1888. | viscous rotating cylinder. 249 
By the method of Greenhill*, the fundamental equations of 
Hydrodynamics for this two dimensional motion of viscous liquid 
are easily shown to be 
OH (v4 «2 tut so (et 0) uae ( =5) gan 
oy p 
ov | dv ov a 2 O fae | 
a tolu-ay)+u(a+o)+o5 —wy=z (7 i (2) 
while the equation of continuity gives 
du dv 
ae ae ay Me aoe latideate batt ote c (3), 
V being the potential due to attraction of the liquid or other 
causes, and » the mean pressure about the point (, ¥). 
From (3) it appears that there is a function , such that 
then the equations (1), (2) become 
( -0¥') ae 2 es 
ot oy Che Boh 6) 
(2_y) 9,34 | 
ot Ox oy Cys 
Differentiating with respect to y, respectively, and adding we find 
Bi a yet 
(=, - 2") Var =0 ee Ce (7). 
3. Let us assume that w (and therefore a) « e~*, where a is 
complex. 
Transform to cylindrical (polar) coordinates, (7, @). A solution 
of (7), which does not become infinite at the origin, is 
Ae = GCE Dale to 3) Lal 078) BBS BRDOS OB BOR (8), 
provided CHD RED OP AED OR EEO SOTO (S) 
J, denoting as usual Bessel’s function of order n and A, B, being 
arbitrary constants. 
* Encyclopedia Britannica, article ‘‘ Hydromechanies,”’ 
