UPPER THERMAL DEATH POINTS 435 



between the limits x = — b (room temperature) and x = p (the 

 highest temperature attained) ; b and p, of course, being measured 

 from the temperature selected as the point of comparison. The 

 constant a is the amount of injury, lo, inflicted in unit time at 

 this temperature. The area of the curve, A, which represents 

 the total injury, I, therefore is: 



A = I 



rQ^ix = af-QL___QrL) 



J-b MogeQi logeQi/ 



Since b (the number of degrees the room temperature lies below 

 the temperature chosen for comparison) is relatively large, the 

 second half of the expression within the parentheses becomes 

 negligibly small and may be disregarded. This is equivalent to 

 calculating the injury that would be inflicted in a rise from an 

 infinitely low temperature instead of from room temperature, 

 but this amounts to practically the same thing, since even 

 considerably above room temperature the injury inflicted in 

 any ordinary time has ceased to be appreciable. 



If instead of raising the temperature at the rate of one degree 

 per minute as implied in the calculation just given, the rate had 

 been slower, say one degree in t minutes, the right-hand side of 

 the equation would have to be multiplied by t. The general 

 expression therefore for the area. A, which represents the total 

 injury, I, inflicted up to the temperature p° when the rate of 

 rise is one degree in t minutes becomes (when a is replaced by 

 its equivalent 1 9) : 



Qf 



I = tL 



logeQl 



In the case of starfish larvae where Qi is equal to approximately 

 2.0 and loge Qi therefore to approximately 0.7 we have finally: 



2P 



I = tIo-^ 



0.7 



In case it is desired to know how high the temperature would 

 have to be raised to inflict just fatal injury, it is only necessary 



