290 LECTURES ON IMMUNITY 



soluble compound, such that one equivalent of it contains 

 one equivalent of precipitate and n equivalents of horse- 

 serum (or in other words n + I equivalents of horse-serum 

 and i equivalent of calf-serum). Then there are present 

 in the solution the following quantities in equivalents of 

 the different substances : 



(A - P p V (n + i) F) of horse-serum, 

 (B-P-p V- Y) of calf-serum ; 



and the following equations of equilibrium are valid : 

 \A-P-pV-(n+i)Y\ {B-P-pV-Yl^ 



If we determine Ffrom the last equation and introduce 

 it into the first one, we obtain : 



/ is found in the experiments to be 2.5. If we put 

 ^ + + i = 345 and ATi/"" - ^i0/ = T 30, we find 



/ A 2 



the calculated values of the total quantity (P) of precipi- 

 tate. The tabulated values of P give this quantity divided 

 with the volume, V t i.e. the quantity of precipitate in i c.c. 



J jjm, + 1 



The last equation gives -~ -- =130. If we suppose 



A 2 0.29 



m = i, i.e. that one molecule of precipitate is formed from 

 one molecule of each of its two components, we obtain 



K+ . K, 3.08 



i = 3.08 ; if we suppose m = 2,we find ^ = = 0.879. 



A 2 A 2 / 



