Arsenic taken without Injury. 379 
By exterminating the second term, every biquadratic may be 
reduced to the form 
x+—qgx*-+rx—S. 
This we assume equal to the product of two quadratic factors 
with indeterminate coefficients, a, 8, y, 
(x? +ax+6—y) x(x?—ar+B+y)- 
This product becomes by actual :multiplication 
_at— (a? —28) 0? + aya + B—y’: 
By equating the terms of this expression with those of the ori- 
ginal equation, we obtain three equations for ascertaining the 
indeterminates, 
a?*—28 = q 
2ay = 7 
(i ONE 
If we find these by means of a, we have Des Cartes’s solution. 
If we find them by means of 8, we have 
B+ 1 e456 + =0 
att—/9+28 x+6-+5=— =0 
Da qe eB 
bach a/q+2zP q—28 r 
Ba org a 5 aa irc 
Here we may observe that the quadratic formula for x, though 
in appearance a quadratic, is in reality and algebraically an equa- 
tion of higher dimensions. ‘This method of exhibiting the two 
quadratic factors under one form with a mere diversity of signs, 
shows the true principle of Des Cartes’s solution, which consists 
in preserving the real dimensions of the biquadratic, while it is 
reduced in form toa quadratic. The value of x expresses all 
the four roots, + being used as usual to denote that either + or 
— may be arbitrarily taken, while + — and — + denote that 
if + be used in the first case, — must be used in the second, 
and conversely. 
If we find the roots by means of y, we have 
OP, ir 1 Be gr, Tae ee) 
ely abl Tia Wil ial = 
r r2—4qy2— + 8y3 
at} — 2p 2. =0 
“Y Sy* 
= DP, 
ty 
which expresses the four roots in a very simple manner. 
ARSENIC TAKEN WITHOUT INJURY. 
The object of this communication is, to diffuse more generally 
the opinion, that charcoal is eminently an antidote to arsenic : 
from 
