322 The University Science Bulletin. 



by the concentric circles. The curve through these points is an 

 hyperbola whose equation is P(T — 2t') = C = 240. 



This constant (240) is the average of 3,817 observations. We 

 may, therefore, conclude that it requires an average accumulation 

 of 240 effective day-degrees to bring the codling moth through the 

 pupa stage. The observed variations from this average in the case 

 of individuals were very great, due in some cases, no doubt, to 

 errors in observation and in part to individual differences, but for 

 the most part to the fact that the day was used as the unit of 

 time. By using the day as the unit of time the actual period might 

 in some cases be nearly a day shorter than the observed period, and 

 in other cases nearly a day longer. 



In midsummer the daily accumulation of effective day-degrees 

 was sometimes as high as 27, so that the accumulation of day- 

 degrees for some of the observed periods might be 27 day-degrees 

 greater or less than for the actual period, or the average 240. 



The following table shows the range of variations: 



Number of individuals. Day-degrees. 



1 166 



1 : 185-194 



4 195-204 



3 205-214 



110 215-224 



602 225-234 



2238 235-244 



653 244-255 



170 254-265 



18 264-275 



7 274-285 



7 284-295 



2 294-305 



Recorded accumulations of less than 205 or more than 275 were 

 probably due to errors in observations; if we add 27 to the former 

 and subtract 27 from the latter, we still have a variation of from 

 232 to 248 due to individual differences, humidity or other causes. 

 The equation for the pupal period may, therefore, be written as 

 follows : 



p (T — 2t')=240± 8. 



This paper was prepared merely to illustrate the method followed 

 in determining the time-temperature factors, or the equation for 

 the period. The method is applicable to the investigation of any 

 stage of an insect. 



If the threshold of development and the degree of the maximum 

 rate of development should be found to be the same for each of 



