356 Mr J. Brill, On Solutions of Differential [May 6, 
x de, (a — bP — 22 (a? +B} 
 B(a2+ a? + BP + wm? [x2 — (a? — b%)}}3 
dz, {(a’ — b*)! — a,’ (a? — b”)} 
— (B(w2 + a2 + 0)? — aa {a2 — (@ — BP 
We may now assume 
Ou _ A {a — BY -y? (a+b) 
Cy [BP (yh + at + bY — aty? {y’ — (a — 8) 
2 2\2 2 2 2 
aa Ou » {(a — bY — wv? (a? + B*)} 
On [b? (a? +0? + BY? — ax? (PIG= aE 
all along the curve «+ y=0, and then the solution may be com- 
pleted in the usual manner. 
8. As a last instance we will take for our boundaries the 
curves whose equations are 
a 2h y? = Cc’, 
and (a? a5 Op y aL ct = Dh? (2° — y’), 
where h>c. 
In the transformed problem the equations of the bounding 
curves will be 
ny =C 
and ay? + ci =h? (a + 9°), 
and we shall consequently have the three equations 
Ly, = C, 
ay? + co =h? (a7 + y,), 
TBO 
Eliminating x, from the first two of these equations, we obtain 
Y:4s —U(Y, +y,') += 0, 
where a =c*/h?, and differentiating this we deduce 
y,dy, (Ys — a") + yay, (ys — a”) = 0. 
If we now write 
Us (y, = Ys) (y,” ay ”) 
and we (CE oh) G2): 
* The choice of signs in these expressions can easily be verified by transform- 
ing the former two into the latter two with the aid of the equations z,+y,=0 and 
tg+Y3=0. 
