THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 

 OCTOBER 1849. 



XXXII. On the Views of the Astronomer Royal respecting the 

 Modificatio7i of Sounds by Distance of Propagation. By 

 the Rev. J. Challis, M.A., F.R.S., F.R.A.S., Plumian 

 Professor of Astronomy and Experimental Philosophy in the 

 University of Cambridge^. 



IN the Number of the Philosophical Magazine for last June, 

 the Astronomer Royal has stated it to be his belief that a 

 musical sound may degenerate into a hiss, abuzz, or a whisper^ 

 and possibly into a roar, by mere distance of transmission. 

 So singular and novel a theory can hardly be expected to 

 pass current without being questioned. I consider myself 

 entitled to call it in question, because a short while before it 

 was promulgated I had proved in this Magazine, by what I 

 conceive to be strict mathematical reasoning, that musical 

 sounds do not by propagation become unmusical. The views 

 of the Astronomer Royal profess to be only conjectures, being 

 neither supported by mathematical reasoning, nor borne out 

 by any experiment, and on this account they cannot well be 

 brought under discussion. They are, however, based on a 

 piece of mathematical reasoning which the Astronomer Royal 

 has adopted from Mr. Stokes, ^nd which admits of being 

 discussed. Now I am prepared to show that this piece of 

 reasoning is faulty in its logic, and that it consequently affords 

 no pretext for the conjectures of the Astronomer Royal. 



The rule of logic against which Mr. Stokes has offended 

 may be stated as follows : — When the equations applicable 

 to a proposed problem have been formed according to the 

 principles of the department of science to which the problem 

 belongs, and a solution of the equations has been obtained, it 

 is not allowable to accept the solution in part and reject it in 

 part : it is either wholly applicable or not at all. In the 

 * Communicated by the Author. 



Phil. Mag, S. 3. Vol. 35. No. 236. Oct. 1849. R 



