382 



The calculation of alpha values by this simple formula is by no means 

 the best method, for it gives various results depending on how many and 

 which combinations are used. The graphic method commonly used con- 

 sists of drawing a straight line through the velocities for the different 

 temperatures. Such a Ime will cross the temperature axis at approxi- 

 mately the hyperbolic zero (alpha value). If averages for points within 

 one degree of each other are used, the results of the graphic method are 

 fairly satisfactory. Where conditions in the different experiments varied 

 as to humidity, air movement, temperature variation, light, etc., weighted 

 averages should not be used, because the variation in mortality leaves 

 widely different numbers completing their transformations. 



The alpha value is best determined by Von Oettingen's method, in 

 which the time is multiplied by the temperature above various assumed 

 alpha values, that one being chosen as correct which gives the most nearly 

 constant product within the widest range of temperatures. To illustrate 

 this method, Table XVI shows the data used in calculating alpha values 

 and in drawing the curve for all experiments having 95 per cent mean 

 humidity (range 90-100%). The alpha value to be used in drawing the 

 curve is the one giving nearest a constant for the data which appear to 

 give an approximate constant. Thus, 54.3° F. (in Table XVI) was used 

 because it gave least deviation for the data between 62. T" and 83° F. 

 Higher and lower temperatures were considered as being outside the 

 range within which the data conform to the equilateral hyperbola. 



The 95 per cent humidity data are shown here, not because they are 

 best to illustrate the principle, but because they indicate the difficulties. 

 The experimental data were unusually heterogeneous and gave much 

 trouble. Some experiments were ventilated, some were not ventilated, 

 and several generations were included. The date were wurked over by all 

 three methods and combined and segregated according to conditions, with 

 unsatisfactory results, suggesting strongly that such experiments for such 

 a purpose should be carried out in the same way and with the correspond- 

 ing generations. Furthermore, an inspection of the data in Table XVI 

 for the alpha value 53.2° F. shows that extending the range of tempera- 

 tures assumed to conform to the hyperbola would give only a slightly 

 larger deviation from a constant. 



b. Velocities of Development of Pupae. Relative velocity is merely 

 the reciprocal of the time for the completion of a process. Usually, for 

 convenience, and for practical reasons, the reciprocal is multiplied by a 

 rather large number such as 100 or 1000, ad lib. Relative velocities based 

 on 300* times the reciprocals of the days from pupation to emergence 

 were computed from the average length of the pupal stage in all the 

 different experiments under approximately constant temperatures. The 

 data (Tables XII, XIII, etc.) were segregated into humidity classes: 

 14-29%, mean 22% ; 30-3;%, mean 31% ; -±0-58%, mean 49% ; 60-08%,, 

 mean 61%; 70-??%, mean 73%; 80-88%, mean 85%; 90-100%, mean 



• This multiple was chosen at first to place the velocity curve approximately on 

 a 4u° angle with the temperature axis. 



