VARIABLE TEMPERATURES 215 



sets of experiments lead to the conclusion that length of time of 

 exposure to given temperatures is of prime importance, and that 

 there is an optimum combination of time and temperature for 

 the given species — the point at which the growth rate attains its 

 maximum value. It is further possible to secure a given growth 

 rate by several combinations of time and temperature. 



Ludwig and Cable (1933) give a useful discussion of the subject 

 of alternating temperatures. They also describe the results of 

 their experiments with pupae of Drosophila which were exposed 

 to daily alternations between two temperatures. When one of 

 the temperatures is above the optimum for development, and the 

 other is between the a point (10°) and the optimum, development 

 appears to be retarded. If, on the other hand, both temperatures 

 lie between the a point and the optimum, the range of development 

 is unaffected as compared with controls at the optimum tem- 

 perature. If one temperature is between the a point and the 

 actual threshold of development the rate is accelerated. This 

 acceleration is due to development having taken place below the 

 a point. These authors further point out that alternating tem- 

 peratures provide a satisfactory method for determining the 

 development threshold. In these experiments, if the pupae of 

 Drosophila be exposed to a high and a low temperature, and the 

 developmental rate is the same as that of controls at the constant 

 high temperature ; it is obvious that no development has occurred 

 at the low temperature. If, however, the time at the high 

 temperature is less than is required in a constant exposure to 

 the same temperature, some development occurs at the low 

 temperature ; the latter, therefore, is above the developmental 

 threshold. By this method it was found that the a point (10°) 

 in the case of Drosophila pupge is considerably above the true 

 threshold, which lies between 7° and 8°. 



In computing the effects of variable temperatures, many 

 entomologists have used the number of " degree-days " for this 

 purpose. The total number of degree-days, for a given stage of 

 development of an insect, is arrived at by taking each day from 

 the commencement to the termination of the stage concerned, 

 and by computing the number of degrees by which each day's 



