values. Upon a comparison
of the computed values with those obtained by actual measurement,
we may base our conclusions concerning the relative merit of various
methods of prediction.
The arithmetical routine is naturally somewhat extensive. It will
be illustrated for only the smallest series — the 17 men omitted by
Gephart and Du Bois from the original Nutrition Laboratory series.
The actual and calculated values and their differences are given for the
individual subjects in the third, fourth, and fifth sections of tables 57-59.
166 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Table 58. — Comparison of actual heat-production and heat-production calculated (a) from
the mean heat per square meter of body-surface by the Meeh formula and (6) from
the equation for the regression of total heat on body-surface by the
Meeh formula in the Gephart and Du Bois selection.
Individual.
Body-
sui-face
by Meeh
formula.
Measured
heat-
production.
Calculated from
mean.
Calculated from
equation.
Heat.
Difference.
Heat.
Difference.
H. F
2.33
1615
1655
2017
1827
1944
2559
1704
1698
1687
1629
1539
1739
1158
1591
1632
1421
1510
1938
1946
2038
1996
1888
2337
1813
1821
1514
1505
1522
1563
1389
1381
1472
1480
1405
+323
+291
+ 21
+ 169
- 56
-222
+ 109
+ 123
-173
-124
- 17
-176
+231
-210
-160
+ 59
-105
1934
1942
2032
1991
1884
2328
1810
1819
1515
1506
1523
1564
1391
1383
1474
1482
1408
+319
+287
+ 15
+ 164
- 60
-231
+ 106
+ 121
-172
-123
- 16
-175
+233
-208
-158
+ 61
-102
Prof. C
2.34
W. S
2.45
0. F. M
M.H.K
H. W
2.40
2.27
2.81
F. A. R
F. E. M
R. I. C
W. W. C
L. D. A
F. M. M
E. J. W
2.18
2.19
1.82
1.81
1.83
1.88
1.67
F. P
1.66
V. G
1.77
C. H. H
B. N. C
1.78
1.69
Table 59. — Comparison of actual heat-production and heat-production calculated (o) from the
mean heat per square meter of body-surface by the Du Bois height-weight chart and (6)
from the equation for the regression of total heat on body-surface by the
Du Bois height-weight chart in the Gephart and Du Bois selection.
Body-
Calculated from
Calculated from
surface by
Measured
mean.
equation.
Individual.
Du Bois
height-
heat-
production.
weight
Heat.
Difference.
Heat.
Difference.
chart.
H. F
1.90
1615
1655
2017
1827
1761
1788
1816
1835
+ 146
+ 133
-201
+ 8
1774
1805
1836
1856
+ 159
+ 150
-181
+ 29
Prof. C
1.93
W. S
1.96
0. F. M
1.98
M.H.K
2.04
1944
1890
- 64
1918
- 26
H. W
2.43
2559
1704
2252
1668
-307
- 36
2318
1672
-241
— 32
F. A. R
1.80
F. E. M
1.81
1698
1677
- 21
1682
- 16
R. I. C
1.76
1687
1631
- 56
1631
- 56
W. W. C
1.67
1629
1548
- 81
1538
- 91
L. D. A
1.67
1539
1548
+ 9
1538
- 1
F. M. M
1.72
1739
1594
-145
1590
-149
E. J. W
1.47
1158
1591
1632
1421
1362
1390
1455
1501
+204
-201
-177
+ 80
1333
1364
1436
1487
+ 175
-227
-196
+ 66
F. P
1.50
V. G
1.57
C. H. H
1.62
B.N.C
1.63
1510
1510
±000
1497
- 13
The average deviation with regard to sign of the calculated from the
observed values are given in table 60. These show that in all series
except one the values predicted from the Gephart and Du Bois selection
average somewhat too high. The prediction of the value of the metab-
A CRITIQUE OF THE BODY-SURFACE LAW.
167
olism of the Gephart and Du Bois selection from the means for the
64 other men is for each method somewhat too low. Similarly, in
dealing "vsath women we note that the values predicted for the supple-
mentary series from the original female series are on the average too
high, while those predicted for the original series are on the average
too low.
Such differences in sign are of course a necessary result of the differ-
ences in the constants of the two standard series of each sex. The
point ^-ill receive further consideration below.
In prediction from the Gephart and Du Bois selection, the average
deviation with regard to sign given by using the mean metabolism
Table 60. — Average defialion vcith regard to sign of total heat-production as predicted by mean
heat-production per unit of body-weight or surface in standard
series from the actual heat-production.
Series
N
Prediction from
body-weight in
kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
body-surface,
height-weight chart.
III.
Men.
Averages based on Gephart and Du Bois
selection:
I. First supplementary series
II. Second supplementary series
III. Indi\-iduals omitted by Gephart and
Du Bois
28
19
17
64
72
-f 11.8= 0.74 p. ct.
+ 38.3= 2.34 p. ct.
+ 67.6= 3.97 p. ct.
+ 34.5= 2.10 p. ct.
- 3.0= 0.18 p. ct.
-i- 6.5 = 0.40 p. ct.
-i- 14.6 = 0.89 p. ct.
+ 4.9 = 0.29 p. ct.
4- 8.5 = 0.52 p. ct.
— 6.5 = 0.40 p. ct.
-f 25.0 =1.56 p. ct.
+ 4.7 = 0.29 p. ct.
-41.1 = 2.42 p. ct.
+ 1.4 = 0.09 p. ct.
- 3.5 = 0.22 p. ct.
IV. All individuals
.\verages based on 64 individuals not in
Gephart and Du Bois selection :
V. Gephart and Du Bois selection. . . .
Women.
Averages based on original series:
VI. Supplementary series
35
68
+ 191.7 = 14.32 p. ct.
-116.6= 8.61 p. ct.
-f 119.0 = 8.89 p. ct.
- 93.9 = 6.93 p. ct.
-1-77.9 = 5.82 p. ct.
— 69.9 = 5.16 p. ct.
Averages based on supplementary series:
VII. Original series
per square meter of body-surface as calculated by the Du Bois height-
weight chart is less than that given by the use of the mean metabolism
per kilogram of body-weight in every case except the first supplement-
ary series. The total series of 64 indi\4duals shows an average plus
deviation of only 1.4 calories per day by the Du Bois height-weight
chart, of 8.5 calories by the Aleeh formula, and of 34.5 calories by body-
weight.
In predicting the values of the 72 individuals from the means based
on the 64 other men, the Du Bois height-weight chart gives better
results for de\'iation with regard to sign than does the Meeh surface
formula, but slightly worse results than prediction from body-weight.
In predicting the total heat-production in the two female series, the
Du Bois height-weight chart gives much smaller de\'iations than either
of the other methods. Apparently, therefore, the Du Bois height-
weight chart gives the smallest average deviation above or below the
168 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
ideal zero deviation, and so far as this test is concerned must accord-
ingly be regarded as furnishing the best basis for predicting the metab-
olism of an unknown subject.
Turn now to the average deviations without regard to sign. These
show the average error either above or below the actually observed
values. The averages are given in table 61. For the whole series of
64 individuals in which prediction is based on the averages per unit
in the Gephart and Du Bois selection ''^ the average error is 100 calories
by the Du Bois height- weight chart as compared with 141 calories by
body-weight, or 6.08 per cent as compared with 8.57 per cent of the
average heat-production of the individuals tested. In predicting the
Table 61. — Average deviation without regard to sign of total heat-production as predicted
from the mean heat-production per unit of body-weight or surface in
standard series from the actual heat-production.
Series.
N
Prediction from
body-weight
in kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
bodj'-surface,
height-weight chart.
III.
Men.
Averages based on Gephart and Du Bois
selection :
I. First supplementary series
28
19
17
64
72
35
68
92.8= 5.78 p. ct.
127.0= 7.75 p. ct.
234.6=13.79 p. ct.
140.6= 8.57 p. ct.
106.4= 6.55 p. ct.
243.7 = 18.21 p. ct.
169.8=12.53 p. ct.
86.8= 5.40 p. ct.
90.5= 5.52 p. ct.
151.1= 8.88 p. ct.
105.0= 6.40 p. ct.
86.9= 5.35 p. ct.
178.4=13.33 p. ct.
115.4= 8.52 p. ct.
94.1= 5.86 p. ct.
99.7= 6.08 p. ct.
109.4= 6.43 p. ct.
99.8= 6.08 p. ct.
88.7= 5.46 p. ct.
149.9 = 11.20 p. ct.
94.6= 6.98 p. ct.
II. Second supplementary series
III. Individuals omitted by Gephart and
Du Bois
IV. All individuals
Averages based on 64 individuals not in
Gephart and Du Bois selection :
V. Gephart and Du Bois selection
Women.
Averages based on original series:
VI. Supplementary series
Averages based on supplementary series:
VII. Original series
'.
metabolism of the 72 individuals of the Gephart and Du Bois selection
from averages based on the 64 other individuals, the average deviations
range from 87 to 106 calories, or 5.35 per cent for surface by the Meeh
formula, 5.46 per cent for surface by the Du Bois height-weight chart,
and 6.55 per cent for body-weight. Errors are much larger in the female
series, ranging from 6.98 per cent to 18.21 per cent, but with the order
of errors always lowest for prediction from body-surface by the Du Bois
height-weight chart, highest by body-weight, and intermediate in
" In working with the subgroups great irregularity must be expected because of the limited
numbers of individuals. In the case of the 17 individuals discarded from the original Nutrition
Laboratory series by Gephart and Du Bois the results of predicting from body-weight are partic-
ularly bad. The error is 6.43 per cent in the case of the height-weight chart and 13.79 per cent
in the case of body-weight. In the first supplementary series prediction from body-weight gives
slightly greater error than prediction from body-surface by the Meeh formula, but slightly less
error than prediction from the Du Bois height-weight chart. In all other series the error by the
height-weight chart is considerably less than by the body-weight method, and in all but two cases
it is less than prediction by the use of means for heat-production per unit of surface-area by the
Meeh formula.
A CRITIQUE OF THE BODY-SURFACE LAW.
169
prediction from area by the Meeh formula. Again the results indicate
the superiority of the Du Bois height-weight chart as a basis of pre-
dicting the metabolism of an unknown.
Table 62 gives (in terms of the square root of mean-square de\'ia-
tion of the predicted from the actual values) a comparison of the results
of predicting by the three different means. The square root of the
mean-square de^aation of the calculated from the actually measured
metabolism is in all series greater in prediction from weight than it is
in prediction from the height-weight chart. This method, Uke the
two preceding, therefore, justifies the conclusion that (as an empirical
basis for the prediction of the heat-production of an individual, on the
Table 62. — Square root of mean-square deviation of total heat-production as predicted from
the mean heat-prodtiction per unit of body-weight and surface in standard
series from the actual heat-production.
Series.
A^
Prediction from
body-weight
in kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
body-surface,
height-weight chart.
III.
Men.
Averages based on Gephart and Du Bois
selection :
28
19
17
64
72
35
68
136.2= 8.49 p. ct.
171.3 = 10.45 p. ct.
268.1 = 15.76 p. ct.
189.5= 11.55 p. ct.
132.2= 8.14 p. ct.
327.8 = 24.49 p. ct.
201.1 = 14.85 p. ct.
107.7= 6.71 p. ct.
135.3= 8.25 p. ct.
173.5=10.20 p. ct.
136.0= 8.29 p. ct.
109.1= 6.72 p. ct.
218.7=16.34 p. ct.
142.0=10.48 p. ct.
117.3= 7.31 p.ct.
134.4= 8.20 p.ct.
139.1= 8.18 p.ct.
128.5= 7.83 p.ct.
110.6= 6.81 p.ct.
174.0=13.00 p.ct.
122.1= 9.01 p.ct.
II. Second supplementary series
III. Individuals omitted by Gephart and
Du Bois
Averages based on 64 individuals not in
Gephart and Du Bois selection :
V. Gephart and Du Bois selection
Women.
Averages based on original series :
VI. Supplementary series
Averages based on supplementary series:
■\1I. Original series
assumption that heat-production bears a definite ratio to some physical
character) the Du Bois height-weight chart measure of body-surface
area furnishes distinctly better means of prediction than does body-
weight. In the series of 64 individuals in which prediction is made
from the Gephart and Du Bois selection the square root of mean
square errors expressed as a percentage of the mean of the measured
heat-production of the individuals stand as 11.5 : 7.8; in the Gephart
and Du Bois selection they stand as 8.1 : 6.8; in the first female series
as 14.9 : 9.0; and in the second female series as 24.5 : 13.0 per cent.
We now turn to the prediction of metabolism by means of a mathe-
matical equation fitted to a series of obser^'ations. Because of its
simphcity and its direct relation to the correlation coefficient we have
naturally first availed ourselves of the linear regression equation.
These follow:
170 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Equations based on 72 individuals chosen by Gephart and Du Bois:
For total heat on body-weight, /i = 565.390+16.707 u).
For total heat on body-surface by Meeh formula, /i = 19.463 -F 821. 567 a y^.
For total heat on body-surface by Du Bois height-weight chart,
/i= - 175.338+1026.173 a^.
Equations based on 64 men not included in the Gephart and Du Bois selection:
For total heat on body-weight, ^1 = 641.261 + 15.392 ip.
For total heat on body-surface by Meeh formula, A = 126.334+763.680 a^.
For total heat on body-surface by Du Bois height-weight chart,
h= -310.884 + 1101.2300^.
Equations based on 68 women of original Nutrition Laboratory series:
For total heat on body-weight, /i =781.408+10.522 uj.
For total heat on body-surface by Meeh formula, /i = 461.758 +506.428 o^^
For total heat on body-surface by Du Bois height-weight chart, /i = 88.493+808.401 o^.
Equations based on the 35 supplementary women:
For total heat on body-weight, /i = 957.468+6.313 u).
For total heat on body-surface by Meeh formula, /i = 741.987+316.101 a^j^.
For total heat on body-surface by the Du Bois height-weight chart,
;i =519.673+500.2520^.
Again we may use the 17 individuals omitted by Gephart and
Du Bois from the original Nutrition Laboratory series to illustrate the
method of calculation. The values are given in the sixth and seventh
columns of tables 57, 58, and 59. Space does not permit the publica-
tion of the calculated values and their deviation from the actually
observed constants in the other series.
Before taking up the question of the relative precision of prediction
of heat-production from equations based on body-weight and on body-
surface by the two formulas, we may consider the relative closeness
of prediction by means of average measures in the standard series and
by means of equations. In doing this we shall draw the comparisons
solely between the results of prediction from means alone and from
equations for the same unit of bodily measurement.
In the tables, 63-65 the differences are given in calories per day
and in percentages of the average heat-production of the group of
individuals dealt with. The positive sign indicates that the prediction
from means gives a larger error, the negative sign that it gives a smaller
error than prediction by the use of the regression equation. In com-
paring the deviations with regard to sign it has been necessary to con-
sider the magnitudes of the deviations only in these difference tables.
The differences show, therefore, which method gives the numerically
larger average error, but give no information concerning the sign of
this error. The latter can, of course, be obtained from tables 60 and 66.
The differences between the average deviations with regard to sign
in table 63 show that in 6 out of the 7 cases prediction by equations
based on body-weight gives a smaller average deviation than prediction
from mean heat-production per kilogram of body-weight. In the
exceptional case the difference is very small {i.e., 4.4 calories or 0.28
per cent), whereas in 5 of the 6 cases in which the differences are posi-
A CRITIQUE OF THE BODY-SURFACE LAW.
171
tive in sign they are also of a very material order of magnitude, ranging
from 24.9 to 113.8 calories or from 1.51 to 8.50 per cent of the average
heat-productions of the groups of individuals. In predictions involving
body-surface as estimated by the Meeh formula the use of equations
gives a smaller net de\^ation than computation of heat-production by
considering it proportional to body-surface. The differences are not
so large when measures of body-surface by the Du Bois height-weight
chart are used, but here 4 out of the 7 comparisons indicate by the
positive sign of the differences the superiority of the regression-line
method of prediction.
Table 63. — Differences in calories between the average deviations with regard to sign resulting
from the use of means and straight-line equations far prediction.
Series.
JV
Prediction from i Prediction from Prediction from
body-weight '■ body-surface, body-surface,
in kilograms. Meeh formula. height-weight chart.
I. ! II. III.
Men.
PredictionfromGephartandDuBois selection:
I. First supplementary series
28
19
17
64
72
35
68
-f 4.3 = 0.27 p. ct. '■ -\- 0.2 = 0.01 p. ct.
-1-25.8 = 1.58 p. ct. 4- nn = 0.0.'i T>. ct.
+ 0.2 = 0.02 p. ct.
- 1.4 = 0.08 p. ct.
-1- 2.9=0.17 p. ct.
- 1.1 = 0.06 p. ct.
- 0.6=0.03 p. ct.
+ 4.7 = 0.35 p. ct,
4-18.4=1.36 p. ct.
III. Individuals omitted by Gephart and
Du Bois
-t-57.9=3.40 p. ct.
4-24.9=1.51 p. ct.
- 4.4 = 0.28 p. ct.
-f-113.8 = 8.50p. ct.
-1- 1.3=0.08 p. ct.
-r 0.6 = 0.04 p. ct.
-1- 0.4 = 0.02 p. ct.
-f40.1=3.00p. ct.
rV. All individuals
Prediction from 64 individuals not in Gephart
and Du Bois selection:
V. Gephart and Du Bois selection
Women.
Prediction from original series:
VI. Supplementary series
Prediction from supplementary series:
VII. Original series
-f63.3 = 4.68p. ct.
-1-38.6 = 2.85 p. ct.
I
If we consider together all of the tests of prediction by equations
as compared vdth prediction from the average values of metabolism
per unit of body-weight or body-surface area made in table 63, we note
that 17 out of the 21 differences are positive. In other words, predic-
tion from the mean heat-production per unit in the standard series
gives a larger average de\dation -with regard to sign than prediction
from equations.
Turning now to comparison of the average deviations without
regard to sign, we have the results set forth in table 64, The first
column of constants shows the differences between the average devia-
tions (without regard to sign) of the predicted from the actually ob-
ser\'ed heat-productions when the predictions are made by the use of
equations and when they are made from the average heat-productions
per unit of body-weight in the check series as a whole. The positive
signs (indicating a greater error of prediction when average heat-
production per kilogram of body-weight is used as a standard) show
that the equations give better results in everj' instance.
■
172 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In comparing the results of predicting total heat-production from
body-surface by equations and by considering it proportional to the
average heat-production per square meter of body-surface, we note
that the differences are far smaller than those found when body-weight
is used. It is not, therefore, so essential to use the equations when
body-surface is to be employed as a basis of prediction as when body-
weight is used. But in predicting from body-surface the equations
give better results in 8 out of the 14 comparisons.
Table 65 gives the comparison of the square root of mean square
deviation of the calculated from the actual values for the prediction
by the use of means only and by the use of linear regression equations.
In prediction from body- weight, the straight line gives far more satis-
Table 64. — Differences in calories between the average deviations without regard to sign
resulting from the use of means and straight-line equations for prediction.
Series.
N
Prediction from
body-weight
in kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
body-surface,
height-weight chart.
III.
Men.
Prediction from Gephart and Du Boia selec-
tion:
I. First supplementary series
28
19
17
64
72
36
68
-1- 1.7 = 0.11 p. ct.
-1-27.6=1.69 p. ct.
-f85.5 = 5.03p. ct.
-h31.6 = 1.92p. ct.
-f 18.3 = 1.12 p. ct.
+93.7 = 7.00 p. ct.
-1-73.7 = 5.44 p. ct.
- 0.7 = 0.05 p. ct.
- 9.5 = 0.58 p. ct.
+ 1.0 = 0.06 p. ct.
- 2.8 = 0.17 p. ct.
- 0.5 = 0.03 p. ct.
+29.4 = 2.20 p. ct.
+ 19.9 = 1.47 p. ct.
+4.5 = 0.28 p. ct.
-1.1=0.07 p. ct.
+3.0 = 0.18 p. ct.
+2.4 = 0.14 p. ct.
±0.0 = 0.00 p. ct.
+3.8 = 0.28 p. ct.
+ 1.5 = 0.11 p. ct.
II. Second supplementary series
III. Individuals omitted by Gephart and
Du Bois
IV. All individuals
Prediction from 64 individuals not in Gephart
and Du Bois selection:
V. Gephart and Du Bois selection
Women.
Prediction from original series:
VI. Supplementary series
Prediction from supplementary series :
VII. Original series
factory results. In the case of the two body -surface measurements
there is less difference. It is important to note that in the case of the
Du Bois height-weight chart, in which body-surface is not merely a
function of weight, the evidence for accuracy of prediction is in favor
of the linear prediction formula. This is shown by the fact that in
6 of the 7 cases prediction from the mean heat-production in the
standard series gives a larger square root of mean square deviation
than prediction by the use of linear equations.
Taking all the three lines of evidence together, a material superiority
of the linear regression equation over the method heretofore used for
purposes of prediction is evident.
We now turn to a comparison of the results of predicting metabo-
lism by means of straight-line equations based on body-weight and
based on body-surface. We shall compare the results of such prediction
A CRITIQUE OF THE BODY-SURFACE LAW.
173
in three ways : by the determination of the mean error with regard to
sign, by the determination of the mean error without regard to sign,
and by the determination of the square root of mean square de\dation
of the predicted from the actuallj^ measured values.
The mean de\iations with regard to sign appear in table 66. With
one exception they indicate that in the nine comparisons with the
three subseries (I-III) prediction from the constants of the Gephart
and Du Bois selection is on the average too high. This is also true of
the whole series of 64 individuals. The actual amount of the deviation
is not large. It ranges from 3.6 to 38.2 calories in the subseries and
from 2.5 to 9.6 calories in the combination series. In terms of per-
centages of the mean heat-production of the groups dealt with these
Table 65. — Differences in calories between square root of the mean-square errors of prediction
by use of means and by use of straight-line equations.
Series.
N
Prediction from
body-weight in
kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
bodj'-surface,
height-weight chart.
III.
Men.
Prediction from Gephart and Du Bois selection :
I. First supplementary series
28
19
17
64
72
35
68
+ 24.4= 1.52 p. ct.
-f- 27.5= 1.68 p. ct.
-f- 97.2= 5.72 p. ct.
-1- 60.3= 3.06 p. ct.
+ 22.0= 1.35 p. ct.
+154.3 = 11.53 p. ct.
+ 80.9= 6.98 p. ct.
— 0.3 = 0.02 p. ct.
— 8.2 = 0.50 p. ct.
-f- 0.9 = 0.06 p. ct.
- 2.3 = 0.14 p. ct.
- 0.4 = 0.03 p. ct.
-h46.9 = 3.50p.ct.
-f-22.2 = 1.64p. ct.
+3.4 = 0.21 p. ct.
— 0.5 = 0.03 p. ct.
+6.2 = 0.37 p. ct.
+2.9 = 0.18 p. ct.
+0.4 = 0.02 p. ct.
+4.9 = 0.37 p. ct.
+ 1.7 = 0.12 p. ct-
II. Second supplementary series
III. Individuals omitted by Gephart and
Du Bois
rV. AH indi\'idual8
Prediction from 64 indiWduals not in Gephart
and Du Bois selection:
V. Gephart and Du Bois selection
Women.
Prediction from original series:
VT. Supplementarj' series
Prediction from supplementary series:
VII. Original series
average de\dations wath regard to sign range from 0.15 to 2.25 per
cent, but only 2 of the subseries show a percentage deviation of over
1 per cent, and the 3 constants for the whole series of 64 individuals
show a deviation of less than 0.6 per cent.
Since the constants based on the Gephart and Du Bois selection
give slightly too high results when used to predict the heat-production
of other indi\aduals, it is necessarj'- that the constants of this other
series give values which are too low when they are used to predict the
heat-production of the individuals of the Gephart and Du Bois selection.
We note, therefore, that the average deviations for the predicted values
of the Gephart and Du Bois selection are negative in sign throughout.
The actual values are roughly comparable with those already con-
sidered, ranging from 4.1 to 7.4 calories, or from 0.25 to 0.46 per cent
of the mean heat-production.
This difference in the sign of the average deviation in the two
174 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
series emphasizes the fact that even series comprising over 60 individ-
uals each are not large enough to give wholly accurate mean predictions
of metabolism. Metabolism constants are highly variable, and this
has as a necessary consequence a high probable error of a mean constant
based on a number of individuals which to the experimental physiol-
ogist would seem to be very large. The reader will of course note that
since the average deviations of predicted values differ in sign in these
two series, the result of combining the two series for the purpose of
predicting standard control values, as we shall do later in this volume,
will be an average deviation much more nearly the theoretical zero in
amount. How close to the theoretical the average of values predicted
from these combined series will lie can, of course, be determined only
in the future when the necessary experimental data have been collected.
Table 66. — Average deviation with regard to sign of total heat-production as predicted by
linear equations from the actual heat-production.
Series.
A^
Prediction from
body-weight
in kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
body-surface,
height-weight chart.
III.
Men.
Equations based on Gephart and Du Bois
selection :
28
19
17
64
72
35
68
+ 7.5-0.47 p. ct.
+ 12.5 = 0.76 p. ct.
+ 9.7 = 0.57 p. ct.
+ 9.6 = 0.58 p. ct.
- 7.4 = 0.46 p. ct.
+77.9 = 5.82 p. ct.
-53.3 = 3.93 p. ct.
+ 6.3 = 0.39 p. ct.
+ 14.1 =0.86 p. ct.
+ 3.6 = 0.21 p. ct.
+ 7.9 = 0.48 p. ct.
- 6.1 = 0.38 p. ct.
+ 78.9 = 5.89 p. ct.
-55.3 = 4.08 p. ct.
+24.8=1.54 p. ct.
+ 6.1 = 0.37 p. ct.
-38.2 = 2.25 p. ct.
+ 2.5 = 0.15 p. ct.
- 4.1=0.25 p. ct.
+73.2 = 5.47 p. ct.
-61.6 = 3.80 p. ct.
II. Second supplementary series
III. Individuals omitted by Gephart and
Du Bois
Equations based on 64 individuals not in
Gephart and Du Bois selection:
V. Gephart and Du Bois selection
Women.
Equations based on original series:
Equations based on supplementary series :
VII. Original series
Comparable results, as far as the opposite signs are concerned, are
found in the two feminine series. The magnitudes of the deviations
are, however, much greater. We find, in fact, averages ranging from
about 50 to about 80 calories, instead of from 2.5 to 9.6 calories, as
in the general male series. Expressed in percentages of the mean,
the deviations are of the order 3.8 to 5.9 per cent, instead of generally
lower than 1 per cent. The conclusion to be drawn from this result
is obvious. Prediction of the metabolism of women can not be carried
out by these equations with the degree of certainty that is possible in
dealing with men. To what extent this may be due to the smaller
number of records of women as yet available, and to what extent it
may be looked upon as due to age heterogeneity or as indicating real
biological differences between the sexes, must remain a problem for
further investigation and consideration.
A CRITIQUE OF THE BODY-SURFACE LAW.
175
Confining our attention to the four general series, IV-VII, in which
the number of indi\dduals is reasonably large, it is apparent that in
every case prediction from the hnear equations based on body-surface
as determined by the Du Bois height-weight chart gives lower average
deviations with regard to sign than do those based on either body-
surface by the IMeeh formula or body-weight. Thus the Du Bois
height-weight chart gives the best prediction, in so far as accuracy of
prediction can be measured by the average deviation of the predicted
from the actually observed value. There seems to be Uttle difference
between the results of prediction from body-weight and from body-
surface as estimated by the jVIeeh formula.
Table 67. — Average deviation vAthout regard to sign of total heat-produdion as predicted
by linear equations frotn actual heat-production.
Series. N
Prediction from
body-weight
in kilograms.
I.
Prediction from 1 Prediction from '
body-surface, 1 body-surface, |
Meeh formula. 1 heights-weight chart.
II. III.
Men.
EiQuations based on Gephart and Du Bois
selection :
I First supplementary series
28
19
17
64
72
36
68
91.1= 5.67 p. ct.
99.4= 6.06 p. ct.
87.5= 5.45 p. ct.
RQ fi= sr^a n. ot.
100.0= fi.10n.ct. 100.S= fi-l.'in. pt. 1
III. Individuals omitted by Gephart and
149.1= 8.76 p. ct. ' 150.1= 8.82 p. ct.
109.0= 6.64 p. ct. 107.8= fi.."!? n. H:.
106.4= 6.25 p. ct.
97.4= 5.93 p. ct.
88.7= 5.46 p. ct.
14fi 1 — 10 Q9 n Pt.
Equations based on 64 individuals not in
Gephart and Du Bois selection:
v. Gephart and Du Bois selection
Women.
Equations based on original series:
VI. Supplementary series
88.1= 5.43 p. ct.
150.0=11.21 p. ct.
87.4= 5.38 p. ct.
14Q 0=11 1.*? r> nt.
Equations based on supplementary series:
VII. Original series
96.1= 7.09 p. ct. Qfi a— 7 n.<; r> nt. OS 1 = R S7 ^ ot.
Turning to the average de\aations without regard to sign, we note
from table 67 that in the whole series of 64 individuals the three
methods give deviations of only 109, 108, and 97 calories or stand in
the ratio 6.64 : 6.57 : 5.93 per cent. Thus the difference in the per-
centage error of predicting from body-weight and body-surface by
the Du Bois height-weight chart is only 6.64—5.93=0.71 per cent.
For the 72 individuals of the Gephart and Du Bois selection the
average de^dations for the three methods of prediction are 88.1, 87.4,
and 88.7 calories, or stand as 5.43 : 5.38 : 5.46 per cent. Thus body-
weight is a little better than body-surface by the height-weight chart
as a basis of prediction. In the two feminine series the absolute error
in calories is considerably larger, the percentages ranging from 6.87
to 11.21. In both feminine series the Du Bois height- weight chart
gives the lowest and body- weight the highest average deviation. The
height- weight chart is therefore the best and body-weight the worst
basis for prediction.
176 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Turning to the square root of mean-square deviation as given in
table 68 for our most critical test of the three methods, we find that for
the first series of 64 men and for the supplementary series of women the
Du Bois height-weight chart gives closer prediction than body- weight.
The differences in terms of percentages of the mean heat-production of
the groups dealt with are 8.48—7.65 =0.83 per cent for the men and
12.96-12.63=0.33 per cent for the women.
In the Gephart and Du Bois selection, body-weight and body-
surface by the Du Bois height-weight chart are equally good as a basis
for prediction, differing by only 6.79 —6.79 = 0.00 =«=per cent. The origi-
nal women also show practical identity in the results of the two methods
of prediction, the difference being only 8.87— 8.89 = —0.02 per cent.
Table 68. — Square root of mean-square deviation of total heat-production as predicted
by linear equations from the actual heat-production.
Series.
N
Prediction from
body-weight
in kilograms.
I.
Prediction from
body-surface,
Meeh formula.
II.
Prediction from
body-surface,
height-weight chart.
III.
Men.
Equations based on Gephart and Du Bois
selection:
I. First supplementary series
28
19
17
64
72
35
68
111.8= 6.97 p. ct.
143.8= 8.77 p. ct.
170.9 = 10.04 p. ct.
139.2= 8.48 p. ct.
110.2= 6.79 p. ct.
173.5 = 12.96 p. ct.
120.2= 8.87 p. ct.
108.0= 6.73 p. ct.
143.5= 8.75 p. ct.
172.6 = 10.14 p. ct.
138.3= 8.43 p. ct.
109.5= 6.75 p. ct.
171.8 = 12.84 p. ct.
119.8= 8.84 p. ct.
113.9= 7.10 p. ct.
134.9= 8.23 p. ct.
132.9= 7.81 p. ct.
125.6= 7.65 p. ct.
110.2= 6.79 p. ct.
169.1 = 12.63 p. ct.
120.4= 8.89 p. ct.
II. Second supplementary series
III. Individuals omitted by Gephart and
Du Bois
Equations based on 64 individuals not in
Gephart and Du Bois selection :
v. Gephart and Du Bois selection
Women.
Equations based on original series :
Equations based on supplementary series:
VII. Original series
Possibly the results slightly favor the prediction of heat-production
from the Du Bois height-weight chart, but the differences are by no
means so large as would be impUed by the statements of those who have
urged that heat-production is proportional to body-surface but not to
body-weight. Thus, in the instance among the larger series (IV-VII)
most favorable to the body-surface theory, i.e., that in which there is
a square root of mean-square deviation of 7.65 per cent in predicting
the metabolism of the individuals of an unmeasured series from body
surface and of 8.48 per cent in predicting from body-weight, the error
of prediction is only 8.48—7.65=0.83 per cent greater when body-
weight is used as a base. We shall return to these problems in a
subsequent section.
Summarizing the results of these tests of body-surface as measured
by the Du Bois height-weight chart in comparison with body-weight
A CRITIQUE OF THE BODY-SURFACE LAW. 177
as a basis of the prediction of the heat-production of a subject, we note
the following points from the two major series of each sex (series
IV-VII, tables 60-62, 66-68).
1. In testing the two bases of prediction, body- weight and body-
surface, by the average de\4ation with regard to sign of the predicted
from the actually obsen^ed values, we find that in predicting by the
use of mean heat-production per irnit of weight and of mean heat-
production per unit of surface area, body-surface gives the lower
average de\'iation in three of the four series (table 60). ^Tien pre-
diction is made by means of the linear regression equations, body-
surface gives the lower average de\'iation in all four series (table 66).
2. In testing the two bases of prediction by means of the average
de\dation without regard to sign of the predicted from the observ'ed
values, we find that in predicting from mean heat per unit of weight
and from mean heat per unit of area, body-surface is the better basis
of prediction in all four cases (IV-VII, table 61). In predicting bj^ the
use of equations we find that surface is the better basis of prediction in
three of the four cases, but sUghtly worse than body-weight in series
V, table 67.
3. In testing the two bases of prediction bj^ the square root of
mean-square de\'iation of the predicted from the observed values, we
find that in predicting from mean heat-production per unit, body-
surface gives lower de\4ations from the actuallj^ measured heat-
productions than body-weight (table 62). In predicting by equations,
body-sm-face gives the closer agreement of prediction with observation
in two of the series (IV, VI), but the two methods are, practically
speaking, equally good in the other two series (V, VII, table 68).
The net result of this analysis seems to be that metaboUsm can be
predicted more accurately from body-surface than from bodj'-weight.
The difference between these two means of prediction depends in a
very large degree upon the method of calculation used, and somewhat
upon the criterion of accuracy of prediction adopted. With the best
methods of calculation the difference between the accuracy of prediction
from body-weight and that from body-surface is not very large.
8. FURTHER TESTS OF THE VALUE OF BODY- WEIGHT AND BODY-SURFACE
FOR ESTIMATING TOTAL HEAT-PRODUCTION.
The practical importance of the solution of the problem of predict-
ing the metabolism of the indi\'idual with the highest attainable degree
of accuracy is so great that we shall apply one further test of the rela-
tive value of body-weight and body-surface area as measured by the
Du Bois height-weight chart. In the preceding tests we have adhered
strictly to the procedure which is theoretically the best and which
fulfills exactly the conditions to be met in practice. That is, in the
case of a subject whose metabolism is assumed to be unknown, we have
178 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
predicted the heat-production from constants based on other series
of individuals taken as the bases of standard constants. The compari-
son of heat-productions thus calculated with those which have been
actually determined furnishes a test of the accuracy of prediction by
the several methods to be tested.
From the theoretical side it is evident that in testing the value of
any method of predicting metabolism, the measurement of an indi-
vidual subject should not be included in the series upon which the
constant or equation used in predicting his own metabolism is based.
In other words, the metabolism of an individual should not be predicted
from itself. This error has in essence been made by earlier writers in
tests of the validity of the body-surface law.
But while a single aberrant subject might have great weight in
determining a standard constant based on a small group of individuals,
the importance of any single metabolism measurement rapidly de-
creases as the number included in the group becomes larger. Thus
in our series of males one individual has a weight of only 1/136 and in
our series of females one individual has a weight of only 1/103 in
determining the constant for the whole series. In predicting the
metabolism of really, and not merely supposedly, unknown subjects
in the hospital ward the clinician should naturally use the constants
based on our 136 men, not on the 72 of the Gephart and Du Bois
selection or the 64 others. The same is true of the 103 women as com-
pared with the two subseries of 35 and 68 individuals.
Since prediction constants based on these series, the largest avail-
able up to the present time, will be used in the calculation of controls,
it seems desirable to determine the error of prediction of the heat-
productions of the individual subjects, considered unknown, from
prediction constants based on the series as a whole. If we follow the
old practice of estimating the metaboHsm of a subject by multiplying
his body-weight by the average heat-production per kilogram of body-
weight, or his body-surface by the average heat-production per square
meter of body-surface, we employ the following average values per
24 hours :
For men, AT = 136:
Mean calories per kilogram 25.697
Mean calories per square meter of body-surface by height-weight chart 925.471
For women, iV = 103 :
Mean calories per kilogram 24.457
Mean calories per square meter of body-surface by height-weight chart 850.010
If, on the other hand, we desire to use the method proposed in
this paper of predicting heat-production by use of regression equations,
we have the following :
For men:
A =617.4934- 15.824 u) A = -254.546+1070.464 a .
D
For women :
A = 884.528+ 8.227w A= 333.618+ 638.610 a .
D
A CRITIQUE OF THE BODY-SURFACE LAW.
179
The results of predicting the heat-production of the 136 individual
men and of the 103 indi\ddual women by these four methods are shown
in table 69. Here the deviations of the calculated heat-production in
calories per day are shown in units of 75 calories per day range as indi-
cated in the first column. The frequencies of de\dations of given grade
are shown for the four different methods of calculation and for the
two sexes in the following eight columns. This table brings out various
facts which are not shown by the other methods of comparison hitherto
employed.
1. The deviations of the predicted from the actually observed
heat-productions may be very great. Differences of 188 calories and
over, either above or below the observed values, occur in many cases.
Table 69. — Comparison of amounts and frequencies of error by different methods of
prediction based on all men and women.
De^'iation of
calculated from
observed heat-
production in
calories per day.
Men.
!
Women.
li
"3 .
.a «
ge
regression
f heat on
weight.
I heat on
surface.
mean heat
r kilogram.
"3 .
(0 u
a »
IS
s s
regression
f heat on
weight.
regression
f heat on
surface.
>>fe
>. ft
>. o
>>
° >> S
>> ft
>> o
>. o
PQ a
pq
a
r<^
K a
«
e
09
+863 to +937
1
+788 to +862
_
+713 to +787
+638 to +712
+563 to +637
3
+488 to +562
1
2
+413 to +487
2
2
+338 to +412
2
3
+263 to +337
6
2
2
2 3
4
+188 to +262
7
5
9
5 7
4
7
7
+ 113 to +187
16
14
13
15 7
13
12
13
+ 38 to +112
20
34
24
J6 12
20
22
21
- 37 to + 37
31
34
39
JO 16
24
23
26
- 38 to -112
23
26
22
29 20
22
23
18
-113 to -187
14
11
19
9 15
8
8
10
-188 to -262
13
6
7
9 6
5
3
5
-263 to -337
1
3
1 6
3
5
3
-338 to -412
1
1
1
••
2. The distribution of the errors of estimation is not chaotic, but
remarkably regular in all cases. The errors form monomodal more
or less symmetrical distributions, i.e., they are distributed around
a maximum control frequency.
3. The errors of estimation in the case of prediction from average
heat-production per kilogram of body-weight are obviously far greater
in both men and women than those resulting from any other method.
The errors by this method tail off in the positive direction with a
number of errors beyond the 338-412 calories class in the women.
Obviously, prediction from mean calories heat-production per kilo-
gram of body-weight gives bad results in both sexes, and particularly
180 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
bad results in the case of the women. From mere inspection of the
frequency distributions of this series of errors it is impossible to dis-
criminate between the value of the three other methods of prediction.
Having recourse to the three tests of accuracy of prediction used
in the foregoing discussion we find the following results from the
ungrouped deviations. The average deviations of the predicted from
the actually observed values with regard to sign are the following:
Calculated from body-weight ^^^- Women. Difference.
By means +15.346 +32.243 +16.897
By equations - 0.007 - 0.019 + 0.012
Difference +15.339 +32.224
Calculated from body-surface
By means - 0.919 + 2.816 + 1.897
By equations + 0.015 + 0.029 + 0.014
Difference + 0.904 + 2.787
This comparison brings out with great clearness three important
results.
1. The average error with regard to sign of prediction from average
heat-production per unit is enormously greater than that in prediction
by the use of regression equations. This is true whether body-surface
or body-weight be used as a basis of prediction.
2. The errors in predictions from body-surface by use of the mean
heat per unit of body-surface in the standard series is far lower than
that resulting from prediction from body-weight.
3. The errors of prediction are in all cases larger in the calculations
for women than the comparable values for men.
As far as it goes, therefore, this test indicates the superiority of
body-surface over body-weight as a basis of prediction.
The superiority of the regression equations for purposes of predic-
tion over the old method of considering heat-production directly
proportional to body-weight or body-surface is the most striking, and
doubtless the most valuable, feature of this table. The old method
of estimation gives average errors of from 0.9 of a calorie to over
32 calories per day, depending on the sex and method of prediction
used. The new method of prediction does not in any case give an average
error of as much as 0.03 calorie per day!
Turning now to the average deviations without regard to sign of
the predicted from the observed values we have the following results :
Calculated from body-weight Men. Women. Difference.
By means 122.5 165.3 +42.8
By equations 97.6 98.0 +0.4
Difference + 24.9 + 67.3
Calculated from body-surface
By means 93.7 99.7 + 6.0
By equations 92.0 97.2 + 5.2
Difference + 1.7 + 2.5
A CRITIQUE OF THE BODY-SURFACE LAW. 181
The constants in this table show:
1. That in all four comparisons prediction from means gives a
higher error than prediction by use of equations.
2. That prediction from body-surface gives lower average devia-
tions than prediction from body-weight. This is true whether predic-
tion is made by considering the production proportional to body-
weight or bodj'-surface, or as given by a linear equation.
3. That by all methods the error of prediction is larger in the
women than that due to comparable methods in the men.
In prediction from body-weight the disadvantage of the method of
estimation from average heat per imit is particularly conspicuous. It
gives an average error of 24.9 calories in men and 67.3 calories per
24 hours in women greater than prediction from equations based on
body-weight. In the case of prediction from body-surface the differ-
ence between the error resulting from the use of means and the use of
equations is not so great, but amounts to 1.7 calories in men and 2.5
calories in women.
Results secured by the use of equations are conspicuously more
consistent than those reached bj' prediction from means of heat-
production per unit of surface. For example, in the men the mean
error of the prediction of heat-production from the mean heat-produc-
tion per kilogram in the series as a whole is 28.8 calories per 24 hours
greater than prediction from the mean heat-production per square
meter of bodj^-surface in the whole series. For the women the differ-
ence is 65.6 calories. But when equations are used the excess error of
28.8 calories in the men shrinks to 5.6 calories and the excess error of
65.6 calories in the women shrinks to 0.8 calorie. Again, in comparing
the men and the women we not€ differences of 42.8 and 6.0 calories
when prediction is made by considering heat-production proportional
to body-weight or body-surface, but these differences are only 0.4
and 5.2 calories per day when prediction is made bj' equations.
Turn now to our third and final standard of comparison — the square
root of mean-square error of prediction.
Calculation from bod}--weight •M'"»- Women. Diferenee.
By means 160.99 225.74 +64.75
By equations 123.88 123.03 — 0.85
Difference + 37.11 +102.71
Calculation from body-surface
By means 119.44 126.81 +7.37
By equations 117.21 122.85 + 5.65
Difference + 2.23 + 3.95
The conclusions to be drawn from this table are in essential agree-
ment with those drawn from the preceding tests. Prediction from
body-surface gives a far lower error than prediction from body-weight
when heat-production is considered directly proportional to weight
182 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
and surface, but the errors of prediction are much more nearly equal
when equations connecting body-weight and body-surface on the one
hand and daily heat-production on the other are used. Thus differ-
ences of 41.55 and 98.93 calories in the results of prediction of metab-
olism by the use of mean calories per kilogram and mean calories per
square meter are reduced to 6.67 and 0.17 calories when equations are
used; and differences of 64.75 and 7.37 calories in the deviation of pre-
dicted from the observed standards in men and women when mean
heat per kilogram and per square meter are used as a basis of predic-
tion reduce to 0.85 and 5.65 calories when equations are employed
for prediction.
Finally, comparing body-weight and body-surface as bases of
prediction when the more satisfactory equation method is used for
prediction, one finds surprisingly little difference between them. For
men body-weight gives a square root of mean-square deviation of
123.88 calories per day, while body-surface gives 117.21 calories or
only 6.67 calories less. For women the difference is only 123.03 — 122.86
=0.17 calorie per 24 hours. The reader must note that these differ-
ences are based on an average metabolism of 1631.74 calories per 24
hours in men and 1349.19 calories in women. Thus the differences
are less than 0.5 per cent of the total metabolism in each case.
On the basis of such differences, who is prepared to assert that
metabolism is proportional to body-surface but not to body- weight?
9. PREDICTION OF HEAT-PRODUCTION FROM TWO PHYSICAL
CHARACTERS,
We shall now approach the problem of the basis of comparison of
the metabolism of various individuals along what we believe to be an
entirely novel line of attack. In a preceding section we have empha-
sized the view that the true test of any method for the reduction of the
metabolism of individuals of different size and shapes to comparable
terms is its capacity for predicting an unknown metabolism. This we
believe to be not merely a logically sound position, but the one upon
which the results of the greatest practical importance can be based.
Aside from the purely physiological problem of the value to be assigned
to the basal metabolism coefficient for the human species, the precise
determination of the metabolism of the normal individual underlies a
wide range of practical medical, economic, and social problems.
Take one illustration merely. A typhoid or goitre subject is placed
in the respiration chamber and basal metabolism is calculated from
gaseous exchange. This is merely a technical matter. The theoretical
question which must be solved before these observational data have
any medical significance is: What value should be assigned to the
metabolism of this individual on the basis of his measurable bodily
characters on the assumption that he is in normal health? In short, we
A CRITIQUE OF THE BODY-SURFACE LAW. 183
are forced to use his predicted metabolism in health as a basis of com-
parison with his measured metaboUsm in disease, in order to reach any
conclusion of value concerning the influence of disease on metabolism.*"
We shall now consider the possibility of predicting the basal metab-
oHsm of an individual by the simultaneous use of two physical charac-
ters. Should the method of the use of two or more characters prove
more advantageous than the use of a single character, the selection of
the most suitable physical characters for use in the estimation of the
normal metabolism of the individual will present a problem of some
practical importance. At present, it is quite natural to take the two
measurements which are most easily and generally made, namely
stature and body- weight.
Let s= stature, ly = weight, /i = total heat-production. Then the
prediction of h from both s and w will be carried out by the formula "
l—rj^ (T^ l—r^,/ (X,
or in terms more convenient for purposes of calculation
n=n— — j — — — - • — 10 — — j 1 — • - 5
Or following another notation *- we may determine the prediction
equations as follows :
The individual partial regression slopes are given by
n . — r '^^^ n — r »'^^^
•rtrA s' tch v>yah — w' sh
where the three standard deviations of the second order, .^o-a, ^<r^
„A 0-, , are given by
.o-A
.ch<^s=(T, Vl-r,,/ Vl-„r,r = o-, Vl-r,,2 \^i-^r,J
sh(^.=<^^ Vl-?-,,/ \/i-^r,f,- = (r^ Vl-r,,2 \/l-,r„.
*> The emphasis which has been laid upon the variation in metabolism from individual to
individual throughout this volume should have convinced the reader that conclusions concerning
the influence of any disease on metabolism can never be safely drawn from the determinations
based on a single individual. It is only when a number of comparisons are made that conclusions
may be safely drawn. This point will be further considered in Chapter "VTII.
»^ In this volume no attempt is made to discuss in detail the statistical theory- employed, or
even to give full citations of the Literature. Multiple prediction formulas are treated by Pearson,
Phil. Trans. Ser. A, 1896, 187, p. 253; loc. cU. 1898, 192, p. 169. Yule, An Introduction to the
Theory of Statistics, London, 1911, Chapter XII gives a general discussion of the subject with
bibliography. Some of the formulas have been given in the form used by Goring in The English
Convict, London, 1913.
*' Yule, Introduction to the Theory of Statistics, 1911, p. 236.
184 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Substituting constants, we have the following prediction equations
based on our principal series.
For the Gephart and Du Bois selection, iV = 72 h= 111.296+14.876 u)+3.300s.
For the 64 men not included in Gephart and Du Bois selection,
h = -603.317 + 12.488 w+8.275 s.
For all men of both series, A^ = 136 /i= -314.613 + 13.129 «;+6.388 s.
For the original women, A^ = 68 h= 664.012+10.441 w+0.753s.
For supplementary series of women, N = 35 h= 477.082+ 5.577 w +3.237 s.
For all women, iV = 103 h= 713.016+ 8.063 ly+l.lies.
These equations have been used for purposes of prediction and the
calculated heat-productions compared with the actually observed pro-
ductions, just as was done in the preceding sections in prediction from
standard average values or by means of a linear equation based on one
bodily measure only.
Thus we have predicted the total heat-production of the 64 indi-
viduals not included in the series selected by Gephart and Du Bois
from equations based on stature and body-weight in the Gephart and
Du Bois selection. Conversely, to secure a more exhaustive test of
the value of our prediction formulas, we have estimated the total heat-
production of the 72 individuals constituting the Gephart and Du Bois
selection from the data of the 64 other males. Similarly, the total
heat-production of the 35 supplementary women has been predicted
from equations involving the constants for stature and body-weight
in the original feminine series, and the values for the individuals of the
original series have been predicted from the data of the supplementary
series of women. Details are given on pages 161-176, tables 60-68.
The reader will bear in mind the fact that these predictions and
comparisons with actually observed constants have been made for the
purpose of determining the most suitable method for estimating the
metabohsm of a subject. The division of our materials to make this
test possible naturally increases somewhat the probable errors of the
constants of the prediction formulas. After the most suitable method
for the calculation of the metabolism of an unknown subject has been
determined, the constants for actual use in the establishment of stand-
ard control or check values will be based upon all the data at our
disposal. In examining the results of the prediction of the metabolism
of series of individuals by means of equations involving both body-
weight and stature, our object has been to ascertain whether this
method gave sensibly better results than other methods of prediction
hitherto employed.
Since it has been shown in a preceding chapter that the correlation
between stature and metabolism is relatively small as compared with
that between body-weight and metabolism, it will be unnecessary to
compare the results of prediction by the use of equations involving
both stature and body-weight with those based on stature only. A
more valuable test of the possible superiority of prediction from both
A CRITIQUE OF THE BODY-SURFACE LAW.
185
stature and body-weight may be obtained by a comparison with the
results of prediction from body-weight only.
Since it has appeared that the prediction from body-surface as
estimated by the Du Bois height-weight chart gives more reliable
results than prediction from body-surface as computed from the Meeh
formula, it seems superfluous to make the comparisons of the prediction
methods here under consideration with those involving body-surface as
measured by this now antiquated formula.
In the following tables we shall, therefore, compare the errors of
estimation found in predicting metabolism from multiple regression
equations invohang stature and body-weight with those found by
considering it proportional to body- weight and to body-surface by the
Table 70. — Comparison of average deviation (in calories, icith regard to sign) from the actual caloric-
output, of heat-production calculated on the one hand from multiple regression equations involving
body-weight and stature and on the other from (a) the mean heat-production per unit of body-weight
and of surface by the Du Bois height-weight chart and from (b) the regression of total heat on body-
weight and on surface area by the Du Bois height-weight chart.
Prediction from
Comparison with res\ilts obtained by other methods.*
regression
Difference from
Difference from
Difference from
Difference from
Series.
equations
prediction from
prediction from
prediction from
prediction from
involving stature
average heat per
regression equation
average heat per
regression equation
and weight.
square meter of
for total heat on
kilogram of
for total heat on
body-siirface.
body-surface.
body-weight.
body-weight.
I.
II.
III.
IV.
V.
I
+ 14.8 = 0.92 p. ct.
-10.2 = 0.64 p. ct.
-10.0 = 0.62 p. ct. + 3.0 = 0.18p. ct.
+7.3 = 0.45 p. ct.
II
+ 10.0 = 0.61 p. ct.
+ 5.3 = 0.32 p. ct.
+ 3.9 = 0.24 p. ct. - 28.3 = 1.73 p. ct.
-2.5 = 0.15 p. ct.
III...
- 5.1 = 0.30p.ct.
-36.0 = 2.12 p. ct.
— 33. 1 = 1.95 p. ct. — 62.5 = 3.67 p. ct.
-4.6 = 0.27 p. ct.
IV. . . .
+ 8.1 =0.50 p. ct.
+ 6.7 = 0.41 p. ct.
+ 5.6 = 0.35 p. ct. - 26.4 = 1.60 p. ct.
-1.5 = 0.08 p. ct.
V
- 6.5 = 0.40 p. ct.
+ 3.0 = 0.18 p. ct.
+ 2.4= 0.15 p. ct.
+ 3.5 = 0.22 p. ct.
-0.9 = 0.06 p. ct.
VI. ...
+77.7 = 5.80 p. ct.
- 0.2 = 0.02 p. ct.
+ 4.5 = 0.33 p. ct.
-114.0 = 8.52 p. ct.
-0.2 = 0.02 p. ct.
VII .. .
—49.8 = 3.68 p. ct.
-20.1 = 1.48 p. ct.
- 1.7 = 0.12 p. ct.
- 66.8 = 4.93 p. ct.
-3.5 = 0.25 p. ct.
Men. .
=±=00.0 = 0.00p. ct.
— 0.9 = 0.06 p. ct.
± 0.0 = 0.00 p. ct.
- 15.4 = 0.94 p. ct.
±0.0 = 0.00 p. ct.
Women
i 00.0 = 0.00 p. ct.
- 2.S = 0.21p. ct. ; ± 0.0 = 0.00p.ct.
- 32.2 = 2.39 p. ct.
±0.0 = 0.00 p. ct.
* The differences in these columns are obtained from the first column of this table and the entries of pre-
ceding tables as follows: column II from III of table 60; column III from III of table 66; column IV from I
of table 60; column V from I of table 66.
Du Bois height-weight chart, and when given by a linear-regression
equation in which heat is predicted from body-weight or from body-
surface by the height-weight chart.
Table 70 gives the average deviations with regard to sign of the
theoretical heat-productions calculated by the multiple-prediction
equation from the observed values and compares these deviations with
those computed by the four other methods. Comparing the average
deviations w4th regard to sign of the constants computed by the various
methods in table 70, we note that in 2 of the 4 larger series (IV-VII),
in which the prediction of the metaboHsm of the individuals of one
series is made from the equations based on another series of individuals
of the same sex, prediction by the simultaneous use of stature and
186 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
body-weight gives a slightly larger average error than prediction from
body-surface by the Du Bois height-weight chart when prediction
from body-surface is made by considering that the heat-production of
an individual is given by _
h = ajij)
where ar, is the superficial area of the individual by the Du Bois height-
weight chart and hf, the average heat-production per square meter in
the standard population. In two cases, VI and VII, it gives a smaller
average deviation from the ideal zero error.
When the best measure of heat-production on the basis of a single
physical measurement is supposed to be given by
as we have demonstrated to be the case, the multiple regression equa-
tion gives slightly higher error in three of the four larger series.
The difference between the results of predicting heat-production
by the use of multiple regression equations involving stature and
weight and those due to the use of linear equations for prediction
from body-surface by the Du Bois height-weight chart is, however,
very slight indeed. In only 1 of the 8 comparisons is the difference
over 7 calories. The difference in the percentage value of the average
deviations with regard to sign of the two methods of prediction is in only
1 case over 0.5 per cent in the 8 comparisons based on larger series.
When the values of the individual subjects are computed from
equations based on the entire material for each sex (136 men and 103
women, as given in the two lower rows of the table) the average devia-
tion with regard to sign is theoretically 0, and for all practical purposes
empirically 0 in our actual observational data. As far as this criterion
can show, all three regression methods seem equally good when predic-
tions of individual values are made from the constants of the population
to which they belong. Therefore, either of these three methods neces-
sarily gives better results as measured by this criterion than either of
the two methods of calculation from average heat-production per unit
of weight or per unit of body-sm-face area in the standard series.
Turning now to the average deviations without regard to sign, as
shown in table 71, we note practically the same relationship between
the results for the 3 sets of formulas as in the preceding comparisons.
Confining our attention to the 4 larger groups (IV-VII), in which
prediction is made from the constants of another series of individuals,
we note that in 5 of the 8 comparisons the multiple prediction equation
shows (as indicated by the positive sign) a slightly larger, but only
slightly larger, error than prediction from body-surface. The difference
is in no case as much as 4.5 calories. In percentages of the average
A CRITIQUE OF THE BODY-SURFACE LAW.
187
i
measured heat-productions for the group under consideration, the
differences in the errors of prediction range from 0.00 per cent to
0.29 per cent.
If the test be based upon the whole series of men and of women
we find that the multiple regression equations give better results in
every case but one. In this case prediction from the linear equation
for total heat on body-surface area gives a mean deviation 0.2 calorie
per day less in the men than the multiple regression equations. This
represents a difference of 0.01 per cent only.
The comparison on the basis of square root of mean-square devia-
tion is made in table 72. The results show that in 6 of the 8 larger
series (IV-VII) in which prediction is made from constants based upon
Table 71. — Comparison of average deviation (in calories, without regard to sign) from the actual caloric-output,
of heat -production calculated on the one hand from multiple regression equations iruolving body-weight and
stature and on the other from (a) the mean heat-production per unit of body weight and of surface by the
Du Bois height-weight chart and from (b) the regression of total heat on body-weight and on surface area
by the Du Bois height-weight chart.
Series.
Prediction from
regression
equations
involving stature
and weight.
I.
Comparison with results obtained by other methods.*
Difference from
prediction from
average heat per
square meter of
body-surface.
II.
Difference from
prediction from
regression equation
for total heat on
body-surface.
III.
Difference from
prediction from
average heat
per kilogram of
body-weight.
IV.
Difference from
prediction from
regression equation
for total heat on
body-weight.
V.
I
87.9= 5.48 p. ct.
99.1= 6.04 p. ct.
127.2= 7.48 p. ct.
101.7= 6.20 p. ct.
88.6= 5.46 p. ct.
150.0= 11.21 p. ct.
94.0= 6.94 p. ct.
92.2= 5.65 p. ct.
93.6= 6.94 p. ct.
- 6.2 = 0.38 p. ct.
- 0.6 = 0.04 p. ct.
+ 17.8 =1.05 p. ct.
+ 1.9 = 0.12 p. ct.
- 0.1 = 0.00 p. ct.
+ 0.1 = 0.01 p. ct.
- 0.6 = 0.04 p. ct.
- 1.5 = 0.10 p. ct.
- 6.1 = 0.45p. ct.
- 1.7 = 0.10p.ct.
- 1.7 = 0.11 p. ct.
+20.8=1.23 p. ct.
+ 4.3 = 0.27 p. ct.
- 0.1 = 0.00 p. ct.
+ 3.9 = 0.29 p. ct.
+ 0.9 = 0.07 p. ct.
+ 0.2 = 0.01 p. ct.
- 3.6 = 0.26 p. ct.
- 4.9 = 0.30 p. ct.
- 27.9=1.71 p.ct.
-107.4 = 6.31 p. ct.
- 38.9 = 2.37 p.ct.
- 17.8= 1.09 p.ct.
- 93.7 = 7.00 p.ct.
- 75.8 = 5.59 p.ct.
- 30.3 = 1.86 p.ct.
- 71.7=5.31 p.ct.
- 3.2 = 0.19 p.ct.
— 0.3 = 0.02 p.ct.
-21.9 = 1.28 p.ct.
- 7.3 = 0.44 p.ct.
+ 0.5 = 0.03 p.ct.
=±= 0.0 = 0.00 p.ct.
— 2.1 =0.15 p.ct.
— 5.3 = 0.33 p.ct.
- 4.4 = 0.32 p.ct.
II
Ill
IV
V
VI
VII
Men
Women
* The differences in these columns are obtained from the first column of this table and the entries of preceding
tables as follows: column II from III of table 61; column III from III of table 67; column IV from I of table 61;
column V from I of table 67.
a different group the error of prediction is greater by the equations
here being tested than by prediction from body-surface by the Du Bois
height-weight chart. The difference between the two methods is, how-
ever, very sUght. In working units, it ranges from 1.1 to 4.7 calories
per day. In terms of percentages of the average daily heat-production
of the series of indi\dduals dealt with, the differences in the errors of
estimation by the multiple-regression equations and the prediction
method based on body-surface range from 0.04 to 0.33 per cent.
Turning to a comparison of the various methods of calculation
when the whole series of men and women are used, it appears in every
case except one that the multiple regression equations give the more
accurate prediction of metabolism.
188 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Now, if we return to the differences in these three tables and con-
sider together the three criteria of excellence of prediction — each of
which has some advantages but neither of which is perfect — as a basis
for a generalization concerning the value of the two methods under
consideration, we note the following points :
1. The results in the first difference column show that prediction
from the two direct measurements stature and body-weight gives more
accurate results than the method of calculation from body-surface
area by the Du Bois height-weight chart heretofore employed.
2. The second difference column suggests that when the more
accurate method of prediction by means of linear regression equations
suggested in this volume is substituted for the old method slightly more
Table 72. — Comparison of square root of mean-square deviation {in calories) from the actual caloric-output,
of heat-production, calculated on the one hand from multiple regression equations involving body-weight and
stature and on the other from (a) the mean heat-production per unit of body-weight and of surf ace by the
Du Bois height-weight chart and from (b) the regression of total heat on body-weight and on surface area
by the Du Bois height-weight chart.
Series.
Prediction from
regression
equations
involving stature
and weight.
I.
Comparison with results obtained by other methods.*
Difference from
prediction from
average heat per
square meter of
body-surface.
II.
Difference from
prediction from
regression equation
for total heat on
body-surface.
III.
Difference from
prediction from
average heat
per kilogram of
body-weight.
IV.
Difference from
prediction from
regression equation
for total heat on
body-weight.
V.
I
110.7= 6.90 p. ct.
139.4= 8.50 p. ct.
148.6= 8.73 p. ct.
130.3= 7.94 p. ct.
111.3= 6.86 p. ct.
173.5 = 12.96 p. ct.
121.0= 8.93 p. ct.
117.4= 7.19 p. ct.
117.4= 8.70 p. ct.
-6.6 = 0.41 p. ct.
+5.0 = 0.30 p. ct.
+9.5 = 0.55 p. ct.
+ 1.8 = 0.11 p. ct.
+0.7 = 0.05 p. ct.
-0.5 = 0.04 p. ct.
-1.1 = 0.08 p. ct.
— 2.0 = 0.13 p. ct.
-9.5 = 0.70 p. ct.
- 3.2 = 0.20 p. ct.
+ 4.5 = 0.27 p. ct.
+ 15.7 = 0.92 p. ct.
+ 4.7 = 0.29 p. ct.
+ 1.1 = 0.07 p. ct.
+ 4.4 = 0.33 p. ct.
+ 0.6 = 0.04 p. ct.
+ 0.2 = 0.01 p. ct.
- 5.5 = 0.41 p. ct.
- 25.5= 1.59 p. ct.
- 31.9= 1.95 p. ct.
-119.5= 7.03 p. ct.
- 59.2= 3.61 p. ct.
- 20.9= 1.29 p. ct.
-154.3 = 11.53 p. ct.
- 80.1= 5.92 p. ct.
- 43.6= 2.68 p. ct.
-108.4= 8.03 p. ct.
- 1.1 = 0.07 p. ct.
- 4.4 = 0.27 p. ct.
-22.3 = 1.31 p. ct.
- 8.9 = 0.54 p. ct.
+ 1.1 = 0.07 p. ct.
=t 0.0 = 0.00 p. ct.
+ 0.8 = 0.06 p. ct.
- 6.5 = 0.40 p. ct.
- 5.7 = 0.42 p. ct.
II
Ill
V.:::::::
VI
VII
Men
Women . . .
* The differences in these columns are obtained from the first column of this table ajid the entries of the pre-
ceding tables as follows: column II from III of table 62; column III from III of table 68; column IV from I of
table 62; column V from I of table 68.
accurate predictions may be made from body-surface area than from
multiple regression equations involving height and weight.
3. The third difference column shows that practically without
exception (25 out of 27 tests) better prediction can be made from
multiple regression equations than by considering heat-production in
the individual as given by (body- weight X mean heat-production per
kilogram in the control series).
4. Even when the superior method of predicting from the regression
of heat-production on body-weight introduced in this paper is employed
instead of the older method, the multiple regression equation in which
prediction is based on both stature and body-weight gives far better
results (as shown by the preponderance of negative signs in the final
difference column) than prediction from weight alone.
A CRITIQUE OF THE BODY-SURFACE LAW. 189
10. PREDICTION OF HEAT- PRODUCTION FROM TWO PHYSICAL
CHARACTERS (STATURE AND BODY- WEIGHT) AND AGE.
In the foregoing section we demonstrated the efficiency of equations
invoMng stature and body-weight for the prediction of the heat-
production of the individual. From the analyses in the preceding
chapter it is clear that age is another factor which should be taken
into account in estimating the basal metabolism of the individual.
Our problem in this section is therefore twofold: First, we must
determine some means of including an age factor in our prediction
equation. Second, we must, on the basis of the available observational
data, replace the symbols in these equations by numerical constants
and determine empirically whether equations invohdng age as well as
body-weight and stature show a superiority for the prediction of the
heat-production of the unknown subject. While Du Bois has given a
tentative correction for age we have not considered it worth while, in \dew
of the very approximate nature of his terms as given on page 123 to
apply his age correction in drawing a comparison between equations
based on body-surface and those based on stature, weight, and age.
Working in terms of partial correlations and variabilities, the
multiple-prediction formulas for the estimation of total heat-production
from stature, body-weight, and age require :
Partial correlation between weight and total heat-production for constant stature and
age, saT-u.h.
Partial correlation between stature and total heat-production for constant weight and
age, -itaTsh.
Partial correlation between age and total heat-production for constant weight and stature,
TL'sTak*
Partial correlation between age and stature for constant body-weight and daily heat-pro-
duction, h-.,Tas.
Partial correlation between stature and weight for constant age and daily heat-production.
These are:
^itA —
T.k =
ICO' th
T„h —
res' ah
T =
lA^rtT
V(l -r,,2-r^2-r„,/-h2r„,r„^0 V(l -r„2-r,;,*_r„,2-f-2r„.r,,r„)
^gA ( 1 ^atr ) ^aa ^g A fws^'vh "T^gir (^os^trA I ^ah''ws)
V(l -r,«« -r^s'-rJ-\-2r,„r,^^^,) V(l -r,J-r^^^-r,,,^-{-2r^^r,hr,,h)
^a;i(l fgyj ) fsaTth T\rafwh~TTtm{TgaTv:h'\~Tsh'fxca)
^»a(l ^Aw ) '^'kifka Tivsfva'T'1'h-a!\Thsfva'\~fhaTvi»)
\/( 1 - Th^^ - T^:- - r^/ +2r*^A/«.) V(l - TkJ - r„J^ - r,,^ -f-2r,,,r,,r« J
rswC^ -Tg/) -rasra,c-rh,rh,c-hraHirasrhtc+r^wrhs)
V(l -r„,2_r,,2 -r«2+2r^r<„rjV(l -r,,2_r,^2-r,.»+2r„Ar,^0
190 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The first three lead to the partial regressions which are required
for computing the variations in heat-productions associated with differ-
ences in weight, stature, and age. The last two are useful in checking
the partial variabilities. The partial regressions are :
ga wh sa' wh tea sh wa' sh ws ah ivs' ah
ihrw wah^s wsh^a
where the partial variabilities are given by
= (T, Vl -r,,2 Vl-„r,,2\/l-,„r„„2
,/T =/T -s/x—r 2 -v/i _ ^ 2 \/l _ « 2
= a^ Vl -r,,,2 Vl-,r,,„2 Vl-„,r«,.2
^,„;.o-. = 0-. Vl -rj Vl -vv^ Vlj-^^
= (r ■y/l—r 2\/l_ r.2\/l_, r 2
"s * -i # gt/j * X to' sA V X hw' ta
wsk<ra=<Ta Vl -r„,^ Vl -,r J Vl -.^r^''
^O'aVl— r 2\/l — r 2-y/l_ |. J
" * -•■ 'as '^ -•• «' ato '^ -"■ w»' ah
These give the characteristic equation
h = (h —sa^whW —waPsh's—waPahO) + .a^ wh^ -^ wa^ ah^ + wgP ah^
Substituting constants and having /i = total heat-production per 24
hours, ?x;= weight in kilograms, s= stature in centimeters, and a = age
in years, we have for the six series of adults dealt with :
Gephart and Du Bois selection, i\r = 72, /i= +175.4866+13.0642 w+4.9520s-9.1252a
Men other than Gephart and Du Bois selection, N = 64,
h=- 67.3458+13.6734 «)+5.7310s-6.1234a
Grand total men, A^ = 136, h = -\- 66.4730+13.7516u;+5.0033s-6.7550a
Original women, iV = 68, /i = +657.4595 + 10.3698 u;+1.3988s-3.5332a
Supplementary women, iV = 35, A = +491.3238+ 8.4793 u; +3.2667 s -4.8748 a
All women, iV = 103, /i = +655.0955+ 9.5634 «7 + 1.8496s -4.6756 a
The testing of these formulas is carried out in precisely the same
manner as that employed in dealing with those in which total heat-
production was predicted from body-weight and stature in the preced-
ing section. Thus tables 73 to 75 are quite comparable with tables
70 to 72. The first column gives the results of predictions of total heat-
production from weight, stature, and age. The five following columns
show the differences between these results and those obtained by other
methods. The final column shows the difference between prediction
from weight and stature as given in the first column of tables 70 to 72
and that from weight, stature, and age as given in the first column of
tables 73 to 75. The subtractions are so made that a minus sign denotes
a smaller error of prediction when the equation involving weight,
stature, and age is used. In taking these differences in the case of
A CRITIQUE OF THE BODY-SURFACE LAW.
191
I
the average de\iation of the calculated total heat-production with
regard to signs, the signs of the constants in the first column of table 70
and in the first column of table 73 are disregarded, and the differences
represent merely the difference in the numerical magnitudes of the
discrepancy between observation and prediction.
Considering the values in table 73, we see that in some cases the
equations involving weight, stature, and age give closer and in some
cases slightly wider average de\Tiations above or below the true value.
In the larger series (IV-VII and total men and women) the equations
Table 73. — Comparison of average deiiation {in calories, with regard to sign) from aztual, color ic-otUput
of heat-production calculated on the one hand from multiple regression equations involving stature,
body-iceight, and age and on the other from (a) the mean heat-production per unit of body-ueight and
bcay-surface by Du Bois height-weight chart, from (b) the regression of total heat on body-weight and
on bony-surface by the Du Bois height-weight chart, and from (c) the regression of total heat-production
on stature and body-weight.
Series.
Prediction from
regression
equations
involving
stature, weight,
and age.
I.
Comparisons with results obtained by other methods.*
Difference from
prediction from
average heat
per square
meter of
body-surface.
II.
Difference from
prediction from
regression
equation for
total heat on
body-surface.
III.
Difference from
prediction from
average heat
per kilogram of
body-weight.
IV.
Difference from
prediction from
regression
equation for
total heat on
body-weight.
Difference from
prediction from
regression
equation for
total heat on
stature and
weight.
VI.
I...
II..
III.
IV..
V...
VI..
VII.
Men
Women
cal. pet.
-1-20.0=1.25
-51.0 = 3.11
-36.8 = 2.16
-16.2 = 0.99
-\- 7.6 = 0.47
-1-30.8 = 2.30
- 2.7 = 0.20
± 0.0 = 0.00
± 0.0 = 0.00
cal. p.ct.
- 5.0 = 0.31
-1-46.3 = 2.82
- 4.3 = 0.25
-1-14.8 = 0.90
-f 4.1=0.25
-47.1=3.52
-67.2 = 4.96
- 0.9 = 0.05
- 2.8 = 0.21
cal. p.ct.
— 4.8 = 0.30
-^44.9 = 2.74
- 1.4 = 0.08
-f- 13.7 = 0.83
-h 3.5 = 0.22
-42.4 = 3.17
-48.8 = 3.60
=fc 0.0 = 0.00
=fc 0.0 = 0.00
cal. p.ct.
+ 8.2= 0.51
4- 12.7 =
- 30.8 =
- 18.3 =
-f 4.6 =
-160.9 = 12.02
-113.9= 8.41
- 15.3= 0.94
- 32.2= 2.39
0.77
1.81
1.11
0.28
cal. p.ct.
-1-12.5 = 0.78
-f38.5 = 2.35
-f-27.1 = 1.59
-f 6.6 = 0.40
-f 0.2 = 0.01
-47.1 = 3.52
-50.6 = 3.74
± 0.0 = 0.00
=fc 0.0 = 0.00
cal. p.ct.
+ 5.2 = 0.32
-1-41.0 = 2.50
4-31.7 = 1.86
+ 8.1=0.49
-I- 1.1 = 0.07
-46.9 = 3.50
-47.1 = 3.48
=•=00.0 = 0.00
=±=00.0 = 0.00
* The differences in these columns are obtained from the first column of this table and the entries of pre-
ceding tables as follows: column II from III of table 60; column III from III of table 66; column IV from I
of table 60; column V from I of table 65; column VI from I of table 70.
which take into account weight, stature, and age give somewhat better
results than those in which prediction is made by the other methods
employed.
The figures set forth in tables 74 and 75 are so striking that they
require but few words of discussion. Consider table 74 showing the
average de\4ations without regard to sign of the calculated from the
actually determined heat-productions in the several series of individuals
when the former are computed in various ways. With one single and
numerically insignificant (+0.7 =0.04 per cent) exception the 45 differ-
ences are negative in sign, showing that the error of prediction is smaller
when multiple regression equations involving weight, stature, and age
are used than when any of the other 5 methods of estimating the heat-
production of a subject is employed. In the larger series (IV-VII and
192 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
Table 74. — Comparison of average deviation (in calories, without regard to sign) from the actual coloric-
output, of heat-production calculated on the one hand from multiple regression equations involving
body-weight, stature, and age and on the other from (a) the mean heat-production per unit of body-
weight and of surface by the Du Bois height-weight chart, from (6) the regression of total heat on
body-weight and on body-surface, and from (c) the regression of total heat-production on stature and
body-weight.
Series.
Prediction from
regression
equations
involving
stature, weight,
and age.
I.
Comparisons Tvith resulte obtained by other methods.*
Difference from
prediction from
average heat
per square
meter of
body-surface.
II.
Difference from
prediction from
regression
equation for
total heat on
body-surface.
III.
Difference from
prediction from
average heat
per kilogram of
body-weight.
IV.
Difference from
prediction from
regression
equation for
total heat on
body-weight.
V.
Difference from
prediction from
regression
equation for
total heat on
stature and
weight.
VI.
I...
II..
III.
IV..
V...
VI..
VII.
Men
Women
cal.
88.6
98.8
86.8
91.1
79.1
109.7
75.8
81.2
84.6
p.ct.
= 5.52
= 6.02
= 5.10
= 6.55
= 4.87
= 8.20
= 5.60
= 4.98
= 6.27
cal. p-ct.
■ 5.5 = 0.34
- 0.9 = 0.05
-22.6 = 1.33
- 8.7 = 0.53
- 9.6 = 0.59
-40.2 = 3.00
-18.8 = 1.39
-12.5 = 0.77
-15.1 = 1.12
cal. p.ct.
- 1.0 = 0.06
- 2.0 = 0.12
-19.6=1.15
- 6.3 = 0.38
- 9.6 = 0.59
-36.4 = 2.72
-17.3 = 1.28
-10.8 = 0.66
-12.6 = 0.93
cal. p.ct.
- 4.2 =
- 28.2 =
-147.8 =
- 49.5 =
- 27.3 =
-134.0=10.01
- 94.0= 6.93
- 41.3= 2.53
- 80.7= 6.98
0.26
1.72
8.69
3.02
1.68
cal. p.ct.
■ 2.5 = 0.16
- 0.6 = 0.04
-62.3 = 3.66
-17.9 = 1.09
- 9.0 = 0.55
-40.3 = 3.01
-20.3 = 1.60
-16.4=1.01
-13.4 = 0.99
cal. pet.
+ 0.7 = 0.04
- 0.3 = 0.02
-40.4 = 2.37
- 10.6 = 0.65
- 9.5 = 0.59
-40.3 = 3.01
-18.2=1.34
-11.0 = 0.67
- 9.0 = 0.67
* The differences in these coliunns are obtained from tlie first column of this table and the entries of the
preceding tables as follows: column II from III of table 61; column III from III of table 67; column IV from
I of table 61; column V from I of table 67; column VI from I of table 71.
Table 75. — Comparison of square root of mean-square deviation (in calories) from the actual caloric-output
of heat-production calculated on the one hand from multiple regression equations involving body-weight,
stature, and age, and on the other from (a) the mean heat-production per unit of body-weight and of
surface by the Du Bois height-weight chart, from (b) the regression of total heat on body-weight and on
body-surface by the Du Bois height-weight chart and from (c) the regression of total heat on stature
and body-weight.
Series.
Prediction from
regression
equations
involving
stature, weight,
and age.
Comparisons with results obtained by other methods.*
Difference from
prediction from
average heat
per square
meter of
body-surface.
II.
Difference from
prediction from
regression
equation for
total heat on
body-surface.
III.
Difference from
prediction from
average heat
per kilogram of
body-weight.
IV.
Difference from
prediction from
regression
equation for
total heat on
body-weight.
V.
Difference from
prediction from
regression
equation for
total heat on
stature and
weight.
VI.
I...
II..
III.
IV..
V...
VI..
VII.
Men
Women
cal.
104.3 =
137.5 =
94.4 =
112.9 =
98.3 =
136.4 =
94.2 =
101.7 =
106.3 =
p.ct.
: 6.50
■■ 8.38
: 5.55
■■ 6.88
■■ 6.05
10.19
■■ 6.95
6.23
■ 7.88
cal. p.ct.
-13.0 = 0.81
-H 3.1 = 0.19
-44.7 = 2.63
-15.6 = 0.95
-12.3 = 0.76
-37.6 = 2.81
-27.9 = 2.06
-17.7 = 1.08
-20.5 = 1.52
cal.
- 9.6 =
-f 2.6 =
-38.5 =
-12.7 =
-11.9 =
-32.7 =
-26.2 =
-16.5 =
-16.6 =
p.ct.
= 0.60
= 0.16
= 2.26
= 0.77
= 0.73
= 2.44
= 1.93
= 0.96
= 1.23
cal. p.ct.
■ 31.9= 1.99
■ 33.8= 2.06
•173.7 = 10.21
■ 76.6= 4.67
■ 33.9= 2.09
■191.4 = 14.30
•108.9= 7.89
■ 69.3= 3.63
•119.4= 8.86
cal.
- 7.5 =
- 6.3 =
-76.5 =
-26.3 =
-11.9 =
-37.1 =
-26.0 =
-22.2 =
-16.7 =
p.ct.
= 0.47
= 0.38
= 4.60
= 1.60
:0.73
= 2.77
= 1.92
= 1.36
= 1.24
cal. pet.
— 6.4 = 0.40
- 1.9 = 0.12
-54.2 = 3.19
-17.4=1.06
-13.0 = 0.80
-37.1 = 2.77
-26.8=1.98
-15.7 = 0.96
-11.1=0.82
* The differences in these columns are obtained from the first column of this table and the entries of pre-
ceding tables as follows: column II from III of table 62; column III from III of table 68; column IV from I
of table 62; column V from I of table 68; column VI from I of table 72.
A CRITIQUE OF THE BODY-SURFACE LAW. 193
totals) the differences range from 6.3 to 134.0 calories, or from 0.38
to 10.01 per cent of the average (24-hour) heat-production of the group
of subjects under consideration.
If one prefers to base his judgment concerning the value of the
different means of estimating the basal metabohsm of an unknown
subject upon the square root of the mean-square de\'iation of the
computed from the actually observed values, he may examine the
results set forth in table 75. Here again the 45 tests of the suitabiUty
of the multiple regression equation invoh-ing stature, weight, and age
with two tri\'ial exceptions (+2.6 calories = 0.16 per cent and +3.1
calories = 0.19 per cent) indicate the superiority of these equations
over the 5 other methods which have been tested. The values for the
larger series (IV-VII and totals) range from 0.73 to 14.30 per cent.
Considered in their relation to the problem of the present chapter,
that of the body-surface law, the tables of this and the preceding
section show that results as good as or better than those obtainable from
the constant of basal metabolism per square meter of body-surface can be
obtained by biometric formulas involving no assumption concerning the
derivation of surface-area but based on direct physical measurements.
To the practical appUcation of these formulas we shall return in
the two following chapters.
II. COMPARISON OF BODY- WEIGHT AND BODY-SURFACE AS BASES OF
PREDICTION IN MALE AND FEMALE INFANTS.
Unfortunately our series of new-bom infants are not large enough
to justify di\dsion into subseries for the purpose of testing the suita-
bility of different methods of prediction by the treatment of the indi-
viduals of one subseries as unknown. We must, therefore, test the
value of the different methods of predicting the total heat-production
of an infant by comparing the actually m.easured heat-production with
that computed from constants based on the series to which it belongs.*'
It seems worth while to test only the methods of predicting total
heat-production from body-weight and from body-surface by the linear
regression equations, and by multiple-regression equations based on
both weight and stature.
The linear equations required are :
For male babies: For female babies:
h= 25.156+ 34.517 w A=. 26.184+ 34.229 u;
h= -31.703+749.914 a^ /i= -32.048+751.548 at
" Unfortunately the Du Boisea have not as yet prepared a height-weight chart for infant*
and we are in consequence limited to the Lissauer formula, which may in time be discarded like
the Meeh formula for adults. An extensive series of measurements made in conjunction with
Dr. Fritz B. Talbot and according to the Du Bois plan of measurement has shown quite re-
markable agreement between the surface areas of infants computed (l) by the Lissauer formula
(2) by the Du Bois linear formula, t. e., so far as normal infants weighing up to approximately
10 kilograms are concerned. For infants weighing more than 10 kilograms the Lissauer for-
mula gives results unquestionably too small. Measurements are now being collected for under-
nourished and atrophic infants.
194 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In male and female infants the deviations of the heat predicted
by use of these equations from the actually measured heat-productions
are:
Boy babiet. Girl babies
Average deviations with regard to sign:
Prediction from weight —0.020 —0.093
Prediction from surface +0.118 +0.047
Average deviations without regard to sign:
Prediction from weight 11.04 11.16
Prediction from surface 11.10 11.02
Square root of mean-square deviations :
Prediction from weight 13.81 13.77
Prediction from surface 13.80 13.61
These results show how slender is the evidence furnished by infants
for the assertion that "heat-production is proportional to body-surface
and not proportional to body- weight." By the first criterion, surface-
area is slightly better in the females but slightly worse in the males.
The average deviations without regard to sign show that in the females
prediction from body-surface there is an average error of 0.14 calorie
per day less than in prediction from body-weight, but that in the males
prediction from body-surface area by the Lissauer formula gives 0.06
calorie worse prediction ! Relying upon the square root of mean-square
deviation for the most critical test, we note that there is a difference
between the two methods of only 0.01 and 0.16 calorie per day! The
differences are trivial in comparison with the average daily metabolism
of over 140 calories for infants of both sexes. In short, body-weight
and body-surface area are equally good for purposes of prediction.
Turning now to the prediction of total heat-production from mul-
tiple regression equations based on the whole series, we have the
equations.
For boy babies ;i= -22.104+31.050 u;+1.162 s
For girl babies ^= -44.901 +27.836 ly+l. 842 s
The theoretical heat-production for each infant has been cal-
culated by these formulas and compared with the actually observed
heat-production.
The theoretical average deviation with regard to sign is zero and
is actually —0.078 calorie per day in the males and —0.047 calorie
per day in the females. The average deviation without regard to sign
is 11.02 calories in the males and 10.84 calories per 24 hours in the
females. Measuring the suitabihty of the formulas by the square root
of mean-square deviations we find 13.78 calories for the males and
13.53 calories for the females.
Comparing these results with those secured by prediction from
body-weight and body-surface above, we note that prediction from
stature and body-weight simultaneously has given slightly better results
than prediction from either body-weight or body-surface alone.
A CRITIQUE OF THE BODY-SURFACE LAW. 195
12. RECAPITULATION AND DISCUSSION.
According to Rubner's ''law" or the body-surface "law" the heat-
production of an organism is proportional to its superficial area.
Otherwise stated, heat-production measured in calories per square
meter of body-surface is a constant.
In this chapter we have outhned the historical development of the
physiologist's beUef in the vaUdity of this "law," have discussed
certain experimental e^ddences for its inapphcabiUty to man, and have
tested its vaUdity by the appUcation of statistical criteria to the largest
available series of data on human basal metaboUsm.
Historically, the idea of proportionaHty between body-surface and
heat-production was originally based upon the assumed physical law,
confused by many physiologists with Newton's law of cooling, that
heat-loss is proportional to the surface-areas of similar soUds, and upon
the further assumption that heat is produced to maintain the body-
temperature constant. The idea of a causal relationship between
body-surface and heat-production has frequently been strongly empha-
sized in foreign writings and is distinctly to be inferred from those of
a number of American "UTiters.
The validity of the body-surface law has long been held in question
by the workers at the Nutrition Laboratory. In a series of papers ^*
its universal applicabihty was challenged and it was stated that the
loss of heat from the body-surface could not be considered as the deter-
mining factor of metabohsm. Certain factors, such as sex, age, and
athletic training, were shown to affect the basal metabolism, even when
measured on the basis of calories per square meter of body-surface,
thus affording illustrations of exceptions to the so-called law.
In dealing with the problem of the constancy of heat-production
per square meter of body-surface in the human species two phases
must be recognized. The first is that of the constancy of heat-produc-
tion within the same individual at different times. The second is that
of the constancy of heat-production per square meter of body-surface
from individual to individual.
From the side of controlled individual experimentation it has been
shown that animals at different nutritional levels, or under varjdng
external conditions, differ in their heat loss to a degree which can not
be explained by differences in body-surface.
A man who fasted 31 days showed a decrease of 28 per cent in heat-
production per square meter of body-surface. Squads of college men
recently investigated on prolonged reduced diet at the International
Y. M. C. A. CoUege at Springfield gave ample corroborative evidence.
Such experiments can be interpreted only as proof of the inapplicability
** Benedict, Emmes, Roth, and Smith, Journ. Biol. Chem., 1914, 18, p. 139; Benedict and
Roth, ibid, 1915, 20, p. 231; Benedict and Smith, ibid., 1915, 20, p. 243; Benedict and
Emmes, ibid., 1915, 20, p. 253; Benedict, ibid., 1915, 20, p. 263.
196 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
of the surface-area law to subjects in widely varying states of nutrition.
Criticism will of course be at once directed against the use of such
evidence. It will be contended that prerequisite conditions for the
application of the surface law as outlined by Rubner ^^ are like physio-
logical conditions, such as nourishment, climatic influences, tempera-
ture, and capacity for work. Just such adverse criticism has been
made of conclusions drawn at the Nutrition Laboratory concerning
the basal metabolism of normal and atrophic infants.
In reply to such comment it is necessary to point out merely that
the physiological states of the fasting man are by no means incompar-
able with the conditions commonly existing in pathological subjects.
Notwithstanding the fact that enormous variations in the previously
mentioned physiological factors are invariably found, their metabolism
has been treated by authors just as though the body-surface law were
fully applicable. For example, in a report on a series of observations
made in the Nutrition Laboratory on patients with severe diabetes ®'
the metabolism of the diabetics was compared with that found in
normal individuals of like height and weight, i.e., of a somewhat thin
and emaciated type. The marked difference in metabohsm found with
diabetics when acidosis was present as compared with that when it
was diminished or absent ®^ led to the conclusion that diabetes increases
the metabolism approximately 15 to 20 per cent above that of the
normal individual. When a wholly arbitrary normal standard value
(obtained with a large number of individuals of whom the greater
proportion were in full vigor) was used for comparison, Graham Lusk
concluded ^^ that the emaciated diabetics with acidosis showed little
or no increase in metabolism. If it is erroneous to apply the surface-
area law to an individual normal subject throughout a prolonged fast,
it is difficult to see the validity of applying it when there are such
marked variations in conditions of nourishment and bodily vigor as
exist between the large group of normal persons and the group of
emaciated diabetics. We must, however, in this connection, refer to
the detailed discussion of the influence of rapid changes in nutritional
level upon the basal metabolism on pp. 102-103.
With the fasting individual it is evident that the body-surface law
does not obtain. The differences in the fasting man at the beginning
and end of the fast are by no means so great as the differences between
pathological individuals, including diabetics, and the average normal
vigorous individuals from whom the standard of comparison proposed
by other writers has been derived.
« Rubner, Arch. f. Hyg., 1908, 66, p. 89.
*• Benedict and Joslin, Carnegie Inst. Wash. Pub. No. 176, 1912.
" It has been demonstrated that when the diabetics are without acidosis (for example, when
following the remarkable Allen treatment), the metabolism is distinctly lower (Joslin,
Am. Joum. Med. Sci., 1915, 150, p. 485) than with acidosis, so that unquestionably the
acidosis per se materially increases the metabolism.
«s Lusk, Science, 1911, n. s. 33, p. 434; ibid.. Journ. Biol. Chem., 1915, 20, p. 599; Ibid.,
Science, 1915, n. 8. 42, p. 818.
A CRITIQUE OF THE BODY-SURFACE LAW. 197
There are even very real purely phj^sical difficulties in the way of
assuming that the superficial body-area can be considered a true meas-
ure of the heat-loss which is assumed to bear a causal relation to heat-
production. Heat-loss does not occur exclusively from the skin. A
considerable proportion of the total heat generated is given off from the
lungs through the warming of the air and through the vaporization of
water. From a large number of experiments with human subjects at
rest, either with or without food, it is found that on the average 2,3
per cent of the total heat for 24 hours is required to warm the inspired
air; 10 per cent is lost as the result of vaporization of water from the
lungs and 12.3 per cent from the vaporization of water from the skin.^®
A recent critical study by Soderstrom and Du Bois ^^ indicates that
with normal individuals somewhat more than 25 per cent of the total
heat is lost in the vaporization of water from the lungs and skin.
Turning from purely experimental tests to those in which the results
of experimentation are subjected to statistical analysis, we may first
note that the estimates of body-surface area upon which most of the
conclusions have been based have been shown to be open to serious
criticism. It is to the credit of D. and E. F. Du Bois that they have
made possible greater precision in this phase of the work.
In testing by statistical methods the vaUdity of this "law" which
has held a conspicuous place in the hterature of metaboUsm for over a
quarter of a century, we have started out from two interdependent
fundamental assumptions which seem axiomatic.
(a) The primary requisite in testing any biological law is to deter-
mine quantitatively the degree of interdependence of the magnitudes
of the variables which it connects.
(6) The true test of the validity of a law is its capacity for predict-
ing an unknown result.
The chief argument used in the past in support of the body-surface
law has been that heat-production shows the least variation from
individual to individual when expressed in calories per square meter
of body-surface. We have shown that this argument is nulhfied by
the simple physical relationship between body-weight and body-surface.
The surface areas of similar solids are not directly proportional to their
weights, but to the two-thirds powers of their weights. Thus, in a
series of individuals whose body-surface area has been determined by
the Meeh formula, body-surface area must necessarily be less variable
than body-weight. The ratio Bod\^-surface ^^s^» therefore, also be less
• i_i i.1- Total heat
vanable than 5— i r-r--
Body-weight
Since the body-surface measurements by the Meeh formula and
by the Du Bois height-weight chart are very closelj^ correlated, the
*» Benedict, Carnegie Inst. Wash. Pub. No. 77, 1907, p. 476.
•0 Soderstrom and Du Bois, Arch. Intern. Med., 1917, 19, 946.
198 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
same conclusion must also applj' for the more modern method of body-
surface measurement.
The question as to whether heat-production is more closely related
to body-weight or to body-surface can be answered only by (a) deter-
mining the correlation between each of these two characters and heat-
production, or by (b) determining which of these two characters will
give the closest prediction of the heat-production of an individual.
The correlations between body-weight, body-surface as approxi-
mated by the Meeh formula, and body-surface as indicated by the
Du Bois height-weight chart on the one hand and gaseous exchange and
total heat-production on the other have been determined. The correla-
tions between body-weight and heat-production are of approximately
the same magnitude as those between body-surface and heat-production.
These results do not, therefore, justify the conclusion that metabolism
is proportional to body-surface and not proportional to weight. Metab-
olism is not proportional to either of these physical characters in an
absolute sense. It is correlated very closely indeed with all three
bodily measurements, stature, weight, and surface.
While the differences between the constants are very slight and
can in no case be looked upon as statistically significant in comparison
with their probable errors, the correlation coefficients indicate a some-
what closer relationship between body-surface and total heat-produc-
tion than between body-weight and total heat-production. That this
closer relationship between area and heat-production can not be taken
as proof of the validity of "Rubner's law" as appUed to human indi-
viduals has been indicated. This point will receive attention below.
In the past many physiologists have assumed that the heat-
production of an individual should be given by
h=whk
where h = the heat-production of the individual, w = the weight of the
individual, and h^. the mean heat-production per kilogram of body-
weight in the standard series, or by
where a = superficial area and ha =mean heat per square meter of body-
area in the standard series.
We have shown that far better results are given by the use of
equations of the type
{h-h)=ru,h~(w-w) {h-h)=r^h—{a-0')
where h, w, and a denote total heat, body-weight, and surface-area,
the bars denote means, the sigmas standard deviations, and r the
coefficient of correlation between the characters. WTien these equa-
tions are used the heat-production of an individual can be calculated
A CRITIQUE OF THE BODY-SURFACE LAW. 199
from body-weight with essentially the same degree of accuracy as
when body-surface is used as a basis of prediction.
Since it has been showTi in Chapter IV that both stature and body-
weight have independent significance in determining the amount of the
metabolism, we have attempted to predict heat-production by the
simultaneous use of stature and body- weight.
With such equations the errors of prediction from stature and
weight are about the same as when using body-surface as a basis of pre-
diction. Apparently there may be a sUght superiority of prediction from
body-surface area as estimated from the Du Bois height-weight chart,
especially when the superior methods of prediction by the use of linear equa-
tions developed in this volume are employed, but on the basis of the data
at hand this superiority can not be asserted to be more than apparent.
The investigation of the validity of the body-surface law has not
merely a theoretical interest but possesses material practical impor-
tance. TMiile of recent years Rubner's law has taken on the nature of
an empirical formula to be practically appUed, in origin it was groimded
on the hj-pothesis that thermogenesis is determined by thermolysis.
Or, it was assumed that coohng obtains as a cause of heat-production
in the organism. As we look at the matter, the "body-surface law"
is at best purely an empirical formula. It has furnished a somewhat
better basis for the prediction of the metaboUsm of an unmeasured
subject than does body- weight.
The demonstration in the course of this investigation that by the
use of proper biometric formulas the metabolism of an indi\'idual can
be predicted from stature and body-weight with practically the same
accuracy as from body-surface area robs "Rubner's law" of its unique
empirical significance in cUnical and other applied calorimetry. It also
casts grave doubts upon any evidence which its superior power of
prediction as compared with body-weight may be supposed to furnish
in favor of its being a real physiological law.
We have shown that the great supposed difference between body-
surface area and body-weight as bases of predicting the metaboUsm
of an unknown subject is largely due to the fact that fallacious methods
of calculation have been employed. In so far as body-surface area, as
estimated from the Du Bois height-weight chart, has any superiority
as a basis of prediction, we believe that this has not been due to any
causal relationship between body-surface area as such and metabolism,
but that it is merely incidental to the fact that body-surface takes
somewhat into account both body-weight and stature, each of which
we have showTi to have independent significance as proximate factors
in determining the total metaboUsm.
In this volume we have limited our investigation of the body-surface
law strictly to its applicabiUty to variations within the hurnan species,
in short to its intra-specific and not its interspecific applicabiUty. It is
200 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
proper, however, to point out that smce the long existing doubts as
to the vaUdity of the older methods for the measurement of body-
surface have been fully substantiated by the development of the linear
formula of the Du Boises for adults and the photographic method, it
is quite possible that more intensive work will draw into question the
validity of the surface measurements upon which the evidence of the
applicability of the law to animals in general depends. If the errors
in the Meeh formula are as large as those pointed out by the Du Boises,
one may also reasonably question the formulas for lower animals. It
is thus probable that the computations of E. Voit, recently approved
by Armsby, will need a radical revision. What influence this revision
may have upon the general acceptance of the wider applicability of the
so-called body-surface law awaits determination.
Finally, in view of the facts that (a) the equations developed in
this volume and the convenient tables ^^ which have been provided for
the prediction of the basal metabolism of the individual from stat-
ure, weight, and age deprive the "body-surface law" of its unique
practical significance, and that (6) the evidence of an actual physio-
logical nexus between body-surface area and metabolism is altogether
inconclusive, it seems to us that the "body-surface law," as far as its
supposed appUcation to the human individual is concerned, must play
a very minor r61e indeed in future physiological discussions.
The equations which we have given were designed primarily for
the most exact work in the problem of metabolism during the period of
adult human life. While for this period they are decidedly superior
to prediction by means of the average heat production per unit of body
surface in a standard series we would not at present recommend the
discarding of the older methods of correcting for body size in compara-
tive studies of metabolism.
Body-weight, the two-thirds power of body-weight, and the more
recent attempts at actual siu*face measurement must be considered
in comparing organisms of very different physical configuration.
We must, however, point out that our experience with the "body-
surface law" in its application to the human individual indicates that
extraordinary caution must be used in regard to all of these methods.
Eventually they will probably have to be replaced by standards similar
to those developed for human adults in this volume.
Until this can be done on the basis of adequate physical and experi-
mental data we do not desire to have our results for adults generalized
beyond the range of physical characters and age to which we have
ourselves applied them. If this were done they might tend to hinder
rather than to assist in the advancement of research. For the present
at least, the older methods of comparison must still be appealed to
in the inter-specific comparisons.
" See Chapter VIII for a full discussion of these tables.
Chapter VII.
A COMPARISON OF BASAL METABOLISM OF NORMAL
MEN AND WOMEN.
1. HISTORICAL.
Consideration of the problem of the relative metabolism of men
and women dates from 1843, when Scharling/ whose results have been
recalculated by Sonden and Tigerstedt,^ found that a girl 19 years of
age excreted a considerably smaller amount of carbon dioxide and a
considerably smaller amount of carbon dioxide per kilogram of body-
weight than a boy 16 j-ears of age. Her actual carbon-dioxide produc-
tion was less than that of two men of 28 and 35, but her carbon dioxide
per kilogram of body-weight lay between that of the two adult men.
He also found that a girl of 10 produced both absolutely and relatively
less carbon dioxide than a boj' of about the same age. Scharling con-
cludes from these observ-ations that there is a greater production of
carbon dioxide by men than by women of the same age.
Andral and Gavarret ^ worked with 37 men and 22 women. They
conclude that throughout the whole of life there is a greater production
of carbon dioxide by men than by women, and that between the ages
of 16 and 40 men produce about twice as much carbon dioxide as women
do. Unfortimately Andral and Gavarret have not recorded the
weights of their men and women; it is therefore, impossible to make
comparisons on the basis of relative heat-production, i.e., on the num-
ber of calories per kilogram of body-weight or on the basis of the
nimiber of calories per square meter of bodj^-surface.
The data of Speck,* restated by Sonden and Tigerstedt,* show
higher metabolism in men than in women over 17 years of age, but the
difference is reversed in the case of a boy of 10 and a girl of 13.
In their classical monograph on the respiratory exchange and
metaboUsm, Sonden and Tigerstedt ® published an extensive series of
observations on both men and women, in which the large respiration
chamber in Stockholm was used. These results are comparable for the
two sexes, although the observations were made under such conditions
^ Scharling, Ann. d. Chem. u. Pharm., 1S43, 45, p. 214. Reprinted in detail in Ann. de chim.
et phj-s.. 1843, 3 ekt., 8. p. 478.
* Sond6n and Tigerstedt, Skand. Arch. f. Physiol., 1895, 6, p. 54.
» Andral and Gavarret, Ann. d. chim. et phys., 1843, 3 s^r., 8, p. 129.
* Speck, Physiologie des menschlichen Athmens, Leipzig, 1892.
* Sonden and Tigerstedt, loc. cit., p. 57.
' Sonden and Tigerstedt, loc. cit., p. 58.
201
202 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
as to exclude them for use as indices of basal metabolism. These
authors based their comparisons on the carbon-dioxide excretion per
hour per kilogram of body-weight and per square meter of body-surface.
They express the relationship between the gaseous exchange of men
and women as a proportion. Their end results are summarized in
table 76. They conclude that in youth the carbon-dioxide production
of boys is considerably greater than that of girls of about the same age
and body-weight, but with increasing age this difference gradually
becomes less and less, and finally in old age it disappears entirely. It
must be noted here that the authors specifically state that it appears
to them that new experiments are necessary before this problem can
be completely solved.
Table 76. — Comparison of carbon-dioxide -production in men and women: data of Sondin
and Tigerstedt.
COj per
kilogram
per hour,
males.
CO2 per
kilogram
per hour,
females.
Relative
CO2 per
CO2 per
Relative
Age
of
males.
Age
of
females.
COj
production
per
kilogram.
hour per
square
meter,
males.
hour per
square
meter,
females.
CO2
production
per square
meter.
7
7
1.149
1.133
100 : 101
26.27
26.61
100 : 99
9
9
1.207
0.850
100 : 142
26.89
20.78
100 : 144
10 to 11
11
1.085
0.845
100 : 131
27.88
21.75
100 : 128
12
12
0.997
0.743
100 : 134
26.49
20.14
100 : 132
13 to 14
14
0.980
0.6G1
100 : 148
27.12
18.22
100 : 149
15
15
0.813
0.601
100 : 135
23.54
17.16
100 : 137
17
17,30
0.814
0.522
100 : 156
24.18
15.53
100 : 156
30 to 50
40 to 60
0.499
0.554
100 : 90
16.55
17.94
100 : 90
67
65
0.407
0.390
100 : 104
14.24
12.64
100 : 113
In 1899 Magnus-Levy and Falk ^ published an extended series of
observations on both men and women in which the Zuntz-Geppert
respiration apparatus was employed. Although Johannson ^ had
shortly before emphasized the importance of controlHng muscular
repose and had outlined his experience in the voluntary exclusion of
muscular activity, these observations of Magnus-Levy and Falk
represent the first comparative observations made upon both men and
women in which particular attention was given to complete muscular
rest; hence they are more nearly comparable with our experiments
than any series published previous to 1899. The series with men
comprise observations on 16 boys, 10 men between 22 and 56 years
of age, and 5 men 64 years old and over. The series of women include
observations on 9 girls, 15 women between 17 and 57, and 7 women of
71 years or older. The data as to age, weight, and height are recorded.
The authors have likewise computed the values per kilogram per
minute and per square meter of body-surface per minute. In their
comparisons of the values obtained with men and women on the basis
^ Magnus-Levy and Falk, Arch. f. Anat. u. Physiol., Physiol. Abt., Suppl., 1899, p. 314.
» Johannson, Skand. Arch. f. Physiol., 1898, 8, p. 86.
BASAL METABOLISM OF XOR\L\L MEN AND WOMEN. 203
of body-weight, they conclude that in middle life the gaseous metab-
oUsm of women is approximately the same as that of men of the
same age and body-weight. With children and old men and women,
the females have a sHghtly less (5 per cent) metaboUsm than the men.
The authors also point out that, owing to the larger proportion of
body-fat, women would have a metabolism per unit of active pro-
toplasmic tissue greater than would men.
Following the work of Magnus-Levy and Falk there was a period
of about 16 years in which Uttle was done on the problem of the differ-
ences in the metaboUsm of men and women. ^Many observations were
made on men, but there were relatively few determinations of basal
metaboUsm on normal women. In 1915, however, Benedict and
Emmes ^ returned to the problem, basing their calculations on the
89 men and the 68 women designated as the original Nutrition Labora-
tory series. In this study they introduced what we have here called
the selected-group method of comparison, a method which marked a
distinct advance in the comparison of the metaboUsm of classes of
individuals. This method, in a somewhat modified form, we shall
employ extensively in this chapter.
2. COMPARISON OF METABOLISM OF MEN AND WOMEN ON THE
BASIS OF GENERAL CONSTANTS.
In this section we shall base our comparisons of the basal metabol-
ism of the sexes upon the constants for the series of indi\'iduals as a
whole. This method of testing the existence of a sexual differentiation
in metaboUc activity is not, in our opinion, so valuable as the further
development of the selected-group method of Benedict and Emmes in
the following section. For the sake of completeness, however, both
methods of analysis must be employed.
Consider, first, the average gross heat-production in calories per 24
hours in series of adults. For the 72 indi\dduals of the Gephart and
Du Bois selection, the 64 others, and the 136 men the averages are 1623,
1641, and 1632 calories, respectively. For the 68 original, the 35 sup-
plementary, and the total 103 women the dailj^ heat-productions are
1355, 1339, and 1349 calories, respectively. Thus the heat-production
of the average woman is roughly 300 calories per day less than that of
the average man, when both are measured in muscular repose and at a
period 12 hours after the last meal. Thus in adults gross metaboUsm
is markedly less in women than in men. Note, however, that these
values are uncorrected for weight, stature, and age in both sexes.
But women are on the average smaUer than men. In either sex
large indi\'iduals produce on the average more heat than smaller ones.
In any discussion of the relation of metabolism to sex it is necessary
to correct for this difference in size. Turning to average heat-produc-
• Benedict and Emmea, Joum. Biol. Chem., 1915, 20, p. 253.
204 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
tion per unit of body-weight or body-surface, we note that in the 72
men constituting the Gephart and Du Bois selection the average heat-
production is 25.8 calories per kilogram of body-weight, in the 64 other
men it is 25.6 calories, while for the total 136 men it is 25.7 calories.
In the 68 original women it is 25.4 calories, in the 35 supplementary
women it is 22.7 calories per kilogram, while in the whole series of
103 women it is 24.5 calories.
On the basis of body-surface area the average heat-productions per
square meter as estimated by the Meeh formula are 832 calories in the
Gephart and Du Bois selection, 828 calories in the 64 men not included
in the Gephart and Du Bois selection, and 830 calories in the whole
series of 136 men. The comparable values for the women are 772
calories for the 68 original women, 715 calories for the 35 supplementary
women, and 753 calories for the whole series of 103 women.
With the measurement of body-surface area furnished by the
height-weight chart we find average heat-productions per square meter
of body-surface area of 927 calories for the Gephart and Du Bois
selection, 924 calories for the 64 other men, and 925 calories for the
whole series of men. For women the values are 865 calories for the
68 original women, 820 calories for the 35 supplementary women, and
850 calories for the whole series.
If we extend the comparison to the 8 men and 7 women studied
by Palmer, Means, and Gamble, ^° we find that the average daily heat-
production of men is 1657.4 calories, whereas in women it is 1468.7
calories. In men the average heat-production per kilogram of body-
weight for a 24-hour period is 23.36 calories, whereas in women it is
21.77 calories. Expressing heat-production in calories per square
meter of body-surface per 24 hours we find that the results for men and
women stand in the ratio 784 : 718 calories when surface is estimated
by the Meeh formula and in the ratio 941 : 919 calories when surface
is estimated by the Du Bois method. These results, due to the experi-
ence of other investigators, will be tested by other criteria on p. 217,
and shown to be in full accord with our own findings throughout.
It is now desirable to look at the evidence from a quite different
angle. Instead of depending upon average heat-production or average
heat-production per unit of body-weight or body-surface for a basis
of comparison of men and women, we may inquire what amount of
change in heat-production would be associated with a variation of a
definite amount from the mean body-weight or the mean body-surface
in the two sexes. If women show a smaller change in heat-production
associated with a variation of the same amount in a physical dimension
we must conclude that metabolism- is less in women than in men. If we
consider these variations in quantity of heat set free per unit of body-
" Palmer, Means, and Gamble, Joum. Biol. Chem., 1914, 19, p. 239; Means, »6id., 1916, 21, p. 263.
BASAL METABOLISM OF NORMAL MEN AND WOMEN. 205
weight or body-surface we note from equations on page 170 that in the
72 individuals of the Gephart and Du Bois selection heat-production
increases 16.7 calories per 24 hours for each increase of 1 kilogram of
body-weight above the average. In the 64 men not included in the
Gephart and Du Bois selection the increase is 15.4 calories. In the
136 men it is 15.8 calories. For comparison we note that in the 68
original women the increase is 10.5 calories, in the supplementary series
it is 6.3 calories, and in the whole series of women it is 8.2 calories.
Turning to the change in heat-production with variation in body-
surface, we note from the variable term of the appropriate equations
(page 170) that the change for body-surface as measured by the height-
weight chart is very different from that for body-surface as measured
by the Meeh formula. Working, therefore, with each of the two
formulas separately, we find that with surface measured by the Meeh
formula the two groups of men show^ a change of 822 and 764 calories
for a variation of 1 square meter of body-surface, while for the 136
men the change is 783 calories. In the 68, 35, and 103 women the
values are 506, 316, and 400 calories respectively.
"V\Tien superficial area is measured by the height-weight chart the
change in heat-production for a variation of 1 square meter of body-
surface is 1026, 1101, and 1070 calories in the 72, 64, and 136 men of
the three groups compared, whereas in the groups of 68, 35, and 103
women the values are 808, 500, and 639 calories respectively.
Turning back to the diagrams of preceding chapters showing the
heat-production of subgroups of men and women, we note that the
smoothed averages, and generally the actually observed averages as
well, are higher in men than in women. This is clearly showTi in dia-
grams 13 and 17 of Chapter IV, in which the individuals are arranged
according to stature and according to body-weight.
Again in diagrams 20-22 of Chapter V, showing the gross heat-
production and heat-production per unit of body-weight and body-
siu-face in men and women of different ages, the Unes for the men are
consistently higher than those for the women. The same is true,
with few exceptions, of the empirical means.
Now the highly important result of all these methods of comparison
is this: Without exception the tests based on general population
constants indicate higher metabohsm in the man.
3. COMPARISON OF METABOLISM OF MEN AND WOMEN BY USE OF
GRADUATION EQUATIONS.
We now turn to a comparison of men and women on the basis of a
method which is in essence an extension and modification of the selected-
group method of Benedict and Emmes.^^ Instead of comparing the
" Benedict and Emmea, loc. cii. Magnus-Levy and Falk, he. cit„ used essentially the se-
lected-group method but with wholly inadequate data.
206 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
averaged constants of a group of women with the empirical average
of a group of men selected for their approximate agreement in stature
and body-weight, we compare the averages for the groups of women
selected for stature, body-weight, or both stature and body-weight,
or for stature, body-weight, and age with the smoothed or theoretical
averages for men of the specified physical dimensions.
The method is essentially the same as that which has been followed
in certain preceding sections. We calculate the theoretical heat-
production of female individuals from constants based on the series
of men, and by comparison of the empirical means with the average
of the theoretical values we determine whether the women have a
higher or a lower metabolism than would be expected if they were men
of the same physical dimensions.
For a first test of the existence of sexual differentiation we classify
the women according to (a) body-surface area as determined from the
Du Bois height-weight chart, (6) body-weight, (c) stature, and (d) age.
The predicted total heat-production has been estimated by means
of the regression equations for total heat on physical characters and
age in the total male series. ^^
In using these equations we have started from the simplest and
advanced to the more complex, laying the results attained by each
of the methods before the reader, who may therefore trace the growth
of the underlying conceptions of our methods and convince himself that
the results due to the more complicated processes are not attributable
to some error in the more recondite reasoning. We first of all compare
the values of the metabolism constants actually obtained for women
with those which are calculated from their weight, from their stature,
and from their body-surface area considered independently of each
other and of age. Thus in working with body-surface we determine
whether women as a class have a higher or a lower basal metabolism
than men of the same superficial area. In doing this we disregard
body-weight, stature, and age. Similarly, in dealing with equations in-
volving constants for body-weight we disregard stature, body-surface,
and age.
In the second attack upon the problem we base our predictions
of heat-production in wom.en upon an equation involving the con-
stants for body-weight and stature in men. Thus body-surface (which
is of course largely determined by stature and weight) and age have
been disregarded.
'^ The analysis in Chapter VI has fully demonstrated the fallacy of predicting total heat-
production by multiplying body-weight or body-surface by the average heat-production per unit
weight or per unit surface in the standard series. We shall not, therefore, give the results of com-
parison on that basis further than to say that with individuals grouped according to body-weight
and body-surface area, as in tables 80 and 81, the average actual heat-production of the groups
of women is lower than that based on male constants in all the 12 subgroups classified with respect
to body-surface and lower than that calculated from the average production per kilogram of
body-weight in the men in 10 of the 13 groups of women classified according to body-weight.
BASAL METABOLISM OF NOR^L^.L MEN AND WOMEN. 207
Finally we have employed an equation in which prediction of heat-
production is made from weight, stature, and age.
The characteristic equations for the calculation of total heat-
production from age, surface, weight, and stature considered alone are :
h= 1823.80-7.15 a
h = -254.546+1070.454 a^
h= 617.493 + 15.824 w)
/i=- 1237.637+ 16.589 s
where h = total heat, a=age, a£,= body-surf ace area by the Du Bois
height-weight chart, iy= body- weight, and s= stature.
Employing these equations, we have calculated the theoretical
heat-production of each individual woman on the assumption that
she is a man of like character. The difference between her observed
metaboUsm (24-hour period) and her theoretical metaboUsm has then
been determined by taking
(measured metaboUsm) less (theoretical metabolism)
Thus a negative sign denotes a deficiency in the actual as com-
pared with the normal heat-production.
Table 77. — Differences in the metabolism of men and women, women classified according to age.
Age.
N
Mean
total
heat-
produc-
tion.
Prediction from age.
Prediction from weight
and stature.
Prediction from weight,
stature, and age.
Mean
predicted
total
heat.
Actual
less pre-
dicted.
Percent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less pre-
dicted.
Percent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less pre-
dicted.
Percent-
age
differ-
ence.
15 to 19
20 to 24
25 to 29
30 to 39
40 to 54
55 to 74
12
35
20
13
13
10
1371.4
1370.9
1334.7
1347.3
1368.0
1253.1
1698.0
1666.1
1635.6
1569.2
1487.2
1379.3
-326.6
-295.2
-300.9
-221.9
-119.2
-126.2
19.2
17.7
18.4
14.1
8.0
9.1
1392.9
1444.3
1399.9
1466.6
1600.2
1540.1
- 21.5
- 73.3
- 65.2
-119.2
-232.2
-287.0
1.5
5.1
4.7
8.1
14.5
18.6
1464.7
1487.1
1412.0
1416.6
1479.3
1313.2
- 93.3
-116.2
- 77.3
- 69.3
-111.3
- 60.1
6.4
7.8
5.5
4.9
7.5
4.6
In basing our conclusions concerning the existence of a sexual
difference in metabolism upon these differences we have examined
them in three ways: (a) We have compared the average values of
observed and theoretical metaboUsm in groups of women classified
with respect to age, stature, body surface, and weight. (6) We have
compared the average values of observed and of theoretical heat-
production in groups of individuals classified by both stature and body-
weight. FinaUy, (c) we have arranged the differences in order according
to sign and magnitude and considered the evidence furnished by the
frequency distributions of the individual deviations.
The results of a comparison of the total heat-productions with
those computed from age and classified according to the age of the
women are shown in the first panel of table 77. The differences are
without exception negative in sign, thus indicating that the metabol-
208 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
ism of the women is lower than it would be in men of the same age if
physical differences were disregarded. The differences range from
119.2 to 326.6 calories, or from 8.0 to 19.2 per cent. The results are
represented graphically in the lower figure, A, of diagram 27. In this
and the following four diagrams the upper row of dots represents the
theoretical and the lower row the actually observed average basal
metabolism for the groups of individuals.^^
Diagram 27. — Comparison of metabolism of men and women. Women
classified according to age.
The differences between the theoretical and the actual heat-
production is not as great in the older groups of women as in the
younger. This point will be touched upon later.
" In this and the following diagrams the theoretical heat-productions calculated from the
linear equations should of course lie in a straight line except for the divergences due to the devia-
tions of the individuals in the subgroups from the mid-ordinate values for age, stature, body-
weight, and body-surface due to the errors of random sampling. The remarkable agreement of
the best-fitting straight line and the calculated mean theoretical heat-production of the several
groups of women furnishes a most gratifying justification of the system of grouping adopted.
BASAL IVIETABOLISM OF NORMAL MEN AND WOIVIEN.
209
For the sake of a further comparison on the basis of an age grouping
of the women we have used the metabolism calculated from the equa-
tion for the regression of heat-production on body-surface as estimated
by the Du Bois height-weight chart in the men. The comparison is
made in table 78. The results, which are represented graphically in
the uppermost figure, D, of diagram 27, fully confirm the preceding.
Without exception the groups of women show average values of
metabohsm from 13 to 273 calories or from about 1 to 18 per cent lower
than values computed on the assumption that their heat-production is
identical with that of men of like weight, stature, and age.
Table 78. — Differences in the metabolism of men and women, women classified according to age.
Age.
N
Mean
total
heat-
production.
Prediction from body-surface.
Mean
predicted
total
heat.
Actual
less
predicted.
Percentage
difference.
15 to 19
20 to 24
25 to 29
30 to 39
40 to 64
55 to 74
12
35
20
13
13
10
1371.4
1370.9
1334.7
1347.3
1368.0
1253.1
1384.1
1432.2
1391.8
1454.2
1568.6
1525.6
- 12.7
- 61.3
- 57.1
-106.9
-200.6
-272.5
0.9
4.3
4.1
7.4
12.8
17.9
Table 79. — Differences in the metabolism of men and women, women classified according to stature.
Stature.
N
Mean
total
heat-
produc-
tion.
Prediction from
stature.
Prediction from
weight and stature.
Prediction from
weight, stature, and age.
Mean
predicted
total
heat.
Actual
leas
predicted.
Per-
cent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
149 to 151
152 to 154
155 to 157
158 to 160
161 to 163
164 to 166
167 to 169
170 to 172
173 to 175
176 to 178
2
6
14
18
24
19
12
6
1
1
1259.5
1315.7
1310.8
1298.2
1375.8
1367.3
1379.0
1413.2
1430.0
1383.0
1267.0
1300.7
1353.9
1403.9
1450.7
1494.4
1550.7
1591.0
1666.0
1682.0
- 7.5
+ 15.0
- 43.1
-105.8
- 75.0
-127.1
-171.7
-177.8
-236.0
-299.0
0.6
1.2
3.2
7.5
5.2
8.5
11.1
11.2
14.2
17.8
1295.0
1327.2
1352.4
1407.8
1478.7
1531.5
1532.7
1545.2
1561.0
1894.0
- 35.5
- 11.5
- 41.6
-109.6
-103.0
-164.2
-153.7
-132.0
-131.0
-511.0
2.7
0.9
3.1
7.8
7.0
10.7
10.0
8.5
8.4
27.0
1335.0
1374.6
1346.5
1406.0
1445.4
1494.1
1503.4
1513.8
1580.0
1786.0
- 75.5
- 58.9
- 35.7
-107.8
- 69.6
-126.8
-124.4
-100.6
-150.0
-403.0
5.7
4.3
2.7
7.7
4.8
8.5
8.3
6.6
9.5
22.6
The results of a comparison of the actual heat-production in the
women with that computed from stature in groups of women classified
with respect to stature are shown in table 79. With one single excep-
tion, that of the 6 subjects 152 to 154 cm. in height, the women of each
grade of stature show a smaller actual average metabohsm than that
computed on the assumption that they were men of hke stature. The
lower figure, A, in diagram 28, which represents these results brings
210 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
out clearly the difference between the actual metabolism in women
and the metabolism which would be found in men of the same stature.
The width of the shaded zone increases from the lower to the higher
statures. Thus the taller women show a greater deficiency in their
metaboUsm than the shorter ones.
ISO IS3 ise
ISO 'S3 IS6
Diagram 28.^ — Comparison of metabolism of men and women. Women
classified according to stature.
Calculating the total heat-production of the women from the equa-
tions for the regression of total heat-production on body-surface in
men, and classifying with respect to body-surface, we have the mean
calculated and the mean actual heat-production in the first section of
table 80.
Again the actual heat-productions of the women are without
exception lower than those which they would have if they were men
of like body-surface area.
1
BASAL METABOLISM OF NORMAL MEN AND WOMEN.
211
The graphic representation of the results for the grouping by sur-
face area in the lowermost figure, A, of diagram 29, shows a deficiency
in metabolism throughout the whole range of variation in body-surface
area. Apparently the difference between the actual and the computed
metabohsm is greater in the women of larger as compared with those
of smaller area.
Table 80. — Differences in the metabolism of men and loomeii, women classified according to surface.
Prediction fron:
Prediction from
Prediction from
Body-
surface.
A'
Mean
total
heat-
produc-
tion.
body-surface.
weight and stature.
weight, stature, and
age.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
1.28 to 1.34 1
985.0
1137.0
-152.0
13.4
1167.0
-182.0
15.6
1005.0
- 20.0
2.0
! 1.35 to 1.41 9
1191.8
1223.9
- 32.1
2.6
1246.2
- 54.4
4.4
1257.2
- 65.4
5.2
,1.42 to 1.4813
1276.1
1299.3
- 23.2
1.8
1313.6
- 37.5
2.9
1294.1
- 18.0
1.4
1.49 to 1.5526
1285.1
1371.0
- 85.8
6.3
1380.8
- 95.7
6.9
1390.5
-105.4
7.6
i 1.66 to 1.62 IS
1368.4
1443.8
- 75.4
5.2
1450.6
- 82.2
5.7
1439.4
- 71.0
4.9
1.63 to 1.69 11
1463.4
1514.5
- 51.2
3.4
1518.5
- 55.1
3.6
1526.5
- 63.1
4.1
1.70 to 1.76 12
1447.0
1592.1
-145.1
9.1
1599.7
-152.7
9.5
1552.0
-105.0
6.8
1.77 to 1.83; 7
1416.6
1657.0
-240.4
14.5
1677.0
-260.4
15.5
1566.7
-150.1
9.6
1.84tol.90i 1
1334.0
1769.0
-435.0
24.6
1797.0
-463.0
25.8
1621.0
-287.0
17.7
1.91 to 1.97 2
1673.5
1822.5
-149.0
8.2
1895.0
-221.5
11.7
1965.0
-291.5
14.8
1.98 to 2.04 3
1521.7
1890.0
-368.3
19.5
1945.7
-424.0
21.8
1834.3
-312.6
17.0
Table 81. — Differences in the metabolism of men and women, women classified according to body-weight.
Body-
weight.
N
Mean
total
heat-
produc-
tion.
Prediction from
body-weight.
Prediction from
stature and weight.
Prediction from
weight, stature, and age.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
Mean
predicted
total
heat.
Actual
less
predicted.
Per-
cent-
age
differ-
ence.
34.6 to 39.5
39.6 to 44.5
44.6 to 49.5
49.6 to 54.5
54.6 to 59.5
59.6 to 64.5
64.6 to 69.5
69.6 to 74.5
74.6 to 79.5
79.6 to 84.5
84.6 to 89.5
89.6 to 94.5
2| 1063.0
S| 1197.9
18! 1255.8
27; 1303.8
19! 1422.2
11 1449.2
41 1491.3
7| 1381.7
11 1334.0
2 1494.5
1 1591.0
3 1646.0
1195.0
1284.0
1370.4
1441.3
1525.1
1597.7
1677.5
1745.7
1861.0
1905.0
2015.0
2083.7
-132.0
- 86.1
-114.6
-137.6
-102.9
-148.5
-186.3
-364.0
-527.0
-410.5
-424.0
-437.7
11.0
6.7
8.4
9.5
6.8
9.3
11.1
20.9
28.3
21.5
21.0
21.0
1203.0
1253.4
1324.8
1400.5
1477.9
1552.5
1628.5
1658.0
1797.0
1817.0
1873.0
1953.3
-140.0
- 55.5
- 69.0
- 96.7
- 55.7
-103.3
-137.3
-276.3
-463.0
-322.5
-282.0
-307.3
11.6
4.4
5.2
6.9
3.8
6.7
8.4
16.7
25.8
17.7
15.1
15.7
1060.5
1264.8
1308.8
1411.0
1484.9
1552.9
1552.0
1502.8
1621.0
1728.0
1944.0
1901.0
+ 2.5
- 66.9
- 63.0
-107.2
- 62.7
-103.7
- 60.7
-121.1
-287.0
-233.5
-353.0
-255.0
0.2
5.3
4.0
7.6
4.2
6.7
3.9
8.1
17.7
13.5
18.2
13.4
The results of predicting the total heat-production of women from
the regression of total heat on body- weight in men are shown in com-
parison with the average actual heat-productions of women in the
first section of table 81.
212 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In every group the observed total production of the women is
distinctly lower than it would be if the group were composed of men
of Uke body-weight.
The graphic representation of these results for grouping b}^ body-
weight in the lowermost figure, A, of diagram 30, shows the widest
divergence of the actual from predicted heat-productions found in any of
Diagram 29. — Comparison of metabolism of men and women. Women
classified according to body-surface.
the four groupings, i.e., by age, stature, body-surface, and body- weight.
The discrepancy is particularly great in the case of the heavier women.
The largest divergence between the theoretical and the actual heat-
productions is found when the theoretical values for the women are
computed by assuming that the heat-production of a woman should
BASAL IMETABOLISM OF NORMAL AfEN AND WO]VrEN. 213
be the same as that of a man of like weight. The greatest increase in
the amount of divergence between the theoretical and the actual heat-
production is apparently found toward the upper limit of the range
of the bases of classification. It seems reasonable, therefore, to assume
(as a working hypothesis for further investigation) that body-weight
DiAOBAM 30. — Comparison of metabolism of men and women. Women
classified according to bodj'-weight.
rather than stature or body-surface is the primarj'' proximate factor
in bringing about this obser\''able tendency' for the women with greater
stature and greater body-surface to show a relatively greater deficiency
in metabohsm. If this ^dew be correct, the observed relationships for
stature and body-sm-face would be the resultant of this primary inter-
relationship and the correlations of both stature and area wath weight.
214 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
We now apply a further test of the existence of a sexual differentia-
tion with respect to metabolic activity in the human adult. In Chapter
VI the value of multiple-regression equations, involving both stature
and body-weight, for purposes of prediction has been conclusively
demonstrated. We may now make use of equations of this type for
predicting the amount of heat in calories per 24 hours which a woman
would produce if she were a man of the same stature and body-weight.
We shall thus avail ourselves of all the advantages of the selected-group
method employed in earlier papers from the Nutrition Laboratory,^*
but by the use of suitable statistical methods shall avoid certain real
difficulties encountered, but not overcome, by them.
What we have done is in effect this : We have expressed the rela-
tionship between heat-production and stature and weight in men as
a mathematical plane, the coordinates of which give the most probable
heat-production in individuals of any combination of stature and
weight. Using this plane to predict the heat which a woman of given
weight and stature would produce if she were a man, we have a series
of check or control values which is free from the disadvantages of the
empirical selected-group system.
Using the equation
h = -314.613-M3.129 w; -1-6.388 s
based on men we have computed the theoretical heat-production for
each woman.
We have treated the differences between the actual and the cal-
culated heat-production in three ways.
The distribution of the deviation of the actual heat-production of
each woman from her computed production is shown in table 84, to
be discussed below.
The mean theoretical and actual heat-productions for groups of
individuals classified by age, stature, body-surface by the Du Bois
height-weight chart, and body-weight have been calculated, and the
differences between theoretical and actual heat-production are recorded
under the caption ''Prediction from weight and stature" in tables
77, 79, 80, and 81.
Without a single exception the 39 comparisons indicate a lower
metabolism in women. The differences between observed and theo-
retical values range from 1.5 to 18.6 per cent in the case of groups
classified according to age, from 0.9 to 27.0 per cent in the case of
women grouped according to stature, from 2.9 to 25.8 per cent in the
case of subjects arranged according to their body-surface, and from
3.8 to 25.8 per cent in the case of groups of women assembled on the
basis of body-weight.
14 Benedict and Emmes, op. cit.
BASAL METABOLISM OF NOR^LVL MEX AND WOMEN. 215
These results are expressed graphically in the second figure, B, of
diagrams 27 to 30. These figures differ from those representing pre-
diction from linear equations (A) in that the mean theoretical heat-
productions do not lie in sensibly a straight line. The discrepancy is
especially great in the classification by statiu"e, where the disturbing
influence of weight is very obvious.
The difference between the graphs for body-weight and body-sur-
face area is not quite so clearly marked as in the case of the linear
equations, but the more conspicuous deficiency in the metaboUsm of
the heavier women is manifest.
The results fully confirm the analysis on the basis of the linear
equations.
We now turn to the results secured when age as well as body-weight
and stature is taken into account in determining the theoretical heat-
productions of the women. The equation, based on the 136 men, is
/i =66.4730 -hl3.7516 W7 -{-5.0033 s -6.7550 a
By the evaluation of this equation for each woman by inserting her
weight w, stature s, and age a, we obtain her probable heat-production
on the assumption that she is a man of like weight, stature, and age.
A comparison of the calculated average heat-productions of women
grouped by age, weight, body-surface, and by stature is made in the
final sections of tables 77, 79, 80, and 81.
With one exception — that of the lowest-weight group containing
only 2 women — which is numerically insignificant, the 39 comparisons
indicate that the actual heat-production is lower than it would be if
these indi\dduals were men of the same age, statiu-e, and body- weight.
The amount by which the women fall short of their computed metab-
olism is measured by differences ranging from 4.9 to 7.8 when the classi-
fication is on an age basis, from 2.7 to 22.6 when grouping is made by
stature, from 1.4 to 17.7 when body-smrface sers-'es as a basis of classi-
fication, and (disregarding the one exceptional case) from 3.9 to 18.2
per cent when the women are thrown into groups of like body-weight.
The results are represented graphically in the third figure, C, of
diagrams 27 to 30. Correction for age has perhaps tended to reduce
slightly the differences between the obser\'ed and predicted-heat
productions, but (with the one slight exception already noted) they are
nevertheless conspicuous and persistent throughout the whole range
of whatever scale of classification is employed.
The reader will note that when the correction for age, stature, and
weight is made and the indi\'iduals are classified by age, the theoretical
and the empirical heat-productions are separated by roughly the same
distance throughout the whole age range.
As far as this method of analysis is concerned, more conclusive
proof of the existence of a sexual difference in the metabolism of male
216 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
and female adults could not be obtained. We now turn to another
method of analysis.
For purposes of comparison by group averages we have classified
the women in a table of double entry, table 82. The entries with signs
in this table are the differences between the theoretical and the actual
average heat-productions for the groups of individuals having the
weights and statures, indicated by the marginal columns. The differ-
ences are given in calories and in the average percentage of the com-
puted heat-production of each individual. The percentages follow the
Table 82.—
-Differences in metabolism of men and women, women classified
according to stature and weight.
Weight
in
kilograms.
Stature in centimeters.
General
averages.
149 to 157.
158 to 160.
161 to 163.
164 to 166.
167 to 178.
f
34.6 to 44.5 -j
44.6 to 49.5 1
49.6 to 54.5 -j
f
54.6 to 59.5 j
59.6 to 69.5 •
69.6 to 94.5
f
General -j
averages . [
- 76.6= 6.4
- 84.6= 6.7
N=5
- 48.5= 3.8
- 67.5= 5.2
iV = 2
'n=6
-131.0=10.1
- 53.0= 4.3
N=l
- 56.5= 4.5
+ 40.0= 3.4
A^ = 2
- 72.4= 5.9
- 53.1= 4.1
A^=10
- 61.4= 4.7
- 6.66= 5.1
^■ = 7
— 6.2= 0.4
- 32.6= 2.3
A^=5
— 32.0= 2.4
- 64.0= 4.6
N=2
-172.0=12.6
± 00.0= 0.3
N=3
-201.0=14.7
-198.0 = 14.5
A^=l
- 69.0= 5.1
- 53.5= 3.9
A^=18
- 39.5= 2.9
- 53.5= 3.8
Ar=4
-102.2= 7.4
-148.2 = 10.5
N=6
- 90.8= 6.4
- 75.7= 5.4
N=9
- 105.0= 7.4
-129.3= 8.8
A^=6
- 196.5 = 13.4
-168,5 = 11.8
Ar = 2
- 96.7= 6.8
-107.3= 7.5
N = 27
+ 48.3= 3.2
+ 9.0= 0.4
iV = 4
-222.0 = 15.1
-209.0 = 14.4
N=2
- 91.0= 6.3
- 38.6= 2.6
N=5
- 44.0= 2.9
- 94.0= 6.1
N = 3
- 44.2= 2.9
- 67.2= 4.3
N=5
- 55.7= 3.8
- 62.8= 4.2
N=19
+ 189.0=12.8
+ 125.0= 8.1
N=l
'n='6
-103.7= 6.7
- 38.5= 2.3
A' = 6
- 165.0=10.5
-187.0 = 11.7
-155.3= 9.7
-155.9= 9.7
N = 7
-112.3= 7.0
- 92.3= 5.7
N = 15
-134.0= 7.7
- 64.0= 3.8
N=l
-263.0=15.9
-112.0= 7.0
A' = 3
-256.5=14.6
-220.0=11.2
A^ = 2
-309.4=16.9
-222.4=12.7
A' = 5
-421.0 = 23.3
-256.0 = 15.2
A^=3
-303.3 = 17.1
-194.3 = 11.3
A^=14
- 32.9= 2.7
- 45.7= 3.6
iV = 22
-109.7= 7.3
-107.8= 7.5
N=18
-103.0= 6.8
- 69.7= 4.5
A^ = 24
-164.3 = 10.3
-126.8= 7.9
A^=19
-163.9 = 10.1
-132.5= 8.3
A^ = 20
-112.3= 7.3
- 94.0= 6.2
A^=103
equality sign. A negative sign indicates that the women show a lower
heat-production than would men of like characteristics . The theoretical
heat-productions were calculated in two ways. The entries with signs
in ordinary type are the differences between the observed and the
theoretical heat-productions when the latter are computed from weight
and stature only. The entries with signs in black-faced type are the
differences between the actual and the theoretical heat-productions
when the latter are calculated from weight, stature, and age.
In arranging the data for this table the individuals have been
assembled into somewhat larger and more arbitrarily limited groups
for both stature and weight than when they were classified with respect
BASAL IMETABOLISM OF XOEMAL AIEN AND WOMEN,
217
to one of these physical characters merely. This has been necessary
in order to secure a number of individuals in the several compartments
of the table. With the grouping of weight and stature adopted in the
accompanying table, 28 of the 30 different combinations of stature and
weight are represented by from 1 to 9 individuals each. When the
theoretical heat-productions are computed from weight and stature,
26 of the 28 groups of women classified with regard to both stature
and weight show lower average heat-productions than they would if
they were composed of men falling in the same range of stature and
weight. When weight, stature, and age are all taken into account,
24 of the 28 groups of women show lower average heat-productions
than they would if they were men of similar weight, stature, and age.
The general averages for all the individuals of given stature-groups
or weight-groups are by both methods without exception smaller than
would be found in men of like physical dimensions. The average defici-
ency for the whole series of women is 94.0 calories per 24 hours when
stature, weight, and age are taken into account, and 112.3 calories
when stature and weight only are considered. The differences for the
subgroups naturally vary widely because of the small numbers of indi-
viduals. The general average percentage deficiency when weight and
stature only are considered in the calculations of the theoretical heat-
productions is 7.3 per cent. WTien age is taken into accoimt as well
as stature and body-weight, the deficiency is 6.2 per cent.
Table 83. — Differences in the metabolism of men and women. Test based on data of
Palmer, Aleans, and Gamble.
Subject.
Age.
Weight.
Height.
Total
calories
per 24
hours.
Calcu-
lated
heat.
Actual
less
calcu-
lated.
Percent-
age
differ-
ence.
Miss M. A. H
21
24
22
21
20
21
23
57.9
70.9
48.1
76.0
77.7
79.8
67.5
157
169
155
168
166
170
170
1434
1648
1143
1497
1635
1480
1444
1506
1725
1355
1810
1830
1853
1690
- 72
- 77
-212
-313
-195
-373
-246
4.8
4.5
15.6
17.3
10.7
20.1
14.6
Miss R. R
MissH
Miss D. L
Miss F. M. R
Miss L. F. W
Miss R. Rob
More conclusive proof of the existence of a sexual differentiation
with respect to metabohsm could hardly be expected.
As a further test of our method we may compute the daily heat-
productions of the 7 young women studied by Palmer, Means, and
Gamble ^^ from the equation, based on our total men. The results
appear in table 83. For every individual the actual heat-production
is lower than it would have been in men of the same weight, stature,
and age. The differences range from 72 to 373 calories per 24 hours.
" Palmer, Means, and Gamble, Joum. Biol. Chem., 1914, 19, p. 239; Means, Md., 1915, 21, p. 263.
218 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN,
In percentages of the theoretical heat-production they range from 4.5
to 20.1 lower than in men of the same weight, stature, and age. Thus
this series of measurements by another group of observers, whether
analyzed by the simple method of averages, as on page 204, or by the
special methods here employed, fully confirms the conclusions drawn
from our own data.
We must however in this connection refer to certain considerations
to be taken up in the following chapter (p. 232).
A discussion of the data on the metabolism of German men and
women recorded by Magnus-Levy and Falk is reserved for the following
chapter (page 232).
Table 84. — Deviations of metabolism of individual women from, the masculine standard.
(Note the high proportion of cases in which metabolism is lower.)
Deviations
from the
male
standard.
Prediction
from
age.
Prediction
from
body-
surface.
Prediction
from
stature.
Prediction
from
body-
weight.
Prediction
from
stature
and weight.
Prediction
from
stature,
weight, and
age.
+338 to +412
+263 to +337
+ 188 to +262
+ 113 to +187
+ 38 to +112
1
4
3
3
9
1
4
I
7
1
8
2
3
9
1
3
9
- 37to+ 37
9
19
14
11
17
22
- 38 to -112
-113 to -187
-188 to -262
-263 to -337
-338 to -412
-413 to -487
-488 to -562
-563 to -637
-638 to -712
9
5
21
18
20
10
5
1
22
20
16
6
2
2
1
22
20
14
10
5
1
22
18
20
12
5
2
3
i
22
21
17
7
1
2
2
22
25
12
6
2
1
In the foregoing discussion comparisons have been made on the
basis of differences in the empirical and theoretical average metabolism
of individuals of various ages, statures, body-weights, body-surfaces,
of various statures and body-weights, and of various statures, weights,
and ages. As far as we know, these methods of comparison are free
from all objections and give conclusive results. They fail, however,
to give the distribution of the individual errors of predicting female
from male metabolism due to the sexual differentiation which has
been shown to exist.
These errors we have seriated in a grouping of 75 calories range in
table 84. The entries in the first four frequency columns of this table
show the distribution of the deviations of the actual heat-productions
of our women from the values which would most probably be found if
they were men of like age, stature, body-weight, or body-surface area
BASAL JklETABOLISM OF NORilAL MEN AND WOMEX. 219
as measured by the Du Bois height-weight chart. The fifth column
shows the deviations of the observ^ed from the theoretical values when
the latter are calculated by the simultaneous use of stature and body-
weight. Finally, the last colunm shows the de\4ations of the observed
from the theoretical values when body-weight, stature, and age are
simultaneously taken into account.
Taking de\iations of —37 to +37 as representing a central "zero"
class, we note that by all methods there is a large excess of negative
differences — i.e., of differences indicating a lower metabolism in women.
Thus, on the basis of computation invohing age there are only 5
individuals showing a metabolism more than 37 calories per day above
their theoretical heat-production as compared with 89 showing a
metaboHsm of over 37 calories below their theoretical heat-production.
When computation is based on body-surface area, only 15 women
show more than 37 calories per day above their theoretical heat-
production as compared with 69 who are in defect by the same amount
or more. On the basis of stature the individuals of the two classes
stand in the ratio of 17 to 72; on the basis of body- weight in the ratio
of 9 to 83; on the basis of both weight and stature in the ratio of
14 to 72, and on the basis of weight, stature, and age in the ratio of
13 to 68. Thus the results for individuals fully substantiate the
conclusions based on averages above.
4. COMPARISON OF BASAL METABOLISM OF MALE AND FEMALE
NEW-BORN INFANTS.
The foregoing analysis of the data for adults has demonstrated
beyond all question the differentiation of the adult male and female
individual in man in respect to metaboUc activity. From the stand-
point of the student of the physiology of sex it is important to inquire
whether this differentiation obtains only during the period of adult
life or whether it is demonstrable in infancy. To test this matter, we
naturally turn to Dr. Fritz B. Talbot's series of new-bom infants.^®
The method to be followed is identical with that used above. We
shall predict the metabolism of girl infants from constants based on
the boys and determine the sign and the magnitude of the difference
between the obsers^ed and calculated values. We require, therefore,
equations showing the regression of total heat on stature (body-length),
on weight, and on body-surface in the male infants. These are
A =25.156+34.517 wj, /i = -229.576+7.340 s, ;i = -31.703+749.914 a^
where h = total heat per 24 hours, ic = weight, s = stature (length), and
a2,= body-surface area computed by the Lissauer formula.
The results for the infants grouped by body-length are shown under
the caption "Prediction from linear equations" in table 85. In three
'• Benedict and Talbot, Camegie Inst. Wash. Pub. No. 233, 1915.
220 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
groups the average heat-productions predicted on the assumption that
the subjects were boys of like body-length are higher and in three
groups they are lower than the actual mean values. Thus, as far as
this test goes, it furnishes no evidence of a sexual differentiation in
metabolism in new-bom infants.
Table 85. — Tests for differences in metabolism of male and female infants.
Prediction from
Prediction from
Female
infants
Mean
actual
linear equations.
planar equations.
classified
total
Mean
Actual
Percent-
Mean
Actual
Percent-
by stature.
heat.
predicted
less
age of
predicted
less
age of
total heat.
predicted.
predicted.
total heat.
predicted.
predicted.
46.0 to 47.0
111.3
112.0
-0.8
0.7
118.3
-7.0
5.9
47.5 to 48.5
120.1
121.1
-1.0
0.8
119.7
+0.4
0.4
49.0 to 50.0
139.7
134.6
+5.1
3.8
133.5
+6.2
4.7
50.5 to 51.5
142.0
145.3
-3.3
2.3
146.9
-4.9
3.3
52.0 to 53.0
161.1
155.7
+5.4
3.5
158.4
+2.7
1.7
53.5 to 54.5
168.0
167.8
+0.3
0.1
172.3
-4.3
2.5
The differences between the actual heat-production and the theo-
retical heat-production as calculated from the regression of total heat
on body-surface in the boys are shown for groups of girl infants classi-
fied according to body-surface by the Lissauer formula in the first
section of table 86. Those calculated from the equation for the rela-
tionship between total heat-production and body-weight in the boys
appear in groups of various body-weights in the first part of table 87.
Table 86. — Tests for differences in metabolism of male and female infants.
Prediction from
Prediction from
Female
Mean
linear equations.
planar equations.
infants
actual
classified by
total
Mean
Actual
Percent-
Mean
Actual
Percent-
body-surface.
heat.
predicted
less
age of
predicted
less
age of
total heat.
predicted.
predicted.
total heat.
predicted.
predicted.
0.170 to 0.186
109.0
106.0
+3.0
2.8
106.0
+3.0
2.8
0.187 to 0.203
122.1
116.4
+5.7
4.9
115.3
+6.9
5.9
0.204 to 0.220
120.8
125.3
-4.5
3.6
124.3
-3.5
2.8
0.221 to 0.237
137.6
140.3
-2.7
1.9
138.4
-0.8
0.6
0.238 to 0.254
153.1
150.9
+2.3
1.5
150.6
+2.5
1.7
0.255 to 0.271
163.1
164.9
-1.7
1.0
164.9
-1.7
1.0
0.272 to 0.288
181.5
177.0
+4.5
2.5
178.0
+3.5
2.0
By both of these methods of computation and analysis, the results
are very similar to those found in the grouping by stature above.
Some of the groups show a lower, others a higher, metabolism than
the computed value. Taking these data as a whole they afford no
evidence that the sexual differentiation in metabolic activity demon-
strated for the adults obtains in new-bom infants.
Using the multiple-regression equation,
/i = 22.104-h31.049w;+1.162s,
for the boy babies, to predict the heat-productions of the girl babies
BASAL METABOLISM OF NORMAL MEN AND WOMEN. 221
we have the de^^ations of the average actual from calculated heat-
productions shown under the caption "Prediction from planar equa-
tions" in tables 85 to 87. These differences are sometimes positive
and sometimes negative in sign. Thej^ show, therefore, that the
actually obsen-ed heat-productions of the girl babies are sometimes
higher and sometimes lower than they would be expected to be if they
were boys of the same phj^sical dimensions. As far as our data go they
indicate, therefore, that on the average there is no sensible difference
between the heat-productions of the two sexes in the first week of Ufe.
Table 87. — Teste for differences in metabolism of male and female infants.
Prediction from
Prediction from
Female
Mean
linear equations.
planar equations.
infants
actual
classified by
total
Mean
Actual
Percent-
Mean
Actual
Percent-
body-weight.
heat.
predicted
less
age of
predicted
less
age of
total heat.
predicted.
predicted.
total heat.
predicted.
predicted.
2.12 to 2.46
109.0
107.0
+2.0
1.9
106.0
+3.0
2.8
2.47 to 2.81
123.6
117.1
+6.5
5.6
116.1
+7.5
6.5
2.82 to 3.16
118.9
125.1
-6.3
5.0
124.6
-5.7
4.6
3.17 to 3.51
137.6
139.7
-2.1
1.5
138.4
-0.8
0.6
3.52 to 3.86
153.1
150.5
+2.6
1.7
150.6
+2.5
1.7
3.87 to 4.21
163.1
164.9
-1.7
1.0
164.9
-1.7
1.0
4.22 to 4.56
181.5
178.0
+3.5
2.0
178.0
+3.5
2.0
5. RECAPITULATION.
Our analj'sis of the available data to ascertain whether men and
women differ in the level of their metabohsm has fully confirmed and
considerably extended the conclusions reached by Benedict and Emmes
in the first critical investigation of the problem. Our finding that the
metabohsm of women is significantly lower than that of men is based
on three lines of evidence.
1. The general averages are higher in men than in women. The
average woman shows a daily heat-production about 300 calories less
than the average man. If correction be made for body-size by expres-
sing heat-production in calories per kilogram of body-weight, she shows
an average heat-production of about 1.2 calories per unit of weight
less than the man. If body-surface area be used as the basis of correc-
tion, the woman shows daily heat-production of 77 calories per 24
hours per square meter as measured bj- the ^Meeh formula and 75
calories per square meter as measured by the Du Bois height-weight
chart less than that of the man.
2. The deviation of heat-production of the indi^'idual woman from
the general average associated -sN-ith a de\'iation in her body-weight
from the general average is less than comparable de^'iations in the man.
When changes in heat-production associated "s^^ith changes in other
characters in men and women are compared by means of equations
222 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
based on the data asa whole, the line for the men is found to lie above
that for the women.
3. When the theoretical heat-production of women is calculated
by inserting their actual physical measurements in equations based on
series of men, the actual heat-production is generally lower than the
theoretical value. Larger women show a relatively larger deficiency
in heat-production than smaller ones. The suggestion is made that
body-weight is the primary factor in determining the greater deficiency
in the heat-production of larger women, and that it is observable in
the case of stature and body-surface area primarily because these are
correlated with body-weight.
The most critical test shows that when body-weight, stature, and
age are taken into account women show about 6.2 per cent lower
metabolism than men.
Our results show that the differentiation of the sexes in metabolism
is not evident in new-born infants. The researches of Sond^n and
Tigerstedt suggest that it is well marked in youth.
Our findings are not in accord with the conclusion of Sond^n and
Tigerstedt ^^ "dass sich der im Kindes - und Jugendalter so deuthch
und scharf hervortretende Unterschied zwischen den beiden Ge-
schlechtern allmahUch verwischt, um endlich bei herannahendem
Greisenalter ganz zu verschwinden." Instead we find the difference
between the metabolism of men and women well marked throughout
the period of adult life.
" Sond6n and Tigerstedt. Skand. Arch. f. Physiol., 1895, 6, p. 96.
Chapter VIII.
STANDARD BASAL METABOLISM CONSTANTS FOR
PHYSIOLOGISTS AND CUNICIANS.
1. THE NECESSITY FOR AND FUNDAMENTAL NATURE OF STANDARD
METABOLISM CONSTANTS.
While the discussions in the foregoing chapters should show that
the determination of basal metabolism, or of variations in metaboUsm,
in normal men and women presents a series of important physiological
problems, it is quite e\4dent that investigations of metabolism will
receive the widest recognition and be of the greatest practical im-
portance if they can be extended to include measurements based on
individuals performing different amounts or kinds of work, subsisting
on different diets, or suffering from various diseases.
All such studies must be comparative. The metabolism of a group
of indi\'iduals affected by any special condition has little interest
unless it can be shown to be the same as or to differ sensibly from the
basal metabohsm of a comparable group of normal individuals. For
example, before any discussion of metabohsm in indi\'iduals suffering
from disease can be of value a series of non-pathological controls
must be established to serve as a basis of comparison. The need for
such control constants has been recognized with varjdng degrees of
clearness by all those who have worked on the problem of the metab-
ohsm of individuals suffering from disease.^
While, as far as v.e are aware, it is now universally considered that
the value of a metabolism determination on a pathological subject is
strictly limited by the trustworthiness of the normal control with
which it is compared, the estabhshment of suitable controls has been
the subject of serious disagreement. ''Controversies have raged more
1 Magnus-Le\T and Falk (Arch. f. Anat. u. Phys., Physiol. Abt., 1S99, Suppl., p. 315) stated
one of the purposes of their research begun in 1895 to have been the determination of normal
metabolism data for comparison with their pathological records. Benedict and Joslin (Carnegie
Inst. Wash. Pub. No. 136, 1910) in 1910 published such determinations on normal subjects as were
then available as a basis of comparison with their diabetic individuals. Lusk (Science, n. s. 1911,
33, p. 433) in reviewing this publication, emphasizes indirectly the importance and the inadequacy
of control series.
Again, in reference to investigations of respiratory metabolism in disease, Du Bois (Am. Joum.
Med. Sci., 1916, 151. p. 785: also Studies Dept. Physiol., Cornell Univ. Med. Bull., 1917, 6,
No. 3, Part II) says: "The main object of all investigators has been to determine the heat-
production of the patient while at complete rest 14 hours or more after the last meal. This is the
BO-called basal metabolism, and is of interest only when compared with the figures obtained on
normal individuals. Since it is impossible to measure the metabolism of many of our patients
when they are entirely recovered, it is necessary to calculate what the man's metabolism would
be were he normal."
223
224 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
fiercely about the normal controls than about the pathological cases." ^
The difficulty has been twofold. First, the measurement of an ade-
quately large series of individuals has been a very heavy undertaking.
Second, the selection of the proper measure of metabolism in the
control series has presented theoretical difficulties. In relation to the
first of these we may quote a statement made as late as 1914: ^
"The impetus given to thje study of gaseous and gross metabolism during
the past decade has resulted in a large number of observations, both in the
domain of physiology and pathology. Investigators in pathology are, how-
ever, continually confronted by the paucity of normal data with which to
compare their observations."
Somewhat later Gephart and Du Bois ^ wrote :
"The importance of the normal control has been emphasized so strongly
by the serologists and the management of the control has been developed by
them to such an art that it has seemed advisable to apply some of their methods
of critique to the study of the respiratory metabolism These precau-
tions .... have been made necessary by the fact that the normal control is
usually the point of attack in serological controversies. Likewise in the study
of metabolism the normal control is coming to be recognized as the weakest
part of the experiment The literature is notoriously filled with false
theories, of which by far the greater part would never have been promulgated
if sufficient attention had been given to normal controls."
Notwithstanding the confidence which has generally prevailed in
the validity of the expression of metabolism in calories per square meter
of body-surface area, the theoretical difficulties in the selection of
control series have not passed unrecognized. "The selection of the
proper normal base-line is a matter of extreme difficulty."^ The
detailed discussion in the preceding chapters of the factors associated
with variations in basal metabolism suggests that the difficulties of
the selection of proper controls has been underestimated rather than
overestimated in the past.
A brief consideration of the fundamental principles of the estab-
lishment of standard or control constants to be used as a basis of com-
parison in experimental work is in order.
In the simplest cases the metabolism of an individual under any
exceptional condition may be compared with his own basal metabolism
which serves, therefore, as a standard or control. This is true, for
example, in the case of variations in muscular activity, in rationing
or in prolonged fasting. Even in the case of protracted illness, sugges-
tion has been made of the possibility of using basal metabolism deter-
minations upon the same individual, obtained subsequent to recovery,
as a basis of comparison with the constants secured when the subject
* Du Bois, Am. Joum. Med. Sci., 1916, 151, p. 785.
' Benedict, Emmes, Roth, and Smith, Journ. Biol. Chem., 1914, 18, p. 139.
* Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 835.
^ Gephart and Du Bois, Arch. Intern. Med., 1915, 15, p. 858.
STANDARD BASAL METABOLISM CONSTANTS. 225
was in the pathological state. Such a course is, however, obviously
impracticable in the vast majority of instances, since the duties or
inchnations of the former patient may preclude periods of study sub-
sequent to those made during confinement in a hospital. Furthermore,
subsequent to a period of severe illness, there is no assurance in any
single period of determinations that the subject has returned, or
indeed that he ever will return, to the normal condition, or at least
to the condition antecedent to the disease. Finally, because of the
great variations in basal metabohsm from individual to individual,
or under experimentally controllable conditions within the same indi-
vidual, single comparisons have little crucial value as a basis for
generahzation concerning the influence of special conditions on metab-
olism unless the influence be very great.
Practically, therefore, one is reduced in the great majority of cases,
and especially in those of the greatest medical interest, to the statis-
tical method of comparing observations on a group of individuals of a
special class (the metabolism of which is being investigated) with those
on individuals which do not possess the characteristics under considera-
tion, or with "normal" individuals.
In experimental work there are two ways in which control constants
maybe determined : (1) The control observations may be made simul-
taneously with those on the individuals of the special class under
investigation. This method is necessarily followed when it is impossible
to regulate external conditions with exactness and when individuals
which are exactly comparable except for the particular characteristics
under investigation must be employed — for example, in cases in which
two manunals from the same litter, two groups of birds from the same
clutch, or two lots of seedlings from the same parent plant must be
utilized. (2) Standard determinations may be used as a basis of com-
parison for all special groups. This method may be followed in cases
in which it is impossible to obtain for simultaneous observation indi-
viduals which are more nearly alike than those which can be obtained
at other times, and in which the experimental technique is so highly
perfected that there is no question but that measurements made at
different times or by different observers are comparable within the
limits of a very slight physical experimental error.
In work on metabolism the second method is not merely justified
but necessary. The justification for the establishment of a standard
control series instead of making normal control measurements for each
pathological case Hes in the fact that respiration chambers, calorimeters
and other apparatus and technique essential for investigating basal
metabolism have been brought to such a stage of perfection that, with
proper chemical and physical standardizations at frequent intervals,
technical errors may be disregarded. Furthermore, subjects upon
whom basal metaboUsm determinations are made must comply so
226 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
exactly with a generally adopted set of conditions that there is no
advantage in carrying out a normal control determination coincident-
ally with the measurement of the metabolism of subjects suffering
from any disease which may be under investigation.
The necessity for establishing a standard control series rests upon
two fundamental considerations. First, variation in basal metabolism
from subject to subject is so great that to be of critical value a control
series must comprise a relatively large number of individuals. Sec-
ondly, the very limited equipment available in all the scientific insti-
tutions of the world for carrying out trustworthy metabolism deter-
minations and the great expenditure in time and effort necessary for
making these determinations render it practically essential that data
which may be regarded as standard for long periods of time be secured
once for all, in order (in so far as possible) to set the limited equipment
free for investigating the many pressing problems of metabolism under
special conditions of exercise, nutrition, and disease. Hitherto control
values have been estabhshed in two ways.
First, the average value of metabolism per unit of body-weight or
body-surface in a selected group of subjects has been used as a control
value, and the observed metabolism of the hospital patient or other
subject, expressed in terms of the same units, has been compared
directly with this value. This is the method used by the majority of
investigators in the past.
Second, the average of the constants secured from a group of normal
individuals as nearly as possible comparable, in physical characters,
with the subjects of the special group under consideration is used as a
standard of comparison. This is the selected-group method employed
at the Nutrition Laboratory in a study of diabetes, of vegetarians and
non-vegetarians, of athletes and non-athletes, and of men and women.
The obvious objection to the population-average method of com-
puting control values is that, in obtaining the fundamental constant,
individuals of the most diverse physical characters are lumped together
indiscriminately. From the physiological standpoint it is quite unrea-
sonable to compare a standard value obtained from a large number of
normal robust individuals with that derived from an emaciated patient
in the clinic; this is evidenced by the fact that an individual undergoing
a prolonged fast may show a decrease of 28 per cent in his metabolism,
as measured in relation to body-surface, simultaneously with the
assumption of an emaciated condition quite comparable with that
observed in some pathological subjects.
The selected-group method in which pathological or other special
groups are compared with normal individuals of like height and weight,
i.e., of general anatomical and morphological similarity, is free from
this very serious criticism, but is open to two others. (1) There is
considerable opportunity for personal equation in the selection of the
STANDARD BASAL [METABOLISM CONSTANTS. 227
series of mdi\'iduals to be used as a control in any specific instance;
(2) because of the well-known and large variations in the metabohsm
constant from subject to subject the average value based on a small
group of indi^dduals may be either too large or too small bj^ an amount
determined by the probable errors of random sampling.
It seems clear that some form of the selected-group method will fur-
nish the most satisfactory basis of comparison. Ideally one should find
a method which will combine all the advantages, and reduce to a mini-
mima all of the disadvantages, of the two methods hitherto employed.
The results of the analysis in the preceding chapters have shown
that four factors need to be taken into account in estimating the basal
metabohsm of a subject: sex, body-weight, stature, and age.
The importance of body- weight in the selection of controls has been
very generally recognized, at least tacitly, by all those who have
expressed metabolism in terms of oxj^gen consumption, carbon-dioxide
excretion, or calories produced per kilogram of body-weight. While
the relation of stature to metabolism is not so ob\'ious as that of bodj"^-
weight, it has been shown in Chapter IV to be a character of independ-
ent significance in the determination of metabohsm. It has long been
known that metabohsm is related to age. In Chapter V this relation-
ship has been expressed quantitatively.
The method used here for the establishment of standard normal
metabolism constants is essentially an extension of the selected-group
method used earher for various comparisons at the Nutrition Labora-
tory. Instead of using the empirical average heat-production of an
actually obser\'ed group of individuals, we shall give the "smoothed"
or "graduated" values for groups of given age, stature, and body-
weight as determined from equations based on all the available data.
We thus ob\nate, as far as possible, the two main objections to the
selected-group method: (a) the possibihty of the influence of personal
equation in the selection of the normal values to be used as controls
in any specific case, and (6) the probable errors of random sampling
attached to the control constants. The rather detailed apphcation
of the method in Chapters V, VI, and VII should have made the whole
theory perfectly clear. There remains, therefore, merely the restate-
ment of the equations and the tabhng of a series of standard constants
to be derived from them in the form most convenient for practical use.
As shown in Chapter VI, p. 190, the multiple prediction equations
based on the total adults of the two sexes are
For men h = + 66.4730+13.7516 tp+5.0033«-6.75oOa
For women A = +655.0955+ 9.5634 u;+1.8496s-4.6756a
where /i = total heat-production per 24 hours, w = weight in kilograms,
s= stature in centimeters, and a=age in j^ears. The evaluation of
these equations, which are used in the calculation of the theoretical
228 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
heat-production for any individual, requires merely the substitution
of the actually measured weight, stature, and age. The tabling of
these equations for a range of body-weight, stature, and age which will
be encountered in practice results in a multiple-prediction normal
standard, or an adult standard normal, with which the observed basal
metabolism (daily heat-production) of individual subjects may be
compared. While the standard values are so arranged as to facilitate
the comparison of individual subjects the reader must remember that
because of the great variability of metabolism from subject to subject
a comparison of a single subject of any special class furnishes a very
slender basis for generalization concerning that class. It is only when
reasonably consistent results are obtained from series of individual
comparisons that generalizations can satisfactorily be drawn.
The validity of these formulas has been exhaustively tested in
comparison with the methods hitherto employed in calorimetry in the
section devoted to the body-surface law. It has there been shown
that, when applied to the individual subjects of the largest series of
basal metabolism data yet secured by a single group of observers, these
formulas give the most satisfactory prediction of the basal metabolism
of an unknown subject of any method hitherto employed. With certain
reservations concerning the range of age over which these formulas may
be legitimately appUed, we have the highest confidence in their validity.
2. TABLES OF MULTIPLE PREDICTION STANDARD METABOLISM
CONSTANTS.
For the convenience of those who have to estimate the metabolism
of subjects from physical characteristics either in the clinical ward or
in the physiological laboratory, we have prepared tables of the values
of these equations for the various grades of body-weight, stature, and
age. The form adopted for these tables has been determined by purely
practical considerations. Because of the large number of permutations
of weight, stature, and age, it is obviously out of the question to publish
constants for each possible combination of these characters; but two
tables of constants may be constructed from which the worker may
obtain the most probable metabolism of a man {i.e., the average
metabolism of a group of individuals of like weight, stature, and age)
by simply adding together the entry for body-weight in table I and
that for stature and age in table II. For women the comparable
entries in tables III and IV will be used.
These tables have been constructed to be entered by body-weight
recorded to the nearest tenth of a kilogram, stature recorded to the
nearest centimeter, and age to the nearest year. In following this
course we have been under no illusions concerning these physical meas-
urements, but have used the units which have become conventional
among physiologists. A measiu-ement of stature to the nearest centi-
STANDARD BASAL METABOLISM CONSTANTS. 229
meter is about the limit of accuracy. To retain tenths of kilograms is
certainly weighing with a degree of refinement hardly justified by the
continually changing state of the experimental object. Finally, when
individuals are recorded to the nearest year of age we may remember
that the}'^ are on an average a quarter of a year older or younger than
the age to which they are assigned.
Against these objections is to be urged the fact that measurements
which are not made with great refinement are Yery apt to lack essential
accuracy. Since these are the divisions of the scales which have been
most generall}'' emploj'ed bj' physiologists it has certainly not seemed
desirable io replace them by coarser ones. Furthermore, it must be
noted that our equations are not based upon a few observations, but
upon over 100 determinations for each sex. Therefore, as a basis of
generahzation, thej^ have a much higher degree of accuracy than any
single observation or group of a small number of observations.
The sources of error in using the multiple prediction tables are two.
(1) The tables themselves are based upon a finite number of
observ'ations. In comparison with phj'^siological measurements as a
class, the number of measurements is verj^ large; biometricallj' con-
sidered it is small. Everj' constant in these equations is therefore,
somewhat too large or somewhat too small because of the innate varia-
bility of human individuals. If another group of subjects were added
to the series upon which these tables are based the factors would be
slightly changed. The constants are subject to revision with increasing
intensiveness or extensiveness of work, just as all physical and chemical
constants are.^ Until more data are available they must be taken
as they are, with the understanding that the standard has its probable
error, just as have the indi\'idual metabolism measurements which
will be compared with it.
(2) As we have repeatedly emphasized in the foregoing pages, every
individual metabolism measm-ement considered as a basis for general-
ization concerning the peculiarities of the individual upon which it is
based {e.g. physical characteristics, pathological state, etc.) has a large
probable error. Thus one can not compare the metabolism of a single
individual of any specified tj-pe with the standard constant and use
it as a basis of generahzation. It is only when a series of individuals
of the specified type are considered that generaUzations may be di^awTi.
From the standpoint of arithmetical technique, the tables probably
correctly represent the results of the largest series of determinations on
normal men and women with an error of not over 1 calorie per 24 hours.^
• We plan later to prepare a revised edition of these tables based up>on more extensive data.
* The results could have been given in such a form that the final constants would have been
arithmetically correct to less than a single calorie per 24 hours had decimal places been retained
in the tables. This seemed a quite needless refinement. Those who desire may derive the theo-
retical values to more places directly from the equations. The theoretical values in the series
of illustrations in this chapter were determined in this way.
230 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
In constructing these tables the constant term of the equation and
the corrective term for body-weight are combined in table I for men
and table III for women. The corrective term for stature and age is
given in table II for men and table IV for women. These tables must he
used in conjunction only. Thus table I or III must not be used to esti-
mate the metabolism of an individual whose weight only is known.
Tables II or IV must not be used to estimate the metabolism of an
individual whose weight is unknown.
The use of the tables presents no difficulty whatever. Three exam-
ples follow:
Man 27 years Woman 22 years Woman 66 years
old, 172 cm. in old, 166 cm. in old, 162 cm. in
height, 77.2 height, 77.2 height, 62.3
kilos, weight. kilos, weight. kilos, weight.
From table I 1128 From table III 1393 From table III 1251
From table II 678 From table IV 204 From table IV - 9
Predicted calories 1806 Predicted calories .... 1597 Predicted calories .... 1242
3. ILLUSTRATIONS OF PRACTICAL APPLICABILITY OF STANDARD
MULTIPLE PREDICTION TABLES OF BASAL METABOLISM.
In a foregoing chapter (VII) the practical usefulness of the equa-
tions upon which these tables are based has been fully demonstrated in
their application to a specific problem, that of the sexual differentiation
in metabolic activity. It now remains to supply further illustrations
of their range of usefulness by applying them to certain cases in which
the individuals were measured by workers outside of the Nutrition
Laboratory, in which the individuals fall outside the range of age or
of physical form upon which the equations were based, or in which
the subjects were in a particular physiological or pathological state,
the influence of which upon metabolism is under investigation.
Illustration A. Tests of Normality of Series of Determinations.
In applied calorimetry the need to be met is practically always the
same. One requires to know whether a special series of metabolism
measurements agrees with a larger series of determinations taken as a
standard. If the special series is made up of individuals characterized
by some specific condition, e.g., rationing, exercise, or disease, the
result of the comparison shows whether this specific peculiarity may
or may not be considered to have a determining influence on the basal
metaboUsm. Some special cases of this sort will be examined.
As a first illustration of the practical usefulness of our multiple-
prediction equations, we may consider the agreement between certain
series of measurements by other observers and the standard which
has been based upon the Nutrition Laboratory experience. Take
first a series of young men and women studied by Palmer, Means, and
Gamble * and discussed in relation to the problem of the body-surface
* Palmer, Means, and Gamble, Joum. Biol. Chem., 1914, 19, p. 239.
STANDARD BASAL METABOLISM CONSTANTS.
231
law by Means.® The data for the application of the equations and the
results of their application are shown in table 88 for the 8 men and in
table 89 for the 7 women.
In these and the following comparisons the differences are taken
(actual metabolism) less (calculated metabolism)
so that a positive sign indicates supernormal and a negative sign
subnormal metabolism in a subject. In this regard the constants of
this chapter differ from those in Chapter VI. The reason for the differ-
ence seems a logical one. In that place we were seeking to determine
empirically which of a series of methods proposed for predicting metab-
Table 88. — Comparison of metabolism of men studied by Palmer, Means, and Gamble irith
normal (multiple prediction) standard.
Actual
Calculated
Actual
Subject.
Age.
Weight.
Stature.
daily
heat-
production.
daily
heat-
production.
less calcu-
lated meta-
boli.sm.
Percentage
difference.
Dr. W. W. P
32
93.9
187
2004
2077
- 73
- 3.5
Mr. H. L. H
27
62.0
172
1574
1597
- 23
- 1.4
Dr. W. S. W
25
73.8
177
1660
1798
-138
- 7.7
Dr. L. W. H
25
68.4
169
1671
16S4
- 13
- 0.8
Dr. P. H. P
27
77.2
172
1620
1S06
-186
-10.3
Dr. J.H.M
29
70.7
175
1599
1718
-119
- 6.9
Dr. J. L. G
30
68.1
181
1679
1706
- 27
- 1.6
Dr. L. H. N
31
58.1
169
1452
1502
- 50
- 3.3
Table 89. — Comparison of metabolism of veomen studied by Palmer, Means, and Gamble with
normal [multiple prediction) standard.
Subject.
Age.
Weight.
Stature.
Actual
daily
heat-
production.
Calculated
daily
heat-
production.
Actual
less calcu-
lated meta-
bolism
Percentage
difference.
Miss M. A. H.
Miss R. R
Miss H
MissD. L
Miss F. M. R.
Mbs L. F. W .
MissR. Rob..
21
24
22
21
20
21
23
57.9
70.9
48.1
76.0
77.7
79.8
67.5
157
169
155
168
166
170
170
1434
1648
1143
1497
1635
1480
1444
1401
1534
1299
1594
1612
1634
1508
+ 33
-1-114
-156
- 97
+ 23
-1S4
- 64
+ 2.4
+ 7.4
-12.0
— 6.1
+ 1.4
— 9.4
— 4.2
olism actually gives the closest approximation to the true value in a
large series of subjects. We therefore determined which predicted
with the smallest error, i.e., which gave the lowest value of
(calculated metabolism) less (actual metabolism).
But having established the best method and utilized the largest avail-
able series of data uniformally obtained as the basis of our constants,
we feel fully justified in taking these equations as our standard, and
in considering that smaller series either do or do not agree with this
» Means, Joum. Biol. Chem., 1915, 21, p. 263.
232 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
standard, as the actual constants may indicate. The differences are
therefore taken
(actual metabolism) less (calculated metabolism)
to give the proper sign to the difference.
Without exception the 8 men are subnormal in their daily heat-
production. The differences range from 13 to 186 calories and are on
an average 78.6 calories. Expressed as a percentage of the calculated
heat-production, the differences range from 0.8 to 10.3 with a general
average of 4.4 per cent.
In the case of the women, in which the theoretical heat-production
is calculated by inserting the values for weight, stature, and age of the
individual under consideration in our equation based on 103 women,
the deviation of the actual from the theoretical values is not so great.
In 3 cases metabolism is higher and in 4 cases lower than would be
expected. The average difference is (-f-170— 471)/7 = —43.0 calories.
Thus while the young women are more nearly typical than the young
men studied by Palmer, Means, and Gamble, their individuals of both
sexes show a tendency to a defective metabolism rate.
We have no suggestion to offer concerning the technical or physio-
logical explanation of the apparent tendency of this series to subnormal
metabolism. The suggestion may of course be offered that it is our
standards which are at fault. There are various evidences that this is
not the case. First of all, the observations upon which our standards
are based have been made by a carefully standardized technique but
by a number of observers. Thus the probability of an influence of
personal equation is to a considerable extent reduced. The large
number and great diversity of individuals dealt with furnishes a strong
guarantee for the validity of the constants. Furthermore the applica-
tion of our method to other series of data indicates supernormal metab-
olism in comparison with our standards. Thus we have abstracted
from the classical paper of Magnus- Levy and Falk ^° the ages, weights,
and statures of a number of men and women and have calculated the
total calories per 24 hours from their measurements of the respiratory
exchange. The essential values are given in table 90. Of the 10 men
7 show a heat-production above standard as compared with 3 which
show heat-production below standard. The deficiencies range from
—13 to —61 calories, whereas the excesses range from -\-Q to -{-203
calories. With one exception the 14 women show a daily heat-produc-
tion above normal. The excess ranges from 22 to 359 calories per
24 hours or from 1.6 to 25.7 per cent.
The average excess for the 10 men is 54.5 calories, while for the 14
women it is 110.2 calories per 24 hours. The average percentage
deviation from standard without regard to sign is 5.3 for men and 8.5
JO Magnus-Levy and Falk, Arch. f. Anat. u. Physiol., Physiol. Abt., Suppl. 1899, pp. 314-381.
Tables I and IIL
STANDARD BASAL METABOLISM CONSTANTS.
233
for women. Regarding signs, the men show an excess of 3.7 per cent
and the women an excess of 8.5 per cent.
Thus the adult series of Magnus-Le^'y and Falk show supernormal
metabolism when compared vdth. the standard which we have adopted,
whereas the subjects examined by Palmer, Means, and Gamble show a
subnormal metaboUsm. If, as judged by the Palmer, Means, and
Gamble series, our standards predict a metabolism somewhat too high,
when judged by the ^Magnus-Levy and Falk series they predict a basal
metabohsm somewhat too low. Our standards can not be changed
without making the results of one or the other of these groups of
obsen-ers appear much more abnormal than they now seem.
Table 90. — Metabolism of the German men and women studied by Magnus-Levy and Folk
compared with American normal {multiple prediction) standard.
Name and
number.
'Age.
Weight.
Stature.
Actual Calculated Actual
daily [ daily | less calcu- ; Percentage '
heat- I heat- Jated meta-; difference. |
production, production., holism.
Men.
1. Rud
2. L
3. Rutt
4. W
6. B
6. Prof. Z
7. Dr. M.-L. .
8. Dr. L.-Z...
9. Sp
10. Schm
Women.
1. B.K
2. G. D
3. W. Spr
4. O.K
5. L. Gr
7. M.W
8. H. M
9. H. Sch
10. M. Kl
11. E. Spl
12. L. W
13. Schw. M...
14. A. Sche....
15. Br. K
24
43.2
30
50.8
26
53.0
56
56.5
32
58.0
43
65.0
25
67.5
22
67.5
29
82.7
22
88.3
40
31.0
38
32.2
35
37.9
25
39.0
21
47.2
20
49.4
28
51.2
18
54.0
17
54.0
28
61.3
20
61.0
26
62.7
22
68.2
27
76.5
148(*)
153
153
170(±)
161
161(±)
167
167
175
176
135
133
142
139
147
159
157
152
156
156
167
15o(?)
159
169
1333
1239
1315
1328
1527
1385
1519
1316
1510
1453
1498
1475
1608
1661
1621
1682
2030(?)
1883
2019(?)
2013
1073
1014
1109
1031
1204
1117
1344
1168
1345
1280
1355
1328
1466
1304
1529
1368
1403
1381
1758
1399
1508
1454
1602
1420
1612
1499
1571
1573
+ 94
- 13
4-142
+203
+ 57
+ 23
- 53
- 61
-f-147
+ 6
+ 59
+ 78
+ 87
-1-176
-1- 65
+ 27
+162
+ 161
+ 22
+359
+ 54
+ 182
+ 113
- 2
+ 7.6
- 1.0
+10.3
+13.4
+ 3.9
+ 1.6
- 3.2
- 3.6
+ 7.8
+ 0.3
+ 5.8
+ 7.6
+ 7.8
+15.1
+ 5.1
+ 2.0
+12.4
+ 11.8
+ 1.6
+25.7
+ 3.7
+12.8
+ 7.5
- 0.1
— . : I
Possibly such tendencies to subnormal or supernormal metabolism
as those seen in the two groups of men and women just studied may be
due merely to errors of random sampling in the selection of the subjects.
This seems, however, highly improbable. To another possible explana-
tion we shall return in a moment. That such tendencies are not
necessarily characteristic of subseries is evident from the following
further illustration.
Table 91 contains the physical data and the actual and computed
heat-production of a number of men studied at the Nutrition Labora-
234 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
tory after the tables" for the present volume were closed." For per-
mission to use the constants of these men in advance of their publi-
cation elsewhere we are indebted to our associates Dr. T. M. Carpenter,
Mr. L. E. Emmes, Miss M. F. Hendry, and Dr. P. Roth. In 13 cases
these subjects showed a basal metabolism of from 24 to 328 calories
less than would have been expected from their stature, weight, and
age, whereas in 18 cases they were characterized by a basal metab-
Table 91. — Comparison of metabolism of series of men recently investigated by Carpenter,
Emmes, Hendry, and Both, with normal {multiple prediction) standard based on earlier
Actual
Calculated
Actual
Subject.
Age.
Weight.
Stature.
daily
heat-
production.
daily
heat-
production.
les3 calcu-
lated meta-
bolism.
Percentage
difference.
W. G. S
19
63.5
171
1704
1667
+ 37
+ 2.2
E. R. K
20
69.0
168
1812
1721
+ 91
+ 5.3
A.S.P
21
69.3
169
1733
1723
+ 10
+ 0.6
J. L. G.*
21
65.5
163
1600
1641
- 41
- 2.5
G. C. G
22
71.3
171
1874
1754
+ 120
+ 6.8
R.T.V
22
65.8
175
1610
1698
- 88
- 5.2
H. H. H
22
71.5
173
1793
1767
+ 26
+ 1.5
J. F. T
22
63.8
188
1750
1736
+ 14
+ 0.8
P.G.H
22
52.1
176
1549
1515
+ 34
+ 2.2
R. K. B
22
65.8
179
1694
1718
- 24
- 1.4
C.A.C
22
64.9
180
1656
1711
- 55
- 3.2
A.C.B
22
77.6
175
1533
1861
-328
-17.6
H. A.M
23
63.5
174
1702
1655
+ 47
+ 2.8
S. N. G
23
60.8
178
1827
1638
-1-189
+11.5
W. J. S
23
56.5
172
1330
1549
-219
-14.1
H.O
23
67.2
172
1628
1696
- 68
- 4.0
C.F.M
23
51.1
161
1258
1419
-161
-11.3
O.A.G
24
66.8
166
1788
1653
+ 135
+ 8.2
T.H.N
24
69.1
190
1868
1805
+ 63
+ 3.5
A.G.N
24
59.9
172
1600
1589
+ 11
+ 0.7
F.S
24
57.4
172
1515
1554
- 39
- 2.5
W.F.M
24
76.1
181
1863
1857
+ 6
+ 0.3
C.S.B
24
61.4
174
1632
1619
+ 13
+ 0.8
L. J.T
25
59.5
176
1471
1596
-125
- 7.8
L. F. F
25
57.5
167
1606
1524
+ 82
+ 5.4
J. A. C
25
59.6
177
1663
1603
+ 60
+ 3.7
H.B
25
64.6
166
1482
1617
-135
- 8.3
G.A.B
26
61.8
167
1493
1576
- 83
- 5.3
K. B. C
26
79.8
177
1759
1874
-115
- 6.1
K. G. M
32
68.8
171
1889
1652
+237
+14.3
R. W.P
44
64.3
170
1572
1504
+ 68
+ 4.5
* J. L. G., aged 20 years and 6 months is considered 21.
olism from 6 to 237 calories higher than the theoretical value. Had
the sample been exactly typical of the standard control series the ratio
should have been 15.5 : 15.5 instead of 18 : 13. Thus there is a devia-
tion of only 13 — 15.5 =2.5 =±=1.9 from the equality which should result
if prediction could be made without a bias toward too high or too low
values.
*' These subjects will be included with such others as may become available in any subse-
quent revision of our prediction tables.
STANDARD BASAL METABOLISM CONSTANTS. 235
The most widely divergent individuals are A. C. B. with a metab-
olism which is subnormal by 17.6 per cent and K. G. M. with a metab-
olism which is supernormal by 14.3 per cent. Of the remaining 29 men
only 3 deviate more than 10 per cent from the standard.
Taking the series as a whole, the average observed heat-production
is 1653.35 calories whereas the average calculated heat-production is
1661.03 calories. Thus for 31 individuals the average error of our
multiple prediction formula is only -f 7.68 calories per day. This is
only +0.46 per cent of the predicted value. If the individual differences
between the predicted and the measured daily heat-productions of
these men be considered without reference to their sign, i.e., without
regard to the fact that some are subnormal while others are super-
normal, we find that there is an average difference of =±=87.87 calories.
Thus by the use of our equations we have been able to predict the
heat-production of 31 subjects with an average (=«=) error of 5.30
per cent. This series may therefore be regarded as quite tjT)ical of
the standard, and might in consequence be legitimately employed for
any rationing or other metabolism experiment.
Returning to the discrepancy between the series of measurements
by Magnus-Levy and Falk and our standard basal constants, we may
note that in addition to the two possible explanations suggested above
— i.e., faulty technique and errors of random sampling in the selection
of the subjects — another must be considered. It is quite possible that
the German and American populations from which these subjects were
drawn are differentiated with respect to the magnitude of their metab-
olism. Some further light maj-- be thrown upon this question by com-
puting the metabolism of the German girls, women, and old women
from the equation based on the 136 American men. In doing this we
are determining what the heat-productions of these individuals should
be if they were American men of like stature, weight, and age. As
fully discussed in Chapter VII, comparison of the actual with the theo-
retical heat-productions will then show whether German women show
a higher or a lower metabolism rate than American men. The results
are set forth in table 92.
Leaving the girls out of consideration for the moment we note that
of the 17 women from 17 to 86 years of age all but 5 show a daily heat-
production in excess of that computed on male standards. The deficiencies
range from —39 to —211 calories with an average of —94.2 calories,
whereas the excesses range from +36 to +369 calories w^th an average
of 152.0 calories. For all the women the average daily excess is (1824-
471)/17 =79.6 calories.
Expressing these differences in relative terms, we note that the
German women range from 11.8 per cent below to 39.3 per cent above
the standard male values. The average for the 5 women who fall
below the masculine standard is 5.8 per cent, while the average for the
236 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
12 women who have a metabolism above this standard is 14.0 per cent.
For the whole series, regarding signs, the average excess is 8.2 per cent.
Now data are not as yet available for determining the real signifi-
cance of these actually demonstrated differences. They may be due
to defective technique, although we believe that other students of
human metabolism will agree with us in holding the manipulative
features of Magnus-Levy's work in the highest regard. They may
represent real physiological differentiation, possibly due to differences
in plane of nutrition ^^ or in muscular training (to be discussed under
Table 92. — Comparison of metdbolism of German girls and women studied by Magnus-Levy
and Falk with the American masculine normal {multiple prediction) standard.
Actual
Calculated
Actual
Subject.
Age.
Weight.
Stature.
daily
heat-
production.
daily
heat-
production.
less calcu-
lated meta-
bolism.
Percentage
difference.
Girls.
1. A. K ...
7
15.3
107
866
765
-1-101
+ 13.2
3. A. M...
12
24.0
129
962
961
+ 1
+ 0.1
4. Fr. W..
12
25.2
128
938
972
- 34
- 3.5
5. E.Gl...
13
31.0
138
1217
1095
+ 122
+ 11.1
6. H.Sch..
11
35.0
141
1313
1179
+ 134
+ 11.4
7. Fr. Th..
14
35.5
143
1299
1176
+ 123
+ 10.5
9. M. P...
11
42.0
149
1459
1315
+ 144
+ 11.0
Women.
1. B. K...
40
31.0
135
1073
898
+ 175
+ 19.5
2. Gd
38
32.2
133
1109
918
+ 191
+20.8
3. W. Spr.
35
37.9
142
1204
1062
+ 142
+ 13.4
4. O. K...
25
39.0
139
1344
1129
+215
+ 19.0
5. L. Or...
21
47.2
147
1345
1309
+ 36
+ 2.8
7. M.W...
20
49.4
159
1355
1406
- 51
- 3.6
8. H. M...
28
51.2
157
1466
1367
+ 99
+ 7.2
9. H.Sch..
18
54.0
152
1529
1448
+ 81
+ 5.6
10. M. Kl . .
17
54.0
156
1403
1475
- 72
- 4.9
11. E. Spl..
28
61.3
156
1758
1501
+257
+ 17.1
12. L. W. . .
20
61.0
167
1508
1606
- 98
- 6.1
13. Schw.M
26
62.7
155(?)
1602
1529
+ 73
+ 4.8
14. A. Sche.
22
68.2
159
1612
1651
- 39
- 2.4
15. Br.K...
27
76.5
169
1571
1782
-211
-11.8
Old women.
4. Kl
71
49.5
145
1088
993
+ 95
+ 9.6
5. Schm . . .
83
51.0
146
1307
938
+369
+39.3
7. Scha....
86
59.3
150
1143
1052
+ 91
+ 8.7
Illustration D, below) in the women of the German and the men of the
American classes from which the subjects were drawn. The solution
of this question must be a problem for the future. The results show
with the greatest clearness the value of standard tables based upon
three characters for the direction of future research.
Again the results exemplify the importance of large groups as a
basis for conclusions. Five of the 17 women show heat-productions
less than the male standard. Had a smaller number beefi' examined,
one or more of these might have been included and the result have been
far less conclusive than it seems with 17 determinations.
" See Chapter VI, p. 196.
STANDARD BASAL METABOLISM CONSTANTS.
237
Illustration B. Metabolism in Childhood and Youth and in Extreme Old Age.
In Chapter V we discussed in detail the changes in metaboUsm
which occur with increasing age during the period of adult life. As we
indicated there, the limits which mark off the stages of development
from the period of maturity and the period of old age from that of
extreme old age are very indefinite, or at least are deterniinable only
with difficulty.
Our equations do not fully represent the metabolism of the develop-
mental period. Neither do the observations upon which they are
based contain numbers of very old men or women adequately large to
justify using them as a standard for determining the influence of special
conditions {e.g. the incidence of a specific disease) upon the metabolism
of advanced old age. For these very reasons our equations are par-
ticularly adapted to determining whether the metabolism of individuals
in these extremes of the life-cycle differs from that characteristic of the
wide central range of mature Ufe. In applying them to this problem
we calculate the metabolism of the individuals of extreme age on the
assumption that it is given by inserting the weight, stature, and age
of the subjects in the equations based on our adult series. Comparison
of the values obtained by actual measurement with that given by the
equations then shows whether the metabolism of the age in question
differs from that in adult life.
Table 93. — Comparison of metabolism of Du Bois boy sands tvith the adult masculine normal
(multiple prediction) standard.
Name.
Weight
Height
Actual
Calculated
Actual
Age.
in kilo-
in centi-
daily daily
less calcu-
grams.
meters.
heat- heat-
production, i production.
lated meta-
bolism.
12
34.5
153
1340
1225
4-115
13
28.5
141
1300
1076
-f224
13
30.4
141
1415
1102
-f313
13
35.4
148
1485
1206
-f279
13
32.1
142
1375
1131
-h244
14
30.6
147
1348
1128
-t-220
14
36.6
146
1401
1206
-fl95
14
36.0
148
1432
1207
-f225
Percentage
difference.
J. D. D. B..
Leslie B. . . .
Raymond M
Reginald F . .
F. R. S
Arthur A. . .
Harry B....
Henry K
4- 9.4
-1-20.8
4-28.4
4-23.1
4-21.6
4-19.5
4-16.3
4-18.6
Consider first the boy scouts studied by Du Bois.^^ The essential
details are given in table 93. The computed values are in all cases
lower than the observed. The differences range from 115 to 313
calories per 24 hours, with an average of 227 calories. Thus boys of
12 or 14 years of age have a basal metabolism from 115 to 313 calories
per day higher than would be expected if they were adult individuals
of the same weight and height. Expressing these results in terms of
percentages of the adult standard, as must be done in comparing boys
with men, we note that the boys have a metaboUsm from 9.4 to 28.4
^» Du Bois, Arch. Intern. Med., 1916, 17, p. 887.
238 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
per cent higher than they would be expected to have if they were
adults of the same height and weight. The average superiority of the
boys is 19.7 per cent of the standard. Thus if the boys were able to
remain in complete muscular repose during the experimental periods,
and if the light breakfast had no measureable influence on their metab-
olism, so that the constants niay be looked upon as truly basal, it is
evident that the metabolism is relatively high at the onset of puberty,
and that the decrease from this period to that of maturity is more
rapid than during adult life.
Table 94. — Comparison of metabolism of German boys and girls studied by Magnus-Levy
and Falk with American normal {multiple prediction) adult standards.
Actual
Calculated
Actual
Name and
Age.
Weight.
Stature.
daily
daily
less calcu-
Percentage
nvunber.
heat-
heat-
lated meta-
difference.
production.
production.
bolism.
Boys.
2. M. N...
6
14.5
110
926
776
-1-150
+19.3
3. Fr. H...
6
18.4
110
970
829
-1-141
+ 17.0
4. G. H...
7
19.2
112
1067
844
-i-223
+26.4
5. K. W...
7
20.8
110
1153
856
+297
+34.7
6. E. J....
9
21.8
115
1036
881
-1-155
+ 17.6
7. P. Oe...
11
26.5
129
1151
1002
+ 149
+ 14.9
8. A. T....
10
30.6
131
1338
1075
+263
+ 24.6
9. 0. Gr...
14
36.1
142
1310
1179
+ 131
+ 11.1
10. E. K. . .
14
36.8
142
1285
1188
+ 97
+ 8.2
11. K. Ke..
16
39.3
149
1352
1244
+ 108
+ 8.7
12. R. D...
17
40.0
154
1397
1272
+ 125
+ 9.8
13. A.N...
14
43.0
149
1525
1309
+216
+ 16.5
14. K. W...
17
44.3
154
1525
1331
+ 194
+ 14.6
15. L. Z....
16
57.5
160
1636
1550
+ 86
+ 5.5
16. B
16
57.5
170
1681
1600
+ 81
+ 5.1
Girls.
1. A. K. ..
7
15.3
107
866
967
-101
-10.4
3. A.M...
12
24.0
129
962
1067
-105
- 9.8
4. Fr. W . .
12
25.2
128
938
1077
-139
-12.9
5. E. Gl...
13
31.0
138
1217
1146
+ 71
+ 6.2
6. H.Sch..
11
35.0
141
1313
1199
+ 114
+ 9.5
7. Fr. Th..
14
35.5
143
1299
1194
+105
+ 8.8
9. M. P. ..
11
42.0
149
1459
1281
+ 178
+ 13.9
Turning to the data for youth presented by Magnus-Levy and
Falk, the comparison of observed and theoretical values in table 94
shows that without exception the boys are characterized by a higher
heat-production than would be expected if metabolism showed the
same rate of change from childhood to maturity as it does from matur-
ity to old age, and if the relationship between physical dimensions
and metabolism were the same in developing as in mature individuals.
The excess ranges from 81 to 297 calories and on the average is 161.1
calories for the 15 boys and youths. On a relative scale, the differences
between observation and theory are from 5.1 to 34.7 per cent of the
latter, with a general average of 15.6 per cent.
The results for the few girls are not so consistent. As to the reason
STANDARD BASAL METABOLISM CONSTANTS. 239
for this difiference between boys and girls we have no suggestion to
offer. It emphasizes the need for more numerous and more minutely
recorded data.
It appears that the metaboHsm is much higher in boyhood than in
manhood, but in passing we must note that practically all of Magnus-
Levy and Falk's determinations are higher than the American stand-
ard. Thus the values of their constants for j'outh are probably too
high (when used in connection with American values for adults) for
the plotting of a curve of metabohsm throughout hfe, as has been done
by Du Bois.'*
To avoid all possible misunderstanding concerning the line of
reasoning employed in this section, we may reiterate that the age factor
in these immature subjects has for purposes of investigation been
assumed to be given by an extension of the hne found vahd for the
period of adult life. If the measured metabohsm of the growing sub-
jects is higher than the value predicted by the standard equation for
adult life, we conclude that (if all sources of experimental error were
ruled out) the decrease in metabolism rate is much more rapid in the
period of growth than in the period of maturity. This seems to be
the indication of the series of measurements by Du Bois^^ and Magnus-
Levy and Falk.
To show how large an influence correction for age by the adult
formula has had upon these metabolism constants we have predicted
the metabolism of the j'oung subjects by means of the equations for
adult hfe ignoring the influence of age changes during adult life itself.
The equations are ^^
For aU men A = -314.613+13.129 to+6.388«
For all women h= 713.016+ 8.063 tr+1.116s
The results are given in table 95. The first difference column shows
that the age term in our equations has made a difference in the predicted
value of from 74 to 199 calories per 24 hours.
The second section of the table shows the percentage excess of the
measured over the theoretical heat-production when the latter is
computed in the two ways. Here there is an influence not merely of
the actual differences in calculated and measured heat-production, but
of the theoretical heat-productions used as bases for the calculation
of the percentage excesses.
'*DuBois, Am. Journ. Med. Sci., 1916, 151, p. 781. Also Stud. Dep. Physiol., Cornell
Univ. Med. Bull., 1917, 6, Xo. 3, part II, p. 1.
^* Just as this manuscript was being completed for the press, a second paper on the same sub-
jects appeared (Olmstead, Barr and Du Bois, Arch. Intern. Med., 1918, 21, p. 621). In this
investigation they find that the boy scouts had shown a material decrease in metabolism during
the two years since they were last studied. The influence of a small breakfast upon metabolism
has also been investigated (Soderstrom, Barr, and Du Bois, Arch. Intern. Med., 1918, 21, p. 613),
and the authors conclude that it has no significant influence upon the metabolism constant.
" See Chapter VI, p. 184.
240 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
The final difference column shows how much greater the excesses
are when the age term is ignored and the regression equation involv-
ing stature and weight only is used.
We now turn to the problem of the metaboUsm rate at the other
extreme of the life cycle, and shall consider the metabolism of the 6
old men studied by Aub and Du Bois.^'^ Table 96 contains the essen-
tial measurements and the comparison of the observed heat-production
Table 95. — Comparison of metabolism of boys calculated from adult normal (multiple predic-
tion) standard when the age factor is considered and when it is ignored.
Calciilated metabolism
Percentage excess
in calories per 24 hours.
on basis of standard.
Name.
Age
Age
Difference.
Age
Age
Difference.
considered.
ignored.
considered.
ignored.
American boys.
J. D. D. B. ..
1225
1116
+ 109
9.4
20.1
+ 10.7
Leslie B
1076
960
+ 116
20.8
35.4
+ 14.6
Raymond M .
1102
985
+ 117
28.4
43.7
+ 15.3
Reginald F . . .
1206
1096
+ 110
23.1
35.5
+ 12.4
F. R. S
1131
1014
+ 117
21.6
35.6
+ 14.0
Arthur A
1128
1026
+ 102
19.5
31.4
+ 11.9
Harry B
1206
1099
+ 107
16.2
27.5
+ 11.3
Henry K
1207
1103
+ 104
18.6
29.8
+ 11.2
German boys.
2. M. N....
776
578
+ 198
19.3
60.2
+40.9
3. Fr. H . . . .
829
630
+ 199
17.0
54.0
+37.0
4. G.H
844
653
+ 191
26.4
63.4
+37.0
5. K. W....
856
661
+ 195
34.7
74.4
+39.7
6. E.J
881
706
+ 175
17.6
46.7
+29.1
7. P. Oe . . . .
1002
857
+ 145
14.9
34.3
+ 19.4
8. A. T
1075
924
+ 151
24.6
44.8
+20.2
9. 0. Gr....
1179
1066
+ 113
11.1
22.9
+ 11.8
10. E. K
1188
1076
+ 112
8.2
19.4
+ 11.2
11. K. Ke....
1244
1153
+ 91
8.7
17.3
+ 8.6
12. R. D
1272
1194
+ 78
9.8
17.0
+ 7.2
13. A.N
1309
1202
+ 107
16.5
26.9
+ 10.4
14. K. W. ...
1331
1251
+ 80
14.6
21.9
+ 7.3
15. L. Z
1550
1462
+ 88
5.5
11.9
+ 6.4
16. B
1600
1526
+ 74
5.1
10.2
+ 5.1
in calories per 24 hours (indirect calorimetry) with the values predicted
by the use of our formula from the constants for body-weight, stature,
and age.
The difference column shows that our formula has in all cases but
one predicted a lower metabolism for these subjects than that found
by actual observation. The difference between observation and
theory in these 5 cases is rather large, amounting to about 245 calories
per 24 hours.
For comparison we may show the results of applying our equations
to the physical measurements of the old men and women studied by
" Aub and Du Bois, Arch. Intern. Med., 1917, 19, p. 823.
STANDARD BASAL METABOLISM CONSTANTS.
241
Magnus-Le^T and Falk.^^ The comparison of observed and theo-
retical values in table 97 shows that with one exception the observed
are higher than the calculated values. The differences range from
2.2 to 27.5 per cent higher than the standard. The results tend,
therefore, to confirm those of Aub and Du Bois. At first glance this
might seem to indicate that our formula is erroneous, at least when
appHed to individuals falhng quite outside the age range covered by
the series of observations upon which it is based. We make no claim
whatever for the strict vahdity of our formula in extreme old age. Such
a claim can only be made when far more extensive series of old men and
women are included in the standard series.
Table 96. — Comparvsan of metabolism of old men studied by Aub and Du Bois with adtdt
nomval (muUiple prediction) standard.
Name.
Age.
Weight
in kilo-
grams.
Height
in centi-
meters.
Actual
daily
heat-
production.
Calculated
daily
heat-
production.
Actual
less calcu-
lated meta-
bolism.
Andrew O'C ....
Henry L
Charles H
Charles W
WUliam C
John B
77
78
79
80
83
83
69.7
68.9
52.9
69.1
62.9
50.5
171
167
163
164
163
158
1600
1568
1416
1220
1426
1240
1360
1323
1076
1297
1186
991
-f240
-1-245
-1-340
- 77
-1-240
-i-249
Table 97. — Comparison of metabolism of old men and women (German) measured by Magnus-
Levy and Falk with American ru/nnal {multiple prediction) standard.
Name and
number.
Age.
Weight.
Stature.
Actual
daily
heat-
production.
Calculated
daily
heat-
production.
Actual
leas calcu-
lated meta-
bolism.
Percentage
difference.
Old men.
1. A. Kr....
2. Be
3. Ki
4. Wa
5. He
Old women.
4. Kl
5. Schm....
7. Scha
71
70
78
77
64
71
83
86
47.8
60.0
68.5
69.3
70.4
49.5
51.0
59.3
164
165
162
172
160
145
146
150
1124
1320
1215
1479
1760
1088
1307
1143
1065
1244
1292
1360
1403
1065
1025
1098
-f 59
+ 76
- 77
-t-119
-f357
-f 23
-1-282
-f- 45
-f- 5.5
+ 6.1
- 6.0
-1- 8.8
-h25.4
-H 2.2
-1-27.5
+ 4.1
In emphasizing the fact that our equations predict a metabolism
for these octogenarians below their observed heat-productions we must
point out that exactly the same relationship is found if the original
line as dra\\Ti by Du Bois is used. Thus in the explanation of their
figure 1, Aub and Du Bois remark '}^ *' In accordance with the findings
in the present series, the line is somewhat higher in old age than in
** Magnus-Levy and Falk, loc. cit.
M Aub and Du Bois, Arch. Intern. Med., 1917. 19, p. 824.
242 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
the curves published in previous papers." Thus their earlier diagram
agrees with our equation in indicating that the observed metaboUsm
of these old men is abnormally high. The remarkable agreement of
5 of the men in their figure 2 with the old-age portion of their line
and the obvious bad results with our equation are, therefore, due to
the fact that their prediction line has been redrawn to fit the special
observations, while our own has not.
The explanation of these results is a problem of considerable diffi-
culty. Of course, one thinks first of all of the question of muscular
repose. Were these octogenarians as quiet as the younger individuals
with whom they are compared? We must note that even for the years
of matiu-ity the constants of Magnus-Levy and Falk are higher than
the American standards. If this result be due to faulty technique it
may account for the high values of the old men and women measured
by them.
It seems to us quite as possible that the discrepancy indicates not
the invahdity of our formula but the selected character of the 6 old
men studied by Aub and Du Bois. In the course of their discussion
they remark:
"It will be noted that the metabolism of Charles W. was unusually low.
This may be accounted for by the fact that he was much more senile than the
others. While this finding is of importance in showing the great depression
in metabolism which may occur in old age, we are not justified in using it to
obtain the average figure which represents the heat-production of men of his
age The results on Charles W. show a deviation of 21 per cent from
the average of the other old men. He is therefore excluded from the averages
as the result of the rule which debars an observation in which the deviation
from the mean is greater than 4 times the average deviation."
Our formula gives the metabolism of Charles W. within slightly
more than 77 calories per day, or with an error of only 5.9 per cent of
the calculated metabolism. On purely general grounds there seems
to be no more reason to exclude Charles W. because he was too senile
for his age than to exclude the other 5 men because they were too
juvenile for their age.^°
It must not be forgotten that men who reach 75 or 80 years are
by virtue of this very fact a selected class. By this time a large pro-
portion of humanity has succumbed to the wear and tear of life. Few
are able to totter forward many paces further. Those who march
with vigor are not typical of their age. But in selecting subjects for
metaboUsm work, individuals in presumably good health are chosen.
In examining the case-histories of the old men studied by Aub and
Du Bois one is rather impressed by the idea that they must have been
physically very remarkable individuals. Certainly in reading that
^ If Charles W. is to be excluded, this should certainly have been done before his metabolism
was measured.
STANDARD BASAL METABOLISM CONSTANTS.
243
Andrew O'C. had never been sick until 75 years of age, and that
during most of his hfe he drank about a pint of whiskey a day, that
ten of the brothers and sisters of Charles H. hved to be over 70 years
of age, that Charles W. at 80 "was formerly very alcoholic," that the
health of WiUiam C. has always been good, and that the mother of
John B., 83 years old, died at 93, the biologist must feel that the octo-
genarians upon whom this series of determinations was based must
have been in their prime men of rare physical capacity.
If this suggestion of the strong influence of selection in the case of
old men and women be vahd, one might expect that a standard based
on a period of life in which selection is not such an important factor
would give values lower than the actually measured heat-productions
of old age. The anomalous results (in comparison with our standards)
of these two independent series of measurements on old people show the
pressing need for further investigations of metaboUsm at the maximmn
age. We of course freely admit the possibiUty that our standards
may be inadequate for this period. If so, the equations must be modi-
fied. We hope that data on this problem may be secured at an early
date. Divergence of results of different observers has shown by a
comparison with our normal standards of illustrations A and B, how
great is the danger of combining the results of different series in order
to obtain a curve of the change of metabolism with age as has been
done by Du Bois.
iLLtTBTRATION C. METABOLISM OP InDITIDTJALS OF ABERRANT PHYSICAL FoRM.
We now turn to the problem of the basal metabohsm of individuals
of highly aberrant physique. For this purpose we avail ourselves of
Table 98. — Comparison of the metabolism of dwarfs as studied by Aub, Du Bois, McCrudden,
and Lusk with normal {multiple prediction) standard for men.
Name.
Subject.
Patrick W . . . ■ Rachitic dwarf .
Raphael De P Achondroplasia
Samuel G . . . . Achondroplasia
Irwin E M>-xedema ....
Hypopituitary.
^HjT)othyroid.. .
Intestinal
\ Infantilism . . . .
George F .
J. P.*....
Age.
Height
in centi-
meters.
38
35
29
32
^48
^17
124
135
124
134
149
113
Weight
j in kilo-
Actual 1
daily '
heat- 1
1 grams.
production. '
37.31
1180
40.86
1256
34.92
1266
37.37
828
53.05
1159
21.3
733
Calculated Actual less
daily calculated
heat- I metab-
production. ' olism.
943
1067
971
1035
1217
810
-237
-189
-295
+207
+ 58
+ 77
* J. P. was studied by McCrudden and Lusk, the others are due to Aub and Du Bois.
the data for dwarfs pubhshed by Aub and Du Bois ^^ and the single
dwarf studied by McCrudden and Lusk.-^ Table 98 gives the essential
data and the comparison of the theoretical and measured heat-produc-
" Aub and Du Bois, Arch. Intern. Med., 1917, 19, p. 840.
** McCrudden and Lusk, Journ. Biol. Chem., 1912-13, 13, p. 447.
244 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
tions for 24-hour periods. In 3 instances our formula has predicted
too large and in 3 cases too small a daily heat-production. The
average error without regard to sign is 177 calories, but with regard
to sign it is —63 calories per day. Thus, while in the individual
instance the error of prediction may be fairly large, the average
result is, considering the small number of subjects, reasonably close.
Physiologically the comparison suggests that the metabolism of
dwarfs is essentially the same as that of normal adults.
Illustration D. Metabolism of Athletes.
As an example of the application of these equations, or tables, in
the solution of a specific physiological problem, we may take the data
for a series of 16 athletes ^^ studied in the Chemical Laboratory of
Syracuse University by Dr. H. Monmouth Smith, now of the Nutri-
tion Laboratory staff. These all fall well within the age range of
our equation, and an observed deviation from the standard values
can not in this case be attributed to a distinct difference in metabolism
due to age, as is certainly the case in the series of boy scouts studied
by Du Bois, or to possible inadequacy of our formulas for extreme old
age, as in the octogenarians recorded by Aub and Du Bois.
Table 99. — Comparison of basal metabolism of H. Monmouth Smith's athletes with adult male
normal (multiple prediction) standard.
Actual
Calculated
Actual less
Subject.
Age.
Weight.
Stature.
daily
daily
calculated
Percentage
heat-
heat-
metab-
difference.
production.
production.
olism.
M. A. M...
29
66.0
177
1695
1664
+ 31
-f-1.9
F. G. R. . . .
20
74.0
179
1914
1845
+ 69
-1-3.7
W. F. M . . .
21
62.4
180
1816
1683
-fl33
-K7.9
E.G
20
78.9
184
2126
1937
-H189
+9.S
D. H. W...
22
82.1
186
2034
1977
+ 57
-f-2.9
J. H. R
23
82.2
187
1978
1977
+ 1
+0.1
M. H. K. ..
19
79.0
188
1944
1965
- 21
-1.1
H. W
19
108.9
198
2559
2426
-1-133
-f-5.5
C. J.D
27
56.7
160
1524
1464
+ 60
+4.1
W.S
22
88.5
165
2017
1960
+ 57
+2.9
W. A. S . . . .
21
56.3
169
1562
1544
+ 18
+ 1.2
R. D. S. ...
21
63.5
170
1619
1648
- 29
-1.8
M. Y. B....
20
63.5
172 .
1677
1665
+ 12
+0.7
C. D. R. ...
22
74.0
173
1908
1801
-f-107
+5.9
H. R. W. ..
24
73.9
175
1842
1796
-f- 46
+2.6
P. D. F....
23
71.2
176
1810
1771
+ 39
+2.2
Table 99 gives the age, weight, and stature, from which the theo-
retical basal metabolism of the men has been calculated and entered
in the fifth column of the table. As is clearly shown by the entries in
the sixth and seventh columns, the athletes are, with two slight exceptions,
supernormal in their metabolism. The excesses over the standard values
range from 1 to 189 calories per 24 hours, or from 0.1 to 9.8 per cent
a Benedict and Smith, Joum. Biol. Chem., 1915, 20, p. 243.
STANDARD BASAL METABOLISM CONSTANTS. 245
of the standard value. On an average the athletes show an excess of
56.37 calories or 3.03 per cent over the standard. These results fuUj-
confirm the conclusions concerning the influence of athletic training
already drawn, although the percentage differences are materially
lower by the new methods of analysis.
The authors ^^ expressed their results for selected groups of athletes
and of non-athletic indi\'iduals in terms of heat-production per 24
hours per square meter of body-surface as estimated by the Meeh
formula and on the average found for athletes 863 calories and for
non-athletes 807 calories. Thus athletes were 6.84 per cent higher.
Subsequent revision of these calculations on the basis of the Du Bois
height-weight chart shows 978 calories for athletes and 912 calories
for non-athletes. Thus the athletes are 7.24 per cent higher.
By the method of analysis here employed we find a difference of
only 3 per cent. This difference in percentage results is probably due
to (1) the inherent defects in the selected-group system of comparison
which have been pointed out above; and (2) to including athletes in
the data from which the normal standard was derived. Had athlete
been excluded from the standard normal series the differences would
have been greater. Why, therefore, were they not excluded? Because
athletic training is in some degree characteristic of men at large.
Blacksmiths, riveters, stone-masons, lumbermen, cowboys, miners, and
stevedores are quite as typically men as are bar-tenders, book-keepers,
floor-walkers, and college professors. Out of 136 men, 16 with special
athletic training is perhaps not too large a proportion for a series
which is intended to serve as a standard for normal men, in good health,
as a class.
iLLUs-mATiON E. Metabolism of Vegetarians.
As a further illustration of the applicability of these equations in
human physiology, we may consider the metabohsm of vegetarians,
a question which has already been discussed elsewhere ^^ on the basis
of a series of men and women well within the age-range over which
our equations may be held to apply. The observed daily heat-produc-
tions are compared wath the standard productions in table 100 for men
and in table 101 for women. Of the 11 men, 6 show a subnormal and
5 show a supernormal metabolism. Of the 11 women, 5 are character-
ized by a subnormal and 6 by a supernormal metabolism. Disregarding
sex, as we may quite properly do since it has been taken into account
in the equations used, we note that 11 vegetarians have a subnormal
and 11 have a supernormal metabolism. The average metabolism of
the 11 men is subnormal by 24.64 calories per 24 hours, whereas that
of the women is supernormal by 5.91 calories per 24 hours. Disre-
garding sex, the metabolism of vegetarians differs from the multiple
^* Benedict and Smith, Journ. Biol. Chem., 1915, 20, p. 251, Table II.
^ Benedict and Roth, Journ. Biol. Chem., 1915, 20, p. 231.
246 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
prediction standard values for individuals of like sex, age, weight, and
stature, on the average by 9.37 calories per 24 hours. These results
furnish a full substantiation for the conclusion already drawn: ^^ ''We
may, therefore, fairly conclude that living upon a vegetarian diet for
a longer or shorter period does not fundamentally alter the basal
gaseous metabolism."
Table 100. — Comparison of basal metabolism of Roth's male vegetarians with normal
{multi-pie prediction) standard for men.
Subject.
Age.
Weight.
Stature.
Actual
daily
heat-
production.
Calculated
daily
heat-
production.
Actual
less calcu-
lated meta-
bolism.
Percentage
difference.
B. K
39
32
27
58
21
41
38
29
22
25
25
58.2
50.6
60.0
50.0
49.3
55.2
75.0
59.3
59.2
64.7
55.4
178
179
179
155
163
164
164
164
169
170
171
1393
1510
1530
1158
1365
1341
1698
1451
1605
1499
1545
1494
1442
1605
1138
1418
1369
1662
1507
1578
1638
1515
-101
+ 68
- 75
+ 20
- 53
- 28
+ 36
- 56
+ 27
-139
+ 30
-6.8
+4.7
-4.7
+ 1.8
-3.7
-2.0
+2.2
-3.7
+1.7
-8.5
+2.0
B. N. C
L. H. W
E. J. W
V. E. H
Dr. P. R
F. E. M
W. B. L
T. H. Y
E. H. T
O.N. A
Table 101. — Comparison c
/ metabolism of Roth's female vegetarians
prediction) standard for women.
with normal {multiple
Subject.
Age.
Weight.
Stature.
Actual
daily
heat-
production.
Calculated
daily
heat-
production.
Actual
less calcu-
lated meta-
bolism.
Percentage
difference.
21
53
26
27
44
27
27
22
29
36
39
90.2
58.0
53.8
47.0
93.6
49.1
44.8
56.8
44.9
40.0
67.2
164
163
160
167
165
151
157
166
159
168
170
1756
1415
1215
1168
1765
1178
1189
1365
1272
1269
1521
1723
1263
1344
1287
1650
1278
1248
1402
1243
1180
1430
+ 33
+ 152
-129
-119
+ 115
-100
- 59
- 37
+ 29
+ 89
+ 91
+ 1.9
+ 12.0
- 9.6
- 9.2
+ 7.0
- 7.8
- 4.7
- 2.6
+ 2.3
+ 7.5
+ 6.4
Mrs. E. B
Miss J. N. B
Miss L. B
Dr. M. D
Miss M. H
Miss M.J
Miss L. K
Mrs. A. L
Miss J. T
Miss C. Z
Illustration F. Metabolism in Disease.
The purpose of many clinical calorimetric researches is to determine
whether a significant modification of metabolism is associated with the
specific disease under investigation. To solve this problem one must
compare the actually measured calories of the subject with the calories
calculated from weight, stature, and age on the assumption that he
is in normal health. To illustrate the applicabihty of these equations
(or tables) to such pathological problems, we may avail ourselves of
Dr. Elliott P. Joslin's series of diabetics. ^^
'* Benedict and Roth, loc. cit., p. 240.
^ Benedict and Joslin, Carnegie Inst. Wash. Pub. No. 176, 1912.
STANDARD BASAL METABOLISM CONSTANTS.
247
Table 102 gives the key number of the subjects,^^ their age, weight,
stature, and actually measured basal heat-production for 24-hour
periods. The fifth colunm gives the theoretical heat-production, the
sixth the absolute deviation of the measured from the calculated, and
the seventh the relative deviation of the actually determined from the
theoretical (normal) heat-production.
Table 102. — Metabolism of Joslin's series of diabetics in comparison with normal
{multiple prediction) standard.
Subject.
Age.
Weight.
Stature.
Actual
daily
heat-
production.
Calculated
daily
heat-
production.
Actual
less calcu-
lated meta-
bolism.
Percentage
difference.
Men.
A(2)
49
50
30
30
31
34
25
21
46
47
22
24
14
17
15
48
57
44
36
40
38
16
37
61.6
46.1
55.5
62.7
48.8
67.1
40.0
54.0
59.1
55.6
63.0
66.5
31.5
40.0
51.7
55.3
58.0
51.4
60.0
41.4
52.4
52.6
39.5
171
171
166
166
173
178
176
171
180
180
183
183
146
173
168
181
177
180
173
158
159
173
leo
1481
1255
1610
1728
1382
1978
1608
1670
1596
1728
1898
1884
1186
1414
1538
1812
1428
1553
1S94
1195
1440
1498
1385
1301
1218
1458
1557
1394
1650
1328
1523
1469
1414
1700
1734
1136
1367
1517
1408
1365
1377
1514
1156
1273
1403
1156
+180
+ 37
+152
+171
- 12
+328
+280
+147
+127
+314
+198
+150
+ 50
+ 47
+ 21
+404
+ 63
+ 176
+380
+ 39
+167
+ 95
+229
+ 13.8
+ 3.0
+ 10.4
+ 11.0
- 0.9
+ 19.9
+21.1
+ 9.7
+ 8.6
+22.2
+11.6
+ 8.7
+ 4.4
+ 3.4
+ 1.4
+28.7
+ 4.6
+ 12.8
+25.1
+ 3.4
+13.1
+ 6.8
+ 19.8
A(l)
C(l)
C (2)
D
G
I
J
K (2)
K (1)
L (2)
L (1)
N
P
Q
R
s
T
V
Women.
B
H
0
u
With one single exception of 12 calories per 24 hours in the case of
subject D, the observed are all higher than the theoretical metaboUsm
constants. The excess ranges from 21 to 404 calories per 24 hours in
men and from 39 to 229 calories in women. In relation to the computed
heat-production taken as a standard, the excess in the men ranges from
1.4 to 28.7 per cent. In the women the range is from 3.4 to 19.8 per
cent. The average de\dation of the 19 male determinations is 169.11
calories, while the average deviation of the 4 female determinations
is 132.50 calories. On the average the heat productions of the men are
11.55 per cent above normal, whereas those for the women are 10.78
per cent above normal.
These results are fully confirmatory of the general conclusions
" Observations on the same patient at different ages or different body-weights are in some
cases available. These are recorded as 1 and 2.
248 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN.
already drawn.^^ Here the application of the formulas to diabetics
serves merely as a particular example of a general method.
It may not be out of place, however, to look at certain quantitative
aspects of the subject more closely. On examining the increments in
metabolism due to diabetes found by this method, we note that they
are on the average only about 11 per cent as compared with 15 to 20
per cent as asserted in earlier publications from the Nutrition Labora-
tory.^'* In partial explanation of this percentage difference we may
note that our prediction equation for men includes about 16 athletes.
This represents about 12 per cent of the whole control series. But in
a preceding illustration we have shown that athletes themselves have
a higher metabolism than normal men at large. Our reasons for
including athletes in our standard series have been given above. It
should be a fixed scientific principle that standards should not be
changed whenever convenience demands. ^^ The inevitable conse-
quence of this inclusion of the athletes has been to reduce the per-
centage difference between diabetics and non-diabetics. In short, it
has made the comparison as disadvantageous as possible to the views
concerning diabetes long held at the Nutrition Laboratory. Notwith-
standing this fact, the validity of the general conclusions already
drawn is fully supported.
A study of the individual entries in this table has considerable
value as indicating the limits of trustworthiness of conclusions from
single subjects even when compared with a standard control based on
large numbers. For example, had the one subject examined chanced
to be D the incautious clinician might have concluded that diabetes
decreases metabolism. Had the second subject chanced to be Q he
might have concluded that a defect of 12 calories in one case and an
excess of 21 calories in the other indicated no relationship at all
between diabetes and metabohsm. Had V or R been the only subject
examined, a quite exaggerated impression of the influence of diabetes
might have been drawn, for these men show an excess of 25.1 and
28.7 per cent. It is only when a considerable number of pathological
cases are available for comparison with the standard that dependable con-
clusions concerning the influence of any disease can be drawn. This
principle is a fundamental one, and must be applied in all comparisons
of special groups with standard control series in all nutritional research.
■^ Benedict and Joslin, loc. cit., p. 121.
•o Benedict and Joslin, Carnegie Inst. Wash. Pub. No. 136, 1910, p. 193; also Carnegie Inst.
Wash. Pub. No. 176, 1912, p. 121.
" Criticism has been made from the Nutrition Laboratory of the Du Bois method of excluding
undersized individuals in obtaining their normal, and the specific statement has been made that
we should not compare standard normals based primarily upon robust, vigorous individuals
with emaciated, weak, under-weight diabetics. We still hold these criticisms to be valid, and we
have avoided them in the comparisons in table 102 by utilizing equations which enable one to
compare each diabetic with a standard value for an individual of like height, weight, and age.
But in determining the equations for these standard values we have included athletes among the
normals, even though their inclusion has minimized the difference between diabetic and non-diabetic
individuals.
STANDARD BASAL METABOLISM CONSTANTS. 249
IixusTRATiON G. Rationing in Periods of Emergency.
The problem of rationing in national crises involves so many factors
(biological, social, and economic) that general principles only can be
established.
It is evident, however, that the fairest and the most advantageous
plan for the allotment of rations is that which is based on the phj-sio-
logical needs of the individuals of the population under consideration.
For instance in an editorial ^^ on the Inter-Allied Scientific Food
Commission we read :
"The basal heat production of an average man weighing 156 pounds
(70 kg.) will be 70 calories an hour at rest and without food, or 1680 calories
in twenty-four hours."
Body-weight is not, however, an adequate standard. The analysis
in the present volume shows that stature, weight, and age must all be
taken into account in determining the basal metabolism of the indi-
\idual, and hence in determining most exactly the food requirements
of a population.
Our 136 men show an average weight of 64.1 kilograms instead of
the 70 kilograms ordinarily assumed as an average value. They show
an average basal metaboUsm of 1632 calories as compared with 1680
calories. Our men are on the average 26.9 years of age and 173
centimeters in height. If we assume that the men of a population
average 70 kg. in weight, 170 cm. in stature, and 35 years of age, we find
from tables I and II a basal requirement of 1029+614 = 1643 calories.
If we are considering a population of adult women weighing on the
average 56.0 kg., 162 cm. in height, and 35 years of age the values from
tables III and IV are 1191+136 = 1327 calories.
These factors must, in practical rationing, be multiplied by the
requisite factors for the increased metaboUsm due to muscular and
other activity.
4. RECAPITULATION.
The purpose of this chapter, in which the principles underlying the
estabhshment of standard control series have been discussed, has been
three-fold.
1. To emphasize the necessity for the estabhshment of statistical
normal basal metabolism standards, which may serve as a basis of
comparison in all special nutritional investigations.
2. To supply convenient tables of such standards based on the
most extensive series of normal data as yet available.
3. To illustrate the practical use of such tables in the solution of
problems in nutritional physiology.
The analysis of this and the preceding chapters leads to the conclu-
sion that biologically the most rational and practically the most satis-
'*Journ. Am. Med. Ass., 1918, 71, p. 1660. Incompletely quoting Lusk, Joum. Am. Med.
Ass., 1918, 70, p. 821.
250 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN,
factory standard is that secured by taking into account the body-
weight, stature, and age of the subject in predicting basal metaboUsm.
This method is therefore an extension and modification of the selected
group method, employed earUer at the Nutrition Laboratory. In the
new method, which we have designated as the multiple-prediction
method, we replace the empirical determinations of the metabolism of
individuals of specific weight, stature, and age by values given by
multiple prediction equations based on the statistical constants of all
available normal data.
These equations have been tabled for both men and women for a
range of weight, stature, and age which will be met in practical work
with adult subjects, and give a set of multiple prediction tables of stand-
ard normal adult basal metabolism constants.
The illustrations of the practical application of these multiple pre-
diction tables show first of all their great usefulness in the detection of
differences between series of metabolism measurements. Thus, as
far as we are aware, the anomalous nature of the series of determina-
tions by Magnus-Levy and Falk and those by Palmer, Means, and
Gamble, has heretofore quite escaped the notice of physiologists, and
their data have been combined freely with other series for the purpose
of generalization. The aberrant nature of these series becomes evident
as soon as comparison of the actual measurements with the theoretical
values from the multiple prediction tables is made.
The use of the tables shows the clear differentiation of athletes and
diabetics from other individuals in their metabolic level, thus confirm-
ing conclusions already drawn at the Nutrition Laboratory.
The use of the standards shows the existence of a well-marked
differentiation in the level of metabolism of men and women, and shows
that the differences are persistent throughout adult life instead of
disappearing in later years as maintained by Sonden and Tigerstedt.
There is no evidence for such differentiation in new-bom infants.
While the novelty of the conception underlying these standards
will probably limit somewhat their immediate adoption by physiolo-
gists, the illustrations show that for purposes of more refined analysis
they have great practical value. We believe that ultimately the great
convenience of these multiple prediction tables will result in their
general adoption as standards of reference in all work on human
nutritional physiology.
\'\Tien larger series of basal data are available we expect to revise
these tables so that they may represent the broadest and most secure
foundation for comparative nutritional investigation.
APPENDIX.
STANDARD
MULTIPLE PREDICTION TABLES
FOR
NORMAL BASAL METABOUSM
(For method of use see page 230. Chapter VIII
gives illustrations of practical application).
PREDICTION TABLES FOR BASAL METABOLISM.
253
Table I.
— Factor for body-xeeighi in men.
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
25
410
412
413
414
416
417
419
420
421
423
26
424
425
427
428
430
431
432
434
435
436
27
438
439
441
442
443
445
446
447
449
450
28
452
453
454
456
457
458
460
461
463
464
29
465
467
468
469
471
472
474
475
476
478
30
479
480
482
483
485
486
487
489
490
491
31
493
494
496
497
498
500
501
502
504
505
32
507
508
509
511
512
513
515
516
518
519
33
520
522
523
524
526
527
529
530
531
633
34
534
535
537
538
540
541
542
544
545
546
35
548
549
551
552
553
555
556
557
559
560
36
562
563
564
566
567
568
570
571
573
574
37
575
577
578
579
581
582
584
585
586
588
38
589
590
592
593
595
596
597
599
600
601
39
603
601
606
607
608
610
611
612
614
615
40
617
618
619
621
622
623
625
626
628
629
41
630
632
633
634
636
637
639
640
641
643
42
644
645
647
648
650
651
652
654
655
656
43
658
659
661
662
663
665
666
667
669
670
44
672
673
674
676
677
678
680
681
683
684
45
685
687
688
689
691
692
694
695
696
698
46
699
700
702
703
705
706
707
709
710
711
47
713
714
716
717
718
720
721
722
724
725
48
727
728
729
731
732
733
735
736
738
739
49
740
742
743
744
746
747
749
750
751
753
50
754
755
757
758
760
761
762
764
765
766
51
768
769
771
772
773
775
776
777
779
780
52
782
783
784
786
787
788
790
791
793
794
53
795
797
798
799
801
802
804
805
806
808
54
809
810
812
813
815
816
817
819
820
821
55
823
824
826
827
828
830
831
832
834
835
56
837
838
839
841
842
843
845
846
848
849
57
850
852
853
854
856
857
859
860
861
863
58
864
865
867
868
870
871
872
874
875
876
59
878
879
881
882
888
885
886
887
889
890
60
892
893
894
896
897
898
900
901
903
904
61
905
907
908
909
911
912
914
915
916
918
62
919
920
922
923
925
926
927
929
930
931
63
933
934
936
937
938
940
941
942
944
945
64
947
948
949
951
952
953
955
956
958
959
65
960
962
963
964
966
967
969
970
971
973
66
974
975
977
978
980
981
982
984
985
986
67
988
989
991
992
993
995
996
997
999
1000
68
1002
1003
1004
1006
1007
1008
1010
1011
1013
1014
69
1015
1017
1018
1019
1021
1022
1024
1025
1026
1028
70
1029
1030
1032
1033
1035
1036
1037
1039
1040
1041
71
1043
1044
1046
1047
1048
1050
1051
1052
1054
1055
72
1057
1058
1059
1061
1062
1063
1065
1066
1068
1069
73
1070
1072
1073
1074
1076
1077
1079
1080
1081
1083
74
1084
1085
1087
1088
1090
1091
1092
1094
1095
1096
254
PREDICTION TABLES FOR BASAL METABOLISM.
Table 1
. — Factor for body-weight in men. — Concluded.
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
75
1098
1099
1101
1102
1103
1105
1106
1107
1109
1110
76
1112
1113
1114
1116
1117
1118
1120
1121
1123
1124
77
1125
1127
1128
1129
1131
1132
1134
1135
1136
1138
78
1139
1140
1142
1143
1145
1146
1147
1149
1150
1151
79
1153
1154
1156
1157
1158
1160
1161
1162
1164
1165
80
1167
1168
1169
1171
1172
1173
1175
1176
1178
1179
81
1180
1182
1183
1184
1186
1187
1189
1190
1191
1193
82
1194
1195
1197
1198
1200
1201
1202
1204
1205
1206
83
1208
1209
1211
1212
1213
1215
1216
1217
1219
1220
84
1222
1223
1224
1226
1227
1228
1230
1231
1233
1234
85
1235
1237
1238
1239
1241
1242
1244
1245
1246
1248
86
1249
1250
1252
1253
1255
1256
1257
1259
1260
1261
87
1263
1264
1266
1267
1268
1270
1271
1272
1274
1275
88
1277
1278
1279
1281
1282
1283
1285
1286
1288
1289
89
1290
1292
1293
1294
1296
1297
1299
1300
1301
1303
90
1304
1305
1307
1308
1310
1311
1312
1314
1315
1316
91
1318
1319
1321
1322
1323
1325
1326
1327
1329
1330
92
1332
1333
1334
1336
1337
1338
1340
1341
1343
1344
93
1345
1347
1348
1349
1351
1352
1354
1355
1356
1358
94
1359
1360
1362
1363
1365
1366
1367
1369
1370
1371
95
1373
1374
1376
1377
1378
1380
1381
1383
1384
1385
96
1387
1388
1389
1391
1392
1394
1395
1396
1398
1399
97
1400
1402
1403
1405
1406
1407
1409
1410
1411
1413
98
1414
1416
1417
1418
1420
1421
1422
1424
1425
1427
99
1428
1429
1431
1432
1433
1435
1436
1438
1439
1440
100
1442
1443
1444
1446
1447
1449
1450
1451
1453
1454
101
1455
1457
1458
1460
1461
1462
1464
1465
1466
1468
102
1469
1471
1472
1473
1475
1476
1477
1479
1480
1482
103
1483
1484
1486
1487
1488
1490
1491
1493
1494
1495
104
1497
1498
1499
1501
1502
1504
1505
1506
1508
1509
105
1510
1512
1513
1515
1516
1517
1519
1520
1521
1523
106
1524
1526
1527
1528
1530
1531
1532
1534
1535
1537
107
1538
1539
1541
1542
1543
1545
1546
1548
1549
1550
108
1552
1553
1554
1556
1557
1559
1560
1561
1563
1564
109
1565
1567
1568
1570
1571
1572
1574
1575
1576
1578
110
1579
1581
1582
1583
1585
1586
1587
1589
1590
1592
111
1593
1594
1596
1597
1598
1600
1601
1603
1604
1605
112
1607
1608
1609
1611
1612
1614
1615
1616
1618
1619
113
1620
1622
1623
1625
1626
1627
1629
1630
1631
1633
114
1634
1636
1637
1638
1640
1641
1642
1644
1645
1647
115
1648
1649
1651
1652
1653
1655
1656
1658
1659
1660
116
1662
1663
1664
1666
1667
1669
1670
1671
1673
1674
117
1675
1677
1678
1680
1681
1682
1684
1685
1686
1688
118
1689
1691
1692
1693
1695
1696
1697
1699
1700
1702
119
1703
1704
1706
1707
1708
1710
1711
1713
1714
1715
120
1717
1718
1719
1721
1722
1724
1725
1726
1728
1729
121
1730
1732
1733
1735
1736
1737
1739
1740
1741
1743
122
1744
1746
1747
1748
1750
1751
1752
1754
1755
1757
123
1768
1759
1761
1762
1763
1765
1766
1768
1769
1770
124
1772
1773
1774
1776
1777
1779
1780
1781
1783
1784
PREDICTION TABLES FOR BASAL METABOLISM.
255
Table
II. — Factor for stature and age in men
21
22
23
24
25
26
27
28
29
30
151
614
607
600
593
587
580
573
566
560
553
152
619
612
605
598
592
585
578
571
565
558
153
624
617
610
603
597
590
583
576
570
563
154
629
622
615
608
602
595
588
581
575
568
155
634
627
620
613
607
600
593
586
580
573
156
639
632
625
618
612
605
598
591
585
578
157
644
637
630
623
617
610
603
596
590
583
158
649
642
635
628
622
615
608
601
595
588
159
654
647
640
633
627
620
613
606
600
593
160
659
652
645
638
632
625
618
611
605
598
161
664
657
650
643
637
630
623
616
610
603
162
669
662
655
648
642
635
628
621
615
608
163
674
667
660
653
647
640
633
626
620
613
164
679
672
665
658
652
645
638
631
625
618
165
684
677
670
663
657
650
643
636
630
623
166
689
682
675
668
662
655
648
641
635
628
167
694
687
680
673
667
660
653
646
640
633
168
699
692
685
678
672
665
658
651
645
638
169
704
697
690
683
677
670
663
656
650
643
170
709
702
695
688
682
675
668
661
655
648
171
714
707
700
693
687
680
673
666
660
653
172
719
712
705
698
692
685
678
671
665
658
173
724
717
710
703
697
690
683
676
670
663
174
729
722
715
708
702
695
688
681
675
668
175
734
727
720
713
707
700
693
686
680
673
176
739
732
725
718
712
705
698
691
685
678
177
744
737
730
723
717
710
703
696
690
683
178
749
742
735
728
722
715
708
701
695
688
179
754
747
740
733
727
720
713
706
700
693
180
759
752
745
738
732
725
718
711
705
698
181
764
757
750
743
737
730
723
716
710
703
182
769
762
755
748
742
735
728
721
715
708
183
774
767
760
753
747
740
733
726
720
713
184
779
772
765
758
752
745
738
731
725
718
185
784
777
770
763
757
750
743
736
730
723
186
789
782
775
768
762
755
748
741
735
728
187
794
787
780
773
767
760
753
746
740
733
188
799
792
785
779
772
765
758
751
745
738
189
804
797
790
784
777
770
763
756
750
743
190
809
802
795
789
782
775
768
761
755
748
191
814
807
800
794
787
780
773
766
760
753
192
819
812
805
799
792
785
778
771
765
758
193
824
817
810
804
797
790
783
776
770
763
194
829
822
815
809
802
795
788
781
775
768
195
834
827
820
814
807
800
793
787
780
773
196
839
832
825
819
812
805
798
792
785
778
197
844
837
830
824
817
810
803
797
790
783
198
849
842
835
829
822
815
808
802
795
788
199
854
847
840
834
827
820
813
807
800
793
200
859
852
845
839
832
825
818
812
805
798
I
256
PREDICTION TABLES FOR BASAL METABOLISM.
Table 11. ^F actor j
or stature and age in men
. — Continued.
31
32
33
34
35
36
37
38
39
40
151
546
539
533
526
519
512
506
499
492
485
152
551
544
538
531
524
517
511
504
497
490
153
556
549
543
536
529
522
516
509
502
495
154
561
554
548
541
534
527
521
514
507
500
155
566
559
553
546
539
532
526
519
512
505
156
571
564
558
551
544
537
531
524
517
510
157
576
569
563
556
549
542
536
529
522
515
158
581
574
568
561
554
547
541
534
527
520
159
586
579
573
566
559
552
546
539
532
525
160
591
584
578
571
564
557
551
544
537
530
161
596
589
583
576
569
562
556
549
542
535
162
601
594
588
581
574
567
561
554
547
540
163
606
599
593
586
579
572
566
559
552
545
164
611
604
598
591
584
577
571
564
557
550
165
616
609
603
596
589
582
576.
569
562
555
166
621
614
608
601
594
587
581
574
567
560
167
626
619
613
606
599
592
586
579
572
565
168
631
624
618
611
604
597
591
584
577
570
169
636
629
623
616
609
602
596
589
582
575
170
641
634
628
621
614
607
601
594
587
580
171
646
639
633
626
619
612
606
599
592
585
172
651
644
638
631
624
617
611
604
597
590
173
656
649
643
636
629
622
616
609
602
595
174
661
654
648
641
634
627
621
614
607
600
175
666
659
653
646
639
632
626
619
612
605
176
671
664
658
651
644
637
631
624
617
610
177
676
669
663
656
649
642
636
629
622
615
178
681
674
668
661
654
647
641
634
627
620
179
686
679
673
666
659
652
646
639
632
625
180
691
684
678
671
664
657
651
644
637
630
181
696
689
683
676
669
662
656
649
642
635
182
701
694
688
681
674
667
661
654
647
640
183
706
699
693
686
679
672
666
659
652
645
184
711
704
698
691
684
677
671
664
657
650
185
716
709
703
696
689
682
676
669
662
655
186
721
714
708
701
694
687
681
674
667
660
187
726
719
713
706
699
692
686
679
672
665
188
731
724
718
711
704
697
691
684
677
670
189
736
729
723
716
709
702
696
689
682
675
190
741
734
728
721
714
707
701
694
687
680
191
746
739
733
726
719
712
706
699
692
685
192
751
744
738
731
724
717
711
704
697
690
193
756
749
743
736
729
722
716
709
702
695
194
761
754
748
741
734
727
721
714
707
700
195
766
769
753
746
739
732
726
719
712
705
196
771
764
758
751
744
737
731
724
717
710
197
776
769
763
756
749
742
736
729
722
715
198
781
774
768
761
754
747
741
734
727
720
199
786
779
773
766
759
752
746
739
732
725
200
791
785
778
771
764
757
751
744
737
730
PREDICTION TABLES FOR BASAL METABOLISM.
257
Table U.— Factor J
or stature and age in men
— Continued.
41
42
43
44
45
46
47
48
49
50
151
479
472
465
458
452
445
438
431
425
418
152
484
477
470
463
457
450
443
436
430
423
153
489
482
475
468
462
455
448
441
435
428
154
494
487
480
473
467
460
453
446
440
433
155
499
492
485
478
472
465
458
451
445
438
156
504
497
490
483
477
470
463
456
450
443
157
509
502
495
488
482
475
468
461
455
448
158
514
507
500
493
487
480
473
466
460
453
159
519
512
505
498
492
485
478
471
465
458
160
524
517
510
503
497
490
483
476
470
463
161
529
522
515
508
502
495
488
481
475
468
162
534
527
520
513
507
500
493
486
480
473
163
539
532
525
518
512
505
498
491
485
478
164
544
537
530
523
517
510
503
496
490
483
165
549
542
535
528
522
515
508
501
495
488
166
554
547
540
533
527
520
513
506
500
493
167
559
552
545
538
532
525
518
511
505
498
168
564
557
550
543
537
630
523
516
510
503
169
569
562
555
548
542
535
528
521
515
508
170
574
567
560
553
547
540
533
526
520
513
171
579
572
565
558
552
545
538
531
525
518
172
584
577
570
563
557
550
543
536
530
523
173
589
582
575
568
562
555
548
541
535
528
174
594
587
580
573
567
560
553
546
540
533
175
599
592
585
578
572
565
558
551
545
538
176
604
597
590
583
577
570
563
556
550
543
177
609
602
595
588
582
575
568
561
555
548
178
614
607
600
593
587
580
573
566
560
553
179
619
612
605
598
592
585
578
571
565
558
180
624
617
610
603
597
590
583
576
570
563
181
629
622
615
608
602
595
588
581
575
568
182
634
627
620
613
607
600
593
586
580
573
183
639
632
625
618
612
605
598
591
585
578
184
644
637
630
623
617
610
603
596
590
583
185
649
642
635
628
622
615
608
601
595
588
186
654
647
640
633
627
620
613
606
600
593
187
659
652
645
638
632
625
618
611
605
598
188
664
657
650
643
637
630
623
616
610
603
189
669
662
655
648
642
635
628
621
615
608
190
674
667
660
653
647
640
633
626
620
613
191
679
672
665
658
652
645
638
631
625
618
192
684
677
670
663
657
650
643
636
630
623
193
689
682
675
668
662
655
648
641
635
628
194
694
687
680
673
667
660
653
646
640
633
195
699
692
685
678
672
665
658
651
645
638
196
704
697
690
683
677
670
663
656
650
643
197
709
702
695
688
682
675
668
661
655
648
198
714
707
700
693
687
680
673
666
660
653
199
719
712
705
698
692
685
678
671
665
658
200
724
717
710
703
697
690
683
676
670
663
258
PREDICTION TABLES FOR BASAL METABOLISM.
Table II. — Factor for stature and age in men. — Continued.
51
52
53
54
55
56
57
58
59
60
151
411
404
397
391
384
377
370
364
357
350
152
416
409
402
396
389
382
375
369
362
355
153
421
414
407
401
394
387
380
374
367
360
154
426
419
412
406
399
392
385
379
372
365
155
431
424
417
411
404
397
390
384
377
370
156
436
429
422
416
409
402
395
389
382
375
157
441
434
428
421
414
407
400
394
387
380
158
446
439
433
426
419
412
405
399
392
385
159
451
444
438
431
424
417
410
404
397
390
160
456
449
443
436
429
422
415
409
402
395
161
461
454
448
441
434
427
420
414
407
400
162
466
459
453
446
439
432
425
419
412
405
163
471
464
458
451
444
437
431
424
417
410
164
476
469
463
456
449
442
436
429
422
415
165
481
474
468
461
454
447
441
434
427
420
166
486
479
473
466
459
452
446
439
432
425
167
491
484
478
471
464
457
451
444
437
430
168
496
489
483
476
469
462
456
449
442
435
169
501
494
488
481
474
467
461
454
447
440
170
506
499
493
486
479
472
466
459
452
445
171
511
504
498
491
484
477
471
464
457
450
172
516
509
503
496
489
482
476
469
462
455
173
521
514
508
501
494
487
481
474
467
460
174
526
519
513
506
499
492
486
479
472
465
175
531
524
518
511
504
497
491
484
477
470
176
536
529
523
516
509
502
496
489
482
475
177
541
534
528
521
514
507
501
494
487
480
178
546
539
533
526
519
512
506
499
492
485
179
551
544
538
531
524
517
511
504
497
490
180
556
549
543
536
529
522
516
509
502
495
181
561
554
548
541
534
527
521
514
507
500
182
566
559
553
546
539
532
526
519
512
505
183
571
564
558
551
544
537
531
524
517
510
184
576
569
563
556
549
542
536
529
522
515
185
581
574
568
561
554
547
541
534
527
520
186
586
579
573
566
559
552
546
539
532
525
187
591
584
578
571
564
557
551
544
537
530
188
596
589
583
576
569
562
556
549
542
536
189
601
594
588
581
574
567
561
554
547
540
190
606
599
593
586
579
572
566
559
552
545
191
611
604
598
591
584
577
571
564
557
550
192
616
609
603
596
589
582
676
569
562
555
193
621
614
608
601
594
587
581
574
567
660
194
626
619
613
606
599
592
586
579
572
565
195
631
624
618
611
604
597
591
584
577
570
196
636
629
623
616
609
602
596
589
582
575
197
641
634
628
621
614
607
601
594
587
580
198
646
639
633
626
619
612
606
599
592
585
199
651
644
638
631
624
617
611
604
597
690
200
656
649
643
636
629
622
616
609
602
695
PREDICTION TABLES FOR BASAL METABOLISM.
259
Table II. — Factor for stature and age in men. — Ckincluded.
61
62
63
64
65
66
67
68
69
70
151
343
337
330
323
316
310
303
296
289
283
152
348
342
335
328
321
315
308
301
294
288
153
353
347
340
333
326
320
313
306
299
293
154
358
352
345
338
331
325
318
311
304
298
155
363
357
350
343
336
330
323
316
309
303
156
368
362
355
348
341
335
328
321
314
308
157
373
367
360
353
346
340
333
326
319
313
158
378
372
365
358
351
345
338
331
324
318
159
383
377
370
363
356
350
343
336
329
323
160
388
382
375
368
361
355
348
341
334
328
161
393
387
380
373
366
360
353
346
339
333
162
398
392
385
378
371
365
358
351
344
338
163
403
397
390
383
376
370
363
356
349
343
164
408
402
395
388
381
375
368
361
354
348
165
413
407
400
393
386
380
373
366
359
353
166
418
412
405
398
391
385
378
371
364
358
167
423
417
410
403
396
390
383
376
369
363
168
428
422
415
408
401
395
388
381
374
368
169
434
427
420
413
406
400
393
386
379
373
170
439
432
425
418
411
405
398
391
3&4
378
171
444
437
430
423
416
410
403
396
389
383
172
449
442
435
428
421
415
408
401
394
388
173
454
447
440
433
426
420
413
406
399
393
174
459
452
445
438
431
425
418
411
404
398
175
464
457
450
443
437
430
423
416
409
403
176
469
462
455
448
442
435
428
421
414
408
177
474
467
460
453
447
440
433
426
419
413
178
479
472
465
458
452
445
438
431
424
418
179
484
477
470
463
457
450
443
436
429
423
180
489
482
475
468
462
455
448
441
434
428
181
494
487
480
473
467
460
453
446
440
433
182
499
492
485
478
472
465
458
451
445
438
183
504
497
490
483
477
470
463
456
450
443
184
509
502
495
488
482
475
468
461
455
448
185
514
507
500
493
487
480
473
466
460
453
186
519
512
505
498
492
485
478
471
465
458
187
524
517
510
503
497
490
483
476
470
463
188
529
522
515
508
502
495
488
481
475
468
189
534
527
520
513
507
500
493
486
480
473
190
539
532
525
518
512
505
498
491
485
478
191
544
537
530
523
517
510
503
496
490
483
192
549
542
535
528
522
515
508
501
495
488
193
554
547
540
533
527
520
513
506
500
493
194
559
552
645
538
532
525
518
511
505
498
195
564
557
550
543
537
530
523
516
510
503
196
569
562
555
548
542
535
528
521
515
508
197
574
567
560
553
547
540
533
526
520
513
198
579
572
565
558
552
545
538
531
525
518
199
584
577
570
563
557
550
M3
536
530
523
200
589
582
575
568
562
555
548
541
535
528
260
PEEDICTION TABLES FOR BASAL METABOLISM.
Table III. — Factor for body-weight in women.
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
25
894
895
896
897
898
899
900
901
902
903
26
904
905
906
907
908
909
909
910
911
912
27
913
914
915
916
917
918
919
920
921
922
28
923
924
925
926
927
928
929
930
931
931
29
932
933
934
935
936
937
938
939
940
941
30
942
943
944
945
946
947
948
949
950
951
31
952
953
953
954
955
956
957
958
959
960
32
961
962
963
964
965
966
967
968
969
970
33
971
972
973
974
975
975
976
977
978
979
34
980
981
982
983
984
985
986
987
988
989
35
990
991
992
993
994
995
996
997
997
998
36
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
37
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
38
1019
1019
1020
1021
1022
1023
1024
1025
1026
1027
39
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
40
1038
1039
1040
1041
1041
1042
1043
1044
1045
1046
41
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
42
1057
1058
1059
1060
1061
1062
1062
1063
1064
1065
43
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
44
1076
1077
1078
1079
1080
1081
1082
1083
1084
1084
45
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
46
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
47
1105
1106
1106
1107
1108
1109
1110
1111
1112
1113
48
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
49
1124
1125
1126
1127
1128
1128
1129
1130
1131
1132
50
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
51
1143
1144
1145
1146
1147
1148
1149
1150
1150
1151
52
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
53
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
54
1172
1172
1173
1174
1175
1176
1177
1178
1179
1180
55
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
56
1191
1192
1193
1194
1194
1195
1196
1197
1198
1199
57
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
58
1210
1211
1212
1213
1214
1215
1216
1216
1217
1218
59
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
60
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
61
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
62
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
63
1258
1259
1260
1260
1261
1262
1263
1264
1265
1266
64
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
65
1277
1278
1279
1280
1281
1281
1282
1283
1284
1285
66
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
67
1296
1297
1298
1299
1300
1301
1302
1303
1303
1304
68
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
69
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
70
1325
1325
1326
1327
1328
1329
1330
1331
1332
1333
71
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
72
1344
1345
1346
1347
1347
1348
1349
1350
1351
1352
73
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
74
1363
1364
1365
1366
1367
1368
1369
1369
1370
1371
PREDICTION TABLES FOR BASAL METABOLISM.
261
Table III
— Factor for body-weight in women. —
Concluded.
.0
.1
.2
.3
.4
.5
.6
.7
.8
.9
75
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
76
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
77
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
78
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
79
1411
1412
1413
1413
1414
1415
1416
1417
1418
1419
80
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
81
1430
1431
1432
1433
1434
1435
1435
1436
1437
1438
82
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
83
1449
1450
1451
1452
1453
1454
1455
1456
1457
1457
84
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
85
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
86
1478
1479
1479
1480
1481
1482
1483
1484
1485
1486
87
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
88
1497
1498
1499
1500
1501
1501
1502
1503
1504
1505
89
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
90
1516
1517
1518
1519
1520
1521
1522
1522
1523
1524
91
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
92
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
93
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
94
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
95
1564
1565
1566
1566
1567
1568
1569
1570
1571
1572
96
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
97
1583
1584
1585
1586
1587
1588
1588
1589
1590
1591
98
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
99
1602
1603
1604
1605
1606
1607
1608
1609
1610
1610
100
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
101
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
102
1631
1632
1632
1633
1634
1635
1636
1637
1638
1639
103
1&40
1641
1642
1643
1644
1645
1646
1647
1648
1649
104
1650
1651
1652
1653
1654
16&4
1655
1656
1657
1658
105
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
106
1669
1670
1671
1672
1673
1674
1675
1676
1676
1677
107
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
108
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
109
1698
1698
1699
1700
1701
1702
1703
1704
1705
1706
110
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
111
1717
1718
1719
1720
1720
1721
1722
1723
1724
1725
112
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
113
1736
1737
1738
1739
1740
1741
1741
1742
1743
1744
114
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
115
1755
1756
1757
1758
1759
1760
1761
1762
1763
1763
116
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
117
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
118
1784
1785
1785
1786
1787
1788
1789
1790
1791
1792
119
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
120
1803
1804
1805
1806
1807
1807
1808
1809
1810
1811
121
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
122
1822
1823
1824
1825
1826
1827
1828
1829
1829
1830
123
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
124
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
262
PREDICTION TABLES FOR BASAL METABOLISM.
Table IV. — Factor for stature and age in teamen.
21
22
23
24
25
26
27
28
29
30
151
181
176
172
167
162
158
153
148
144
139
152
183
178
174
169
164
160
155
150
146
141
153
185
180
175
171
166
161
157
152
147
143
154
187
182
177
173
168
163
159
154
149
145
155
189
184
179
174
170
165
160
156
151
146
156
190
186
181
176
172
167
162
158
153
148
157
192
188
183
178
173
169
164
159
155
150
158
194
189
185
180
175
171
166
161
157
152
159
196
191
187
182
177
173
168
163
158
154
160
198
193
188
184
179
174
170
165
160
156
161
199
195
190
186
181
176
172
167
162
158
162
201
197
192
187
183
178
173
169
164
159
163
203
199
194
189
185
180
175
171
166
161
164
205
200
196
191
186
182
177
172
168
163
165
207
202
198
193
188
184
179
174
170
165
166
209
204
199
194
190
185
181
176
171
167
167
211
206
201
197
192
187
183
178
173
169
168
213
208
203
199
194
189
184
180
175
170
169
214
210
205
200
196
191
186
182
177
172
170
216
212
207
202
198
193
188
184
179
174
171
218
213
209
204
199
195
190
185
181
176
172
220
215
211
206
201
197
192
187
183
178
173
222
217
212
208
203
198
194
189
184
180
174
224
219
214
210
205
200
196
191
186
182
175
225
221
216
211
207
202
197
193
188
183
176
227
223
218
213
209
204
199
195
190
185
177
229
225
220
215
210
206
201
196
192
187
178
231
226
222
217
212
208
203
198
194
189
179
233
228
224
219
214
210
205
200
195
191
180
235
230
225
221
216
211
207
202
197
193
181
237
232
227
223
218
213
209
204
199
195
182
238
234
229
224
220
215
210
206
201
196
183
240
236
231
226
222
217
212
208
203
198
184
242
237
233
228
223
219
214
209
205
200
185
244
239
235
230
225
221
216
211
207
202
186
246
241
236
232
227
222
218
213
208
204
187
248
243
238
234
229
224
220
215
210
206
188
250
245
240
236
231
226
221
217
212
207
189
251
247
242
237
233
228
223
219
214
209
190
253
249
244
239
235
230
225
221
216
211
191
255
250
246
241
236
232
227
222
218
213
192
257
252
248
243
238
234
229
224
220
215
193
259
254
249
245
240
235
231
226
221
217
194
261
256
251
247
242
237
233
228
223
219
195
262
258
253
248
244
239
234
230
225
220
196
264
260
255
250
246
241
236
232
227
222
197
266
262
257
252
247
243
238
233
229
224
198
268
263
259
254
249
245
240
235
231
226
199
270
265
261
256
251
247
242
237
•232
228
200
272
267
262
258
253
248
244
239
234
230
PREDICTION TABLES FOR BASAL METABOLISM.
263
Table I\
'. — Factor fat
stature and
age in women
. — Continued.
31
32
33 j
34
35
36
37 i
38
39
40
151
134
130
125
120
116
111
106
102
97
92
152
136
132
127
122
117
113
108
103
99
94
153
138
133
129
124
119
115
110
105
101
96
164
140
135
131
126
121
117
112
107
102
98
155
142
137
132
128
123
118
114
109
104
100
156
144
139
134
130
125
120
116
111
106
102
157
145
141
136
131
127
122
117
113
108
103
158
147
143
138
133
129
124
119
115
110
105
159
149
144
140
135
130
126
121
116
112
107
160
151
146
142
137
132
128
123
118
114
109
161
153
148
143
139
134
129
125
120
115
111
162
155
150
145
141
136
131
127
122
117
113
163
157
152
147
143
138
133
128
124
119
114
164
158
154
149
144
140
135
130
126
121
116
165
160
156
151
146
142
137
132
128
123
118
166
162
157
153
148
143
139
134
129
125
120
167
164
159
155
150
145
141
136
131
127
122
168
166
161
156
152
147
142
138
133
128
124
169
168
163
158
154
149
144
140
135
130
126
170
169
165
160
155
151
146
141
137
132
127
171
171
167
162
157
153
148
143
139
134
129
172
173
169
IW
159
154
150
145
140
136
131
173
175
170
166
161
156
152
147
142
138
133
174
177
172
168
163
158
154
149
144
139
135
175
179
174
169
165
160
155
151
146
141
137
176
181
176
171
167
162
157
153
148
143
139
177
182
178
173
168
164
159
154
150
145
140
178
184
180
175
170
166
161
156
152
147
142
179
186
181
177
172
167
163
158
153
149
144
180
188
183
179
174
169
165
160
155
151
146
181
190
185
180
176
171
166
162
157
152
148
182
192
187
182
178
173
168
1&4
159
154
150
183
194
189
184
180
175
170
165
161
156
151
184
195
191
186
181
177
172
167
163
158
153
185
197
193
188
183
179
174
169
165
160
155
186
199
194
190
185
180
176
171
166
162
157
187
201
196
192
187
182
178
173
168
164
159
188
203
198
193
189
184
179
175
170
165
161
189
205
200
195
191
186
181
177
172
167
163
190
206
202
197
192
188
183
178
174
169
164
191
208
204
199
194
190
185
180
176
171
166
192
210
206
201
196
191
187
182
177
173
168
193
212
207
203
198
193
189
184
179
175
170
194
214
209
205
200
195
191
186
181
176
172
195
216
211
206
202
197
192
188
183
178
174
196
218
213
208
204
199
194
190
185
180
175
197
219
215
210
205
201
196
191
187
182
177
198
221
217
212
207
203
198
193
189
184
179
199
223
218
214
209
204
200
195
190
186
181
200
225
220
216
211
206
202
; 197
192
188
183
264
PREDICTION TABLES FOR BASAL METABOLISM.
Table IV. — Factor for stature and age in women. — Continued.
41
42
43
44
45
46
47
48
49
50
151
88
83
78
74
69
64
60
55
50
46
152
89
85
80
75
71
66
61
57
52
47
153
91
87
82
77
73
68
63
59
54
49
154
93
88
84
79
74
70
65
60
56
51
155
95
90
86
81
76
72
67
62
58
53
156
97
92
87
83
78
73
69
64
59
55
157
99
94
89
85
80
75
71
66
61
57
158
101
96
91
87
82
77
72
68
63
58
159
102
98
93
88
84
79
74
70
65
60
160
104
100
95
90
86
81
76
72
67
62
161
106
101
97
92
87
83
78
73
69
64
162
108
103
99
94
89
85
80
75
71
66
163
110
105
100
96
91
86
82
77
72
68
164
112
107
102
98
93
88
84
79
74
70
165
113
109
104
99
95
90
85
81
76
71
166
115
111
106
101
97
92
87
83
78
73
167
117
113
108
103
98
94
89
84
80
75
168
119
114
110
105
100
96
91
86
82
77
169
121
116
112
107
102
98
93
88
83
79
170
123
118
113
109
104
99
95
90
85
81
171
125
120
115
111
106
101
97
92
87
83
172
126
122
117
112
108
103
98
94
89
84
173
128
124
119
114
110
105
100
96
91
86
174
130
125
121
116
111
107
102
97
93
88
175
132
127
123
118
113
109
104
99
95
90
176
134
129
124
120
115
110
106
101
96
92
177
136
131
126
122
117
112
108
103
98
94
178
138
133
128
124
119
114
109
105
100
95
179
139
135
130
125
121
116
111
107
102
97
180
141
137
132
127
123
118
113
108
104
99
181
143
138
134
129
124
120
115
110
106
101
182
145
140
136
131
126
122
117
112
108
103
183
147
142
137
133
128
123
119
114
109
105
184
149
144
139
135
130
125
121
116
111
107
185
150
146
141
136
132
127
122
118
113
108
186
152
148
143
138
134
129
124
120
115
110
187
154
150
145
140
135
131
126
121
117
112
188
156
151
147
142
137
133
128
123
119
114
189
158
153
149
144
139
134
130
125
120
116
190
160
155
150
146
141
136
132
127
122
118
191
162
157
152
148
143
138
134
129
124
119
192
163
159
154
149
145
140
135
131
126
121
193
165
161
156
151
147
142
137
133
128
123
194
167
162
158
153
148
144
139
134
130
125
195
169
164
160
155
150
146
141
136
132
127
196
171
166
161
157
152
147
143
138
133
129
197
173
168
163
159
154
149
145
140
135
131
198
175
170
165
160
156
151
146
142
137
132
199
176
172
167
162
158
153
148
144
139
134
200
178
174
169
164
160
155
150
145
141
136
PREDICTION TABLES FOR BASAL METABOLISM.
265
Table IV. — Factor for stature and age in women. — Continued.
51
52
53
54
55
56
57
58
59
60
151
41
36
31
27
22
17
13
8
3
-1.2
152
43
38
33
29
24
19
15
10
5
0.6
153
45
40
35
31
26
21
16
12
7
2
154
46
42
37
32
28
23
18
14
9
4
155
48
44
39
34
30
25
20
16
11
6
156
50
45
41
36
31
27
22
17
13
8
157
52
47
43
38
33
29
24
19
15
10
158
54
49
44
40
35
30
26
21
16
12
159
56
51
46
42
37
32
28
23
18
14
160
57
53
48
43
39
34
29
25
20
15
161
59
55
50
45
41
36
31
27
22
17
162
61
57
52
47
42
38
33
28
24
19
163
63
58
54
49
44
40
35
30
26
21
164
65
60
56
51
46
42
37
32
27
23
165
67
62
57
53
48
43
39
34
29
25
166
69
64
59
55
50
45
41
36
31
26
167
70
66
61
56
52
47
42
38
33
28
168
72
68
63
58
54
49
44
40
35
30
169
74
69
65
60
55
51
46
41
37
32
170
76
71
67
62
57
53
48
43
39
34
171
78
73
68
64
59
54
50
45
40
36
172
80
75
70
66
61
56
52
47
42
38
173
82
77
72
67
63
58
53
49
44
39
174
83
79
74
69
65
60
55
51
46
41
175
85
81
76
71
67
62
57
52
48
43
176
87
82
78
73
68
64
59
54
50
45
177
89
84
80
75
70
66
61
56
52
47
178
91
86
81
77
72
67
63
58
53
49
179
93
88
83
79
74
69
65
60
55
51
180
94
90
85
80
76
71
66
62
57
52
181
96
92
87
82
78
73
68
64
59
54
182
98
93
89
84
79
75
70
65
61
56
183
100
95
91
86
81
77
72
67
63
58
184
102
97
93
88
83
78
74
69
64
60
185
104
99
94
90
85
80
76
71
66
62
186
106
101
96
92
87
82
78
73
68
63
187
107
103
98
93
89
84
79
75
70
65
188
109
105
100
95
91 '
86
81
77
72
67
189
111
106
102
97
92 ■
88
83
78
74
69
190
113
108
104
99
94
90
85
80
76
71
191
115
110
105
101
96
91
87 ■
82
77
73
192
117
112
107
103
98 !
93
89
84
79
75
193
119
114
109
104
100 ;
95
90
86
81
76
194
120
116
111
106
102
97
92
88
83
78
195
122
118
113
108
104
99
94
89
85
80
196
124
119
115
110
105
101
96
91
87
82
197
126
121
117
112
107 1
103
98
93
89
84
198
128
123
118
114
109
104
100
95
90
86
199
130
125
120
116
111
106
102 1
97
92
88
200
131
127
122
117
113 1
108
103
99
94
89
266
PREDICTION TABLES FOR BASAL METABOLISM.
Table IV.
^-Factor for stature and age in women
— Concluded.
61
62
63
64
65
66
67
68
69
70
151
-6
-11
-15
-20
-25
-29
-34
-39
-43
-48
152
-4
- 9
-13
-18
-23
-27
-32
-37
-41
-46
153
-2
- 7
-12
-16
-21
-26
-30
-35
-40
-44
154
-0
- 5
-10
-14
-19
-24
-28
-33
-38
-42
155
1
- 3
- 8
-13
-17
-22
-27
-31
-36
-41
156
3
- 1
- 6
-11
-15
-20
-25
-29
-34
-39
157
5
1
- 4
- 9
-14
-18
-23
-28
-32
-37
158
7
2
- 2
- 7
-12
-16
-21
-26
-30
-35
159
9
4
- 0
- 5
-10
-15
-19
-24
-29
-33
160
11
6
1
- 3
- 8
-13
-17
-22
-27
-31
161
13
8
3
- 1
- 6
-11
-15
-20
-25
-30
162
14
10
5
0
- 4
- 9
-14
-18
-23
-28
163
16
12
7
2
- 2
- 7
-12
-16
-21
-26
164
18
13
9
4
- 1
- 5
-10
-15
-19
-24
165
20
15
11
6
1
- 3
-.8
-13
-17
-22
166
22
17
12
8
3
- 2
- 6
-11
-16
-20
167
24
19
14
10
5
0
- 4
- 9
-14
-18
168
26
21
16
11
7
2
- 3
- 7
-12
-17
169
27
23
18
13
9
4
- 1
- 5
-10
-15
170
29
25
20
15
11
6
1
- 4
- 8
-13
171
31
26
22
17
12
8
3
- 2
- 6
-11
172
33
28
24
19
14
10
5
0
- 4
- 9
173
35
30
25
21
16
11
7
2
- 3
- 7
174
37
32
27
23
18
13
9
4
- 1
- 5
175
38
34
29
24
20
15
10
6
1
- 4
176
40
36
31
26
22
17
12
8
3
- 2
177
42
37
33
28
23
19
14
9
5
0
178
44
39
35
30
25
21
16
11
7
2
179
46
41
37
32
27
22
18
13
8
4
180
48
43
38
34
29
24
20
15
10
6
181
60
45
40
36
31
26
22
17
12
8
182
51
47
42
37
33
28
23
19
14
9
183
53
49
44
39
35
30
25
21
16
11
184
55
50
46
41
36
32
27
22
18
13
185
57
52
48
43
38
34
29
24
20
15
186
59
54
49
45
40
35
31
26
21
17
187
61
56
51
47
42
37
33
28
23
19
188
63
58
53
48
44
39
34
30
25
20
189
64
60
55
50
46
41
36
32
27
22
190
66
62
57
52
48
43
38
33
29
24
191
68
63
59
54
49
45
40
35
31
26
192
70
65
61
56
51
47
42
37
33
28
193
72
67
62
58
53
48
44
39
34
30
194
74
69
64
60
55
50
46
41
36
32
195
75
71
66
61
57
52
47
43
38
33
196
77
73
68
63
59
54
49
45
40
35
197
79
74
70
65
60
56
51
46
42
37
198
81
76
72
67
62
58
53
48
44
39
199
83
78
74
69
64
59
55
50
45
41
200
85
80
75
71
66
61
57
52
47
43
I
QP Harris, Janes Arthur
171 A biometric study of basal
H37 metabolism in man
8c Me<iK»l
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