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-Grove, 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.iii.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- 

 Jution 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 f, 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 I 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 Co/mnissance dcs Terns for 1834. 



