4o6 ON INCREASE IN SIZE [pt. iii 



pre-natal life, when the yolk was becoming exhausted. Thus the wet 

 weight of an embryo plotted against the time gave an S-shaped 

 curve, which, however, was not symmetrical, for it had a point of 

 inflection after about 70 per cent, instead of 50 per cent, of the 

 development had been completed. This was of course well shown on 

 the increment curve, which was skewly bell-shaped. Assuming that 

 growth was proportional to the amount of yolk remaining as well 

 as to the size of the embryo already formed, Gray developed an 

 equation ^ 



(where x is the weight of the embryo at time t,yQ the total yolk in 

 the unfertilised egg, K^, the amount of yolk combusted by one gram 

 of embryo divided by the constant k in the equation 



dx J 



It = '"^' 



X and y being weight of embryo and weight of yolk respectively) 

 which he considered accounted very well for the observed facts. He 

 deduced from it that there should be a period at the end of develop- 

 ment when the wet weight of the larva (the whole system, embryo 

 plus yolk) is decreasing, although the wet weight of the embryo itself 

 is still increasing. During the major part of development the wet 

 weight of both would increase, owing to the absorption of water 

 from outside. From the equations the maximum weight of the larva 

 should be reached when o-86 gm. of yolk is still unconsumed, and 

 in actual fact Gray found the peak at a point when i*io gm. \^as 

 yet remaining. 



Another possibility used by Gray to test his hypothesis was that 

 as it was unlikely that the temperature coefficient of the growth 

 process would be the same as that of the catabolism going on, there 

 ought to be a measurable difference in the size of fishes raised at 

 various temperatures at the end of their development. Experiments 

 designed to reveal such differences gave the following results : 



Mean weight of 100 embryos at 

 Temperature (°C.) the end of incubation (gm.) 



15 i3-35±o-i6 



ID i507±o-i8 



so that the higher temperature not only accelerated the process, but, 

 by accelerating the combustion more than the storage, led to a 



