445] A MEMOIR ON QUARTIC SURFACES. 181 
difficult to actually develope the equation ; in fact, starting from the term w 8 [(a, b, c) 2 ] the 
other terms are obtained therefrom by changing a, b, c into a,+~(hy—gz), b+^(—hx+fz), 
c + — (gx —fy) respectively; the equation may therefore be written in the symbolic form 
w 8 . exp. i {(hy - gz) 8 a + (- hx +fz) 8 b + (gx -fy) S c } . [(a, b, c) 2 ] = 0. 
or, what is the same thing, 
w 8 . exp. ^ {x (g8 c - h8 b ) + y (h8 a ~/8 c ) + z (f8 b - g8 a )}. [(a, b, c) 2 ] = 0, 
where exp. 6 (read exponential) denotes e d , and [(a, b, c) 2 ] represents a determinant as 
above explained. The equation contains, it is clear, the four terms 
& [(«, - K 9f\ + V s [(- K b, -ff\ + ^ [(- g, f c) 2 ] + w 8 [(a, b, c) 2 ]. 
I am not sure whether this surface of the eighth order has been anywhere considered.