40 ON THE EFFECT OF THE IKTEENAL FBICTION OF FLUIDS
27. Let a be the radius of the cylinder ; and as before let the cylinder's motion be defined by the equation
c^'** ....................... (78);
then we have for the equations of condition which relate to the surface of the cylinder
dt „,
, whenr=a...(79).
~^ dr dt }
The general equations (75), (76), as well as the equations of condition (79), may be satisfied by taking
%i = &™H sin 6 F± (r), ^ = &'**' sin (9 ^ (r) ......... (80).
Substituting in (75), (76), and (79), we get
F:(r)+^(r)Fz(r)-m^(r) = 0 ......... (82),
JT1(a) + JT2(a) = ac, J/ (a) + F9f (a) = c ............ (83),
besides which we have the condition that the velocity shall vanish at an infinite distance.
28. The integral of (81) is
F^^ + Br ........................ (84).
The integral of (82) cannot be obtained in finite terms.
To simplify the latter equation, assume J?2 (r) = FB' (r). Substituting in (82), and integrating once, we get
(85).
It is unnecessary to add an arbitrary constant, because such a constant, if introduced, might be got rid of by writing F (r) + G