No. 614] 



PHYSIOLOGICAL PROBLEMS 



137 



straight-line limits the effects of constant and variable 

 temperatures should be the same. This is due to the fact 

 that the product of time units X temperature above the 

 threshold of development is a constant within the straight 

 line limits. Where it is not a constant, the actual values 

 may be plotted approximately for any temperature. 



Using the data of Krogh (Fig. 3), I have drawn an 

 approximate total temperature curve for the development 

 of the first cleavage plane for the egg of the frog. The 

 number of degree-minutes required for completion of the 

 cleavage furrow is the same for all temperatures between 

 7° and 21° C. That is time X temperature is constant 

 between 7° and 21° C, where it is about 2,475 time- 

 temperature units or minute-degrees, and the curve is a 

 straight line. Above 21 degrees the total temperature is 

 greater than the constant, and below the lower limit of 

 the constant it is less than the constant. At 2.7 degrees 

 it should be infinity if the hyperbola held good, but is 

 actually 1,844 minutes. The time-temperature units are 

 not expressible at this point, so the actual time is given. 

 If development takes place below the zero of the hyper- 

 bola, the time-temperature units may be considered as 

 having a negative value, but are expressible. From this 

 curve it is possible to tell how long it takes for the cleav- 

 age furrow to develop at any temperature shown ; for ex- 

 ample, take 6 degrees (bottom of chart = 3.3 degrees at 

 top). We find from the curve that the total temperature 

 for this is approximately 2,200 degree-minutes. Thus, 

 2,200 divided by 6.0 — 2.7 gives 666 minutes. It is true that 

 the same result could be obtained by reading off the time 

 on a time-temperature curve (near to hyperbola) with 

 less labor, but the region in which the total temperature 

 is a constant cannot be shown on such a curve; and the 

 time for different temperatures is obtained with less sim- 

 ple calculations from the reciprocal. The total tempera- 

 ture curve exaggerates the straight-line limits, and brings 

 out sharply the fact that high temperatures retard and 

 low temperatures accelerate as compared with the veloci- 



