95 
So and a 2 h 2 , &c., have the same meanings with reference 
to another element. The letters cq b lf a 2 b 2 , & c., may have 
any positive integral value including 0. Then a chemical 
compound may he denoted by S 2 oq S 2 a 2 &c., which for 
brevity may be denoted by A. So B will denote a com- 
pound of the form Si b l S 2 b 2 &c., and so on for other com- 
pounds. Hence the chemical equation may be written in 
the form 
Pi A + PoB + 8cc. = Q X M + QoN + &c (1) 
Pi, P 2 , Qj, Q 2 , &c., being undetermined. Then equating the 
terms containing S x S 2 , &c, we have equations of the form 
S 1 (P 1 « 1 + P 2 6i + &c.) = S^Qi^j + Q 2 %i + &c.) 
S 2 (Pl «2 + P 2^2 + &c) - S 2 (QiW 2 + Qo??. 2 + &c.) 
S?i(Pia rt + P 2 ft„ + &c.) - Sw(QiW b + Q o?i n + etc.) 
From the above equations the letters S 1? S 2 , &c., might 
have been omitted, but are retained to show that there will 
be as many equations as elements. Hence if the number of 
elements be equal to the number of compounds we shall 
have sufficient equations to determine P t , P 2 , Q ls Q 2 , &c. 
If the number of compounds exceed the number of elements 
by unity, take any one of the undetermined coefficients, 
then all the rest may be determined as multiples of that 
one, and replacing these values in equation (1), both sides 
will be multiplied by the same arbitrary quantity, which 
may therefore be omitted. 
Within the last few years chemical compounds of con- 
siderable complexity have been obtained, and for their 
quantitative reactions such a method as that suggested 
might be serviceable. Annexed are two examples of the 
method applied to well known chemical equations. 
I. Copper and nitric acid yield water, copper nitrate, and 
nitric oxide. 
PA + P 2 (HN0 3 ) = Q^O) + Q 2 (Cu(N0 3 ) 2 ) + Q 3 (N 2 0 2 ) 
