I 



387 



73 per cent data, for which 52.0° proved better than 54.0°, the use of the 

 lower alpha value is further justified by the fact that some of the hiber- 

 nated pupae included in these data had not been soaked, winter dryness 

 accounting partly for the low velocity values at 83° F. 



Preparation of the Equal- Velocity Chart. 



After the curves for data covering medial temperatures and experi- 

 mental humidities (roughly 65°-87° F. and 45-95yf ) had been smoothed 

 as in Fig. 14A, the points with velocity 35 at the various combinations of 

 temperature and humidity shown in the solid-line curves of Fig. 13 were 

 plotted on a large sheet of co-ordinate paper scaled for temperature and 

 humidity as in Fig. 14B, and a line was drawn through these plotted 

 points, both below and above the maximum velocity, and connected 

 around the low humidity to make the greater part of an ellipse, as shown 

 between 85° and 90° in Fig. 14B. In the same way, other equal-velocity 

 lines were drawn roughly parallel to the 35 line until the scheme was 

 completed for the high temperatures. The velocity values on the lower 

 ends of curves similar to those in Fig. 13, but drawn according to the 

 formula 10 y = x'-^ K, were transferred to the equal-velocity chart, and 

 lines were drawn through them so as to complete that portion for low 

 temperatures. (Fig. 14B is the final form, resulting from much refine- 

 ment of this rough draft.) 



Data from the variable-temperature experiments was then plotted 

 on this rough draft of the chart. The march of temperature and 

 humidity is shown on Fig. 15 for each of these experiments. Only about 

 half of these experiments were sufficiently accurate to use. The velocity 

 values for the experiment DD in Table XVIII (indicated by the line DD 

 on Fig. 15) were then plotted, as is shown in Fig. 16, to determine the 

 alpha value. The alplia values for experiments AW and AD were 

 determined similarly. 



As indicated in Fig. 16, the velocity curves in part of the experiments 

 turn downward at high temperatures. The "summing of temperatures" is 

 done on the assumption that the velocities for the temperature fall on a 

 straight line. In these curves it may be seen that they do not fall in a 

 straight line. Throughout this part of the paper, therefore, wherever the 

 velocity for a temperature does not fall on the straight line, a straight- 

 line temperature zt-'ith the same velocity value is substituted for the actual 

 temperature recorded by the thenuograph for the hour in question. The 

 high-temperature slope of the curve shown in Fig. 16 was modified until 

 the sum of temperatures above alpha came out approximately 6,480 (or, 

 in other words, until the substitution-quotient came out approximately 

 270) as it did with AW and AD in Fig. 15, which were concerned with 

 variations within the straight-line limits only. Thus, in Fig. 16, instead 

 of 90°, 95°, 100°, and 105°, which were recorded for two-hour readings, 

 the following temperatures were used respectively: 89.5°, 84.1°, 74.6°, 

 64.6°. By means of trials with the data of the variable-temperature 

 experiments, the upper part of the equal-velocity chart was tentatively 



