204 Prof. Challis 07i the Hydrodynamical Theory of 



TTork involve two unknown constants Hj and H.2, for which no 

 analytical expressions are obtained^ and their values are conse- 

 quently left undetermined. On this account the theories which 

 attribute the forces of Jieat, molecular attraction, and gravity to 

 action on the atoms by pressure of the aether in vibration are 

 incomplete. Recently, however, a different course of reasoning 

 has occurred to me, which, although it does not directly meet the 

 difficulties of the second approximation, seems to give an intel- 

 ligible account of the way in which vibrations of an elastic fluid 

 are capable of producing an accelerated motion of translation of 

 a small sphere. This new process I shall now endeavour to 

 explain. 



31. Supposing at first the small sphere to be fixed, let a series 

 of plane-undulations be incident upon it in a given direction. 

 Then, if a line of abscissae [x] be drawn in that dh'ection through 

 the centre of the sphere, it is evident that the whole of the mo- 

 tion and condensation will be symmetrical with respect to this 

 line as an axis, and that the condensation [a) on the surface of 

 the sphere wdl be a function of x and t. We may therefore 

 make the general assumption that (t-=.o-J{x, t), and take a, to 

 be the condensation at the time t in the plane perpendicular to 

 the axis through the centre of the sphere, so far as it is unaf- 

 fected by the disturbance of the motion by the reaction of the 

 sphere. (I have reason from previous researches to say that 

 throughout this plane, and therefore where it cuts the surface of 

 the sphere, the condensation has that same value a^.) The un- 

 dulations are supposed to be incident in the positive direction 

 of X, 



32. Now there are three circumstances which determine the 

 distribution of condensation on the surface of the sphere : first, 

 the reaction of the sphere against the incident vibrations causes 

 a certain amount of condensation, which is so -much the smaller 

 as the sphere is smaller, and for spheres the diameters of which 

 are very small compared with X is extremely small; secondly, after 

 taking account of the condensation produced by this reaction, 

 the proper condensation of the incident undulations is not im- 

 mediately disturbed, and is therefore, ccsteris paribus, the same 

 at the surface of the sphere that it would have been at the same 

 points if the sphere had not been there ; but, thirdly, the distri- 

 bution of the condensation is modified by the circumstance that 

 the undulations are com.posed of spontaneous direct and trans- 

 verse vibrations, in consequence of which, when they are dis- 

 turbed by incidence on the sphere, lateral action is brought into 

 play. The kind of effect thence resulting may be conceived of 

 as follows. If undulations of very small breadth were incident 

 on a very large sphere, the condensations which reach the further 



