132 Prof. Sylvester on Elimination and Derivation 
oxide of iron. If therefore one of these sulphates is mixed with 
the latter in solution, by far the greater portion of the iron 
may be precipitated by saturating, as nearly as possible, the 
solution with potash, and the remaining portion of iron may 
be thrown down by dilution and boiling. It remains only 
to be observed that no other acid than sulphuric acid must 
be present, and that the solution nearly saturated must be 
diluted with at least twice or three times its quantity of 
water. 
This method may not only be employed with advantage in 
preparing pure oxide of cobalt, but also in analysis. When 
no error has occurred, the iron is perfectly free from cobalt, 
although the cobalt may sometimes contain a slight trace of 
iron. 
During the preparation of pure oxide of cobalt from the 
roasted ores, arsenious or arsenic acid is constantly present. 
This need not first be separated by sulphuretted hydrogen, 
for it is precipitated, on treating it in the manner above de- 
scribed, as arseniate or arsenite of iron. It is, however, better 
in this case to add to the solution previously to saturation a 
quantity of the sulphate of the peroxide of iron, as other- 
wise there might not be a sufficient quantity of iron present 
to take up the whole of the arsenious acid, and then arseniate 
or arsenite of cobalt would also be thrown down. 
XXIII. A Method of determining by mere Inspection the de- 
rivatives from two Equations of any degree. By J. J. Syl- 
vester, F.R.S. and R,A.S,, Professor of Natural Philosophy 
in University College, London,^ 
L et there be two equations, one of the nth, the other of the 
mih. degree in x ; let the coefficients of the first equation 
be an an— I an—^ a^, each power of x having a co- 
efficient attached to it, belonging to x"^ and a^ to the con- 
stant term. 
In like manner let 
hm bm^\ ^0 the coefficients of the second 
equation. 
I begin with 
A Rule for absolutely eliminating {x). 
Form out of the {a) progression of coefficients (m) lines, 
and in like manner out of the (b) progression of coefficients 
form {n) lines in the following manner : 
* Communicated by the Author. See the December and January Num- 
bers of this Magazine. 
