496 Invariant Theory of Conies.

Dem. — Let

\ &c.;

'i - 8 -

<7'a = S - («'.)», &c.

then, multiplying the determinants

0 1 &i a* #3 01

0 1 #! &> h 01

0 1 d c2 c3 01

0 I di d» d3 01

0 . 1 *, * *3 01

-62 -

the proposition is evident.

The foregoing proof is adapted to the case where the mutual
power is of the form 1 - £12 ; but if it should be of the form
1 -f .#12, the necessary alteration is obvious.

401. If the anharmonic angle of the conies Cm, C"nbe denoted
by mnf, it follows from the equations

cos ft,

12 = v/0 -

- a COS

that the determinant (1023) can be transformed into the follow-
ing:—

cos 11', cos 12', cos 13', cos 14', cos 15',

cos 21',

c°s 31',

cos 41', „ „

cos 51', „. „

5)
5J
J)

= 0.

(1024)