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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 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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44 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



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INDIVIDUALS AND MEASUREMENTS CONSIDERED. 45 



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46 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



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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- 















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■75 








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40 


4S 


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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 




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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 
=- 62.07+1.565 
=+ 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. 





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• 






V 






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■IS8S 














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• • 






Q. 


■I48S 






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< 








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■385 




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/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 
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^ 




^ 




/\ 






■24 








^ 




' \ 




A 


-23 








v\ 




\: 




^M^ 


■22 












VN 




\a\ 


-21 
■20 
















\r\ 


■19 


22 


27 


32 


31 


42 


4-7 


S2 


V ^ 

S7 $2 67 
... i..._.t__. . 1 J — 



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 m ost 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 


-10 

- 7 

- 4 
+ 11 
+ 3 


+ 7 

- 1 


F. A. R 

E. F. D. B.... 

John L 

J. J.C 

J. R 


R. H. H 

L. C. M 

F. C. G 

Louis M 

T. M. C 


Average 


1.05 


34.2 


±8.1 


±4.6 



The average of the percentage deviations of the individual measures 
of heat production in terms of calories per kilogram of body-weight 
from the general mean of this measure is clearly higher than the average 
of the percentage deviations of the measures in units of calories per 
square meter of body-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, 
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 shr inks 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 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„,^ V l -,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 





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 


- 


- 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 





- 4 


- 9 


-14 


-18 


-23 


-28 


163 


16 


12 


7 


2 


- 2 


- 7 


-12 


-16 


-21 


-26 


164 


18 


13 


9 


4 


- 1 


- 5 


-10 


-15 


-19 


-24 


165 


20 


15 


11 


6 


1 


- 3 


-.8 


-13 


-17 


-22 


166 


22 


17 


12 


8 


3 


- 2 


- 6 


-11 


-16 


-20 


167 


24 


19 


14 


10 


5 





- 4 


- 9 


-14 


-18 


168 


26 


21 


16 


11 


7 


2 


- 3 


- 7 


-12 


-17 


169 


27 


23 


18 


13 


9 


4 


- 1 


- 5 


-10 


-15 


170 


29 


25 


20 


15 


11 


6 


1 


- 4 


- 8 


-13 


171 


31 


26 


22 


17 


12 


8 


3 


- 2 


- 6 


-11 


172 


33 


28 


24 


19 


14 


10 


5 





- 4 


- 9 


173 


35 


30 


25 


21 


16 


11 


7 


2 


- 3 


- 7 


174 


37 


32 


27 


23 


18 


13 


9 


4 


- 1 


- 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 





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 



PLEASE DO NOT REMOVE 
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UNIVERSITY OF TORONTO LIBRARY 



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