173] THE GOLDFISH AS A TES T A NIMA L— POWERS 53 



Ki-ogh (1914, 1914a) and Sanderson and Peairs (1913) almost at the same 

 time and independently of each other noted that a similar curve was formed 

 when rate of development of eggs of frogs, insects and sea-urchins and also 

 larv'ae and pupae of insects was plotted as ordinate and temperature as abscissa. 

 Sanderson and Peairs determined the reciprocal curve which they designated 

 as the rate of development and considered it a straight Hne crossing the X-axis 

 at the actual zero of development. They disregarded the variations from a 

 straight Une at the extremes altogether and made all calculations on the assump- 

 tion that the temperature above their theoretical zero times the time required 

 for the organism to pass through certain stages of development is a constant. 

 Krogh in his work called attention to the variations of the rate of development 

 begun below the point at which the straight line cut the X-axis, i.e., the lowest 

 temperature at which development will take place is below the theoretical 

 temperature for the initiation of development. Reibisch (1902) called this 

 the threshold of development. 



Finally, Osterhout has shown that the dying curve of Laminaria when killed 

 in an NaCl or a CaCl2 solution of the same conductivity as that of sea-water 

 as shoum by the fall of electrical resistance after having passed the point of 

 stimulation of the latter salt follows the course of the same general curve when 

 resistance is plotted as ordinate and time as abscissa. 



The close similarity of the curves found by different workers in entirely 

 different fields suggests that the extremes of the reciprocal curves should be 

 more thoroughly investigated. The possibility is that no portion of the curve 

 is a straight Une. This supposition is evidenced by the equation l/t= (MK2-I- 



KiXV loge ( — — H ) • This is further emphasized by the fact that 



M-z Ki(]M-z) X 



Ostwald's data fits almost equally well the formulae y(x-a)= k, i.e., l/t= (x-a) 

 /K = Ki(x-a) and t(C-n) =Ki, i.e., logg t+mlogg (C-n)=loge Ki. These 

 two equations represent hyperbolae of entirely different orders and are never 

 similar except when m=\. Thus the evidence is that neither of the two equa- 

 tions fits exactly. But for all practical purposes in pharmaceutical work and 

 in insect pest prediction (Shelford 1918) the equation l/t=y=Ki(x-a) can 

 be considered as holding in very narrow limits i.e., when the temperature to 

 which the insect pest is subjected is never below the temperature at which 

 the velocity of development curve ceases to approach a straight Une; otherwise, 

 some modification of the equation used by entomologists must be employed. 



