THE RELATION O F WEIGHT TO CHEST-GIRTH, STATURE, AND STEM-LENGTH'

HORACE GRAY, ill. D. Boston

THE PROBLEM

Chest measurement, poignantly complained Corbin in 1831,' though practised since Laennec in 1819 by many of the most justly eminent members of the Paris faculty, remained surprisingly scorned. And this in spite of the ease of its performance, compared with the ex- perience necessary for satisfactory auscultation. The same neglect has continued for a century.

Five years ago, in an attempt to discover which of the many-and therefore obviously inadequate-weight standards was the soundest, experimental application to normals showed us2 that weights predicted by the scarcely recognized formula of the Russian military surgeon Bornhardt3 came nearest to the observed weights. Now this formula differed from the less accurate methods in that it utilized in addition to the height on which the others depended, the circumference of the chest.

The fundamental necessity of securing this measurement has more and more struck home to us in subsequent of the much mooted topic of normal weight. These examinations of fact have repeatedly proven that those weight tables excel, which take notice of the perimeter of the thorax.

Full recognition however, of its primary importance has been de- layed by the claim of Pirquet" that the critical measurement is the sit- ting-height, and by the independent but parallel insistence of D r e ~ e r ' ~ + ' ~ on the stem-length, a nearly identical but, as we agree,14 more reliable measurement aiming to reproduce the distance between the bony landmarks; Vertex and ischial tuberosities.

A still shorter section of the body length has also been fancied on theory that, if the weight be more nearly related to the body length with-

1 For valuable assistance in this paper the author is indebted to Dr. Wade Wright. AMER. JOUR. PHYS. ANTHROP., Vol. V, No. 3.

25 1

252 HORACE GRAY

out the legs (sitting-height or stein-length), it may be even inore closely proportional to one of those two minus the head and neck. This torso length may be talien anteriorly from suprasternal notch to the seat, or posteriorly from vertebra proininens to seat. The former has seemed to us both untrustworthy owing to the mobility of the upper landmark during respiration, and also inconvenient to measure in women. The spine of the seventh cervical vertebra on the other hand has struck us as a more fixed point, especially with the subject placed in the steni- length position so well defined by Wallier’s and by Dreyer. We have therefore measured from the nychion to the seat as representing the distance of the seventh cervical spine to ischial tuberosities. It might be called the short stem-length, niid for convenience’ sake will be ab- breviated below as 7C.

METHOD OF ATTACK

In order to determine as indisputably as inay be, the correlation be- tween body weight and these rival gauges of body frame, we have undertaken the laborious method of bioinetric analysis. Our series is small: 80, but that is larger than several of the groups considered adequate for the far more complex problem of nietabolisin by such authorities as Harris and Benedict.16

The technic of biometrica! figuring and interpretation may be briefly stated. Any physician venturing into this field will find today we believe no clearer exposition than Harris and Benedict’s monograph, nor any more helpful manual of statistics than Yu1e’s.l’ For the mechanical work a calculating machine is not necessary, but niuch time can be saved by using Pearson’s Tables1* and Henselin’s Rechentafel.l9

Two methods have been used to calculate each average, each standard deviation, each numerator for the fraction yieldibg the fundamental correlation coefficient r ; while the remaining arithmetical work has been checked throughout by a second person. The numerical results therefore are believed correct.

SUBJECTS MEASURED

The material consisted of 80 healthy men, aged 18 to 71, mostly 20 to 35. These included 36 oarsmen a t the Harvard crew quarters a t Red Top in 1921,20 and a number of former athletes in medical school or active professional life. In short, there was little likelihood of either obesity or wasting disease.

All measurements were taken without clothes.

RELATIOhT O F WEIGHT 253

RELATION O F WEIGHT TO VL4RIOUS BODY MEASUREMENTS

Graphic Correlation by Senii-logarithniic Paper.-The simplest manner of gaining some conception of the degree of correspondence between the weight and the physical measurements previously discussed, is to plot a ratio chart. For such a study of the parallelisin between curves, the simple co-ordinate paper usually employed in medical articles gives an impression which is sometimes fallacious and often obscure.

In the present study, and probably inore generally than realized by scientific inen using statistics, greater lucidity may be obtained with a logarithmic ruling. This is a t first confusing, but can be mastered in a few minutes and that without an understanding of logarithms. The resulting graph is inueh easier to interpret, both by maker and reader, for one needs oiily to know that on semi-log or arithilog paper the curves representing two variables which are increasing a t the same rate tend to be parallel, no matter which curve is situated nearer the top of the diagram. In other words, during interpretation, the absolute values can be disregarded, a convenience non-existent in the case of many of the charts plotted on squared paper. Semi-log paper exhibits the customary equal divisions along the base line, while the vertical scale is divided into logarithmic spaces as on a slide rule.

Let us now sort our 80 cases serially beginning with the smallest weight, and plot these, then turn over the cards again and plot the height, chest-girth, stem-length and the seventh cervical length. In Chart 1. we notice:

1. The irregularity of all the measurement curves. 2 . That parallelisin to the weight curve is most striking in the case

of the chest ciwve, while the other three seein much alike. In order now to make the facts in Chart 1 more intelligible, each

variable was averaged for each successive group of five cards, then the 16 averages were plotted, and a demarcating high and low line drawn for each variable. It so happened that each pair of these bound- ary lines showed such parallelism that i t was easy to draw through the zone a single straight line to represent the general trend. These five trend lines are reproduced in Chart 2, from which the weight appears to be correlated to the bodily ineasurements in the following order: (1) Chest-girth, at nipple level, halfway between full inspiration and complete expiration.

Now hazardous this interpretation may be, and how inexpressively subjective at best, will appear below.

(2) Height; (3) 7-Cervical; (4) Stem.

254 HORACE GRAY

CHART 1. RELATION OF WEIGHT TO BODY MEASUREMENTS W=W7eight in pounds (log scale) of 80 normals arranged consecutively from left

to right; H = height in cm. corresponding to each W;

C=chest-girth in cm. corresponding to each W. =stem-length in cm. corresponding to each W:

7c = sho

CHART 2. SMOOTHING OF THE CURVES FOR BODY MEASUREMENTS SHOWN IN CHART 1.

RELATION O F WEIGHT 255

Numerical Correlation by the Coeficient r.-This basic value is shown with other usual statistical constants in Table 1.

TABLE S STATISTICAL CONSTANTS

MEASUREYENTS MEAN STANDARD DEVIATION VARIABILITY COEFFICIENT OF

CORRELATION

N -80 If k p.e. u rtr p.e. V ~ w x f p . e .

Weight W 163.3750 f 1.575 20.89 f 1.114 12.79 Chest-girth C 92.2563 rt0.4429 5.873 f 0 . 3131 6.37 + O . 879 f 0 . 0172 Height H 179.425020.5636 7.474f0.3985 4.17 +0.639+0.0446 Stem A 92.5063 LO. 2587 3.430 20.1829 3.71 $0.575 + O . 0505 Short stern 7C 65.0689 rt 0.1899 2.144 k 0.1343 3.29 +O. 440 f 0.0714

The inference from these coefficients of correlation is plain a t a glance when we remember that the nearer r is to unity, the greater the inter- dependence of the two variables considered. A trained statistician might state mathematically the significance to be attributed to the differences between the four coefficients of correlation, but the following general deduction is believed to be for our purposes adequate and true.

The weight of adults is most nearly related to (1) chest-girth, next best to (2) height, then (3) stem-length and least t o (4) 7-Cervical length. The first two of these therefore should be taken into account in constructing a normal weight standard.

Davenport and Love in 1921, reported for U. S. Soldiers a t demobiliza- tion, a much less striking figure: rwc (deflated chest a t nipple level) =0.6598, but it definitely exceeded the r wHwhich was 0.4810 and the principle they deduced is harmonious with ours. They wrote: “This indicates that the development of muscles and the deposition of fat upon the chest go hand in hand with increasing weight, so that the two are closely interdependent. . . . The weight and chest circumference (expiration) are more closely correlated measurements than are the stature and weight.” These statements, none the less, they seem unwilling to accept a t their face value for they end with “the conclusion that in accordance with the findings of Gould, and before him, Quetelet, the ratio of weight divided by the second power of the height seems to be the most satisfactory index of build.”

For boys from 7-16 years, similar laws may be seen in the coef- ficients published by Baldwin in 1921,22 which afford most satisfactory confirmation of the tenets demonstrated in the paper, and seem strong evidence that they hold true for children as well as for adults. He found:

256 HORACE GRAY

rwc = O . 859 (compared with our 0.879), rWH = 0.809 (compared with our 0.639), rwsi=0.785 (compared with our 0.575 for rwx).

His comment however was brief: “Between the yearly measurements of weight and the girth of the chest the correlations are higher than for weight and any other physical trait measured. The coefficients are fairly uniform throughout the ten years.”

SUMMARY Indirect evidence has increasingly impressed upon us the close con-

nection between weight in man and the thoracic girth, together with uncertainty as to the next best measurement.

Direct biometric data have therefore been sought in the literature and determined from personal observations on 80 unusually fit men. From these facts we deduce the principles that the weight is correlated with the physical measurements in the following order:

(1) Chest-girth, taken as the mean between full inhalation and com- plete exhalation a t mammillary level.

( 2 ) Height. (3) Stem-length. (4) Short stem-length, or distance 7-cervical spine to seat. Application of these principles to the construction of a practical weight

standard will be suggested in a subsequent paper.

REFERENCES

1. Corbin (E.)-Instraction pratique sur les diverses mithodes d’exploration. Paris, 1831.

2. Gray (H.) & K. M. Gray-Normal Weight. Bosf. Med. & Surg. J., Dec. 27, 1917, CLXXVII, 894.

3. Bornhardt (A.)-Die Korperwagungen der Einberufenen als Mittel zur Bestim- mung der Tauglichkeit zum Militardienst. St. Petersb. med. Wchsehr., 22 March (3 April) 1886, N . S. 111, 108, and 24 May (5 June) 1886, N . S. 111, 196.

Ibid., 26 November ( 8 Dec.), 1888, N . S. V, 413.

4. Gray (H.) & J. F. Mayall-Body Weight in 229 Adults; Which Standard is the Best. Arch. Int. Med., Aug. 1920, XXVI, 133.

5. Gray (H.) & H. F. Root-Weight Prediction by the Formulae of Bornharclt, of Von Pirquet and of Dreyer. Bost. Med. & Surg. J., July 7,1921, CLXXXV, 28.

6. Gray (H.)-Size and Weight in 130 Boarding School Boys (Middlesex). Med. Clinics No. Anzer., May 1921, IV, 1899.

7. Gray (H.) 8 W. J. Jacomb-Size and Weight in 136 Boarding School Boys (Groton). Am. J . Dis. Child., Sept. 1921, XXII, 259.

8. Gray (H.)-Ideal Tables for Size and Weight of Private School Boys. Ibid. 272.

do.-Uber die Bezeichnung der Korperbeschaffenheit durch Ziffern.

RELATION O F WEIGHT 257

9. Gray (H.) & A. RII. \\ralker-Length and Weight. A71z. J . Phys. Antkrop., July-

10. Gray (H.) & G. H. Edmands-Indices of the State of Nutrition in Children.

11. Pirquet (C.)-Sitzhohe und Korpergewicht. 2. j .

12. Dreyer (G.)-Investigations on the Normal Vital Capacity in Man and its Rela-

13. Dreyer (G.) & G. F. Hanson-The Assessment of Physical Fitness. London,

14. Gray (H.)-Sitting-height and Stem-length in Private School Boys. A m J . Dis.

15. Walker (E. W. A.)-The Growth of the Body in Man; The Relationship between Proc. R. Soc. Lond., Jan. 1, 1916,

16. Harris (J. A,) & F. G. Benedict-A Biometric Study of Basal Metabolism in

17. Yule (G. U.)-Introduction to the Theory of Statistics. 5th ed., Lond., 1919. 18. Pearson (I<.), Editor-Tables for Statisticians and Biometricians.

19. Henselin (8.)--Rechen taf el. Berlin, 1912. 20. For these measurements we are greatly obliged to Dr. George P. Denny. 21. Davenport (C. B.) & A. G. Love-Army Anthropometry. Publ. by the J4ed.

Dept., U. S. Army, Wash., 1921, 260, 175, 163. 22. Baldwin (B. T.)-Physical Growth of Children. 8", Iowa City, 1921, 120, 124.

Sept. 1921, IV, 231.

A7n. J . Dis. Child., March, 1922, XXIII, 226.

Kinderheillc., 1916, XIV, 211.

tion to the Size of the Body. Lancet, Aug. 9, 1919, 11, 227.

1920; repr. N. Y., 1921.

Child. May, 1922, XXIII , 406.

the Body \'\reight and the Body Length.

System der Erniilirung 11.

LXXXIX, 157.

RIIan. Pub. No. 279, Carneg. Inst., Wash., 1919.

Caazbridge Univ. Press, 1914.