On the Hall Effect in Liquid and Solid Mercury. 109 



In one complete period t, nVt//na undergoes the increment 

 2tt. The exponential factor giving the decrement in one 

 period is thus 



0-2ir(39)M ....... (41) 



(42) 



or with regard to the smallness of (39) 



■np sinh /3 



This is the factor by which the amplitude is reduced after 

 each complete period. 



In the case of ordinary gases p/cr = p?. As an example, 

 take p, = cosh/3 = 1/3 ; then (42) gives 



1--581W- 1 «-•»*« (43) 



When n rises beyond 10, the damping according to (43) 

 becomes small ; and when n is at all large, the vibrations 

 have very great persistence. 



In the derivation of (42) we have spoken of stationary 

 vibrations. But the damping is, of course, the same for 

 vibrations which progress round the circumference, since 

 these may be regarded as compounded of two sets of 

 stationary vibrations which differ in phase by 90°. 



Calculation thus confirms the expectation that the whis- 

 pering gallery effect does not require a perfectly reflecting 

 wall, but that the main features are reproduced in trans- 

 parent media, provided that the velocity of waves is 

 moderately larger outside than inside the surface of transition. 

 And further, the less the curvature of this surface, the 

 smaller is the refractive index (greater than unity) which 

 suffices. 



X. Note on the Hall Effect in Liquid and Solid Mercury. 

 By W. N. Fenninger *. 



ALTHOUGH Bagard f and others have announced that 

 they observed a Hall effect in certain liquid electro- 

 lytes, negative results obtained by other experimenters have 

 been strongly supported by the theoretical work of Donnan J, 

 which appears to show conclusively that the effect must be 

 far too small to be detected by such apparatus as these 

 experimenters used. As to liquid metals, Amerio § has 



* Communicated by Prof. S. J. Barnett. 



t C. II. cxxii. p. 77 (1896) ; J. de Phys. (3) v. p. 499 (1896). 



X Phil. Mag. xlvi. p. 465 (1898). 



§ N. Cimento (5) i. p. 342 (1901). 



