XVIII. On the Reflexion and Refraction of Sound. By G. Green, Esq., 



of Cuius College, Cambridge. 



[Read December 11, 1837-] 



The object of the communication which I have now the honour of 

 laying before the Society, is to present, in as simple a form as possible, 

 the laws of the reflexion and refraction of sound, and of similar pheno- 

 mena which take place at the surface of separation of any two fluid media 

 when a disturbance is propagated from one medium to the other. The 

 subject has already been considered by Poisson, {Mem. de I'Acad., &c. 

 TomeX. p. 317, &c.) The method employed by this celebrated analyst is 

 one that he has used on many occasions with great success, and which he 

 has explained very fully in several of his works, and recently in a digres- 

 sion on the Integrals of Partial Diffei-ential Equations. {Theorie de la 

 Chaleur, p. 129, &c.) In this way, the question is made to depend on 

 sextuple definite integrals. Afterwards, by supposing the initial dis- 

 turbance tp be confined to a small sphere in one of the fluids, and to 

 be everywhere the same at the same distance fi'om its centre, the formulse 

 are made to depend on double definite integrals ; from which are ulti- 

 mately deduced the laws of the propagation of the motion at great dis- 

 tances from the centre of the sphere originally disturbed. 



The chance of error in every very long analytical process, more 

 particularly when it becomes necessary to use Definite Integrals affected 

 with several signs of integration, induced me to think, that by employ- 

 ing a more simple method we should possibly be led to some useful 

 Vol. VI. Paet III. 8F 



