^ + e -- = ~T' 
100 
[733 
733. 
ON A FORMULA OF ELIMINATION. 
[From the Proceedings of the London Mathematical Society, vol. XI. (1880), pp. 139—141. 
Read June 10, 1880.] 
Consider the equations 
{a, If =0, 
i) m = o, 
where a, ..., A, ... are functions of coordinates. To fix the ideas, suppose that each 
of these coefficients is a linear function of the four coordinates x, y, z, w. Then, 
eliminating 6, we obtain V = 0, the equation of a surface; and (as is known) this 
surface has a nodal curve. 
It is easy to obtain the equations of the nodal curve in the case where one of 
the equations, say the second, is a quadric: the process is substantially the same 
whatever may be the order of the other equation, and I take it to be a cubic; 
the two equations therefore are 
(a, h, c, d\6, 1 ) 3 = 0, 
(A, B, Cp, l) 2 = 0; 
giving rise to an equation 
V, ={a, h, c, d) 2 (A, B, Gf, =0. 
And it is required to perform the elimination so as to put in evidence the nodal 
line of this surface. 
Take dj, do the roots of the second equation, or write 
(A, b, c\e, 1 ) 2 =a (0-00(0-02); 
that is,