1077 
Ponti=0, B=), Zon4i=0, €2n41=0 , Wo,=0, wan =O , Ponti 
En Anke Wy , wonin + 1)ka2"+1po,44 , Wn=2nkaryon , | (14) 
pan=2nka "na, 
From the foregoing discussion it appears, that, when a body of 
revolution in a liquid oscillates about its axis in a simple harmonic 
damped motion (how the motion is sustained, is of no account), the 
liquid will assume a motion which consists partly of a compound 
harmonie damped oscillation of liquid shells, where the amplitude 
may be represented by 
aza, ta, Ja, d...=ap get Hap, o3kt 4 a'p ekt...) . (15) 
and for the rest of a motion of circulation in meridian planes. 
The above reasoning still holds, if the motion of the oscillating 
body itself is a compound harmonie one of the form: 
a ae NT ert Lp aS emt ge ae (5) 
the functions g2,41 are, however, not then zero at the surface of 
the body, but equal to 62,41. 
The motion of the body. 
7. The question now arises: of what nature will the motion be 
which tbe body assumes in the liquid, when without friction it 
would perform a simple harmonic oscillation? Certainly not a simple 
damped motion, for, even if by some artifice the body was for some 
time made to swing exactly in the simple damped motion, which it 
must assume according to the first approximation, the higher terms 
of the liquid motion would still by friction’ give rise to forces which 
would try to disturb the simple motion and which would certainly 
create this disturbance, as soon as the body was left to itself. It is 
obvious that they would impart to the body a composite motion, 
corresponding to equation (16) where the even terms would not occur, 
seeing that the liquid motions of even order only give friction along 
the meridians and thus cannot have any influence on the oscillation’). 
1) The quantities © are functions of p, 2 and b which are exclusively determined 
by the boundary conditions. In the case, when the body is an infinitely long 
cylinder, all p's are zero, with the exception of ©). At the ‘solid boundaries of 
the liquid the p's become zero (except 9, = 1). If the liquid is partly bounded by 
a free surface, a special condition will hold there. 
2) The friction along the meridians can only produce an imperceptible deformation 
of the body. It might seem as if the circulational motion in the liquid, although 
it is kept up by the body and damped by friction in the liquid, did not occasion 
a loss of energy of the body. The explanation of this seeming contradiction may 
be found in the circumstance, that the motions of different order are not mutually 
independent and a loss of energy of even order is provided by products of 
velocities of uneven order, 
