The figure 28.4 now becomes that part of the figure 38.0, which is inter- 
polated into the number of days for the fourth instar, which is 7. That part 
is 28.4 over 38.0 multiplied by 7, equaling 5.2 days (line 2, step 2, table 4). 
Again we assume that all the fourth instar specimens have gone through at least 
6.545 = 16 days of development, to which is added 5.2 days, which equals 21.2 
days. This last figure is then subtracted from 41, giving 19.8 as the number 
of days after May 31 when 20 percent had hatched, as shown in table 3. 
It is not necessary to go through all these subtractions to obtain each of 
the next two figures for the 30 and 40 percent hatch. Instead we can successive- 
ly subtract 10 from the remainder 28.4 in line 1, step 2, table 4, until it 
cannot be subtracted further without running into negative numbers. Thus 
28.4-10 = 18.4 and 18.4-10 — 8.4, which is as far as we can go. Further inter- 
polation into the number of days in the fourth instar consists in multiplying 
7 days by 18.4 over 38.0 and 8.4 over 38.0, which equals 3.4 and 1.5 days, 
respectively. These numbers are, in turn, added to the total of 16 days in the 
first three instars, equaling 19.4 and 17.5 days, respectively. Subtracting 
these from 41 we obtain 21.6 days for the 30 percent hatch and 23.5 days for the 
4O percent hatch, as given in table 3, for the number of days after May 31 when 
these percentages of hatch had occurred. 
We are still left with the calculations for a 50 to 90 percent hatch, and 
the procedure is the same as shown in steps 3 and 4, table 4. 
Table 3 has now all the data necessary to plot a hatching curve for the end 
population of differentialis in Butte County, S Dak., in 1946 The YY axis or 
ordinates represent the percentage of hatch 0, 10, 20, 30, ples 4 
100 percent and the abscissa or XX axis represents the number of aaa nee 
May 31 converted to a period of time marked by actual dates. Hatching curves 
show a marked similarity in form, with the part of the curve between 10 and 90 
percent hatch being in an almost straight line. Before the former and beyond 
the latter points, the curves trail off, indicating that, at the beginning and 
end of the period, hatching is somewhat prolonged and dragged out. This 
phenomenon has been verified by direct observation. 
Hatching Period of Melanoplus sanguinipes 
In order to show the wide variation in the hatching period of sanguinipes 
and to compare this with temperature and rainfall, figure 1 was prepared from 
data accumulated between 1939 and 1948, inclusive. The vertical axes show the 
degrees of daily maximum air temperature and inches of rainfall on the left and 
the number of accumulative degrees above 60° F. of daily maximum temperatures 
on the right. This latter measurement had been used before with some precision 
to predict the beginning of the hatch of sanguinipes, bivittatus, and differen- 
tialis. The horizontal axes show the period of time, March 2 to June 29 or July 
29, in inclusive, divided into equal intervals of 5 days. 
All data were divided into eight groups on the basis of when 10 percent of 
the hatch had taken place. From the top left-hand corner of figure 1 to the 
bottom right-hand corner, the grouping for the time when 10 percent had hatched 
was as follows: (1) April 21-30, (2) May 1-10, (3) May 11-20, (4) May 21-30, 
(5) May 31-June 9, (6) June 10-19, (7) June 20-29, and (8) June 30-July 9. The 
two vertical dotted lines in each grouping show the average period on the 
