SECT. 2] AND WEIGHT 503 



attended with very great difficulty. Bayliss has drawn attention 

 forcibly to this. The position as regards the embryonic growth- 

 process is therefore doubtful, and, although its temperature coefficient 

 has been many times estimated, we cannot yet be certain what the 

 real significance of this is. Nevertheless, the recent researches of 

 Crozier and his school have brought us nearer to a sound judgment 

 upon the matter. 



2-15. Temperature Coefficients 



The older quantitative observations were few in number and not 

 very accurate; we owe them to Fere; Lillie & Knowlton; Higgin- 

 bottom; Driesch; Chambers; Edwards; Semper; and Bury. Some of 

 them are shown in Table 68. They were too few in number to lead 

 to any well-based conclusions, though they certainly demonstrated 

 the fact that, within certain limits, the higher the temperature, the 

 higher the growth-rate. But the classical paper on this subject is 

 that of O. Hertwig, who in 1898 subjected developing frog embryos 

 to various temperatures. He had been preceded by Baudrimont 

 & de St Ange, who, as early as 1846, had observed the accelerating 

 effect of temperature on the developing egg of the frog. His figure, 

 which has often been reproduced, is shown as Fig. 76, and from it 

 one can easily see that the time taken to reach the seventh stage, for 

 instance, is 16-7 days at 20° but 55-6 days at 10°. The time taken 

 at the lower temperature, therefore, is just 3-33 times as long as 

 that at the higher temperature, so x^° of the van't Hoflf equation 



Vt 



= X" 



will be 3-33, where Vt is the reciprocal of the weight gained at a 

 certain temperature and V {t -\- n) is the reciprocal of the weight 

 gained at n degrees higher temperature. Therefore 10 log a: = 

 log 3-33 = 0-5224; therefore log a: = 0-05224 and a; =1-128. In 

 other words, if m days are taken to complete a certain stage of de- 

 velopment at 10°, it will take m x 1-128" days when the temperature 

 is n degrees less for the same stage to be arrived at, D'Arcy Thompson 

 calculated all the values of Hertwig's experiments from this simple 

 exponential formula, and obtained a series of curves convex to the 

 abscissa, which showed fair agreement with those plotted from the 

 experimental observations. 



