335 



23° travels S3.SS mm. farther per minute, and so on up to 28°, where a 

 change takes place. The unit of progression is -11. 4-1 mm., based upon the 

 effect of one degree Centigrade within the range of medial temperatures, 

 which are marke'd by the straighl-line limits of the velocity curve CD. 

 This same imit is the basis of determining the points at which the eft'ect 

 of one degree higher or lower temperature upon the rate of progression 

 is greater or less than 41.4-4 mm. in one minute. The alpha value (hyper- 

 bolic zero) for the data of Crozier is approximately 10° C, a fact of very 

 little actual significance except in the determining of the constant product 

 of the temperature above alpha and the time for a definite total distance. 

 This total distance is here assumed to be 5967.3 mm. The portion of the 

 time-temperature curve AB between 22° and 28° C. is a portion of an 

 equilateral hyperbola. The time is that required to travel 596?. 3 mm. at 

 the temperatures plotted. An inspection of the curve will show that the 

 mathematical product of time (as plotted) and temperature above 10° C. 

 (as plotted) is 144, and that for each point plotted the reciprocal of the 

 time units multiplied by 144 equals the number of progression units. 

 These relationships are characteristic of the equilateral hyperbola. 



The total distance was here arbitrarily taken as 144 X 41.44 mm. 

 units, or .")!»(JT.3 mm. (calculated). If another distance were chosen, the 

 velocity for each temperature would be the same, because the milliped 

 would travel at the same rate, but the number of progression units would 

 differ. The same principle holds good in respect to the different stages 

 of development of an organism. The amount of metabolism required in 

 each stage is comparable to distance to be traveled, while the rate of 

 development remains basically of the same order of magnitude not only 

 for the dift'erent stages of the same insect but probably also for all the 

 various insects and, indeed, perhaps for all cold-blooded animals.* 



The next step in the way of experiments with the milliped would be 

 the use of %'ariahlc temperatures from 20° to 28° C. Such variability 

 would probably increase the rate of progression slightly for a mean of 

 the varying temperatures as compared with the constant ones, but this 

 difference will be ignored in the absence of data from variable-tempera- 

 ture experiments in this case. For the present purpose, we may assume 

 that the rate of progression as plotted for a certain degree of constant 

 temperature would hold good for the same degree of mean variable tem- 

 perature; accordingly, we may construct a table of "effective temperature" 

 above 10° C. as the "starting point" (using some of the nomenclattire of 

 those writers who have summed temperatures), by assuming a difl'erent 



