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XXXII. A new Method of Investigating the Resistance of the 

 Air to an Oscillating Sphere. By the Rev. J. Challis, 

 M.A.y Plumian Professor of Astronomy arid Experimental 

 Philosophy in the University of Cambridge* . 



SHOULD have been unwilling to advert again to the 

 subject of discussion between Mr. Airy and myself, unless 

 it had appeared to me, after reading Mr. Airy's Reply in the 

 August Number (p. 143), that something may yet be said in elu- 

 cidation of this confessedly difficult question. Mr. Airy may feel 

 assured that I have no fault to find with the manner in which 

 he supports his own views, and that equally with him I am 

 persuaded of the necessity of adhering to strictly legitimate 

 principles in treating questions of this nature. By placing my 

 reasoning under another point of view, I hope to show that it 

 is not defective in this respect. 



But first I must remark, that the argument by which Mr. 

 Airy concludes that Poisson's solution is possible and mine 

 impossible, is nothing to the purpose. I was fully aware that 

 my solution would not satisfy the equation by which Mr. Airy 

 has tried it; and it was scarcely necessary to prove that an 

 integral obtained by so experienced a mathematician as Poisson 

 satisfied the equation from which it was derived. The ques- 

 tion really at issue is, whether that equation, without any li- 

 mitation annexed, is the one which the conditions of the pro- 

 blem require. The reasoning I am about to adduce will, I 

 think, prove that it is not, and at the same time will be an an- 

 swer to all that Mr. Airy has said in the latter part of his 

 Reply. 



The following general proposition will be necessary for my 

 purpose : — 



If N be a factor which makes udx-\-vdy + wdz an ex- 

 act differential, then will 



N(ud% + vdy + iv dz) = 



be the differential equation of a surface which cuts at right an- 

 gles the directions of the motion of the particles through which 

 it passes. 



The proof that follows is taken from that which Mr. Earn- 



is therefore somewhat too high, and it contains more than one volume of 

 oxygen ; thus it is clear that the atomic weight of carhon, as calculated 

 from this, is also too high. That, calculated from his specific gravity, at 

 the pressure of one- third of an atmosphere, is 75*7. He has as yet, however, 

 only made three weighings, which he considers as little more than intro- 

 ductory experiments of practice. I shall be present tomorrow at the 

 fourth determination." 

 * Communicated by the Author. 



