176 Researches on Chemical Equivalence. 



value of a vanishes and /3 represents an undisturbed combining 

 proportion. 



In Table II. we have stated the result of acting upon a con- 

 stant quantity of sodic carbonate with a varied amount of 

 nickelous sulphate. The equation employed in the calculation, 

 all experiments being taken into account, is 

 1-2816* 

 •^ 1 + 1-2308* W 



Probable error of a single experiment, "014915. Applying 

 the criterion as to (f>, we notice that the equation cannot actu- 

 ally hold good until *=*2288, though the difference between 

 theory and experiment is not great before that stage. 



On the other hand, when (Table III.) nickelous salt is kept 

 constant and sodic carbonate is the varied precipitant, we have 



_ -66641 * 

 y ~\ --52700*' (5) 



with a probable error -0046138 for a single experiment. 

 Similarly, when carbonate is constant and manganous salt 

 varies (Table IV.), 



2-7486* 

 y ~ 1 + 2-6648*' W 



an equation which is not rational until ;c = '6oCr2, and has 

 therefore been necessarily calculated from the last two expe- 

 riments only. 



Again, when manganous salt is constant and carbonate 

 varies (Table V.), 



•98103* 

 y 1--49146* 5 ( 7 ) 



the probable error of a single experiment being -015742. 



If in equation (3) we put <£>= -, we shall find that 



, 1 + a* 



*—T' 



a relation which, when we adopt other constants, may be ex- 

 pressed as follows : — 



(f> = a + bx. 



Hence the precipitability equation is, as we have already seen, 

 a linear one. 



_ The equation to <}>, as thus deduced from the separate preci- 

 pitation experiments [<£,], differs in its constants from that to 

 which the "conjoint" experiments [</> c ] have led us. The 



