1886.] Rev. H. J. Sharpe on Motion of Compound Bodies. 31 
shall vanish when r = a ; we thus get m = 2n + 1 and the following 
series of equations : — 
a 7 r 
a , 4c 1 
<r 
+ 
7 r 
3.5 
= 0, 
4c 1 A 
I T^ = °. 
a J 
7T 
1.3 
4c 1 
a 7 
y ~ — 0 , &c. 
7 7T 5.7 ’ 
We thus get u + c 
2c j a 2 
— i - cos 0 + 7-7 
7T I r l.£ 
2 a 5 
9 
a' 
O 0 COS 30 — “T COS 50 + “7 COS 70 - &c. 
o r 3 0.5 5.7 r' 
v ■ 
2 c 
7T 
a . 
— sm 0 ■ 
r 
2 a 3 . 2 a 5 . 
' 0 , 1 ™ 30 ~ a 5?^ sln50 
It is well known that if we transform from polar to rectangular 
co-ordinates, the above equations can he expressed in the form 
u=f(x + iy) +f (x — iy), 
v = i{f(x + iy) - f\x - iy ) } , 
and when presented in this form we know that the equation of the 
stream lines is 
f{oc + iy) — fix - iy) = constant. 
Determining in the particular case considered the form of the 
function/, and then transferring back again to polar co-ordinates, 
we find for the equation of the stream lines 
A 7r r . A 2 a 2 r . nA 
0 - k - ~ sm 0 + T sm 
2 a 1 . 2.0 r * 
2 a 4 2 a 5 
- . . ■ — sin 4 0 + -Trsin 60 - &c. = constant.. 
3.4.5 r 4 5.6.7?* 
Dor the particular stream line which passes through the point B, 
the above must he satisfied by r = a, 6 =* r, and in this case the 
constant = 0, and we get equation (1), which is strictly a stream 
line, hut which may evidently be considered as a material curve 
joined to AB at B. It is evident that CE is an asymptote to this 
