JOSEPH KRAFKA, JR. 661 



for under these conditions they are normal and expected, since they 

 represent only the continuation of the primary exponential. 



Dr. R. P. Stephens and Dr. David F. Barrow have supplied me 

 with an empirical formula from data on the rate of development of 

 the fruit fly, Drosophila melanogaster, which fulfills the conditions for 

 the flattening of a primary exponential into a linear with a sharp 

 bend at the upper end. 



y CO 2* - 0.002a;» 



This corrective factor at the same time breaks the primary expo- 

 nential at the lower temperatures so that a theoretical zero becomes 

 possible. 



While any number of mathematical functions could be devised 

 whose graphs would fit the experimental points fairly well, the latter 

 formula stated in general terms should have some practical value. 



y CO A'' - BX"" 



where A represents van't Hoff's constant, B and n calculated values 

 to represent the divergence between the linear and exponential at 

 the uppermost points. 



BIBLIOGRAPHY. 



Krafka, J., Jr., J. Gen. Physiol., 1919-20, ii, 409. 



Krogh, A., Z. allg. Physiol., 1914, xvi., 163. 



Loeb, J., and Northrop, J. H., /. Biol. Chem., 1917, xxxii, 103. 



Peairs, L. M., /. Econom. Entomol., 1914, vii, 174. 



Plough, H. H., /. Exp. ZooL, 1917-18, xxiv, 147. 



Sanderson, E. D., /. Econom. Entomol., 1910, iii, 113. 



Snyder, C. D., Z. allg. Physiol, 1913, xv, 72. 



