238 Mr. Albert Griffiths : Some 



little influence. The higher the value of k, the lower is the 

 frequency for which (8) is still true. 



In the preceding it has been assumed that n>p ; it seems 

 impossible to obtain the actual value of n. In general, rapid 

 oscillations are characteristic of small dimensions ; and if the 

 oscillations were due to mechanical causes, as an hypothesis 

 I should feel inclined to take n large. The frequency of the 

 oscillations of a magnetized particle could not depend entirely, 

 however, on mechanical forces, for it would certainly depend 

 on the strength of the field and the relative position of the 

 particle with respect to the field. 



It may be noticed also that r a depends to some extent on p; 

 and it will be shown later that, if the bismuth spiral formed 

 one arm of a Wheatstone bridge, the positions of minimum 

 noise would vary slightly with different frequencies ; so that 

 unless a perfectly harmonic alternating current was employed, 

 the sound in the neighbourhood of the minimum position 

 would differ in constitution from the sound corresponding to 

 the original alternating current. 



The preceding treatment is very incomplete, a fuller 

 examination is given below. 



The adjoining figure represents 

 a Wheatstone bridge. The tele- 

 phone is placed in BD, the bismuth 

 spiral in CD. It will be assumed 

 that the increase in resistance of 

 the bismuth, when measured with 

 a telephone, is altogether apparent. 



Let Y = true resistance of the bismuth spiral. 



Let X = Y, for simplicity. 



T + P 7 Q 



Let us suppose the resistance of BD is so great that an in- 

 appreciable current goes through the telephone. 

 Let E.M.F. at A = 0. 



„ „ C = gcos^. 



Let 2 = current along C D A. 

 Let u = displacement of a bismuth particle, 



_;.:.,. ^+h^+n*„ = ^ (1) 



Let B=back E.M.F. due to motion of bismuth particles; 

 since the back E.M.F. will increase with the number of par- 

 ticles^ if we confine our attention to the same kind of wire, 



