SELIG HECHT 679 



ent results (Hecht, 1919, c). In order to determine exactly the 

 velocity of the inactivating reaction, it is necessary to utilize the 

 dynamics of catenary reactions. This process does not lend itself 

 readily to graphic representation, and must therefore be studied from 

 certain mathematical considerations. 



We have to determine what happens in the case of the two con- 

 secutive monomolecular reactions 



It has been assumed that 1 mol of the substance L is present at the 

 beginning of the latent period. At the end of the time t occupied by 

 the latent period, let the reaction system contain x mols of L, y mols 

 of T, and z mols of N. Therefore 



x + y + z=l. (5) 



According to the mass law the rate of diminution of L will depend 

 on its concentration x, and will proceed according to 



dx , ^ 



-- = kxx (6) 

 at 



where ki is the velocity constant of the reaction L^T. The rate 

 of the formation of the indifferent material N will depend on the 

 concentration y of the substance T, and is 



where k^ denotes the velocity constant of the transformation of T 

 to N . Therefore the rate at which T will accumulate in the sense 

 organ will evidently be the difference between the rate of diminution 

 of L and the rate of formation of N; in other words, 



dy 



-r = kix - hy. (8) 



at 



The speed of the chemical system L -^ T —^ N \s, fully determined 

 by these three simultaneous differential equations. The conditions 



