WILLIAM R. AMBERSON 541 



lated if desired. Thus from the decay curve which is tabulated in 

 Table I and graphed in Fig. 1, we derive the absolute value of k as 

 follows: 



— log 



t ^ A-X 



If X becomes — 

 Then 



(3) ^ = ylog2 



The time t needed to reduce the concentration A to half of its value 

 is determined directly from the graph. For log / at time 0, deter- 

 mined from the straight line intersection in Fig. 1, is 0.17. 



Then 



log — = log / — log 2 

 = T.869 



/ A 



When / becomes — > X becomes — . A reduction of log / from 



0.17 to 1.869 corresponds to a time interval of 30.7 mm. of film, 

 or 7.446 seconds of time. Using the usual time unit employed in 

 calculating velocity constants, 1 minute, we find that, as 7.446 seconds 

 is 0.124 minutes, then from equation (3) 



0.30103 



" 0.124 



= 2.43 

 This gives the absolute value of the velocity constant if we are using 

 Briggs' logarithms. The corresponding value of k for the natural 

 system is: 



2.43 

 " 0.4343 

 = 5.59 



This absolute value of k will indicate the extraordinarily high speed 

 at which this luminescent reaction is proceeding, even at room 

 temperature. 



The Secondary Reaction. — I have mentioned at various places the 

 highly labile character of luciferin solutions wliich oxidize sponta- 



