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of molecular vibration, and the corresponding velocities of 

 waves will be inversely as the lengths of these axes.* 



The six ellipsoids just mentioned perform a very impor- 

 tant part in the problem of elastic solids, as they reappear in 

 the conditions at the limits, and afford a geometrical meaning 

 for many of the results. 



Mr. Haughton then determines from simple considerations 

 the equation of the Sphsero- Reciprocal-Polar of the Wave- 

 surface, or the Surface of Wave-slowness of elastic Solids, 

 which occupies a position in this subject, analogous to that 

 held by the index-surface in light. This surface, and the im- 

 portant results it leads to, are, as far as Mr. Haughton is aware, 

 given by him for the first time; it is of the sixth degree, and 

 has three sheets, and by means of it, the direction of a vibra- 

 tion passing from one medium into another may be determined. 



The paper then proceeds to the discussion of three parti- 

 cular cases of elastic solids : 1. The case where the molecules 

 are arranged symmetrically round three rectangular planes, 

 2. Round one axis. 3. The case of a homogeneous uncrys- 

 talline body. 



In the first case, the following results are deduced : The 

 traces of the surface of wave-slowness on the planes of sym- 

 metry, consist of an ellipse and a curve of the fourth degree. 

 The surface possesses four nodes in one of its principal planes, 

 where the tangent plane becomes a cone of the second degree, 

 and the existence of these points will give rise to a conical 

 refraction in acoustics, similar to what has been established in 

 physical optics. 



In general, for a given direction of wave-plane, three 



* After Mr. Haughton had obtained this construction, he found that M. 

 Cauchy has given analytically, and for a particular case, a solution which 

 involves an analogous ellipsoid ; but M. Cauchy has not follovced out the con- 

 sequences of his analysis in the right direction, and has been misled in his 

 attempt to apply his equations to the problem of light. 



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