1079 
Ee 
EUT tr 
(19) 
or 
VeeK+nklL, + M—0, 
the first of which (n= 1) is the same as equation (26) of Comm. 
N°. 1485, by which & is determined. The other equations determine 
the quantities 5. *). 
Herewith the problem is formally completely solved. Numerical 
application would, however, only be possible, if one succeeded in 
finding the functions w, and y, ?) 
Physics. — “The viscosity of liquefied gases. VU. The similarity 
~ in the oscillatory rotation of a body of revolution in a viscous 
liquid’. By J. B. Verscuarrert. (Communication N°. 151/ 
from the Physical Laboratory at Leiden). (Communicated by 
Prof. H. KAMERLINGH ONNES). 
(Communicated in the meeting of February 24, 1917). 
1. In Comm. N°. 148c -the conditions were derived under 
which similarity would exist between two different modes of motion 
of an oscillating sphere in a viscous liquid. The discussion was at 
that time entirely based on the first approximation of the problem : 
but even then it was anticipated that the conclusions would prove 
to hold in general (Comm. N°. 148c § 5), not only in nearer approxi- 
mations, but also for bodies of different shape to the sphere; this 
will now be shown to be the case. 
Returning once more to the general hydrodynamical equations 
(equation (1) of the previous communication, Comm. N°. 151e), we will 
inquire whether it is possible to introduce units of length, mass and time 
such that everything specific disappears from the equations. The 
external similarity of, the liquid motion of course requires in the 
first place similarity of the body oscillating in the liquid (the latter 
condition is of itself satisfied in the case of a sphere); let R be a 
1) In all this the supposition is retained that the moment of the torsional couple 
is proportional to the angle of torsion and that the ordinary laws of friction 
remain valid. 
2) Not till then would it be possible to settle the exact condition for infinite 
smallness of the velocities (comp. preceding communication § 1 note), i.e. the 
condition for 23 (for the body) to remain below a definite fraction of ej or, as 
would be even more useful for our purpose, thé condition for the decrement 3 
not to deviate by more than a definite amount from the limiting value 3p. 
