]ME. W. H. L. EUSSELL ON THE CAECTJLIIS OE SYMBOLS. 
259 
As there are some peculiarities connected with this form, I shall calculate its value at 
length for the values r=:l and r=2. 
First, let r=l. Then d d 
=£«— 'in. — 
dn — 1 
Let n=l. Then 
Consequently 
<p^pTrz=&7r^ and Hi; 
£ 
6®d7r5(w) 
•~£ * 
— 1 
^W(7r); 
d 
2w:r 1 
£ dTT 1 
■ £ 
— 1 
6{w), 
which coincides with the value of the coefficient of * obtained by the former process. 
Again, 
= 2£ ^(7r)£^^” '^d£r2£ 
g^dvr — 1 
^(tT 2w)£<^’r. 
d s^”dK—\ 
i d-K — 1 
^(tt) 
^(tt 2n) 
g dn- — 1 
d / d \ ® S ott — [ / d \ 
= £^(”->fe 2(s-'’”S^^(7r))£Y^^^^ (£-^”d. 
=£=»-'>l;2[(r‘4«(a-) 
r 
L 
-d 6{'nr 
e dn — 1 
■ L 
£ 
ed-n 
£^^” ^hn'Zz ^“dTT ^(t).— j ^(’^)| 
[_ g^dTT 1 
d d / e— 2n^ 
— * 2Cn— 1)— -/ ® 
1 / '^g’®d;_ 1 ' 
d - — 2n — 
e^TT 
e dir — 1 ^ g^dir — 1 
n£-(^)(5^<^)) 
g dir — 1 g dir — ■ 1 
+-d - 
g^dir — 1 g^dir— 1 
where Ha is a function of (t) to be determined. 
