476 On the Coagiilative Power of Electrolytes. 



occupied by the spheres of influence of the ions and the whole 

 volume of the solution, and may be written as Ac, where A is 

 a constant and c represents the concentration of the solution. 

 The chance that two such ions should be present together is 

 the product of their separate chances, that is (Ac) 2 . Similarly, 

 the chance for the conjunction of three ions is (Ac) 3 , and 

 for the conjunction of n ions (Ac)". 



In order that three solutions, containing trivalent, divalent, 

 and monovalent ions respectively, should have equal coagu- 

 lative powers, the frequency with which the necessary con- 

 junctions should occur must be the same in each solution. 

 We should then have, the constant being assumed equal in 

 each case, 



A 2 "c 3 2 ' l = A 3 "c 2 3 " = A 6n c 1 6w = a constant= B. 

 Therefore 



L L 1 



Ba« B-s» B«3» 



c *=-r C2 =~a> Ci= x' 



Cj, c 2 , c 3 representing the concentrations of monads, diads, 

 and triads in their respective solutions. 



Thus we get tor the ratios of the concentrations of equi- 

 coagulative solutions 



-1 -L - 1 I A 



C| : c 2 : c 3 = B b » : B^» : B^~< = 1 : Be» : B^ 11 . 



11. 

 Put Ben =• ; the ratios can then be written 



1 : i : i- 



X x~ 



The reciprocals of the numbers expressing the relative 

 concentrations of equi-coagulative solutions give values pro- 

 portional to the coagiilative powers* of solutions of equal 

 concentration ; so that, calling the coagiilative powers of 

 equivalent solutions containing monovalent, divalent, and 

 trivalent ions respectively ^>i, p%, Ps, we get 



Pi *ft:.p»=l = « : «?■ 

 Let us now take some numerical examples. Putting x = 32, 

 we get the series 



1 : 32 : 1024, 



which agrees very well with Linder and Picton's results 



1 : 35 : 1023 ; 

 and putting #=40, we get 



1 : 40 : 1600, 

 numbers comparable to Schulze's values 



1 : 30 : 1650. 



