394 Ralph S. Lillie 



From the above experiments it appears that the optimum time 

 of exposure to the high temperatures is shorter the higher the tem- 

 perature employed. In the above two series the best results were 

 obtained at 35° with 70 seconds exposure, at 36° with 40 or 50 

 seconds, at 37° with 30 seconds, and at 38° with 20 seconds. In 

 general the same relative favorability of different periods of expo- 

 sure at different temperatures was found in several other similar 

 series of experiments. The decrease in the optimum time of 

 exposure with a given increase in the temperature is somewhat 

 surprisingly rapid, the difference of three degrees between 35° and 

 38° reducing the optimum exposure from 70 to about 20 seconds. 

 If the process in which the initiation of development depends is 

 a purely chemical one, this would indicate an extraordinarily high 

 temperature-coefficient of acceleration. The conditions in a 

 heterogeneous system like protoplasm must, however, be recog- 

 nized as peculiar; rise of temperature, in addition to accelerating 

 the specific chemical processes (usually about threefold for a rise of 

 10°), has a certain effect (which under some conditions may be very 

 considerable) in altering the surface of interaction between the 

 colloidal bodies concerned and the other chemical substances 

 reacting with them; increased subdivision of the colloidal particles 

 following a rise of temperature would in itself accelerate the reac- 

 tion; and the total acceleration would be measured by the product 

 of this increase in the surface of interaction into the specific acceler- 

 ation of the process itself through the rise of temperature; this com- 

 pound value might exceed many times (as apparently in the case 

 under consideration) the simple temperature-coefficient of acceler- 

 ation of the purely chemical process. The results with membrane- 

 production also indicate a very high temperature-coefficient. So 

 far as regards development I have as yet made no special endeavor 

 to determine the optimum periods of exposure at temperatures 

 above and below those cited. The favorable periods for tempera- 

 tures of 39° and 40° would undoubtedly be found very short, while 

 at 34° and 33° exposures would be more prolonged. Temperatures 

 so low as 30° would in all likelihood be found effective with suffi- 

 cient time of exposure, as Delage's-" results indicate. 



2" Delage: loc. cit., p. 307. 



