ME. W. SPOTTIS WOODE ON THE SEXTACTIC POINTS OF A PLANE CUEVE. 665 
In this the coefficient of — p 
=±{d„X Zb,Y-Yd,Z u +B,Y X^Z-Z^X u +d„Z Y^X-X^Y u) 
^X Z^Y-Y^Z v d,Y Xd,Z-Zd,X v ~b y Z Y^X-Xd.Y v 
d,X Zb.Y—Y'dJZ w b,Y X^Z-Z^X w ~d z Z Yd*X-X^Y w 
=±{p'b x K+qd ie Y+rd x Z P u +ud x K+v'b x Y+w'd;Z P, u}= P, P u 
pbyK+qbyY +rd y Z Q v ub y X-\-vb^-\-wb y Z Q, v Q t Q v 
jpd z X-j-^d z Y-j-rd z Z R w ub^X-\-vb z Y -\-wb z Z R, w R, R w. 
Now 
« «. P, = ^ I {2(»P,+SQ,+4rE l )-y( 1 gP,+jrQ,+CE 1 )} 
v w' Q, 
w t/ R, 
« »' P.=^{*(@P,+4fQ,+CE 1 )- z (aP,+®Q,+®R,)} 
V v , Q, 
w v! R, 
« »' P. = ~ i{y(aP,+®Q 1 +©R 1 )-*(®P I +33Q 1 +J r K,)} 
w id Q, 
w ro, R, ; 
so that multiplying these equations by X, Y, Z respectively, and adding, 
» P P, =^ T {(aP,+BQ, + ©E,)(yZ- 2 Y) 
» QQi +(lP 1 +SQ,+J r E 1 )(zX-xZ) 
w R R, +(eP,+^Q,+CK,X«Y-yX)} 
= 3 t x 2> H { a»+®» + ®ro)P, + ( J) « +33» + Jfw)Q, + ( i6k+ jfo + C»)E, } 
= f^ H ’f p -*+9'?+ E -*) 
= ~ vi ( i"r ^ (Xp+Yg+Zr) 
( 45 ) 
= 0 . 
