1882.] W. Spottiswoode. Geometrical Theorems. 37 



I D«(rfir), DV, D 5 j, D»( :C y) ! 

 + U M D6(^), DV, D 6 !/. r> 6 0'!/) [' 



In the same way Z>, c, d, e are determined, and then /*, i/, p, a are 

 known from the third, second, first, and original equations. 



(6.) In the same way we may proceed to find the 14-pointic contact 

 of a curve of the fourth order. The coefficients will be expressed by 

 series of determinants, each having eight rows and eight columns, 

 divided by a determinant having nine rows and nine columns. And 

 the same method will apply to the general case. 



II. " Note on Mr. Russell's paper ' On certain Geometrical 

 Theorems. No. 2."' By William Spottiswoode, Pres. 

 R.S. Received May 25, 1882. 



If we apply Mr. Russell's formulae to the determination of the sex- 

 tactic points of a curve, we shall have, in addition to the equations 

 (1)— (5), the following — 



*DV + /3D- 5 (^)=Dy>; 



and by elimination of % and (3 from his equations (4) and (5), together 

 with this latter, we shall obtain as the condition for a sextactic point — 



J>% Wzy, Dy=0 <A). 



D% D*zy, BY, 



But Dxy = y + xDy, 



TPxy=ZDy +xB*y, 

 ~D 5 xy = 3Wy +zD s y, 



Dh:y=$T) i y +xD$y, 



T>if = 2yT)y, 



Dy =2^4- 2(D y y, 



Dy=2yD«y+ 6DyD 2 y, 



BY =2yB*y+ 8DyT>hj+ 6(D^) 2 , 



Dy =2z/D 5 j/ + 10D2/D 4 y + 20D 2 ?/D 3 ?/, 



