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V. — On a Classification of Elastic Media, and the Laws of Plane Waves propa- 

 gated through them. By the Rev. Samuel Haughton, Fellow and Tutor of 

 Trinity College, Dublin. 



Read January 8, 1849. 



In a Memoir on the equilibrium and motion of solid and fluid bodies, pre- 

 sented to this Academy in May, 1846, I deduced the laws of such bodies from 

 the hypothesis of attracting and repelling molecules ; since that time I have 

 been led to consider the general laws of continuous bodies, without making 

 any such restriction as to the nature of the molecular action. The present 

 paper contains the results I have arrived at in this investigation, and may, per- 

 haps, be considered interesting on account of the classification suggested as ap- 

 plicable to all elastic media. It consists of five sections ; the first contains the 

 general equations applicable to all media, and the properties of plane waves 

 transmitted through them, which are readily deduced from an extension 

 which I have given to a theorem originally stated by M. Caucht, for a parti- 

 cular case ; the second, third, and fourth sections contain respectively the laws 

 of the three groups into which elastic media may be divided ; these three groups 

 consisting of, — first, bodies whose molecular action consists of exclusively nor- 

 mal pressures ; secondly, bodies whose molecular action produces exclusively 

 tangential forces ; thirdly, bodies composed of attracting and repelling molecules. 

 The fifth section contains a comparison of the mechanical theories of light pro- 

 posed by Mr. Green and Professor Mac Cullagh, with some observations on 

 the present state of the science of physical optics. Whatever theoretic objec- 

 tions may be made to the application of the theory of elastic media to optics, 

 none such' exist as to its application to solid and fluid bodies The mathematical 



VOL. XXII. 



