333 



organisms in each stage. This is more convenient, mathematically, than 

 to regard the developmental total as fixed. These standard velocity values 

 were derived from data on moths under observation at Olney in 1915 and 

 li)l(i; at Olney, Urbana, and Plainview in 191?; and at Urbana in 1918, 

 1919, and 192U. The methods by which these values were derived are 

 too involved for brief description here (see PART THREE), and they 

 need not be completely understood by readers who are interested pri- 

 marily in the use of velocity values and in the modification of develop- 

 mental totals for purposes of estimating progress of life-histories. 



As has been noted, the direct use of weather data in spray calendars, 

 etc., though of some value, has failed to give results of sufficient accuracy 

 in all years and seasons. In the most successful recent attempt at the 

 direct use of temperature, namely, that of Glenn ('22), the temperatures 

 as occurring were extensively corrected to conform to the behavior of the 

 codling moth. If the last century of phenological observation and "tem- 

 perature summing" has proved anything, it is that direct application of 

 weather data is largely a failure. This failure is further emphasized by 

 a growing tendency to use plants as indicators. (McLean, 'IT ; Clements, 

 '21 — Bibliography.) The researches herein described have shown conclu- 

 sively that in the case of the codling moth, estimation of progress in 

 development, of abundance, and of fecundity must be based primarily 

 upon the physiological characters and responses of the species. Weather 

 data cannot be used directly. Temperatures summed above the empirical 

 or imaginary "threshold" selected by ordinary methods do not give correct 

 results because they have diflferent accelerative values under dift'erent con- 

 ditions and because temperatures below it are actually effective. Also, 

 high temperatures, above or near 90° F., have a much smaller accelerating 

 eft'ect than they have been expected to show by most investigators except- 

 ing Glenn ('22). In this paper all attempts at direct use of weather data 

 are abandoned, the chief reliance is put upon velocity of development of 

 the codlhig-moth in its several stages. 



Graphic Representation of Velocity. 



The meaning of velocity is well illustrated by reference to rate of 

 movement, or speed of travel, of a machine or animal or man. In all 

 matters of speed of travel, the reeifrocal of the time required to cover a 

 fixed distance is used to represent relative velocity, or rate of travel. For 

 example, in the case of a tractor pulling a load 12 miles at various speeds, 

 -the relative velocity is obtained from the time as follows : 



