Ml! J. J. WALKER ON THE DIAMETERS OF A PLANE CUBIC. 181 



to the two other points in which it meets the Cotesian v ; and is thus discriminated 

 from them, when all three are real If one only is real, that of course is the COTES- 

 point. 



54. The general form given above (49), 35, for the satellite chord of the line L, 

 may be verified from the form it takes for the present one of u (65), the reciprocal of 

 which as far as the terms giving those which do not vanish in its second differential 

 coefficients for = 0, 17 = 0, = n is 



v = a a>,C- + 6a s &fi,V - 24te*, ; ... (78) 



viz., for those values of 77, , 



while the reciprocal of s ( = e 2 2 z + abxy) being now 



4<r = - 



Also 



3* 3*i , 3*jt . 



^j = 6ar, ^=66y, ^ = 6 ( Cl + c# + cz), 



9*U 



With these values of the second differential coefficients, which do not vanish, for the 

 present forms (64) (65) the satellite chord of L, or nz = 0, is n 4 multiplied by 



(2alri\ + *) ax + (2crbc 2 + *) by + (Sa z b- - 4a6 8 ) 



+ 2( - 4afee 8 + Safte 3 ) + (* + *) (ey + cp) + (* + *) (ex + c,?), 



or, identically, 



Cja: 4- 3a 2 6 2 Cjt/ + (a 2 6 2 c + Sate 8 ) z, 

 which agrees with the form in cr (68). 



