Mr Green on the Vibration of Pendulums. 55 
the motion of a pendulum by the action of the surrounding me- 
dium, we have insisted more particularly on the case where the 
ellipsoid moves in a right line parallel to one of its axes, and 
have thence proved, that, in order to obtain the correct time 
of a pendulum’s vibration, it will not be sufficient merely to al- 
low for the loss of weight caused by the fluid medium, but that 
it will likewise be requisite to conceive the density of the body 
augmented by a quantity proportional to the density of this 
fluid. The value of the quantity last named, when the body of 
the pendulum is an oblate spheroid, vibrating in its equatorial 
plane, has been completely determined, and, when the spheroid 
becomes a sphere, is precisely equal to half the density of the 
surrounding fluid. Hence, in this last case, we shall have the 
true time of the pendulum’s vibration, if we suppose it to move 
in vacuo, and then simply conceive its mass augmented by half 
that of an equal volume of the fluid, whilst the moving force 
with which it is actuated is diminished by the whole weight of 
the same volume of fluid. 
We will now proceed to consider a particular case of the motion of a 
non-elastic fluid over a fixed obstacle of ellipsoidal figure, and thence endea- 
your to find the correction necessary to reduce the observed length of a pen- 
dulum vibrating through exceedingly small arcs in any indefinitely extend- 
ed medium to its true length 7m vacuo, when the body of the pendulum is 
a solid ellipsoid. For this purpose, we may remark, that the equations of 
the motion of a homogeneous non-elastic fluid are 
Vie gain = 1{ aie eS ey + (2) OES EET ICT IS (.) 
2s PoP EPugh B 
on He gh Par tte seetectceeeeeetteettin (2) 
Vide Mec. Cel. Liv. iii. Ch. 8. No. 33, where ¢ is such a function of ‘the 
