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



whence at once x", y", z" are given in terms of x'y'z' by 



x" : y" : z' 



A ... 2F ... being the coefficients of the reciprocal of s. 



Conversely, if x, y', z are to be expressed in terms of x", y", z", they are the 

 coordinates of the point common to the two conies 



3s 9w 9s 9w _ 3s 9?* 9s 9w _ 9s 9w 9s 9?* 

 3z 9y 9y dz 8x 9z dz dx 9y tte dz 9y 

 and the line 



Ix + my + nz = 0. 



46. But the point x'y'z' is more readily determined by the double line of the pencil 

 of chords through that point, having their CoTES-points on the tangent to the poloid 

 at x, y, z, which has been shown to be (54) 



- L") + 0*" - L-) = o. 



At the intersection of this and L 



3V' fflu" 9V 



'" H 2// " = U) 



gving 



x' : y * 



9V 9V , 9V 9V 9V . 9V 



or either of two other analogous sets of values. 

 47. Thus, when L is taken as z = 0, and 



u = 



of the coefficients A ... 2H of the tangential equations of the poloid s, all vanish 

 except 



40 = - 2 6 2 , 4H = 2a6e 2 ; 



