THE COEFFICIENT OF GROWTH-PARTITION 49 



individual growth-ratio with age. But even this does not 

 exhaust the complexity of the phenomenon. The curve for 

 age-change of growth-ratio is obtained by plotting the weights 

 of fully-formed antlers of known age against body-weight for 

 the same age. It will be at once clear that the actual growth- 

 ratio of the antlers can never be the same as that thus obtained, 

 but must always be higher (Fig. 29). For the points on the 

 curve are those which would be obtained if the antler grew 

 with a constant differential growth-coefficient from its incep- 

 tion ; whereas actually, it has to begin its growth anew each 

 year from zero. 



Now this is of considerable importance, since it indicates 

 that it is not necessarily the actual rate of growth which is 

 regulated in accordance with our formula, but the limitation 

 of the total amount of growth achieved. What our results tell 

 us is that at any given body-size the total amount of material 

 which can be incorporated in the organ is proportional to the 

 body-size raised to a power (the exact value of the power also 

 varying with age). The mechanism of this relation is at 

 present obscure. We do not know whether the total bulk 

 of material in the body imposes the relation directly, which 

 is unlikely ; whether some substance is formed in the body 

 in this particular quantitative relation, as an exponential 

 function of body-weight, and the final size of the organ is then 

 directly proportional to the amount of this substance ; or 

 whether there be after all a true constant differential growth- 

 ratio between organ and body, determined by some peculiarity 

 of the organ, but that this growth-ratio represents a limiting 

 value, higher values being possible and indeed necessary 

 whenever the relative size of the organ is below its limiting 

 amount. The last supposition is perhaps the most probable, 

 on the close analogy with regeneration (see below) , but experi- 

 ment alone can decide the point. 



§ 2. The Coefficient of Constant Growth-partition 



In any case, to speak simply of growth-coefficients in such a 

 case is misleading ; yet we require a term for the exponent 

 of body-size according to which relative organ-size is limited. 

 Two terms are possible — either coefficient of growth-limitation, 

 or else growth-partition coefficient ; I shall adopt the latter. 1 



1 Since writing this passage, I find that Robb (1929) had previously 

 suggested the same idea of growth-partition, which has later been 

 adopted by Twitty and Schwind (193 1). 



4 



