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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 Sphero-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 faras 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. 
~Canchy has given analytically, and for a particular case, a solution which 
involves an analogous ellipsoid ; but M. Cauchy has not followed 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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