﻿284 Prof. Challis on Attraction caused 



considered to express the attractive action, is 



/ 1 4tt 2 6 c2 \ 



( 1+ -x^) 



4r 4 (1 + 



From this formula it follows that the attraction is greater as the 

 impressed velocity /jl is greater, and that it decreases rapidly with 

 an increase of the distance r. These inferences agree with the 

 results of the experiments. It appears also from the mathema- 

 tical theory that ceteris paribus the attraction is greater as X is 

 greater. In the description of the apparatus used in making the 

 experiments the author states that the fork made 128 complete 

 vibrations in a second ; whence I infer that the value of \ was 

 8ijr feet. The distance b at which, as measured from a centre, 

 the disturbance might be considered to be made, was very much 

 less than this ; so that the amount of attraction was little influ- 

 enced by the value of \. 



In those experiments in which a fixed card or a fixed vibrating 

 fork was placed near a moveable vibrating fork, the approach 

 of the latter was still caused by the diminution of density in 

 the intervening space due to the non-periodic part of the velo- 

 city. The explanation of the motion in these instances is analo- 

 gous to the theoretical account I have given of magnetic attrac- 

 tion in the Philosophical Magazine for January 1861 (art. 7, 

 p. 68), and in the ' Principles of Mathematics and Physics' 

 (art. (4), p. 607). 



In concluding this communication I wish to call attention to 

 the circumstance that I have employed above the integral of the 

 equation 



d 2 . r<j> _ /2 d 2 . r<f> 



in a manner inconsistent with views I have repeatedly advocated 

 in this Magazine, and more recently in pp. 251-254 of the above- 

 cited work. I have argued, on grounds that admit of no dis- 

 pute, that if the equation 



j„-f(r-a't + c) 



be true, there cannot be a solitary wave of condensation, for in 

 that case the condensation must vary inversely as the square of r; 

 or, if the solitary wave be possible, that equation cannot be true. 

 None of my mathematical contemporaries, as far as I am aware, 

 have recognized the necessity of deciding between these two 

 views, although, till this be done, Hydrodynamics is hardly en- 



