269 



this function will be, in the case supposed, homogeneous, and 

 of the second order, and will contain forty-five constants, 

 if no hypothesis be made as to the nature of the molecular 

 action. Mr. Haughton deduces from it the general laws of 

 propagation of waves, and the particular conditions at the 

 limits, which give the laws oi reflexion and refraction. If any 

 particular form be given to this function, the laws of propa- 

 gation, reflexion, and refraction will be completely deter- 

 mined; but Mr. Haughton shows that this is not the case 

 in the inverse problem, which proceeds from the laws of 

 propagation of waves to the form of the function. In this 

 case, different forms of the function, i. e. difi^erent conditions 

 of molecular action, may produce the same laws of propaga- 

 tion. No such indeterminateness attends the laws of reflex- 

 ion and refraction, and while several forms of the function may 

 give the same laws of propagation, there is but one unique 

 form of function for the laws of reflexion and refraction ; these 

 laws, therefore, give (so to speak) a more intimate and pro- 

 found knowledge of the molecular structure of bodies, than the 

 laws of propagation. If, therefore, two mechanical theories give 

 the same laws of propagation for a given body, it is impos- 

 sible to determine which is the right theory, without having 

 recourse to the laws of reflexion and refraction ; these will 

 aff"ord the true experimentum crucis for such a case, which 

 has actually occurred in the optical theories of Mr. Green and 

 Professor Mac Cullagh, and is discussed by Mr. Haughton in 

 the memoir. 



Mr. Haughton deduces the following, among other results, 

 for the propagation of plane waves. 



1. That M. Cauchy's construction, for determining the di- 

 rection of molecular vibration, holds true for the most general 

 law of molecular action. There will be three possible direc- 

 tions of vibration for the same direction of wave plane, and 

 the equations will contain thirty-six arbitrary constants, which 



x2 



