﻿by Vibrations of the Air. 283 



Also 



ft'a/ r Xr X v y 



V 2 ^<ft 2 

 Hence the non-periodic part of ~- '+ 9 ,T, 2 is 



1 f ibftlfi / X 2 \ 4ttV \ 



4l XV \ + 4ttV/ XV 2 J* 



which is equal to — -j-^. Since this is a negative quantity, the 



pressure of the fluid is least where the velocity is greatest, so far 

 as it depends on the non-periodic terms. Consequently, sup- 

 posing a disk to be submitted to the action of the vibrations, 

 since the motion will be greater on the face which directly receives 

 them than on the opposite face, the disk will be apparently 

 attracted toward the source of the vibrations, as in the known 

 experiment of Clement. It is plain that bodies of other forms 

 will be attracted, if only the condition be fulfilled of the velocity 

 being greater on the side turned toward the source of the vibra- 

 tions than on the opposite side. 



Let it now be supposed that the vibrations are originally pro- 

 duced at the distance b from the centre, and that at this distance 



the velocity at any time t is expressed by yu-sin — - — . Hence, 



X 



putting b for r in the value of V, we must have 



. 2tt a! t 2irm (. X 2 \i . /2tt , . A 



To satisfy this equation independently of the time t, it is suffi- 

 cient to determine the arbitrary quantities m and c by the equa- 

 tions 



. 47r 2 m 2 A, X 2 \ 2tt ., . a 



IT. 



The second equation gives 



2ttc 2irb L , X 



-X- =7r --^- tan 2^ 



whereby c is expressed in terms of known quantities ; and from 

 the other equation 



^b 4 



m' = 



Hence the sum of the non-periodic terms, which sum may be 



