1072 
series of points were found not to be perfectly symmetrical with 
respect to a straight line a = const. : the diameter of the set of two 
lines was slightly curved and approached the zero of the deflections 
asymptotically. This may be interpreted by assuming that this zero 
(a,) changes during the experiment; the shift is very small, however : 
1 mm. about on the scale in the experiments of section 3, 1° at 
the utmost in those of section 4. 
To begin with this shift was looked upon as due to an elastic 
time-effect of the wire, connected with the initial torsion given to it 
at the beginning of each experiment; but when the phenomenon was 
found to be very regular, independent of the original torsion of the 
wire, and the return to the position of equilibrium appeared to 
happen more slowly in liquids of smaller viscosity, some phenomenon 
in the liquid was thought of, the possibility being contemplated, that 
by starting the motion of the oscillating system the liquid acquired 
a one-sided rotational motion which carried the sphere along, and 
which would naturally be a damped motion, so that the sphere 
would gradually return to the position of equilibrium. A calculation 
showed, however, that an influence of that kind could not make 
itself felt during such a long time.') Moreover the change of «, was 
found always to occur in the same direction, independently of the 
direction of the initial rotation of the system. and lastly @, was the 
same function of the amplitude with all the liquids, viz. proportional 
to the square of the amplitude: ¢, = 0.04 a’, that is: the logarith- 
mie decrement of a, was twice that of «. 
The conclusion was drawn, that the shift of the zero was only 
an apparent one, and what was really observed was the effect of a 
1) The damping of this motion of the liquid can easily be calculated. The motion 
is bound to be aperiodic and may thus be represented by equation (56) of 
Comm. N°. 148d; if the sphere is practically at rest, we must have D = 0, in order 
that 4 need not be zero; hence: 
b"(R'—R) 
tg b" (R'—k) = ———— Pg 7 
ED ER (2) 
an equation which allows an infinite number of solutions for 6”, and thus for k, 
but of which only the first solution which is not zero has to be considered. In 
our case R'=3, and R=2; the solution thus becomes b’=3,2 and therefore 
—k=10—. 
u 
In the case of a hollow sphere (R’ = 0, comp. Comm. N°. 148b, § 21) equation (2) 
becomes tg b”’R=b”’R, whence b”’R=4,5 and — k= 20 ei (Comp. LAMB 
ul 
Hydrodynamics p. 577). 
