64 LECTURES ON IMMUNITY 



where A is the quantity of ammonia present at the 

 time / = o, x the quantity of ammonium-acetate formed, 

 and consequently Ax the quantity of ammonia at a 



given time, t. The velocity of reaction is propor- 

 tional to y and to the quantity P of ethyl-acetate, so that 



the equation 



dx = K(A-x) 



dt x + ky 



is also valid. If x is not too small, ky may be neglected, 

 and we find the integral : 



From this formula the values ;r calc-1 are calculated. A 

 is set as 1000. Here KP is 82. The agreement may be 

 regarded as very satisfying. At low values of t the 

 observed value x is less than the calculated one, due to the 

 neglection of ky, as compared with x, which is not allowed 

 if x is small. 



If x is very small compared with A, i.e. in the beginning 

 of the experiment, we may as a first approximation put 



A x = A and 



dsc = KAP 



dt x 

 which gives x* = KAP, 



x is proportional to the square root of the time and also 

 to the square root of the concentration of the ammonia at 

 the beginning of the experiment, and to the square root 

 of the concentration of the ethyl-acetate. This is the rule 

 of Schiitz. 



As is seen from these equations, x is only a function of 





