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Full text of "Scientific Papers - Vi"

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