1668 
the sphere by a different mass. In this the shape of the part 
swinging in the vapour must not be changed; for this reason we 
have added a free mass to the swinging system which could be 
replaced by a different one of exactly the same shape, but made of 
a denser substance. As such we have used hollow cylinders (S in 
the figure) one of aluminium (density u, = 2.72), the other of brass 
(density u,=—=8.45). The difference of the moments of inertia A, 
and A, of these cylinders had to be equal to that of the sphere 
(K), so that, when FR, and A; represent the external and internal 
radii of the two cylinders and 4 their height, the following equation 
had to be satisfied: 
etl (ie hig WAE EE Ve DE PE 
The constants for the aluminium eylinder were in C.G.S. units 
R, = 1,744 , Ri=0,525 , h — 4,42 , m, = 104,4 , K, = 173,2, 
for the brass cylinder 
Nh, eh; 0 Ok a a me "321,02, Ke 104, OF 
In order that with the exchange of the cylinders besides the 
internal friction of the wire also particularly the frictional couple 
M should remain the same, as a change of it would also have 
brought about a change of the time of swing, it was necessary to 
arrange that with the removal of the sphere the tension of the 
wire should remain unaltered, so that the difference of the masses 
m, and m, had to be equal to the mass of the sphere *). A further 
condition had therefore to be satisfied in designing the cylinders, 
namely 
x (RR?) h (u, —u,) =m, 
error resulting from this does not come into account, however, as the difference 
A Al 
between 7’ and 7, is very small in our experiments (J = Si is smaller than 
0 
0.01). Moreover it is here only a question of the determination of a correction; 
it is true that the correction was found to be considerable (qh, about of the total 
amount), but the desired accuracy could still be secured. 
1) When the sphere is at a low temperature Re and thus also Ks become 
smaller; properly speaking the difference of the moments of inertia ought therefore 
to have been taken a little smaller, but again, in view of the degree of accuracy 
aimed at, the equation need not be satisfied with minute exactness and thus in 
the construction the cylinders the variability of Ks could be disregarded. 
*) Zempten (l.c) also used interchangeable cylinders for the same purpose. 
at the same time he only made the tension of the wire equal in the two cases: 
the moment of inertia of the vibrating system changed. Consequently he measured 
the moment of the retarding frictional forces with a time of swing which differed 
from that at which the whole moment was measured, and in these circumstances 
it was not allowable to take the moment in question equal to the difference of 
the two measured ones. 
