412 



each group. By this method, the velocity tends to remain constant for 

 any one temperature, but the sum changes. This variation in the sum is 

 evidence that the developmental total is not the same for different indi- 

 viduals ; that is, the developmental processes, especially where enzymes 

 are concerned, require varying amounts of metabolism to complete the 

 stage. For example, 280 larvae which pupated at various approximately 

 constant temperatures ranging from 53" to 80° were in three successive 

 groups. When an approximately constant velocity value was obtained 

 by dividing the mean substitution quotient for the group by the time (in 

 days) for each individual at a constant temperature, that velocity value 

 was used for that temperature in making the equal-velocity chart. This 

 calculation was based on the fact that all groups at constant temperatures 



Table XXIII. Differences in "Pre-pupaV Time-Temperature Products (above 

 o(l° F.) for Two Collections of Hibernated Larvae Pupating in Three 

 Successive Groups (Sirring of 1920) in Constant- 

 Temperature Experi'm.'ent. 



within the straight-line limits showed a fairly uniform rate of reduction 

 of the time-temperature product, as illustrated in Table XXIII for two 

 collections of larvae wintering out-of-doors. 



A large series of calculations of alpha values, taking the means of 

 the three groups separately, showed no conclusive difference in the 

 "threshold". Some apparent differences were rendered questionable by 

 irregularity of time and small numbers of temperatures within the 

 straight-line limits. There is a suggestion of a slightly lower "threshold" 

 for the later groups, but this is not borne out by calculations based on an 

 assumed alpha value of 50° F. For practical purposes the assumption of 

 the same threshold for all three groups is the simpler. 



On the basis of 300, 525, and 675 as the respective time-temperature 

 products above 50° F. for the different groups, roughly segregated for 



