137 
choose needlessly to introduce three biquadratic instead of the 
usual three quadratic radicals free from J — 1, after 2#, 
4* 0 =S*+^S+H 1 ) ; +(s+H 2 )' + ^S+H 3 ^ i , 
where S=S^ 4 -f 24 • x Q x x x 2 x z — 6hx 2 x\ and 
Hj=:12 (ofycl+ofix i) — 4=^x 0 x 2 (x 2 0 + xl) +%i% 3 (ocl+xl)^ 
-\-4: 1 yXofai ^ 3 ) -f" ( X 2 ^o) + ^]fe X \)-\~ X l{ X 0 ^ 2 )^) 
A being a three-valued, and k a six- valued function, whose square 
Jc 2 is three-valued. We can form with the coefficients of F=:0 the 
two cubics whose roots are the values of h and the values of k 2 . If 
their algebraic roots be Y l Y 2 Y 3 , and Z 2 Z 2 Z 3 , we have, for the 
root of the biquadratic 
F= (x — x 0 ) (oc — Xi)(cc — x 2 ) (x — x 3 ) = 0, 
* 0 =^+l(s+Y 1+ 4Zf|4j(s+Y 3 +4Z|y + -J(s+Y3+4Z|y. 
To transform into this shape the ordinary solution does not 
seem easy. 
It is obvious that x 0 can be represented in like manner in terms 
of x 0 #1 # 2 ‘ ' x n-i by an expression which is true when for x 0 is put 
any one of the n — 1 others. Nothing more is required for the 
algebraic solution of the general equation of the nth degree, than 
to break up the given equation U=0 of the degree ( n — 1) • (n — 2) 
••2*1 into factors of the n — 1th degree. But the inexorable 
theory of groups forbids me to hopo for this reduction of U=0, 
when n, the number of roots, exceeds four. 
Has it been before pointed out, that the problem of algebraic 
resolution of equations is merely that of elimination of imaginaries 
by involution into symmetrical functions under radical signs? 
“ On the Origin of Colour and the Theory of Light,” Part 
II., by J. Smith, M.A., Perth Academy. 
On a former occasion the Author proved experimentally 
