﻿280 Prof. Challis on Attraction caused 



translation of a small sphere by their action upon it, I add the 

 remark (note at the bottom of p. 439), " It is desirable that this 

 inference, which seems to be strictly deduced from admitted dy- 

 namical principles, should be tested experimentally by means of 

 the action of rapid vibrations of the air on a small sphere. 

 Although the effect would in this instance be very small, modern 

 experimental skill might succeed in detecting it." It was 

 therefore with no little interest that I read, in the Proceedings 

 of the Royal Society (vol. xix. No. 123, p. 35), the article by Mr. 

 Guthrie "On Approach caused by Vibration " *. The experi- 

 ments, it is true, were not made with reference to a small sphere ; 

 but they embrace a variety of substances, as a card, a tuning- 

 fork; and a mass of water, and in each case the body was drawn 

 toward the source of the vibrations. From the mathematical 

 theory of this movement which I am about to propose, it will 

 appear that a general explanation of it may be given without 

 reference to the particular form and quality of the body moved. 

 Let p be the pressure, p the density, and V the velocity, at 

 any time t, at any point xyz of a mass of fluid characterized by 

 the relation p = a % p between p and p; and let ds be the incre- 

 ment, at that point, of a line s drawn at the time t in the direc- 

 tion of the motion of the particles through which it passes. 

 Then we have the general equation 



_ «*a*dp __fdV\ 



pds \dt) 3 



\-Tr) being the complete differential coefficient of V with re- 

 spect to time, and k a constant factor which, according to the 

 hydrodynamical principles I maintain, has its origin in the laws 

 of the fluid's motion. If, however, this factor be ascribed to 

 development of heat, the subsequent reasoning will be in no way 

 affected. For the sake of brevity I shall substitute a! for ica. 

 Accordingly we have 



pds dt ds ' 



Since the fluid is supposed to be set in motion by vibratory 

 action, as that of a tuning-fork, no motion of translation is im- 

 pressed upon it, so that at every point the motion is at all times 



vibratory. Hence V, and, by consequence, -j- and I —rrds are 



periodic functions having as much positive as negative value. 



Again, since the motion is vibratory, udx + vdy + wdz is, as is 

 known, an exact differential to terms of the first order. Putting 



[* The complete paper, with a Plate, will be found in the November 

 Number of this Magazine for 1870. —Eds.] 



