The Growth of Children. 



APPENDIX. 



By the kindness of President Runkle of the Massachusetts Institute 

 of Teclmology the writer is enabled to present formulas which express 

 the relation between the weight and height of growing children, from 

 five to eighteen years of age, with considerable accuracy.* 



The figures of Tables Nos. 23 and 24, showing the weights corre- 

 sponding to each inch of height in the whole number of observations 

 were placed by President Runkle in the hands of -Professor Gaetano 

 Lanza, who kindly subjected them to a mathematical discussion, and 

 reported on the subject substantially as follows : — 



The results of Dr. BoAvditch's observations on the relation between the 

 weight and height of boys from 42 to 66 inches, inclusive, are very fairly 

 represented bj'^ the follow' iug empirical equation : — 



Let y == weight in lbs., and o:^ height in inches ; then 



log. y — 0.02007;/; + 0.7772-t, or ?/= lO"-"-'''''-*^ + 0.77724 _ (^p^-^ 



The results of the observations on the relation between the weight and 

 height of girls from 42 to 61 inches, inclusive, are represented with toler- 

 able accuracy by the following empirical equation : — 



Let y :=. weight in lbs., and x-— height in inches ; then 



log. y =0.02164ic + 0.69017, or y — l0'^•"2l6^^•^-"•e■•'"'l^ (B) 



The greatest difference between calculated and observed values is, in 

 the case of boys, 0.65 lb., and in that of girls, 1.41 lbs., with one excep- 

 tion, where it is 3.01 lbs. 

 The equations 



y = 0.002428x--^-' (Ai) 



for the boys, and 



?/ = 0.001277a:'-" (Ri) 



for the girls, represent quite roughly the results. 



The following table, embodying the results of Professor Lanza's 

 discussion, shows at a glance the superior accuracy of the logarithmic 

 equations (A) and (B), as compared with the exponential equations 

 (A^) and (Bi). 



* For older as well as for younger children the formulas are obviously much less accurate. 



