1073 
small term «a, =a, e?4* in equation (1) a term which could not, 
however, originate in the motion of the liquid (an asymmetry of the 
oscillating system was out of the question and, moreover, a, was 
independent of the nature of the liquid), but probably had to be 
ascribed to a want of symmetry in the wire‘). 
Physics. — “The viscosity of liquefied gases. VII. The torsional 
oscillatory motion of a body of revolution in a viscous liquid.” 
By J. E. VerscHarreLT. (Communication N°. 151e from the 
Physical Laboratory at Leiden). (Communicated by Prof. H. 
KAMERLINGH ONNES.) 
(Communicated in the meeting of February 24, 1917). 
1. In Comm. N°. 1485 the theory of the torsional oscillatory motion 
of a sphere in a viscous liquid was developed to a first approxim- 
ation; the results of the experimental investigation described in the 
previous part (VL, Comm. N°. 151d) render it advisable to develop the 
theory to a higher degree of approximation. The present paper is 
an attempt to a solution of the problem, not only for a sphere but 
for an arbitrary body of revolution. This attempt was in so far 
successful as a method of solution is given, in which the motion 
of the liquid and of the body is put into the form of a series; the 
terms of these series, however, centain functions of the coordinates 
which in the mean time owing to the difficulties of the integration 
remain determined by differential equations, and coefficients the 
numerical value of which cannot yet be given. In form these series 
agree with those which were found experimentally (Comm. N°. 151d). 
The motion of the liquid. 
2. We start from the well-known hydrodynamical equations ®) 
1) An asymmetry of this kind is not improbable, as the wire owing to the 
method of preparation showed a permanent twist: on the tension being taken off 
it curls up spirally and the zero changed with the weight suspended from it. 
During the oscillation of the system the wire obtains a higher twist in the one 
direction and is untwisted in the other, which might involve a small deviation 
from Hooxe’s law to be expressed by a term Na? in the equation of motion of 
the oscillating body (Comm. N°. 148), equation 23). 
2) u,v, w are the components of the velocity at a point x, y, 2; p is the pres- 
sure in the liquid, its density being « and its viscosity 4; Xo, Yo, Zo are the 
components of the external field of force, in which the liquid is placed, in our 
