840 



Physics. — "77*1'' viscosity of liquefii'd (jases. I. The lotational 

 (i.scil/iitiiiiis of a sphcri' in n viscous lif/iiid." B^' Prof. J. E. 

 Vkhschaffklt. Comm. N°. 14:8/j from the Physical Laboratory 

 at Leiden. (Conumiiiicated by Prof. H. K.^mkhmngh <)nne8). 



(Communicatf-rl in the meeting of October 30, 1915). 



1. Witii a view to an inve!sti<i;ation of the viscosity of liquefied 

 gases at low teniperatures, especially in the case of hydrogen, which 

 on the invitation of Professor K\mkri,ingh Onnes I hope to under- 

 take, in conjunction with Mr. Ci). Nicaise, by the method of damped 

 rotational oscillations of a S[)here suspended in the liquids in question, 

 I shall here give the theory of the method. The problem has been 

 dealt with before by a number of writers') and the formulae which 

 embody the results of their calculations have also found application 

 ill the discussion of different experiments; still I do not consider it 

 superfluous to publish my method of dealing with the problem, 

 because in my opinion it is simpler and less involved than the one 

 followed by previous writers, while the formulae which I have 

 arrived at are much better adopted to numerical calculations. 



The sphere will be supposed to swing freely about a diameter 

 under the action of a couple of forces (the torsional moment of the 

 suspension) the moment of which J/« is proportional to the angle 

 of deflection k. In the absence of friction the sphere would perform 

 a harmonic oscillation with a time of swing given by: 



-k^L 



K being the moment of inertia of the sphere about a diameter (or 

 more correctly tlie moment of inertia of the vibrating system of 

 which the sphere forms parts), .1/ the angular moment per unit of 

 angle. If the sphere swings in a viscous liquid, the motion is damped 

 and it appears (although properly speaking an experimental confirm- 

 ation is lacking), that when the friction is not too strong the sphere 

 executes a damped harmonic vibration, according to the formida: 



1) G. J. H. Lampe, Programm des stadt. Gymn. zu Danzig, 1866. 

 G. KmcHHOFF, Vorlesungen iiber mathemalische Physiii, No. 26, 1877. 

 1g. Klemencic, Wien Ber. 11. 84, 146, 1882. 

 G. G. Stokes, Math, and Phys. Papers. Vol. V, p 207. 

 W. KoNiG, Wied. Ann. 32, 193, 1887. 

 H. Lamb. Hydrodynamics, 1906, p. 571, 599, 581. 

 G. Zemplén, Ann. d. Pliys. 19, 783, 1906; 29, 899, 1909. 



M. Brillouin. Leqons sur la viscosilé des liquides et des gaz, 1907; 1^^*^ partie 

 p. 96. 



