-1 day after May 31, which is May 30. Since first instar individuals were also 
present in the collections, then 100 percent hatch (table 3) can be considered 
as being true for no date earlier than the date collection was made, which was 
July 11, 41 days after May 31. 
Had there been no first instar individuals present and if the youngest 
specimens in the collections were in the second stage of development, then the 
100 percent hatch could have been considered as being true for the day 41-6 
(days in first instar, item 1, table 2), or 35 days after May 31. Had only the 
first five instars been present, then the O percent hatch would have fallen on 
the day 31 days preceding July 11 or 41-31 = 10 days after May 31 or June 10. 
The figure 31 is the sum of the days in the first five instars (item 1, table 2). 
Having now filled in the figures for O and 100 percent hatches (table 3), 
we can proceed with the method for determining the number of days after May 31 
when 10 to 90 percent hatching had occurred. Table 4 illustrates the method 
used for continuing the calculations. 
Beginning with the 10 percent hatch (step 1, table 4), we can consider 90 
percent as being unhatched. Then subtracting from 90 successively the percent- 
ages from left to right given in item 3, table 2, we reach a figure 0.4 percent 
after making the last subtraction of 38.0 in the fourth instar column of item 3, 
table 2. The next figure in item 3 is 9.3, which cannot be subtracted from 0.4 
and still keep positive numbers. 
We are now ready to interpolate how far this 0.4 percent cuts into the 
number of days in the instar which contains this figure 9.3 percent of the 
collection. It is the fifth instar and has 8 days (item 1, table 2). Continu- 
ing under line 1, step 1, table 4, we multiply the 8 days by the fraction 0.4 
over 9.3, which equals 0.3 days. We can now assume that all fifth instar 
specimens have at least gone through an average of 6,5:;3537 or 23 days 
(item 1, table 2) in their development. This number 23 is then added to 0.3 
days (line 2, step 1, table 4), which equals 23.3 days. Subtracting 23.3 days 
from 41 days we obtain 17.7 days, which represents the number of days after 
May 31 when 10 percent had hatched (table 3). 
The reasoning here becomes clear if we selected the figure found in the 
sixth instar column of table 2, which would 1.1 percent hatch equal to the 
figure 1.1 percent of the collection in the sixth instar. Our reasoning would 
here be that on this date, July 11, all sixth instar specimens had gone through 
a total of 6+5:5+4+7+8 or 31 days' development. Since only 1.1 percent were 
in the sixth instar, then only 1.1 percent had already existed for at least that 
length of time, and a 1.1 percent hatch must have occurred by a date 31 days 
previous to July 11 or 41-31 = 10 days after May 31. 
Continuing the method to line 1, step 2, table 4, we next proceed to 
determine the number of days after May 31 when 20, 30, and 40 percent had 
hatched. First a 20-percent hatch means 80 percent unhatched and, as before, 
we proceed to subtract from 80 successive numbers from left to right found in 
item 3, table 2. The last number subtracted is 31.7, resulting in a remainder 
of 28.4 percent, from which the next number 38.0 cannot be subtracted without 
running into negative numbers. 
