THE PRECIPITINS AND THEIR ANTIBODIES 293 



(A-P) , (I20-P) 



sera are a ^ / and - % and the formula repre- 

 senting the equilibrium is: 



where K is a constant, which according to the experiments 

 is 250. With the aid of this equation the calculated values 

 of P have been found and are written beside the observed 

 values. In the three last tests i c.c. of water containing 

 I per cent of sodium chloride has been added to the mix- 

 ture of the sera, which circumstance has been taken ac- 

 count of in the calculation of the volume F(in c.c.). 



The agreement between the observed and the calculated 

 values may be regarded as very satisfying, especially with 

 respect to the enormous change of A (in the proportion of 

 i : 1000) and of F 2 (i : 2500). 



The simple form of the equation of equilibrium depends 

 upon two circumstances : the extremely low solubility of the 

 precipitate in rabbit-serum (not i in 3000), and in sheep- 

 serum. Probably these two circumstances are connected 

 with each other. The figures obtained with goat-serum 

 were calculated in the same manner and the results are 

 given below. In this case I c.c. of the goat-serum was 

 always equivalent to 40 units of the precipitate, but 0.4 c.c. 

 of the rabbit- serum was equivalent to only 85 units of pre- 

 cipitate. 



The constant K is set at 200. Here the agreement is 

 not so perfect as in the foregoing series. The agreement 

 would have been much closer for the latter part of this 

 series if we had taken K = 160, but then the first part 

 would have shown greater deviations than it does now; 



