in Fluid Media. 61 
af 
ave f 
g: s abe 
We thus perceive, that, besides the retardation caused by the loss of 
weight which the vibrating body sustains in a fluid, there is a farther re- 
tardation due to the action of the fluid itself; and this last is precisely the 
same as would be produced by augmenting the density of the body in the 
proportion just assigned, the moving force remaining unaltered. 
When the body is spherical, we have a’ = b’ =c’, and the proportion 
immediately preceding becomes very simple, for it will then only be requi- 
site to increase p, the density of the body by um or half the density of the 
fluid, in order to have the correction in question. 
The next case in point of simplicity is where a’ = c’, for then 
lee) 
feb Bhs ft allie sda uetac a2, 
a@be ath as 
° ° Vv 
If a’ > VU’, or the body, is an oblate spheroid vibrating in its equatorial 
plane, the last quantity properly depends on the circular ares, and has for 
value 
pee 7 —3 wT es y ( — u ) \ uv 
(a 6”) { F) are { tan = W@? a) —F@x=W ay 
If, on the contrary, a’ —D’, or the spheroid, is oblong, the value of the 
same integral is 
rap a ir ag a sh ice Ci u 
3 (0 — 0) 08 Fae?) | ata) 
Another very simple case is where ¢’ = b’, for then the first of the quan- 
tities (12.) becomes, if a’> DL’ 
2 9) —3 a + J(a? — 6") 2 
(a? —b*)~ * log @— (G78) & GF =O) 
and if a’ = b’, the same quantity becomes 
20207! {ae (n= pegs) —F} tapas 
