662 ME. W. SPOTTISWOODE ON THE SEXTACTIC POINTS OF A PLANE CUEVE. 
=Hjp ff 
3^ 7 
= — Op — (0/ + + <&p’)up — H pq — Qpv + $t>d,0 D + %| 
— (<%' + Jfjp' + Cr, )vp — 0fyr' +36#, +$p')uq 
\ud y "ty v 
+ (W +ffq l +€/ )wp 
—(<3r' +fq x +Cy )ur 
-(W +33$'i +tfp')uq 
+ (9'Mj +^'w'+(B'v')uv 
+ (#i>i +4^ +C^ )w 
+(fe+^' +4^ >2 
+ (3^'te, +2SV + fv'y 
+ (&u t +4fV +CV)w 
Hence • 
-(<gr' +#^+Cp>r 
+(9^ 
+{W + 
+(#/ +4f2i+Cp')wp 
+($P1 
+(?%L+23/ +4^')^ 
+(%i+ JV +C£')n> 
Jac. («, Y, Z)=%^Hp ! -(Q i )-ia,© u ) M 
Jac. («, Z, X)=i£=f> Hp ? -(Qp-i3.,0 o >+J«9^„-i M 9,^ u 
Jac. (w, X, Y)= 4 ^’ i _ 1 2) Hpi — (Qp — ja,0„)w+iw3 t 'I , n — 
4 (72 — 2) 
Jac. («, Y, H#p— (Gj— J9 y 0u)«+^B,^u— 
Jac.(t>, Z,X)=i^Hf-(O 2 -i3,0„)» l . (39) 
Jac. (v, X, Y )=~~ H(?r— (O^— 
4 ( n ~ 2 ) 1 
Jac. (tv, Y, Z)=-^ rr ; Hrp-(Qr-p z 0 u >+i^^ u -i w ^ u 
Jac. (w, Z, X)=^rHi- 2 -(Q,— p,0„)*+i«3,^„-iw3,^ o 
Jac. (w, X , Y)=^|^Hr ! -(Qr-|a,0,)w. 
Again, 
•r Jac. 0, Y, Z)+?/ Jac. (v, Y, Z)+z Jac. (w, Y, Z)=(»— 1) Jac. (U, Y, 7) ; 
whence, bearing in mind that 
^»+?3,^u+*3.^o=2(3»- 7)¥„, 
^*0 o +y3»0 tI +23,©„=2(K-l)0 u , 
