Physics. — “On the resistance of fluids and vortex motion.” By 
Prof. J. M. Burerrs. (Communicated by Prof. P. EHRENFEST.) 
(Communicated at the meeting of September 25, 1920). 
§ 1. Introduction. 
Several writers have drawn the attention to the connection between 
the vortices, generated by a body moving in a viscous fluid, and the 
resistance the body experiences during its motion.') The purpose of 
this paper is an effort to formulate this connection. The resistance | 
couple being neglected, the investigation will be confined to the 
resistance force. 
The following assumptions are made: The motion of the body 
may be an arbitrary one. However, the time since the beginning 
of the motion must be finite and the velocity must always have a 
finite value, while a change of the volume of the body be excluded. 
The fluid is incompressible; it is unlimited and at great distances 
velocity and vorticity become zero according to formulae of the form 
a a 
kim oe — 3: mw 7 ae 
' R=0 Rey? R= Rei ( 
where J >0.?) The pressure approaches a constant value, for which 
zero is taken. 
1) See among others: 
O. ReynoLps, Scientific Papers I, p. 184. 
F. Antporny, Jahrb. d. Schiffbautechn. Gesellschaft 1904, 1905, 1909. 
Tu. v. KARMAN u. H. Rupacu, Physik. Zeitschrift 18, p. 49, 1912. 
9) In connection with the eharacter of the equations for the diffusion of vorticity 
for high values of R w will probably behave according to a formula of 
R? 
the type: exp. (- rl See in connection with this: C. W. Oseen, Acta Math. 
34, p. 222, 1911.) 
In the stationary motion of Srokes — which therefore does not suffice the 
above conditions — w decreases only proportional with R—?; in the motion 
according to the formulae of OsreNn and LamB w decreases as: 
(1 + &R) 
sin O 
li 
that is exponentially for 4 #0; while for 6=0: w—=o. (See H. Lamp, Hydrodynamics 
p. 599, Cambridge 1916). 
exp |— kR (1 — cos 0) }, 
