1667 
of Communication 1485 which only refers to the friction of the 
liquid. For the system experiences, besides friction from the liquid 
on the sphere, also friction from the vapour on the parts not immersed 
in the liquid; finally there is the internal friction in the wire. The 
couple of the frictional forces thus consists of three parts, which are 
independent of each other, so that we may write: 
| imag Dae ae Pel BO 7 
where L,, L, and L, refer to the friction of the liquid, of the 
vapour and of the wire respectively ‘). From the total coefficient 
L found the part LZ, must thus be extracted and this is possible 
by determining separately the sum L,+ L,, namely by making the 
system with the sphere removed swing in the vapour; the determ- 
ination of d in these circumstances (therefore of d, + d,) leads to 
the knowledge of L,-+ L,, by means of the same equations 28 *). 
It must, however, be remembered, that for a given apparatus, 
swinging in a given liquid, Z is not necessarily a constant quantity : 
this coefficient still depends on 7 and on d (comp. equation (30) in 
Comm. 1484); this is certainly also the case with Z, (Z, on the 
other hand seems to be a real constant for a given wire); it follows 
that it is necessary in determining £, + ZL, to give the system the 
same time of swing, as in the determination of the total frictional 
couple ®, i.e. after removing the sphere, the swinging system must 
retain its moment of inertia‘). This may be attained by replacing 
1) It was theoretically proved that the moment of the frictional forces exerted 
da art 
— , but this is not the 
dt 
ease for the two other moments; it may however be considered as very probable, 
and the experiments are in agreement with this supposition that these components 
da aL da 
Pr an 3 SET 
(comp. ZEMPLEN, Ann. d. Phys., (4), 19, p.786, 1906; G. E. Guys, Arch. d. Ge- 
nève, 37, p. 222, 1914’. 
2) By making the system swing in vacuo Lj may be determined separately ; 
but for our experiments this knowledge is of no importance. 
3) Properly speaking the damping ought also to be the same, but that is of 
course impossible; this is, however, of less importance, as the whole damping is 
by the liquid on the sphere may be written in the form Zj 
of the total frictional couple may also be written in the form L, 
d . ; 5 
in arly case small (the ratio y= 5—, on which the influence of the damping depends, 
T 
was in our experiments less than 0.01) and with the degree of accuracy aimed 
at in our experiments the influence of a change of it on Lj Ls will not make 
itself felt. 
#) When the moments of inertia are equal in the two cases, this is also true 
for Ty, but not for 7 (in the vapour T practically coincides with 7). The small 
; 107 
Proceedings Royal Acad. Amsterdam. Vol. XVIII. 
