﻿Amplitude of just audible Aerial Waves. 365 



The very small difference between the two is of course acci- 

 dental, as the measurements of the displacement of the 

 images on which the experimental value of v was founded 

 could not be trusted to anything like 5 per cent. 



The action of a magnetic force in deflecting these rays 

 shows, assuming that the deflexion is due to the action of 

 a magnet on a moving electrified body, that the velocity of 

 the atom must be at least of the order we have found. 



Consider an atom projected parallel to the axis of the tube 

 which is situated in a uniform field of magnetic force, the 

 lines of magnetic force being at right angles to the axis 

 of the tube. Let H be the intensity of the magnetic force. 

 Then, if m is the mass of the atom, v its velocity, and p the 

 radius of curvature of its path, we have 



mv 2 • -rr 

 = i±ev, 



P 

 where e is the charge on the atom; since e/m for hydrogen is 

 10 4 , we have v =pB.xlO\ 



I cannot find any quantitative experiments on the deflexion 

 of these rays by a magnet ; but ordinary observation shows 

 that it would require a strong magnetic field to make p as 

 small as 10 centim., which would mean clearing the tube of 

 phosphorescence except within about 10 centim. of the 

 cathode. If v were 2 x 10 7 , this would give H=200, which 

 is not extravagant. 



XLI. On the Amplitude of Aerial Waves which are but just 

 Audible. By Lord Rayleigh, Sec. R.S.* 



THE problem of determining the absolute value of the 

 amplitude, or particle velocity, of a sound which is but 

 just audible to the ear, is one of considerable difficulty. In a 

 short paper published seventeen years agof I explained a 

 method by which it was easy to demonstrate a superior limit. 

 A whistle, blown under given conditions, consumes a known 

 amount of energy per second. Upon the assumption that 

 the whole of this energy is converted into sound, that the 

 sound is conveyed without loss, and that it is uniformly dis- 

 tributed over the surface of a hemisphere, it is easy to calcu- 

 late the amplitude at any distance ; and the result is neces- 

 sarily a superior limit to the actual amplitude. In the case 



* Read at the Oxford Meeting of the British Association. Communi- 

 cated by the Author. 



t Proc. Roy. Soc. vol. xxvi. p. 248 (1878). 



