THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[THIRD SERIES.] 



JUNE 1849. 



LVIII. The Astronomer Royal on a difficulty in the Pro- 

 blem of Sound. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 A N apparent difficulty in the problem of sound has been 

 ■^■*" discussed in successive numbers of your Journal by Pro- 

 fessor Challis and Mr. Stokes. Upon this subject I beg leave 

 to lay before you a ^evf remarks. My communication will 

 consist, not of strict mathematical investigation, but of ana- 

 logies and conjectures ; and will therefore be fairly liable to 

 the charge of vagueness to which all papers of this character 

 are exposed. At the same time I must assert that I should 

 not think it proper to transmit such a paper for insertion in 

 your respectable Journal, if I were not persuaded that the 

 analogies are valid and the conjectures probable. 



Attention has been called by Professor Challis to the nature 

 of the accurate solution of the partial differential equation 

 applying to plane waves of air. And Mr. Stokes has shown 

 that a distinct meaning can be given to this solution up to a 

 certain point in the progress of the wave. 



This solution, although complete as far as it goes, is still 

 but a functional differential equation of the first order with 

 regard to the co-ordinates of a particle of air. For my present 

 purpose, it will be more convenient to take the differential 

 equation applying immediately to the co-ordinates of the par- 

 ticles ; although in that case also the complete solution cannot 

 (so far as I am aware) be obtained. 



If the original ordinate of a particle of air be w, and its 

 disturbed ordinate be ,2?+X, then the differential equation 

 applying to its motion is 



"" dx''~V^ dx) ' dt^' 

 Phil, Mag. S. 3. Vol. 34. No. 231 . June 1 849. 2 D 



