■ 989 



time, and therefore also how the logarilhmic decrement 



rr,d log n 

 6^ — 1 — '- — chanees with tlie amplitude of the oscillations. For 



db ^ 



a =: 0.05 approximately we thus find tf= 1.052 ff^, and hence 



ff„ = 0.0962 



with an accuracy which may be taken at I'/o- ^ 



The time of swing of the oscillating system with the sphere 

 immersed in liquid hydrogen (temperature of the liquid about 20° K, 

 the temperature of the room and thus also of the wire being 8.7° C) was 



T = 40.20 =b OJO ^) 

 so that (see above) 



7'„ = 40.20—0.44 = 39.8'). 



The hydrogen was under a pressure of 76.9 cms mercury; thus 



according to the latest data about the vapour pressure of hydrogen ""j, 



the temperature of the liquid was: 20.39 + 2W = 20°.43 K. At 



that temperature the sphere (according to the data supplied in Comm. 



N°. 85) had a radius of 2.002 cms, and therefore a moment of inertia of 



/2.002A'' 

 20.26 X =20.23, so that the total moment of inertia of 



^2.005. 



the oscillating system in the experiment in liquid hydrogen was 

 ir= 3.95 4- 5.77 + 20.23 = 29.95. 

 For the moment of the couple exerted on the sphere by the 

 viscosity of the liquid we now find (by equation 28' of Comm. 

 N». I486). 



L\ — -^ — 0.1448. 

 T 



In order to determine the couple of the frictional forces on the 



not-immersed part of the oscillating system the sphere was, as 



previously, removed and cylinder C, was replaced by cylinder C^. 



1) This logarithmic decrement is considerably larger than what was expected 

 from the similarity with carbon disulphide (see above). But it should be borne 

 in mind that on account of the complicated structure of the oscillating system 

 there can only be question of similarity in a very rough sense; for as regards 

 the part which is not immersed in the liquid there is no question of similarity 

 at all. For this reason the reduction of § to <?„ is not so accurate as might have 

 been the case in the case of perfect similarity. 



2) As the decrement of the swings, this time of swing was subject to irregular 

 variations (of a few tenths of a second). 



3) This value agrees closely with that which is to be deduced from those men- 

 tioned above taking into account the changes in the temperature of sphere and 

 wire. 



4) Gomp. Comm. N». 152a. 



69 

 Proceedings Royal Acad. Amsterdam. Vol. XX 



