FORCE OF THE WESTON NORMAL CELL IN SEMI-ABSOLUTE VOLTS. 
153 
It can be shown that 
P\ = 1 ; P' 3 = f (5 cos 2 0 —l); P' 5 = ^(21 cos 4 0—14 cos 2 0 + 1); 
P' 7 = T V (3003 cos 6 0 — 3465 cos 4 0 + 945 cos 2 0 — 35); &c. 
If we neglect temporarily the corrections due to the breadth and depth of the 
windings, it can be shown that the constants G n and cj n are given by 
27T 1ST ! 
G„ = 
and 
(a 2 + d 2 ) 
[cos AOC . P„ (cos AOC) — P„_j (cos AOC)] 
n +1 
g n = 2 xN 2 (a 2 + ci 2 ) 2 [cos BOD . P„ (cos BOD) — P n+1 (cos BOD)], 
where N 7 and N 2 are the number of turns on each of the large and small coils 
respectively, and the angles are those shown in fig. 1. It will be seen that 
d 
cos 
= and cos BOD = 
A0C = ““ “ us ^ = 
We have, by substitution in the above expressions, 
27rN 1 a 2 
G, = - 
( a 2 + d 2 ) 3/ ’’ 
ffi 
= xN 2 a 2 , 
IxNyrfc? 2 --) 
r V 4 ) 
(. a 2 +d 2 ) 7 '• ’ 
g A — 3xN 2 a 2 ^ 
Gf> = - 
6 -Nyr ( d 4 — §a 2 d 2 + 
or 
8 j 
(a 2j rd 2 Y k 
a " 
4 
g 5 = 5xN 2a 2 (^-fa 2 «5 2 + |j, 
g 7 - 7xN 2 a 2 (^—^ ^n^-sV), 
&c. 
f i _ SxNja 2 (d 6 — 1 y-a 2 d i + 1 £ L a 4 d 2 —w±ci 6 ) 
{a 2 +d 2 ) u i> 
&c., 
Substitutions of the values for a, d, a and d for this instrument showed that a = 2d 
and a. = 2S to a degree of approximation such that the term GgPgP'g could be 
neglected as well as all the terms where n> 7. 
It remains to find the corrections due to the breadth and depth of the windings. 
(A short method of calculation is given in Maxwell’s ‘ Electricity and Magnetism,’ 
3rd edition, § 700, Yol. II., p. 337). If £, > ?1 , ^ 2 , % represent the depths and breadths 
of the lai'ge and small coils respectively, it can be shown that we must multiply the 
value of G 7 recorded above by 
tf+ h+r#"‘ 2+negligible terms> 
but if a = 2d approximately, this reduces to 
C 2 
i — jw 
bU q 2 ’ 
VOL. CCXIV.-A. 
X 
