200 



wave propagation ; and, like the corresponding surface in the theory 

 of light, it serves to determine the direction of the refracted waves, 

 in passing from one medium to another, as well as the laws of propa- 

 gation in the same medium. In the most general case considered by 

 the author, — namely, when the molecules of the medium are arranged 

 symmetrically round three rectangular planes, — it is shown that 

 this surface ha.s four nodes, at which the tangent plane is a cone of 

 the second degree ; and thence arises a conical refraction in Sound, 

 similar to that discovered theoretically by Sir William Hamilton 

 in the case of Light. 



That such analogies, and points of correspondence, should exist 

 between the theory of light and any general theory of vibration in 

 crystalline solids, was, of course, to be expected from the common 

 foundation and the common postulates of the two theories. Not- 

 withstanding this, however, the two theories diverge at a very early 

 point. In both, indeed, the form of the characteristic function is de- 

 duced from the assumed molecular constitution of the medium. But 

 that constitution is essentially differentin the two cases, — the funda- 

 mental molecular property of the luminiferous ether, in the theory 

 of Professor Mac Cullagh, being the unchangeableness of its den- 

 sity, while the corresponding basis of the theory of Mr. Haughton 

 is the property that the molecules of the medium act on one another 

 in the direction of the joining line.* 



In conclusion, I may observe that the value of Mr. Haughton's 

 theory — considered on its physical side, and independently of its 

 mathematical elegance — consists in its high degree of generality ; 

 which is such, as necessarily to embrace all the fundamental condi- 

 tions of the problem, and thus to leave to future mathematicians 

 the task only of limiting and interpreting his results. 



In speaking of Dr. Hincks's philological researches I must pass 

 over those which relate to Egyptian Hieroglyphics, and hasten to his 



* The theory of Mr. Haughton bears a much closer resemblance, in many 

 of its results, to the wave-theory of M. Cauchy than to that of Professor Mac 

 Cullagh, although it differs from it wholly in method. The theory of M. Cau- 

 chy is, in fact, a theory of the laws of propagated vibration in solids, and 

 is inapplicable (as was shown by Professor Mac Cullagh) to light. 



