ON THE REFLEXION AND REFRACTION OF SOUND. 



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 phenomena which take place at the surface of 

 separation of any two fluid media when a disturbance is propa- 

 gated from one medium to the other. The subject has already 

 been considered by Poisson (Mem. de VAcad., &c. Tome x. 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 digression on the Integrals of Partial Differential 

 Equations (TMorie de la Chaleur, p. 129, &c.). In this way, 

 the question is made to depend on sextuple definite integrals. 

 Afterwards, by supposing the initial disturbance to be confined 

 to a small sphere in one of the fluids, and to be everywhere 

 the same at the same distance from its centre, the formulae are 

 made to depend on double definite integrals ; from which are 

 ultimately deduced the laws of the propagation of the motion 

 at great distances from the centre of the sphere originally dis- 

 turbed. 



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 employing a more simple method we should 

 possibly be led to some useful result, which might easily be 

 overlooked in a more complicated investigation. With this 

 impression I endeavoured to ascertain how a plane wave of 

 infinite extent, accompanied by its reflected and refracted waves, 

 would be propagated in any two indefinitely extended media of 



