ns 
ON PHOTOGRAPHING THE SOLAR CORONA. 351 
the strongly marked details could be made out on his drawings, a rift 
near the north pole being especially noticeable ; this was in a photograph 
taken on April 3, in which the detail of the northern hemisphere is best 
shown, while the detail of our southern hemisphere most resembles the 
photograph taken on June 6; in fact, our negatives seem to hold an inter- 
mediate position. Afterwards I went with Dr. Huggins and Mr. Woods 
to Burlington House to see the negatives. The outline and distribution 
of light in the inner corona of April 3 is very similar to that on our plate 
which had the shortest exposure; the outer corona is, however, I think, 
hidden by atmospheric glare. As a result of the comparison I should say 
that Dr. Huggins’s coronas are certainly genuine as far as 8! from the 
limb.’ 
On Lamé’s Differential Equation. 
By Professor F. Linpremann, D.Ph. . 
[A communication ordered by the General Committee to be printed in eatenso 
among the Reports. ] 
Ir is known that the integration of Lamé’s equation 
d*y 
dz? 
42(1—2) (1—I?z)— + 2[322? -22(1 422) + 1)! =[n(n+ 1)R2+hly 
has been perfectly settled by Mr. Fuchs and Mr. Hermite for the parti- 
cular case in which 7 is a whole number. In all the other cases one can 
only give the solutions by development in series, each of which is con- 
vergent within a circle, whose centre is to be found in a critical point of 
the above equation (viz., in one of the points z=0, z=1, z=k~*, z=00), 
and whose circumference passes through the next critical point; it remains 
then to establish the relations between the different developments so 
obtained; e.g., one has in the neighbourhood of the point z=0, two 
integrals of the form 
YymCoteysteowe+ .... 
Yo=A[bo t+ byztbor+ ....], 
and at the point z=1, one has the developments 
Y3=Cy' +¢,'(1—z) +e, (l1—z)?4+ 2... 
y= (1—2)![Bo! +B)\(1—2) +by'(1—2)2+ «J 
The difficulty which has to be got over is to determine the constants 
A, B, D, E in such a manner that the equations 
yi, =Ay3+ By,, yo=Dy3+Ey, 
may be satisfied. . 
Supposing now that 2n is a whole number, this problem can be re- 
solved in a remarkably simple way by the same method which I have 
lately applied! to the differential equation of the functions of the elliptic 
cylinder (i.e.,s=0). Finally, I have arrived thus at the following result. 
} Mathematische Annalen, vol. xxii. p. 117. 
