988 



The oscillating system with sphere and cylinder C, had therefore 

 very nearly the same moment of inertia (and thus also the same 

 time of swing) as the system without the sphere but with cylinder Cj. ^) 



The oscillations of the system when immersed in liquid hydrogen 

 were found to be actually strongly damped (ffz= 0.1 about ): but 

 the regularity of the damping left much to be desired, so much so 

 that for a somewhat accurate calculation of rf only a few small 

 portions selected from the series of observations could be utilized. ^) 

 The most regular poi'tion obtained, which was exclusively used, 

 was as follows : the elongations «, expressed in radiants, were 

 observed to the right ( + ) and to the left alternately; in the table 

 are also given the naperian logarithms of the absolute values of 

 the elongations. 



«= + 0.05180 %« = — 2.9599 



— 4925 3.0108 

 -1- 4685 3.0607 



— 4400 3.1101 

 + 4230 3.1632 



From these results it follows that 



<f= 0.1012 dr 0.0003. 



This is, however, not yet the logarithmic decrement ö^ for infi- 

 nitely small amplitudes; in order to find it, we utilize equation c 

 of Comm. N". 151d, § 3 found for carbon disulphide, which equation 

 shows, in what manner the maximum-elongation depends upon the 



diminution of the moment of the torsional couple M with increasing load (the 

 change amounts to -00035 if per gramme); IIq (couple without load = -752+ -002). 

 From a few observations at different temperatures it appeared moreover, that 

 with rising temperature the couple M diminished by -0008 M per degree. 



1) This was the condition laid down in making cylinder C^ (comp. Comm. 149&, 

 IV, § 5); for this reason this cylinder was made of retort-coal (see note on 

 previous page), after cylinder Ci had been made before. In this case the condition, 

 laid down before, that the system with or without sphere should have about the 

 same weight, was not fulfilled; as a matter of fact it had been found, that the 

 weight of the system has but very little influence on the torsional moment, and 

 this was confirmed by the present experiments (comp. previous note). 



2) Indeed, with very small elongations no damping could be observed at all: 

 the oscillating system did not com.e to rest, but continued to oscillate to and fro 

 over a few scale divisions, sometimes more and. sometimes less. This must 

 undoubtedly be partly ascribed to not entirely avoidable convection-currents In the 

 liquid, which was found to receive radiation to a not inconsiderable degree: when 

 the apparatus was closed (as before the liquid was under constant pressure), the 

 vapour-pressure rose at the rate of about 2 cms. mercury per minute, corresponding 

 to a temperature-rise of • 1°. 



