249 
Because all the points seem to be displaced more or less on account 
of using ineffective and retarding temperatures in the temperature axis, 
they afford no means of determining the true reciprocal curve. The two 
points that are least affected are the middle points from 68 to 72 degrees. 
The line determined by these two points cuts the temperature axis at 
51.92 degrees. By using 50, 51, 52, and 53 degrees in turn as the possible 
zero of development it was found that 52 degrees more nearly satisfied 
the conditions than any other of the points. 
To ascertain the degree of the maximum rate of development 86, 
87, 88, and 89 degrees were tried in turn. 87 most nearly satisfied the 
conditions. 
The average daily day-degrees above 52 were computed and the results 
recorded in column 7 of Table 7. Twice the average daily day-degrees 
above 87 degrees were computed and the results placed in column 8. By 
subtracting twice the average day-degrees above 87 degrees from the aver- 
age daily day-degrees above 52 degrees we got the average daily effective 
day-degrees in column 10. By multiplying the daily effective day-degrees 
by the periods, we obtained the total accumulated effective day-degrees 
recorded in column 14. It will be noted that with the exception of that 
portion of the hibernating generation which pupated late, between 60 
and 67 degrees inclusive, the total effective day-degrees are quite uniform 
for all temperatures. The retardation of the late portion of the hiber- 
nating generation due to the daily disturbance to which they were sub- 
jected is shown by the increased accumulation which was necessary to 
bring them through the stage. We concluded, therefore, that the effective 
day-degrees for the pupa might be computed by subtracting from the 
sum of the average daily day-degrees above 52 degrees, twice the average 
daily day-degrees above 87 degrees. The average of the effective day- 
degrees as thus determined is 240.7. 
Graph 6 was prepared by plotting the reciprocals of the periods 
against the average daily effective day-degrees given in columns 4 and 
10 respectively of Table 7. It will be noted that all the points with the 
exception of those which represent the late portion of the hibernating 
generation (10-16) lie nearly in a straight line, which shows that there 
is a quite constant relation between the average daily effective day-de- 
grees as above determined, and the rate of development. 
Observations on the pupal period were made at such a wide range 
of temperatures that the data exemplify very nicely the hyperbolic form 
of the curve of development formed by plotting the periods against the 
average daily effective day-degrees. Graph 7 has been prepared to show 
the different positions of the points occasioned by the use of different 
factors as coordinates and also the curve of development. 
