680 



TEMPERATURE AND LATENT PERIOD 



which govern the behavior of the four variables in the equations are 

 well known, and have been subjected to experimental verification 

 (Mellor, 1916, p. 434). Without going into the details of the mathe- 

 matics of the matter, it is sufficient to say that by combining equations 

 (5), (6), (7), and (8), and integrating under proper conditions, an 

 equation is deduced which gives the amount z of the substance iV 

 formed in a given time / in the terms of the two velocity constants 

 k\ and ki. This equation is 



z- 1 



^1 — hi e' 





(9) 



in which all the terms have their previous significance, and e is, as 

 usual, the Naperian base. 



TABLE n. 



Velocity Constants of the Fundamental Reaction of the Latent Period, and of the 



Inactivation Reaction. Amount of Thertnolabile Substance Inaciivated 



above 21°, and the Time (t) during Which the Inactivation 



Actually Takes Place. 



We already know the values of t, the actual latent period; these 

 are given by the experimentally determined points of Fig. 2 and in 

 part by the triangles in Fig. 3. The amount of N present in the 

 system is the quantity z of thermolabile substance T which has been 

 inactivated. This is also known from Fig. 3, and its value at dif- 

 ferent temperatures is given in Table II. Also, ki is known, its 

 values having been given in Table I. The only unknown in equation 

 (9), therefore, is ^2, the velocity constant of the inactivating reaction 

 T —^ N. Equation (9) may then be solved for ko, which will give us 

 precisely the information we desire: the values of this velocity con- 



