836 SIR B, C. BHODIE ON THE CALCULUS OF CHEMICAL OPERATIONS. 



and 



2yim =3^1+^2™. 



From the first of these equations it appears (since ^2 ^^^ Vx have no common measure) 

 that ^2 cannot be an even number, if the equation is to admit of an integral solution. 

 Making this assumption, we have, putting ^2=1 + 22, 



m =2+z, n =yi, 



Wi=3, 7^^=0, 



m2=l-\-2z, 712=2^1, 

 a minimum, which give 



Symbol of chloride of boron . «''"*^'%'/3I*% 

 Symbol of boron a^'/S?". 



Also, since 5"5 parts of boron are formed by the decomposition of 1 volume of chloride 

 of boron of the density 58*75, putting W as the density of boron-vapour, 



2y, 2 



and putting 1/^^=1 -\-2z, 



Again, putting a^x^'/S"' as the symbol of boric methide, and (as before) - as the 



number of volumes of carbon formed by the decomposition of one volume of marsh-gas, 



and giving to y^ and 1/2 the same values as in the last equation, it is known from 



experiment that 



2y2^ia'"«'"'/3?= dyy^u+Gxy^x." +yyy^^f' ; 

 whence 



2m =9+2^2' 



2mi=6ar, 



and putting ^2=1+2^, and x=l, 



m =zb-\-z, 



mi=3, 



m2=l-f2z, 



and we have for the symbol of boric methide a'^V/Sl^**, 



Proceeding in a similar manner with the other gaseous combinations of boron, we arrive 

 at the following symbols : — 



