Feb. '08] JOURNAL OP ECONOMIC ENTOMOLOGY 63 



tween these curves and a horizontal line at 2 or 3, which would 

 represent the plotting of the increase of velocity, were it uniform 

 between the critical point and maximum. 



If there be a thermal constant for all temperatures between the 

 critical point and maximum, it would be represented by a curve like 

 "T. C. C." in figure 1. But there is evidence to show that the ther- 

 mal constant is lower at the optimum than at temperatures approach- 

 ing the critical point. And if the velocity be plotted from the curve 

 "T. C. C." of figure 1, the same curve in figure 2 shows that the 

 coefficient of increase of velocity with a uniform thermal constant is 

 much less than that observed, being only 1.5 at 25° C. On the other 

 hand, if we plot a curve based on a uniform increase of velocity of a 

 coefficient of 2 or 3 we secure curves V2.C. and V3.C. of figure 1, re- 

 spectively, and by computing the thermal constant for various tem- 

 peratures on these curves, it is found that the thermal constant 

 increases below the optimum to a certain point and then decreases. 

 Thus on V2.C. the thermal constant at 35° is 300, at 25° is 400, at 

 20° is 450, and then decreases to 400 again at 15°, to 300 at 10°, and 

 at the critical point we secure the anomaly of a thermal constant of 

 80°, which is clearly impossible, as no reaction will take place unless 

 above the critical point. The same would hold true of curve V3., or 

 any other curve based upon a uniform coefficient of increase of 

 velocity. 



From a study of these considerations it seems probable that the 

 effect of temperature upon various forms of animal life will be repre- 

 sented by a curve characteristic for each species or group for the 

 various phenomena of growth considered, and that such a curve will 

 be betw^een the curve shown in figure 1 for the uniform thermal con- 

 stant, T. C. C, and that for a uniform rate of increasing velocity, 

 V2.C. Such a curve may be secured by a uniform coefficient of 

 increase for the thermal constant as the temperature decreases from 

 the optimum as shown in curve H. C. — hypothetical curve — figure 1. 



Figure 2. Curves sliowing variation of coefficient of velocity of certain 

 biological phenomena. Hypothetical Curve, based on same in figure 1 ; Terrapin 

 Heart Curve, based on rate of heart beat of Pacific terrapin, from data by 

 Snyder*; Thermal Constant Curve, based on same in figure 1; Toad and Frog Tad- 

 pole Curves, based on rate of growth of toad and frog tadpoles from data of Lillie 

 and Knowlton'^ ; Frog Muscle Curve, based on rate of contraction of gastrocnemius 

 muscle of frog from data of Burnett'' ; Cat Heart Curve, based on rate of beat of 

 isolated cat hearts from data of Langendorff"!. 



!^ Snyder, Univ. Calif. Publications, Physiology, 2, pp 125. 1905, quoted by Arrhenius, 

 Immunochemistry, pp 139. 



b Quoted by Morgan, Experimental Zoology, pp 260. 

 c Burnett, jour. Biological Chemistry, 2, pp 200-1906. 

 d From Snyder, Amer. Journal Physiology, 17, pp 356-1906. 



