1887.] Equations to the Motion of a number of Cylinders, de. 141 
parallel and perpendicular to Oz, y the ordinate of the centre of 
the cylinder A. | 
It is known from the theory of dipolar co-ordinates, that the 
cyclic motion is the same as would be produced by two rectilinear 
7 
A 
P 
B 
vortices of circulations « and —« situated at A and B, hence the 
value of y will be 
AE AL nen 
oT eS TD Tee 
Also, if a be the value of 7 at the surface of the cylinder A, and 
Al = 2G. 
GO COFIINC) =O GOWN Aadsscaononseqgnec (12), 
and > (xy) = «°a/z. 
Since this kind of cyclic motion could be produced by applying 
a uniform impulsive pressure xp to every point of that portion of 
AB which lies between the cylinders, we must have 39=0. Let 
(r, 0) be the co-ordinates of P referred to O, then 
K ri+ce—2rcesin@ xc . 
et ree r+te+2%rcsind | Fee ee 
whence A=0, W=-x«e/r. 
Therefore L=WF + 2xcpu — xp’a/27. 
Also if M be the mass per unit of length of either of the 
cylinders 
3 = (M+ B) (uw +0). 
