140 PROBLEMS OF RELATIVE GROWTH 



But during the early stages of development, the effect of 

 different time of origin will be relatively large, and will com- 

 pletely vitiate the method of comparing absolute sizes (I.e., 

 p. 59). What we require to do, if the organ x is first formed 

 n days after the standard part y, is to compare the size of the 

 organ at n, n + I, n + 2 . . . days with the size of the 

 standard at o, 1, 2 . . . days : from these sizes, the growth- 

 coefficient of the organ could be correctly calculated according 

 to our heterogony formula. But to arrive at these values, we 

 require to know the time-relations of early development, which 

 is precisely what we have been able to neglect, with such 

 economy of time and labour, in our previous approach. 



Unfortunately, owing firstly to the difficulty of estab- 

 lishing the true time of origin of development, and secondly 

 to variations of developmental rate among individuals, which 

 make different embryos arrive at the same developmental 

 stage at different absolute times, accurate time-relations are 

 hard to establish for embryonic life, and not always service- 

 able even when established. These difficulties are extreme in 

 the chick, but serious even in mammals, where, e.g., litter- 

 size has a marked effect on foetal size and consequently upon 

 foetal differentiation. For these reasons, Schmalhausen uses 

 an indirect method for estimating true developmental age. 



In his previous papers, Schmalhausen was able to show 

 that in the chick and apparently in various other vertebrates, 

 the linear growth of the embryo, measured by the cube root 

 of its weight, typ, remained approximately constant through- 

 out embryonic life. Since the specific gravity of the embryo 

 is very close to 1, then if the weight p is taken in milligrams, 

 typ can be taken as giving a value in millimetres ; and the 

 constant rate of growth can be expressed in mm. per day. 

 Thus the cube root of the weight of the embryo can be taken 

 as giving a measure of its age. 



This approximate constancy of linear growth-rate holds also, 

 according to Schmalhausen, for the separate organs of the 

 body. In all cases, there are considerable oscillations in the 

 value of linear growth per day ; and sometimes the value alters 

 progressively during development, so that the method can only 

 be considered an approximate one. None the less, for studies 

 of relative growth, the method appears to be at least as suit- 

 able, and certainly much less difficult to arrive at, than 

 accurate time-measurements. 



Starting from these assumptions, we arrive at the following 



