on Chemical Equivalence. 175 



which we have elsewhere* shown to hold good for niekelous 

 with cobaltous sulphate. "Within the limits of error of expe- 

 riment, the second constant in (1) is the reciprocal of the 

 second constant in (2). The attraction of niekelous sulphate 

 for the reagent is thus the inverse of that of manganous sul- 



In order to ascertain in what proportions the commixed sul- 

 phates are equally precipitable, we have 



•98570 + •61438n=3-0881-l-7203?n, 

 whence 



»»=1-2221— -35714m. 



This equation does not admit of solution except on some 

 further supposition with respect to m or n. Xow Table I. 

 shows that the required values of m or n are very nearly equal 

 to 0"9, and consequently that equal weights of niekelous and 

 manganous sulphates are equally precipitable. If, in fact, in 

 the equation just given we put 7z = - 9, we shall find the sub- 

 stantially identical value 0'9007 for m. 



To calculate in what proportions the two sulphates must be 

 mixed so that they may give equal weights of precipitate, we 

 have 



n _ (-98570 + -61438 »> \ 

 m ~ (3-0881- 1-7203 m)/i ) 

 »=1 — m. 



Putting -=1, and combining these equations, we obtain a 



quadratic, one of whose solutions is m = '6215, and conse- 

 quently v=-3785. Substituting these values in the primitive 

 equations, we find /-t= - 3086, v = "3107 — very nearly equal 

 weights. 



Separate Precipitation. — In cases of precipitation of a single 

 salt, if x be the weight of reagent taken, y the weight of pre- 

 cipitate obtained, and «, /3 constants of condition, some form 

 of the relation 



*=i& « 



is ordinarily valid. The sign of /3 is necessarily positive; but 

 the sign of a depends upon the order of constancy in precipi- 

 tation. The equation can obviously apply only as long as 



6 = - is = or > 1 . There are verv few instances in which, as when 



y 



sodic chloride acts on argentic nitrate in a weak solution, the 

 * Proc. Eov. See. xxix. 181, 



