1891-92.] Prof. Tait on Sylvester’s Elimination ProUein. 131 
Not© on Dr Muir’s Solution of Sylvester’s Elimination 
Problem. By Professor Tait. 
(Read May 2, 1892.) 
The following method of treating the question occurred to me 
while Dr Muir was reading his paper at the last meeting of the 
Society. It seems to throw some new and curious light on the 
intrinsic nature of the problem. I have confined myself to an 
exceedingly brief sketch, but it is clear that the proposed mode of 
treatment opens a wide field of interesting work. 
Write the equations as 
or 
C' 
xy 
+ I- = 0 , &c., 
^AB VAB B 
+ 7^2 = 0 , &c. 
The two values of &c., are evidently reciprocals of one another. 
In fact, if we were to put 
$jr] = tan 0 .^, &c.. 
the equations might be written 
Since we have 
1 - 63 sin 26 'g = 0 , &c. 
L . E . L 
V ^ i 
1, 
while the values of the factors on the left are, respectively, t^ or 
— , or — , ^2 or — , it is obvious that the fourth equation re- 
h h ^2 
quired for the elimination is 
-r— — ~ ~ ~ “ ^2)^ ~ ^ • 
Put T = ^1^2^35 
