385 



as properly omitted from averages, though the computation of these alone' 

 would give a much lower alplia value. In these cases, moreover, there 

 was possibly a considerable error in determining the time of pupation. 



In the preliminary rough drafts of these curves, the velocity values 

 for the experimental data at medial temperatures fell fairly close to a 

 straight line, but those at lower temperatures did not. It was with some 

 difficulty that a curve was found which would fit these lower points. A 

 hint was taken from the insistence of physiologists upon Qi,, as a constant, 

 for this suggested some form of concave curve. Accordingly, a curve 

 x^ ■' K 



with the formula y = was chosen (K being a factor by which the 



10 



curve should be multiplied to make it fit the experimental data) and was 

 slightly modified for each htmiidity group until it would pass through 

 the plotted velocity values. Each of these curves thus marked approxi- 

 matel)' the velocity values from the lower straight-line limit to the 

 approximate threshold of development.* It is noteworthy that the 

 threshold is higher for lower humidities, as is also the lower straight-line 

 limit. 



The highest points of the velocity curves for htuiiidities of 115, 61, 

 and 49 per cent give a fair indication of the temperatures at which 

 development is most rapid, namely, 88°, 90°, and 90.5°, respectively, 

 showing that the maximum velocity shifts to a higher temperature as the 

 humidit}- is lowered. The downward curvatures at the higher tempera- 

 tures were taken roughly through points plotted from the data available 

 at that stage of the calculations and were later brought into their present 

 position by use of the ecjual-velocity chart described below. 



Another step preliminary to the drawing of the solid-line curves 

 which are shown in Fig. 13 was the harmonizing of the equal-velocity 

 values. For this purpose, velocity values at o-unit intervals were taken 

 from the straight-line portions of the broken-line curves of Fig. 13 and 

 plotted on co-ordinate paper scaled for humidity and temperature, as 

 shown in Fig. 14A, and the plotted points were connected by broken- 

 line curves. 



The waves in these curves are not in accord with our general knowl- 

 edge of the effects of external conditions on the behavior of organisms. 

 The curves should be more regular. The irregularities probably result, 

 first of all, from the heterogeneity of the material, the extent of which is 

 suggested in Tables XVIII and XIX. For example, the 95 per cent 

 data include various conditions, ventilated and unventilated. and dift'erent 

 generations, etc. Secondly, the crookedness of these curves may be partly 

 due to errors in the observation and interpretation of the process of 

 development, particularly as regards the beginning and the ending of the 

 pupal stage. Finally, there is the possibility of errors in the calculation, 

 for the methods used give only approximate results at best. 



•Since a curve with this formula doe.s not pass through O, a formula of the form 

 y = K (logx) + c is more nearly correct. 



