I ( 
i[ I I 
si 
ON THE INVERSION OF A QUADRIC SURFACE. 
For x, y, z write x—^^w, y— 2 and put for shortness 
lx + my + nz = u, l 2 + m 2 + n 2 = ol, 
al 4- hm + gn = a, (a, b, c, f, g, fitfl, m, n) 2 = A, 
hi + bm +fn = b, 
gl + fm + cn = c, 
becomes r 2 — ^ + \ ~ w 2 , 
lx + my 4- nz ,, 
(a, ...\x, y, z) 2 
Hence the equation is 
7 [ . ~ „ uw „ (7 a „ u 2 \ . auw 2 , a 2 
d r~ 2r, Y +m 
[498 
U — h -} w, 
“ cl 
(a, ...l[x, y, z) 2 - (ax + hy + cz)™ + ±A ™ 
( „ UW 2 
i a 
( i OL \ 
\ wr - 1T + 
*<P W J 
(a, ...Jx, y, z) 2 - (ax + by + cz) ~ + lA ^[ = 0 ; 
( , a u 2 
+ w ]~^n r,2 --r + (a, ...Jx, y, z) 2