1894-95.] on ProUem of Sylvester' s in Elimination. 371 
Further Note on a Problem of Sylvester’s in Elimination. 
1. A first note on this subject, viz., the elimination of x, y, z 
from the equations 
was communicated to the Society in April 1892. By reason of my 
immediate departure for South Africa, the manuscript was not 
prepared for the press, and the paper was consequently not printed 
until this year. In the meanwhile, both Professor Tait and Lord 
McLaren had written notes on the subject, under the impression, I 
fear, that the object of my original paper was to obtain in any way 
an easy solution of the problem. 
2. The method of elimination which Professor Tait employs 
(Proc., xix. pp. 131, 132) is the so-called Method of Symmetric 
Functions. He puts the equations in the form 
solves as it were for and substitutes in the identity 
Lord M‘Laren’s method (Proc.^ xix. pp. 264, 265) is the same : but 
he solves for ^/r;, in the first and second equations, and sub- 
stitutes in the third. The eliminant is obtained as a square in both 
cases, although in the latter this is overlooked. 
By Thomas Muir, LL.D. 
(Read May 6, 1895.) 
3. If it had formed part of my plan to go outside the dialytic 
