1824.] Application of Mathematics to Chemical Analysis. 99 



Article III. 



An Application of Mathematics to Chemical Analysis. By Mr. 

 JohnDavies,M.W.S. Memberof the Literary andPhilosophical 

 Society of Manchester, &c. 



(To the Editors of the Annals of Philosophy.) 



GENTLEMEN, Manchester, July 4, 1824. 



To determine the quantities of lime and of magnesia when 

 they occur together, has been regarded as a problem of some 

 difficulty ; and though several eminent chemists, who have paid 

 particular attention to the subject, have suggested peculiar 

 methods for the purpose, an accurate and a direct process is, if 

 I mistake not, still a desideratum. 



It occurred to me a short time ago that the object might be 

 best attained by the aid of calculation, applied in a manner 

 which, though very simple and easy, has not, I believe, been 

 hitherto attempted. The method which will be explained in this 

 paper will furnish another example, in addition to the many 

 already known, of the value of the atomic theory in its subser- 

 vience to chemical investigation. 



I designate by the name of atomic multipliers those numbers, 

 whether whole or fractional, by which if we multiply the weight 

 of an atom of any base, we shall obtain that of the correspond- 

 ing salt. Now it appears from the table * of chemical equiva- 

 lents, that when the number denoting the weight of an atom of 

 magnesia is multiplied by 3, and that of an atom of lime by 



17 



— , we obtain the numbers representing the relative weights of 



the sulphates of those earths. 



Suppose, then, that we have a quantity of lime and magnesia 

 weighing together 96 grains, and that, when converted into 

 sulphates, their joint weight is 265J- grains ; it is required to 

 determine by calculation the quantity of each earth. 



Assume x = the quantity of magnesia, and 



y = lime. 



Then x + y = 96, 



And 3 x + ~y = 265-1. 



Hence x = 56, the quantity of magnesia, and y = 40, that of 

 lime. 



If any objection be conceived to arise from the difficulty of 

 procuring the earths in a pure state, it might evidently be 

 obviated by taking the bases in the state of nitrates or any 



* Henry's Chemistry, vol. ii. pp. 637 and G38. 

 II 2 



