Attractive and Repulsive Forces. 203 



vibrations of an elastic fluid agrees, to the first order of small 

 quantities, with, that which is commonly adopted. Forinstance, 

 I solve the problem of the resistance of the air to the vibrations 

 of a ball-pendulum exactly as Poisson has done. Also the re- 

 verse problem of the acceleration of a ball by vibrations of the 

 air, which is more to my present purpose, I have solved to the 

 same approximation in an analogous manner. From the solu- 

 tion of the latter problem it appears that, so far as is indicated 

 by the first approximation, setherial waves produce vibratory 

 motions of the atoms without permanent motion of translation. 

 The impression of such vibrations on the atoms of nerves of the 

 eye may be considered to be the proximate cause of the sensation 

 of light. 



39. In order, therefore, to determine whether the setherial 

 vibrations are capable of giving to atoms a permanent motion of 

 translation, which is a question of essential importance in the 

 proposed theory of the physical forces, it is necessary to proceed 

 to the second approximation. The obvious way of doing this 

 would seem to be to start from the first approximation, and then 

 make use of it, according to the usual rules, in advancing to the 

 second. But this course is liable to the objection that it does 

 not differ, except in having a^ in the place of a, from that which 

 would be proper if it were unnecessary to take account of the 

 effect of the spontaneous movements. Having, in fact, succeeded 

 in overcoming the mathematical difficulty of effecting a second 

 approximation by this means, I have ascertained that the solution 

 contains terms of indefinite increase, whence it must be con- 

 cluded that the logic of the process is somewhere at fault. The 

 failure may, I think, be accounted for as follows. In the first 

 approximation the effect of spontaneous motion is included by 

 assuming that the actual vibrations result from an unlimited 

 number of the spontaneous vibrations so combined as to neu- 

 tralize the transverse vibrations ; and this assumption is allowable 

 for a first approximation on the principle of the coexistence of 

 small motions. But this principle does not extend beyond the 

 first approximation ; and consequently, on proceeding to the 

 second, additional steps are required for including the influence 

 of the spontaneous movements. 



30. Both in this Magazine and in my work on the Mathema- 

 tical Principles of Physics, I have in various ways attempted to 

 solve to the second approximation the problem of the motion of 

 a small sphere acted upon by the vibrations of an elastic fluid. 

 But I must confess that, owing to the difficulty of including the 

 effect of the spontaneous vibrations, my efforts have been only 

 partially successful. The arguments employed for this purpose 

 in pp. 439-455 and in pp. 490-498 of the above-mentioned 



