146 



PROBLEMS OF RELATIVE GROWTH 



quotients, or, as I prefer to call them in accordance with the 

 terminology of this book, the corrected growth-coefficients. 



These corrected growth-coefficients for various organs of 

 five species of birds are as follows (recalculated from Schmal- 

 hausen's Table 9) : 



The heterogony of the brain is always markedly negative, 

 that of the fore-limb slightly negative ; that of the hind-limb 

 is always higher than that of the fore-limb ; while that of 

 the gizzard is the most variable. 



The right-hand part of the table concerns another constant 

 arrived at by Schmalhausen. On the assumption previously 

 arrived at by him that the growth of an organ can be repre- 

 sented by the formula 



v = (at) k (6) 



where v is the weight or volume of an organ, t is the time elapsed 

 since its origin, and a a constant (if the rate of linear growth 

 of the body or organ is constant, then of course k = 3), then 

 a is what Schmalhausen calls the extension factor (Extensit- 

 atsfaktor). The constant a can also be calculated for a given 

 interval of time (t x — t). A derivative constant is what 

 Schmalhausen calls the mass factor, m. This he takes as a h . 

 It can be derived from (6) thus : 



,fc — 



v 



m = cr — -7. , or v 



t k ' 



mt k 



(7) 



This constant m characterizes the initial size of the organ- 

 rudiment. Schmalhausen's exposition is here exceedingly 

 obscure, especially as to how he transforms his absolute 



