THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOUENAL OF SCIENCE. 



[FIFTH SERIES.] 



APRIL 1877. 



XXXIII. On the Theory of an Imperfectly Homogeneous 

 Elastic Solid. By Professor C. Niven, Queen s College, 

 Cork*. 



1. npHE present paper attempts to deal with the theory of a 

 -i- solid composed of elastic material, homogeneous on a 

 large scale but not homogeneous when considered in detail. 

 It may be likened, to use Sir W. Thomson's comparison, to a 

 wall built of rubble, which appears homogeneous enough when 

 looked at from a sufficiently great distance. Inside such a 

 substance the stress across a small plane area will not be a 

 simple force, but may, under certain circumstances, consist of 

 a force and a couple. In fact the investigation was suggested 

 by the theories of the bending and twisting of wires and of 

 the bending of thin plates, in which the stress is thus specified. 

 On forming the equations which determine the small mo- 

 tions of the solid, I found that it was possible to frame a 

 mathematical illustration of the phenomenon of the circular 

 polarization of light in quartz and other substances — and that 

 if we admit that the substance transmits in every direction 

 two waves consisting of transversal vibrations, these waves 

 must necessarily be elliptic and oppositely polarized, according 

 to Professor Stokes's definition. In certain directions the 

 ellipses become circles. The results are thus far the same as 

 those obtained by Clebsch in his geometrical development of 

 Cauchy's theory; but the method of solving the equations of 

 motion is quite different, and the physical foundations of the 

 two theories have nothing in common. It is unnecessary, there- 

 * Communicated by the Author. 



Phil. Mag. S. 5. Vol. 3. No. 18. April 1877. K 



