Mr Walker o/i Elimination. 
rough, and sulphureous taste, which reddened iris paper, which 
grew turbid, and deposited sulphur on standing, and, when 
boiled, gave off sulphurous acid, and finally which, saturated 
with ammonia and concentrated by evaporation, acted upon 
every re-agent exactly as a solution of hyposulphite of ammonia 
would have done. But the acid so obtained was in such small 
quantity compared with that contained in the metallic salt, that 
I will not venture to speak decidedly on the subject, but pro- 
p(3se the earliest opportunity to try, as a last resource, the action 
of the voltaic pile. 
Slough, Jan. 8. 1819. 
Art. III . — Application of tfie Indeterminate Analysis to the 
elimination of the unknown quantities from two Equations. 
By William Wallace, Esa. F. K. S. Edin. Communi- 
cated by the Author, 
When two unknown quantities are to be determined from 
two equations, one of which is of the second order, we may, by 
known theorems in the indeterminate analysis, eliminate both 
the quantities, and derive from them a new equation containing 
only one unknown quantity, of which each of the other un- 
known quantities is a given function. 
1. For example, let us suppose that the equations are, 

a^‘^ -j- hocy -\-cy^^—n’^ (S) 
This last is taken of the second order for the sake of brevity, 
but it might be of any order whatever. 
Let us assume 
(r^ — s’^')m 
y,2_j_^2 ? 
Then -f 
9^r s m 
y ^ 2 1 f. 2 
r^-\-s- 
^4 ^2 ^^2 _|_^4 
m- 
Thus, it appears, that the first equation is satisfied by the na- 
ture of the functions a? and y, independently of any particular 
value of r and s. 
