808 SIK B, C. BEODIE ON THE CALCULUS OF CHEMICAL OPERATIONS, 



The admissible values are limited by the conditions 



2)w(a)-\-piW(b)-\-j)2tv(c) =W, 



qw(a) + q^w{h) + q^w{c) = Wj, . 



rw{a)-\-r^w{b)-{-r^w{c) =W2, 



where %o{a), w(b), w(c) are positive, and W, Wj, Wg, are connected by N equations 



of the form 



mW+m'Wi+m"W2+m"'W3+ =0. 



Section VI.— ON THE CONSTRUCTION OF CHEMICAL EQUATIONS FROM THE DATA 



AFFORDED BY EXPERIMENT. 



Our knowledge as to the identical relations of ponderable matter is derived, as has 

 already been observed, exclusively from the science of chemistry. The next step in this 

 inquiry is to embody in a system of chemical equations the information on this subject 

 which experiment affords to us. The process is very simple by which this may be 

 effected. To take, for example, a single instance. Let it be supposed that we have 

 ascertained by experiment that 3000 cub. centims. of chlorine and 2000 cub. centims. 

 of ammonia have been converted into 6000 cub. centims. of hydrochloric acid and 1000 

 cub. centims. of nitrogen. We hence infer the identity of the ponderable matter of 

 which the two groups respectively consist, and putting 



<p as the symbol of a unit of chlorine, 



<Py as the symbol of a unit of ammonia, 



f 2 as the symbol of a unit of hydrochloric acid, 



^3 as the symbol of a unit of nitrogen, 



we assert this identity in the chemical equation 



3?) +2^1 =6^2+^3- 

 Proceeding in other cases in a similar manner, we should arrive at a system of equa- 

 tions corresponding in number to the experiments of which the results were thus recorded. 

 It would soon, however, be perceived that we could not in this manner indefinitely add 

 to our knowledge, but that the information thus supplied to us was soon exhausted, the 

 equations not being independent, but capable of being derived from one another by the 

 processes of addition and subtraction ; and that, in fact, they could be replaced by a 

 single system of equations connecting every chemical symbol equal in number to the 

 total number of chemical substances, exclusive of the elemental bodies. Such a system 

 is afforded to us by those equations which express the relations of identity which subsist 

 between the ponderable matter of compound substances and the ponderable matter of . 

 the elemental bodies of which they are composed, which we may consider as a solution 

 of the entire system of chemical equations in regard to the symbols of the elements. 

 From this primary system every other chemical equation may be derived, and our total 



