842 Sm B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 



of antimony ; and putting W as the density of bismuth, V the density of chlorine, and 

 Vj the density of terchloride of bismuth, we have, as before, 



and putting V= 35-5 and Vi=157-25, 



^3^=^2X208. 



3*289 

 Now, the specific heat of bismuth, h, =0-03084, and putting ^=q. q^q^ * 



A=106-6. 



We may hence assume that y^=.2y2A^, and, as before, putting 



1. W= A, y,=2y^; 



2. W=2A, y,= y^; 



3. W=4A, 2^3= y^; 



and by precisely similar reasoning to that in the last example, putting oT'y^'^^ as the 

 symbol of terchloride of bismuth, and a"%"'|32' as the symbol of bismuth, from the 



equation 



(a'"x'"'|3?)'*'=(a%')'*<aV/3?>'^ 



we arrive at the following symbols, rejecting, for the same reason as in the case of 

 antimony, the first hypothesis. 



On the second hypothesis, 'W=2A, 



Symbol of bismuth a/Bj, 



Symbol of terchloride of bismuth a'^'iSa. 



On the third hypothesis, W=4A, 



Symbol of bismuth ajSj, 



Symbol of terchloride of bismuth a^jS^. 



We have hence the following system : — 



Combinations of the Prime Factors 05, |, ^, %, . . . . and /3j. 



