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_ the temperature rises; the degree at which development proceeds most 
rapidly ; and to find a temperature constant for each of the stages and for 
_the whole period of development which will apply to all temperatures, 
and a method by which that constant can be determined. 
Before proceeding very far it was discovered that the character of 
_ the climatic data obtained under field conditions was not well suited to 
_ studies of this kind, because the temperature varied constantly throughout 
the day, and consequently the deductions had to be made from averages 
of widely varying degrees of temperature. Early in the season the tem- 
perature during part of the day was in the zone of hibernating tempera- 
tures and during the remaining time in the zone of temperatures which 
stimulated development, and later in the season the temperatures during 
part of the day were in the zone in which the rate of development 
increased as the temperature rises and during the remainder of the day 
in the zone in which the rate of development decreased as the temperature 
rises. For scientific accuracy it is of interest to determine the relative 
effects of each degree of temperature, but from data of the kind here 
used this could not be undertaken. 
It has already been pretty well established that the rate of develop- 
ment increases, approximately at least, as the temperature rises above the 
zero of development, until the temperature at which the rate of develop- 
ment is at its maximum is reached; and our studies have led us to con- 
clude that as the temperature rises above the degree of the maximum rate 
of development the rate of development decreases directly as the tem- 
perature rises. 
] The day has been used as the unit of time, and the day-degree as the 
unit of accumulated temperatures; and it has been assumed that, within 
certain limits of temperature, the period expressed in days multiplied 
by the average daily day-degrees above the zero of development will 
approximate a constant, or at least that the average products of a large 
number of observations will approximate a constant. 
GENERAL PROCEDURE IN THE STUDY OF TEMPERATURE RELATIONS 
The first step taken was to prepare temperature tables from the 
thermographic records, showing the mean daily temperatures. In com- 
puting the mean daily temperatures, the day was regarded as beginning 
and ending at 5 o’clock p. m., that being the hour when observations for 
_ the day usually ended. All mean daily temperatures were ascertained by 
dividing the sums of the temperature readings for the even hours of the 
day by 12. Mean temperatures above 50, 52, 85, 86, 87, and 88 degrees 
_ were computed in the same way. 
q The second step was to tabulate in detail all the data relative to the 
- length of the egg, pupal, and larval periods, tabulating the data for each 
generation and year separately and arranging the data in chronological 
order with respect to dates when the periods began and ended. 
