1075 
3. In the first approximation (velocities infinitely small of the 
first order) we have 
Ou, : 
yy nih eae MS Mee 3 ORE: Soe ru, (9) 
If the motion of the body is an oscillation of the damped harmonic 
kind, the angle of deviation of which can be represented by the 
real part of 
. PRN isd ae ass OTe eB) 
we must put 
Plate) OER 0 rep ein 8S or ese (7) 
where ¢, is now only a function of @, zand 5 LY k determined 
N 
by the differential equation 
Op,  3-p, | 09, 
emia NE Sei eer oor nt nd (= 
and by the boundary conditions, that at the surface of the body 
p‚=l and at the external boundary of the liquid (at infinity, if 
the liquid is infinite) g, — 0)*). 
4. In the second approximation one finds: 
0 
acc +yAu, HX, etc. 
Oa ot (9) 
where es) 
ASSO 7a. YS Oe ae, — 8. 
This represents the first approximation to a motion in the field 
of the centrifugal force *). Moreover: 
1) In the first approximation the distribution of pressure is the same as in 
condition of rest. 
4) k is a complex imaginary quantity; @ may be taken as real. (Comp. Comm. N°. 
1485). 
3) If the body of revolution is a sphere, ¢; becomes a function of r = Wa? + y? + 22 
orly, and equation (8) reduces to equation (11) of Comm. N°. 148d, 
4) In general this field of force has no potential; that is why it causes a movement 
of circulation in the liquid. (Comp. Comm. N°. 148d, Proc. XVII, 2, p. 1038). For 
0 
that reason it is also impossible to put in general +t = p Az, etc, as in the 
& 
distribution of the pressures under the influence of the external field of force. 
Only in the case of an infinitely long cylinder, where 9, is merely a function of », 
the field of force of the centrifugal force has a potential; a movement of circula- 
tion is absent in that case and the motions of higher order disappear at the same time, 
