The Aether as an Elastic Solid. 149 



MacCullagh and Neumann felt that the great objection 

 to FresnePs theory of reflexion was its failure to provide for 

 the continuity of the normal component of displacement at the 

 interface between two media ; it is obvious that a discontinuity 

 in this component could not exist in any true elastic-solid 

 theory, since it would imply that the two media do not remain 

 in contact. Accordingly, they made it a fundamental con- 

 dition that all three components of the displacement must be 

 continuous at the interface, and found that the sine-law and 

 tangent-law can be reconciled with this condition only by 

 supposing that the aether- vibrations are parallel to the plane of 

 polarization : which supposition they accordingly adopted. In 

 place of the remaining three true boundary-conditions, however, 

 they used only a single equation, derived by assuming that 

 transverse incident waves give rise only to transverse reflected 

 and refracted waves, and that the conservation of energy holds 

 for these i.e. that the masses of aether put in motion, 

 multiplied by the squares of the amplitudes of vibration, are 

 the same before and after incidence. This is, of course, the 

 same device as had been used previously by Presnel; it 

 must, however, be remarked that the principle is unsound as 

 applied to an ordinary elastic solid; for in such a body the 

 refracted and reflected energy would in part be carried away 

 by longitudinal waves. 



In order to obtain the sine and tangent laws, MacCullagh 

 and Neumann found it necessary to assume that the inertia 

 of the luminiferous medium is everywhere the same, and 

 that the differences in behaviour of this medium in different 

 substances are due to differences in its elasticity. The two 

 laws may then be deduced in much the same way as in the 

 previous investigations of Fresnel and Cauchy. 



Although to insist on continuity of displacement at the 

 interface was a decided advance, the theory of MacCullagh and 

 Neumann scarcely showed as yet much superiority over the 

 quasi-mechanical theories of their predecessors. Indeed, 

 MacCullagh himself expressly disavowed any claim to regard 



