668 MR, W. SPOTTISWOODE ON THE SEXTACTIC POINTS OE A PLANE CURVE. 
Similarly, it will be found that the coefficients of 
(^X— A#P+2Hb r X) 
(pY — AyP + 2HB ,Y) 
(pZ -AsP+2Hb,Z) 
are 
-(w-2)(3HK+5P>, 
-(w-2)(3HK+5P>, 
_( w _2)(3HK+5P> 
respectively ; and consequently the whole expression 
= — (w — 2)(3HK-f-5P 2 ) { (^>X— A#P -f 2Hb^X)% 
+Q>Y-AyP+2Hd # Y)t> 
+(_pZ - As P + 2Hd,Z )w + ^ 2 HP } 
= -(?*— 2)(3HK + 5P 2 ){—2HP—2(a. .)(«, % w)(b,P, b y P, B,P)-f-«r a HP} 
= _(„_2)(3HK+5P){-2-^=S+- ! }HP. 
2) 
But ro- 2 =l-f- — * so that a bove expression 
=(rc-2)(3HK + P 2 )HP. 
Now 
-(w-2)(3HK+P 2 )=w 
u 
p 
a,p b y p 
v w n\J 
w' v' (n—l)(u—u) 
q r , ‘6{n— 2)H 
5(w— 2)P. 
u w xu -\-yv -\-zw 
w' v' xu t -\-yvo' -\-zv' 
p q r xp -\-yq -\-zr 
b,P B y P BJP a?a.P+yB r P+*a,P 
= — (n — 1 )u u p b^P 
v q d y P 
w r d,P : 
—u 
u 
i-l> 
• ( 48 ) 
so that the whole expression is divisible by u. Similarly, it might be shown that M, 
or M' is divisible by v, and N or N' by w. 
It follows from what has gone before that %, are all divisible by 
H, that %, are divisible by u, iPT by v, by w, and consequently dividing 
