1669 
Where, in view of the upward pressure of the liquid, m’ represents 
not the true mass of the sphere, but this mass diminished by that 
of the liquid displaced. 
As it was our intention to work with different liquids, it was 
originally thought that it would be necessary to have a series of 
sets of cylinders made; it turned out that this was unnecessary, 
however, and that one set sufficed") because the rigidity of the wire 
changed only very little with the tension. This is proved by the 
following table, which gives the times of swing 7’, of the system, 
measured in air at the normal temperature and pressure, at different 
loads on the wire (i.e. different masses of the swinging system) 
and the corresponding values of the torsional moment J/. 
m le Alyy K M 
dt 104,4 + m, 12,406 3,899 201,0 51,56 
UL 250,8 + m, E45E7 7,773 400,3 51,50 
FIL 250,8 + 104,4 + im, 20,979 11,149 573,5 51,44 
IV: 327,6 + m, 20,968 11,136 572,8 51,43 
m, represents the mass of the system without sphere and cylinder 
(m, = 56,2), the corresponding moment of inertia being 27,8 *). M 
will be seen to undergo a small diminution with inereasing tension 
of the wire, about 0,0005 per gramme ®):; the modification of J/ by 
the upward pressure of the liquid (amounting to about 30 grams 
in water or liquid air) lies inside the limits of accuracy of the 
observations. *) 
1) See note 1 p. 1668. 
2) The moment of inertia was derived from the time of swing (7))v = 4,611 
of the unloaded system and the value of M at m= mg (51,63); as the moment 
of inertia has to be known in determining M, its value had to be found by successive 
approximation. 
8) Even without actually calculating M the change of M with the tension appears 
from the measurements I, II, and Ill. If M were independent of the tension the 
following relation between the various times of swing (TZy)J, (Tot. (Ty)r11 and 
(T))v would hold: 
Fur — (T.)v* = (1)? — (7) v7] — [Lu -- (4)? vj 
The deviations from this equation on the assumption of a linear relation between 
M and m lead to the value of the coefficient 0,0005. 
4) Even when the load remained the same, the torsional moment was found to 
undergo small changes; from one day to the next the time of swing showed 
small changes amounting to a few hundredths of a second, evidently through 
small modifications in the condition of the wire (mainly changes of temperature). 
A systematic investigation on this point was not carried out, as in any case 7) 
was determined separately in each experiment. 
107* 
