1914] UNDER CAPILLARY FORCE 265
— -2 T^i = — Vi cos ^ + 4r2 cos 26 4- 9r3 cos 301 ,
asinfl Idr _ r, rz (r, rg 8r,|
+ rcos6>rd0~ 2n 2a [4a r0 4aJ
0 0 0 4sa)
Thus altogether for the coefficient of cos 6 on the right of (29) we get
r0 ...... +'
This will be made to vanish if we take &> such that
&>2a2r0 _ 3r02 r-i 3r2 T ~~ 4a?~ 2a 2r/
The coefficient of cos 20 is
3ar,
2r0 2>0 2T [a, + a "' 2a2j '
or when we introduce the value of o> from (31)
...........................(32)
3ara 3r0 2r8
r02 4*0. r0 The coeiSicient of cos 30 is in like manner
8ars r02 i\
These coefficients are annulled and ap^T is rendered constant so far as the second order of r0/a inclusive, when we take r4, r5, &c. equal to zero and
ra/r0 = r0»/4a«, r8/r0 = - 3ros/64a8 ................ (34)
We may also suppose that rx = 0.
The solution of the problem is accordingly that
_ Jl , '0 t)f\ "' 0 'J/JL ^li\
V ^
gives the figure of equilibrium, provided o> be such that
T
The form of a thin ring of equilibrium is thus determined ; but it seems probable that the equilibrium would be unstable for disturbances involving a departure from symmetry round the axis of revolution.s as before (fig. 3). Now