478 The Rev. George Salmon on the Degree of the 



Substituting these values in the equations (A) and (D), we obtain the follow- 

 ing system of equations, remembering that n' — 2 = (71 — 2) (n' + 1), we have 



n(?i-l) (ra-2) {n'+l) = 3n{n-2)+n{n-2) {71' - n' + n - 12) 



+ 8n(n-2), 



n (71-1) {71 -2) ^'-'^' + "-^^ („_ 2) (n' + 1) = 71 {71 -2) (n' - n^ + n - 12) 



+ in{n-2) (1171-24:) + 12n (71-2) (n-3) (71' + 37i - 16) + 3t' , 



i)i(7i-l) (n-2Y (m2+1) = 8w(w- 2) + 871(71-2) (llw-24) " 



+ 4n(n-2) («-3) (w'+3n- 16), 



n(7i-l) (n-2) (n-+l) (71^-211^ +71-?,) =71 (71 -2) (n^-9) 



+ n-(?i-l)^ (71-2) (n^-7i'' + 7i-12)-\-12n^(7i-iy (7i-2) 



- 4w (71 - 2) (7f - 71- + 71- 12) - 36n (w - 2), 



n(n-l) (n-2)^^^ ?^ (m - 2) (?r-+l) (7i'-27i' + n-3) 



= ik' + ire- (71 -1)' (71-2) (71' -n^ + 7i-12) 



+ 67i^n-iy (71-2)- (71' -n- + 7i-12)-187i(7^ -2) (1171-24) 



-24n(7i-2)(7i-8) (?i' + 3re-16) 



-2?i(n-2) (71' -71- + 71-12), 



47l(n-l)(7l-2)'(7l''+l)(7l'-27l' + 7l-3) 



= S7i(n-2) (16n*-64n'+80?2'-108w+156), 



+ i7i'(7i-l)- (7i-2) + 4n'(7i-l)' (n-2y (n'-?i- + ?i- 12) 



-12re(n-2) (llw-24), 



-16w(?i-2) (n-3) (n' + 3n-l(3)-12n(7i-2). 



On examining these equations it will be found that four of them are satis- 

 fied identically, while the remaining two give the values, 



Qt' =n(n-2) (w'-4re''+7re'-45?zH114re^-lllw= 4-54871- 960) 



8k' = n(7i - 2) (71'" - 67*^ + l&n" - 54n' + 1647i«-288re=-l-547?i*- 1058?i' 



+ 106872^- 121471+1464). 



It would be desh-able to test these results by obtaining the number of triple 

 tangent planes to a surface of the ?i"' degree by a different process. I have 

 endeavoured to determine this number by the same method by which we deter- 



