ME. W. SPOTTISW OODE ON THE SEXTACTIC POINTS OF A PLANE CTTEVE. 663 
because in the differentiations £5, . . . SI', . . are supposed constant, it follows that 
Jac. (U, Y, ] 
Again, 
12 (n 
Jac. (U, 
3 n — 7 
3(n — i 
Jac. (U, 
X, Y)=^ 
Mi d*Y 
~d x Z=u x 
w' B y Y 
a,z «/ 
i/ d 2 Y 
s 2 z 
(40) 
=^ 2 H —(%r r +43?! +Jfp')wp +(<3'u 1 +$ r, w'+€ l v')wu 
+(®p, +#/ +C?')wp+($'w 1 +?I)V +<§V)w 2 
— ((Bq 1 +fj>'+^r l )uj) +(W?L+4$V +4fW)w> 
+(li>i+43r' +#?>?> 
. . JT, . .)(**, v, w){u„ w', v')u. 
Whence 
Jac. (u, Y, Z)=^£^ Hp 2 -O Mp + (g', . . jf', . .)(««, w)(%„ w', v')u 
Jac. (m, Z, X)=^^ Hp?-1%+(ST, . . 4f', . .)(«, v , w)(«/, w> 
Jac. (m, X, Y)=^^ Hpr-Qwr +(3', . . jf', . .)(«, «, w)(®*, < w>. 
(41) 
A similar process of reduction conducts to the relation 
Jac. (X, Y, Z)=— (A, . . f, . .)(p, q, r)(p„ r', ?')X— (£', . . f : . . .)(u, v, w)(u„ w\ t/)X 
— (3, • • S, • -)(JP» A* r )(^ )Y— ($', . . JT, . .)(w, V, w)(w\ w')Y 
—(SI, . . JT, . •)(?> ^)(?',i>', )Z— (S', . . jT, . .)(«*, «, w)(+ w,)z 
= — Jac. (U, H, ^u)— Jac. (U, H, ©„). 
Whence also 
Jac. (wX, %Y, u7i)=v? Jac. (X, Y, Z)+w 2 {X Jac. (w, Y, Z)+Y Jac. (X, u, Z)+Z Jac. (X, Y, u)\ 
= -w 3 Jac.(U, H, ^ D ). 
4 y 2 
