432 OVULATION IN THE DOMESTIC FOWL 



X, present at that moment, which acts as the catalyst of the reaction; 

 that is 



— = Kix {A - x) (1) 

 dt 



dx 

 where -tt stands for the momentary velocity or rate of reaction, and 



Ki is the velocity constant. Equation (1) cannot be applied to 

 experimental data since the momentary velocity of the reaction is 

 not known, and since the velocity is not expressed as a function of 

 time. It is therefore first integrated obtaining 



log -^— = KxAt + C (2) 

 A — X 



where C is the integration constant. The value of the integration 

 constant C is found by an analysis of the meaning of i in equation (2) 

 above. Equation (1) represents a curve of a rising and falling type, 

 the maximum or turning point occurring when x = A — x; thai is, 

 when the reaction is half way completed, and when the reaction is at 



X 



the maximum velocity. At that point, therefore, log -. = 0. 



/i. X 



It is most convenient to count the time from this maximum or turn- 

 ing point, that is t at this point is just equal to zero; therefore, 

 KiAt = and also C = 0; if it is agreed to count time from the max- 

 imum velocity, then C = 0, and equation (2) becomes 



log -^^— = KiAt (3) 

 A — X 



t in equation (3) is then the time on either side of the maximum point, 

 counted from that point as zero. Equation (3) may be more con- 

 veniently written 



log --^- = K,A (t - h) (4) 

 A — X 



where ii is the time from the beginning of the reaction to the maxi- 

 mum point; / is any time from the beginning of the reaction chosen 

 for discussion; and {t — h) is therefore the difference of time from 

 the maximum point to the chosen time t. The minus sign between 

 t and /i indicates difference in time between the maximum and 



