EXTRACT FROM A LETTER TO MR. C. W. MERRIFIELD.
[From the Messenger of Mathematics, vol. I. (1872), pp. 87, 88.]
The general integral of the equations
a /3 7
/3 7 $ ’
, . d 3 z d 3 z
where a, p, 7, 0=^,
Ty’ oan ' 1 th!uk - be found - viz - s ives
r = function s, and - = ^ gives s = function t. But r = function s, is integrated as the
equation of a developable surface (p instead of z), viz. we have
a and g functions of h, and
ax 4- liy + g)
0 = a'x + y + g') ’
a =
da
dh'
J dll) ’
similarly, s = function t, gives
q = hx + by +f,
0 = x + b'y +f,
Observe that the constants have been so taken, that ~ = h, ^ = h; but in order that h
may, in the two pairs of equations, mean the same function of (x, y), we must have