ON THE TABULATION OF BESSEL AND OTHER FUNCTIONS. 91 
A quinquesection test can be applied here of the formulas on page 7, 
Report I., by taking 
¢ — * = 64 (sin 18°) =2 | =5/5—11, 
ct taays (“=I 5 
So.also for K=7K’ from K=K’ ; the transformation formulas would be 
7) = ag? [BEIM , Den? ACs? 
A(r,7) = A(r)7 I ee ante 
(7 ) (r) Lpasep + ace ao 
peers Dey aceas 
pet age DER] 
PBs)? | Di)? Alege) 
Leap + at Dey 
Den =o [+B 
) 
~ 
B( 
A(r)? A( 
[+ Dey By 
2 
~ 
ME(r,7) = E(r) + 3E(7). 
Ar)? AGH)? A(r)?  A(282)? 
AG) | Dor tT BED? | Det Base 
+ D(0)D(2r) Ar)? A( 
u— 1+en;K _Aen7K I+en'?K 
1—cn#K 1—en$K 1—cn!?K 
The calculation has been made at r=45, ... , so as to show the 
general shape of the curve of the elliptic function of penultimate 
character. 
Some applications of the Elliptic Function Table were mentioned in 
Report II., p. 7, including the potential of a spherical bowl, which can be 
given by c&2-+7’0’ instead of the expansion in a series of spherical har- 
monics, as in Maxwell’s ‘ Electricity and Magnetism,’ IT. §694, where it is 
denoted by P; and then 
Pr = crQ. + 070’, leading to o (Pr) = cQ, as in §695. 
