208 REPORTS ON THE STATE OF SCIENCE.—1914. 
Using the transformations 
2é=r+-y 
2n=x— Ly 
we find readily 
ré 10) 8 (OK 
wes fe 2) a a le 
= 2 (9) i aon 2 
SS OTE THES: BP =— 55, 
ed Dy _ &H 
Q—P+2 2S= sa (1) Q—P—2.5 = op (2) 
ako 
Q+P=5- Sy (3) 
From (1) and (2) 
OK eH 
pe —21p — = ae Hi a ee 
Re 52 Re S72 
Apo see 
822 oy? (4) 
Now, the isoclinic lines give ¢ as a function of a, y and therefore of €, y 
for every point. 
On the other hand, it is well known that E satisfies the equation 
7) 0 
vy 
or 
SE 
82. 82 
of which the solution is 
=E, (£)+E.(y)+7E;(€)+-€H,(y) (5) 
K,, Ey, E3, and Hy, being arbitrary functions. 
(4) then gives 
een] By"(Q4- my") ] Bs") +4") () 
Putting 7=0, €=0 successively in the identity (6) 
Ey!" (€) =e 4b) 5 | B,"(0)+48,"(0) | (7) 
By" (yg) =e Cm) ‘ [ #1"0)+7B"(0) (8) 
