170 MR. J. J. WALKER ON THE DIAMETERS OF A PLANE CUBIC. 



35. The presence of the factor v in this result is accounted for by the fact that the 

 solution has been really that of the more general question : "to find the locus of the 

 CoTES-points of all chorda of u (relatively to their intersections with L) which 

 touch s " ; discarding, therefore, this factor, the equation of the tangents to u at the 

 points 



u = 0, L = Ix + my + nz = 0, 







is 



CT = v + 8PLs = (48) 



Reverting now to the form (40) of v, in which 



the equation of the three tangents to u at the points 



u = 0, Jx + my + nz = 

 is found in its standard form ; viz., 



wherein 77, are to be replaced in v and its second differential coefficients by I, m, n. 



36. It will be satisfactory to verify the general expression for the satellite chord of 

 L by applying it to the canonical form of u, for which CAYLEY has obtained the form 

 referred to in 6. 



For 



u EE OKI? -f- fty 3 + C2;3 + 6ea;ys, 



- 8(abc 



8 ' = - 4&W + 32e s (cm*l + Zm 3 /) + 48&ce%, 



, 3% 



i 8 - s = *; 



whence, 



+ 48 ^) ^ = {abc(bd* - ZcamH - 2al>nH) - S(abc + 2e 3 )oem 2 n 2 }x. . . (50) 

 Again, 



