848 SIR B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPERATIONS, 



and putting W as the density of the vapour of silver, 



whence we may infer that 



ygW 35-5 X 75-24 -„„ 

 1^= 24-66 =^"^' 



Also from the general considerations previously given, 



?^=XA, 



where X is a positive integer. 



Hypothesis I. — Let us assume that W=A. Then 



2^=2, ^=X, and ^=1 



There are two cases, according as X is assumed to be odd or even. 



(1) Let X=2a-+1, an odd number. Then yi=2, ^2=^, y^=21L\ and substituting 



these values in the equation 



y\m=yo-\-yin, 

 we have 



2m=(2a:+l)(l+2«), 



to which equation there is no integral solution. This hypothesis is therefore untenable. 



(2) Let X=2a:j, an even number. Then yi=l, y2=-^v ^3=20^1, and 



m = 0^1(1 +2w), 



m2=2ari«2- 

 These equations in all cases admit of the minimum solution, 



m = a^i, n =0, 



mi=:2Xi, TCj = 0, 



m2=2xi, »2=1' 

 In which case the above equation becomes 



the symbols being thus expressed: 



Symbol." ■ Weight in grm. Relative weight. 



Silver gj 4827 54 



Chloride of silver . («%"§?)" a^iX 12-828 arjX 143-5 



Hypothesis II.— Now, let W=2A. Then 



Vs^l^ !y3=X, and ?^=X. 



^2 ' yi ' Vi 



(1) Let X be odd, =2a: + l; then ^1= 2, ^2=^' y3=^> ^^^ 



2m ={2x+l)(l+n), 

 2wii=(2ar+l)(2+«i), 

 2m2={2x-\-iyn^. 



