556 
PROFESSOR G. H. DARWIN ON ELLIPSOIDAL HARMONIC ANALYSIS. 
Note that in this table P* denotes 
{v- - 1)^^ 
2 ' i ! 
\clv 
{v~ — 1)‘, and n is 
V- — 
^ *! 
V- — 1 
If the variable is /r, and if accordingly the factor {v- — 1)^* in P/ is replaced by 
(1 — the signs of all the terms which have /3 as coefficient must be changed. 
n has still the same meaning, but must be written in the form (—C j 
l + j3 
0 \ 1 
Table of the Cosine and Sine Functions. 
1 = 0 (EEC) (10=1. 
^•=I (OEC) 
(OOC) 
(OOS) 
Ci = ffi 
€ 
;} f cos J 
1 = bin 
^ = 2 (EEC) 
(EOC) 
(EOS) 
(EEC) 
(EES) 
(^2= 1 —f/S COS 2(f) 
(jr^ 
SI 
sin 
i=S (OEC) 
(OOC) 
(OOS) 
(OEC) 
(OES) 
(OOC) 
(OOS) 
?’=4 (EEC) 
(EOC) 
(EOS) 
(EEC) 
(EOC) 
(EEC) 
(EES) 
G,=(^[l — S/3 cos 2<^] 
2(f) 
SI ' 
cos 
sin 
S(t) 
sin 
cos 
sin 
S(f). 
(^ 4 = 1 —5/3 cos 2^+y|/3' cos 4</) 
cos 
c: 
[sm 
cos .3 
sm 
|i=A/3={J+i^{r2^+{“A^. 
