828 8IE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEKATIONS. 



Hence, putting y as the number of units of marsh-gas thus decomposed, and x as the 

 number of units of the vapour of carbon formed, and putting a""*"*' as the symbol of 

 marsh-gas, and a"«"' as the symbol of carbon, 



^a'"x'"'=2ya+:ra"x"', (1) 



whence 



and 



my=ly-\-'ax, 



m^y=- n^x. 



Now, whatever be the values of y and x, these equations will admit of a minimum 



integral solution, provided only that y and x be integral numbers. 



This solution is 



m=2, mi=-x, 



n =0, «! =y. 



As determined, therefore, from this equation, we have 



Symbol of marsh-gas . . . aV, 

 Symbol of carbon . . . . k". 



Assuming 8 as the density of marsh-gas, 



2-\-xw{x)=S, 

 whence 



and putting W as the density of carbon-vapour, 



X 



the above equation (1) being thus expressed, 



y(a V) =.2yu-\-xx?. 



We now should proceed to ascertain whether the same symbol, k", for carbon will 

 satisfy the conditions afforded by other equations. I will give one or two examples of 

 the process by which this is effected. 



It is known from experiment that y^ volumes of olefiant gas are decomposed into 2yi 

 volumes of hydrogen and x^ volumes of carbon-vapour. Hence the absolute weight of 



carbon formed by the decomposition of a unit of olefiant gas is ?^ W. 



But this weight is determined by experiment, and is equal to twice the weight 

 of carbon formed by the decomposition of a unit of marsh-gas, which weight is equal to 



-W. Hence ^ = -r- ; and putting aV' as the symbol of olefiant gas, and «*, as before, 



as the symbol of carbon, 



ya^K'"=2yu+2.XK^, 

 and 



p—2, py=2x, 

 whence we have the symbol of olefiant gas a^*" ; and the symbol of carbon can be ex- 

 pressed in this equation also as k", where y has the value given in equation (1). 



