462 Rev. J. Challis on the Motion of a small Sphere 



fects up to this time have been obtained from locomotive en- 

 gines, in which water is heated in contact with brass tubes. 

 How far this may influence the production of electricity, fur- 

 ther experiments must determine. It is certainly somewhat cu- 

 rious to consider the splendid locomotive engines we see daily 

 in the light of enormous electrical machines; but this they un- 

 doubtedly are ; the steam is analogous to the glass plate of an 

 ordinary machine, the boiler to the rubbers ; and a conductor 

 properly exposed to the escaping steam gives out torrents of 

 electricity. I am, Gentlemen, 



Your obedient Servant, 



Bentham-Grcve, Gateshead, H. L. PATTINSON. 



November 21, 1840. 



LXV1II. On the Motion of a small Sphere vibrating in a re- 

 sisting Medium. By the. Rev. J. Challis, Plumian Pro- 

 fessor of Astronomy in the University of Cambridge*. 



IN the London and Edinburgh Philosophical Magazine for 

 September, 1833 (vol. hi. p. 186.), I have given a solution of 

 the problem of the resistance to the motion of a ball-pendulum 

 vibrating in the air, by making use of the principle of the 

 conservation of vis viva, and assuming that for slow vibra- 

 tions the motion of the air surrounding the ball is the same 

 as if the fluid were incompressible. I have given another so- 

 lution in the Cambridge Philosophical Transactions (vol. v. 

 part ii. p. 200.), by adopting the above assumption without 

 using the principle of the conservation of vis viva; and in the 

 latter solution it is not taken for granted, as in the other, that 

 the same considerations apply to fluid motion directed to or 

 from a moving centre, as to motion to or from a fixed centre. 

 The two methods lead to the same result. In 1835, M. Plana 

 published at Turin a Memoir (for a copy of which I am in- 

 debted to the kindness of the author) containing a solution 

 of the problem in question, the same in principle as that of 

 Poisson in vol. xi. of the Memoires of the Paris Academy 

 of Sciences j-, with the difference of treating separately the 

 motions in a compressible and an incompressible fluid, and 

 so obviating some objections to which Poisson's reasoning 

 appeared liable. M. Plana adverts to my communication 

 in the Philosophical Magazine, and subjoins a translation of 

 it, but is unwilling to admit the correctness of the principle 

 of the method 1 have employed, apparently for no other 

 reason than that it leads to a result differing from his own. 



* Communicated by the Author. 



f Poisson's memoir is also inserted in the Connaissance des Terns for 1834. 



