44 
ON THE RATIONALISATION OF CERTAIN ALGEBRAICAL EQUATIONS. [109 
lastly, multiply by x 2 , y 2 , z 2 , yz, zx, xy, xy 2 z 2 , yz 2 x 2 , xy 2 z 2 , reduce and eliminate the 
quantities in the outside row, 
the result is 
1 
xyz, 
x 2 y 2 z 2 , 
yz 2 , zx 2 , xy 2 , 
y 2 Z, Z 2 X, X-XJ 
a 
. 1 . 
. . 1 
b 
. . 1 
1 . . 
c 
1 . . 
. 1 . 
1 
1 . . 
1 . . 
1 
. 1 . 
. 1 . 
1 
. . 1 
. . 1 
1 
C 
, b . 
1 
a 
c 
1 
. b . 
a 
= 0; 
where, as in the case of two cubic radicals, two forms, viz. the first and third forms 
of the rational equation, are not essentially distinct, but may be derived from each 
other by interchanging lines and columns. 
And in general, whatever be the number of cubic radicals, two of the three forms 
are not essentially distinct, but may be derived from each other by interchanging lines 
and columns.