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