360 



nearly all the data of Peairs ('1-1) and Sanderson and Peairs ('13) relat- 

 ing to eggs of Samia cercropia Linn., Malacosoma americana Fabr., Car- 

 pocapsa (Cydia) pomonclla Linn., and Margaropas aniiiilatus Say; and 

 in the full life history of the grain louse and its parasite, as given by 

 Headlee ('14). The development of the Indian corn plant shows a 

 similar curvature, but drops to zero again at high temperatures. (See Le- 

 henbauer, '11:, pp. 27!)-80.) Some work has been done on the germination 

 of fungus spores (Weimer and Harter, '23; Jones, '23), in which similar 

 relations ■ have been found. The authors of the papers did not plot 

 reciprocals or make extended interpretations. These plant curves aie 

 similar to the curves for animal activity. Verworn ('99) showed an 

 irritability curve conforming in its main features to curve C in Fig. 8. 



The physiologists have studied velocities of development according 

 to a special principle. By chance, the rule published by Van't Hofif to the 

 eiifect that an increase of 10° C. approximately doubles the rate of chemi- 

 cal reaction, was found by physiologists to apply roughly to the rate of 

 development of organisms (?'. c, Q,,. is about 2). It was assumed to be a 

 constant within the optimum temperature range. They immediately 

 seized upon this as evidence with which to combat vitalism and anti- 

 evolution and show that life is a physico-chemical process, and the Q,o has 

 been and still is the chief method of expressing the temperature relations 

 of many physiological processes. Until Krogh's 1914 paper there was no 

 important attempt at analysis by other methods. The only matter in 

 point here is that the lower end of the velocity curve is of such a nature 

 as to fit (for a short distance) a Q^ curve with Qm as a constant. Its 

 application by physiologists may be taken as evidence for the curvature 

 of the lower end of the velocity curve. On further analysis, however, it 

 is evident that, as Krogh has pointed out, the Qm is not a constant but, as 

 he shows in the case of the frog's egg, ranges from 53.0 at the lowest 

 temperature to a little more than unity at the highest. This makes it 

 useless for most purposes. 



There is, in addition, a large amount of work on toxicity of salts 

 and other drugs to fishes and crustaceans (Warren, '00; Pittenger and 

 Vanderkleed, '15; Powers, '17) in which the concentration-time-to-deah 

 curve is very similar to our time-temperature curve. The reciprocal, or 

 the curve for the velocity of the toxicity, is similar to our temperature- 

 velocity curve except in its upper limits. Powers, in particular, has made 

 contributions of much importance to the mathematical relations of such 

 curves. He developed a theory of metabolism suited to his facts. 



Altogether, the evidence for the deviation of the developmental 

 velocity from a straight line at low and at high temperatures is strong, 

 and there is no reason why procedure should not be based upon the facts. 

 Glenn ('22) recognized the nature of the upper end of the curve and 

 reduced the high temperatures accordingly. He did not, however, take 

 into account the deviations from a straight line at the lower temperatures. 

 The result is that he figured his sum too small for the pupae ; but the 



