100 Application of Mathematics to Chemical Analysis. [Aug. 



other salts, and then converting them into sulphates. Having 

 determined in this way the respective quantities of the given 

 salts, those of the earths may be deduced by simple proportion. 

 It is easy to get a general formula for all similar cases. Let 

 the atomic multiplier of any simple body, A, to form a given 

 salt, be a ; and that of another, B, b ; and let the joint weight 

 of the simple bodies be m, and that of their salts S ; the absolute 

 weights of A and B may be found as follows : 



x + y = m, 

 ax •+•- by =s S, 



from which equations we obtain y = — —, and x — ^ m . 



1 ^ a ~r o a S- b 



The preceding question may be readily answered by means, 

 of the general formula, the use of which it will serve to illustrate. 



265J - ( — x 96^ 

 s-bm \7 J 1856-1632 224 __ iU 



x = — T = — = 3 = - =56, the 



3 ~T 

 quantity of magnesia, as before: and 96 — 56 = 40 = the lime. 

 The algebraical result from the general equation furnishes the 

 following 



Rule. 



Multiply the joint w r eight of the bases by the atomic multi- 

 plier of one of them (A); then the difference between this pro- 

 duct and the weight of both salts, divided by the difference 

 between the atomic multipliers, will give the absolute weight of 

 the other base (B). 



The base A may be found by subtraction. 



The principle upon which the above rule is founded may be 

 extended to three or more bodies. 



Let a, b, c, be the multipliers of the sulphates, 

 And a', b', c', nitrates. 



Then, by denoting the respective quantities of base by x, ij, 

 and r, we have, 



r x + i/ + z = m~\ 

 < a x + b g + c z = s V 

 La'x + b'u + c'z = n J 



Hence the respective values of x, y, and z, may be deter- 

 mined. 



