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XLIX. Elastic Solid JEther, with two Moduli, satisfying 

 MacCullagh's Crystalline Optical Conditions. By Prof. 

 Alex. McAulay, 21. A., University of Tasmania*. 



1. Description of the solid. 



THREE states of the medium require naming for our 

 purposes. (1) The zero state ; this is a state (not of 

 equilibrium) necessary for descriptive purposes. (2) The 

 intrinsically strained state ; this is a state of stable equi- 

 librium. (3) The actual disturbed state ; this is a state 

 which is obtained from the intrinsically strained state by 

 displacements small compared with those which produce the 

 intrinsically strained state from the zero state. 

 Let an elastic solid of density 



D=10 G gm. per cub. cm (1) 



till space. Let its potential energy per unit volume consist 

 of two terms, a cubic rotational term and a hydrostatic 

 quadratic term. 



The cubic rotational term is 



— efgx(l=— efg x 1*8 X 10 :]s ergs per cub. cm. . (2) 



where <?, /, g are the small fractions expressing the principal 

 elongations necessary to pass from the zero to the actual 

 disturbed state. 



It will be shown below that so long as we retain only the 

 terms of lowest order in the stress, the cubic rotational stress 

 is zero when the curl is zero, so that there is from the cubic 

 term no elastic resistance to irrotational strain. 



Let the medium be irrotationally intrinsically strained 

 from the zero state according to the following specification. 

 First impose everywhere and in all directions a uniform 

 elongation of linear value 



*.=/„=<*,= 10- 11 , (3) 



and call the state of the medium obtained free cether. 

 Secondly, throughout certain volumes, to be called crystals, 

 change the elongations from e to values *i,/i, <ft, given for 

 three mutually perpendicular directions, the principal direc- 

 tions of the crystal; e^f\, g 1 are each less than e in the ratios 

 of the squares of the corresponding velocities of light to the 

 square of the velocity in free aether. Due to the difference 



* Communicated by the Author. Read before the Australasian 

 Association for the Advancement of Science, at the meeting at Brisbane, 

 January 1909. 



