256 
ON THE SEXTACTIC POINTS OF A PLANE CURVE. 
[341 
71. For the first line we have 
•Sr 2 
a °-u=- 
,h, a s u=- 
and hence 
{in — 1 ) 2 
first line of did s U = 
(to — l) 2 
S- 2 
„dH, 
(in - l) 3 
((to - 2) Hd<P + <5>dH). 
72. For the second line, we have 
v (a 2 to= va 2 t7+2(v .a>a u 
= V a 2 77, since V . a = 0, and therefore (V . d) d 77 = 0 ; 
that is 
Va 2 77=V(a 2 17)= V 
to 77 
to — 1 (m — 1)- 
or writing 
this is 
whence also 
Similarly 
^(trv$ + i>VC7)-^- ï? (^V J ff+2^V^); 
77=0, V 77= H, Va = <ï>, 
TO — 1 
va 2 77= — ^F74>- ———- VJ7 
(to-1) 2 (to — l) 2 ’ 
S7d 3 U= V (d 3 U), 
mU 
= V 
^ 2 
a<F — 7——y s# , 
TO— 1 (to —l) 2 
=sfiri ( v PStI> + №) - (^-T). v № + »vaeff) : 
or putting 
77=0, V 77= 
TO — 1 
H, V^ = cp, 
and observing also that V (aF7), = VaFT + ( V. d) H is equal to VdH, that is to dWH, 
we obtain 
and then from the above value of d(Wd-U), we find 
a cva 2 T0- va 3 7/ = (- 2#a$ + m<&dH) + (-acvh) + d 1 vh) ;