304 
MR. G. T. WALKER ON REPULSION AND ROTATION 
10. In order to justify the approximation we observe :— 
(a). For ordinary values of the letters, 27rap is comparable with cm; in the case, for 
instance, of a copper shell of diameter 10 cm., and thickness -g- cm., 
and if 
a = 5, 
a = 3 X 1640 about; 
2 Trap = cm, 
then p = 160 n about, which means that the number of reversals per second is about 
55n. 
Hence, as far as we are concerned, we regard iirapcr/D^ or 87ra 2 p 2 /D 3 as of no 
degree in a. 
((3). It only remains to remark that the degree in a, a of the most important term 
of each of the coefficients N 1; Q 3 , &c, is that of their suffix 1, 3, &c. 
11. We have 
Q'i 
R'i 
Aira'pcr' a'b' 
Dd 
(tV 2 + c 2 ) 
+ 
4 : 7 ra'pcr' 
a'c 
Dd 
b ' 2 + c 2 
+ 
87 rW 2 p 2 
a'b' 
D'i 
b ’ 2 + c 2 1 
87 r 2 a' 2 p 2 
a'c -j- 
— I + cubes. 
DY b ' 2 + c 2 
I + . • 
Hence, as far as the fourth degree, in a, a', 
M, 
N x 
27 Taper 
^T 
27 rapa 
21 ab 8 ttW aa' 2 b' ^ 
O I -n / 70 7 /o 2 
D 
l L 
+ 
b 2 + c 
21 ac 
b 2 + L 
D\d 2 b ' 2 + c~ _ 
aa “c 
87 r 2 a' 2 p 2 
D\ ~ d 2 (b ' 2 + c 2 ) Y 
I 67 T s a?a'p z <r' aa n V _ 
+ I), D \d 2 V 2 + c 2 1 
167r 3 a 2 aY 3,T/ aa’ 2 c 
(viii.), 
DjD'j d 2 (b ' 2 + c 2 ) 
I 
with similar values for Q 2 and R x . 
M 3 = I . 
4:7rapa T a 2 (Jr — c 2 ) 
d 2 L (& 2 + c2 ) 2 
+ 
87 r 2 a' 2 p 2 a 2 a' 2 b' 
d P (b ' 2 + c 2 )_ 
+ 
16 ’jr s a 2 a'p'<r' a 2 a' 2 b' ^ 
B\ D 3 # (b ' 2 + c 2 ) L ’ 
with similar values for N 2 , Qo, and R 3 . 
The values of the coefficients may be determined by the same method to a further 
degree of accuracy, and since the current w is given when the H due to it is given, 
