THE AMEBIC AX XATUBALIST [Vol. LII 



ture on the rate of fish development, particularly during 

 the late embryonic stages. Reibisch ('02) showed that 

 time X temperature is a constant, using the hyperbola. 

 He called the temperature at which development could be 

 initiated by the slightest increase the "threshold tempera- 

 ture/' which is the same as the zero of development and 

 physiological zero of other authors. He calculated this 

 from the hyperbola formula, thus anticipating the work 

 of Sanderson and Peairs by about eleven years. In fact, 

 the idea of ineffective temperature below a minimum and 

 a sum of temperatures which is the product of time X 

 temperature dates from de Candolle's 1830 article. 



Johansen and Krogh worked over the data of Danne- 

 vig and showed that the velocity is different for different 

 fishes (Fig. 2, A, B, C). They note further that tempera- 

 ture is not absorbed by the organism and that the constant 

 is only a convenience. They call attention to the fact 

 that the velocity-of-development curve is a straight line 

 which, prolonged downward, crosses the axis of abscissas 

 at a point mathematically corresponding to Reibisch 's 

 threshold temperature. The threshold of development 

 would be where the velocity curve crosses the axis of ab- 

 scissas if the straight-line velocity curve held good and 

 the time-temperature curve were a true hyperbola. Krogh 

 ( '14) showed that while 2.7 degrees is the mathematical 

 threshold of development for cleavage of the frog's egg, 

 the first cleavage appeared at this temperature 1,844 min- 

 utes after fertilization. If the curve were an hyperbola, 

 at 2.7 degrees the development of the cleavage plane 

 should have required an indefinitely long time; or, in 

 other words, it should not have appeared at all. Also, at 

 4.9 degrees the appearance of the cleavage plane should 

 have required 1,100 minutes, while the observed time was 

 approximately 730 minutes. Further, it required 138 

 mi nutes for the cleavage furrow to appear at 22.1 degrees, 

 which is more than at 20.7 degrees, showing a decrease in 

 velocity at higher temperatures. Thus Krogh points out 

 that the velocity curve is a straight line only between 7 



