THE EQUILIBRIUM OF ELASTIC SOLIDS. 73 



These particular cases were 



That of an elastic hollow cylinder, the exterior surface of which was fixed, while the 

 interior was turned through a small angle. The action of a transparent solid thus twisted 

 on polarized light, was calculated, and the calculation confirmed by experiment. 



The second case related to the torsion of cylindric rods, and a method was given by 



Q-Wiw 



which m may be found. The quantity E= T~^~ was found by elongating, or by bending 

 the rod used to determine TO, and p. is found by the equation, 



Em 



/* = 



9m -6E' 



The effect of pressure on the surfaces of a hollow sphere or cylinder was calculated, 

 and the result applied to the determination of the cubical compressibility of liquids and 

 solids. 



An expression was found for the curvature of an elastic plate exposed to pressure on 

 one side ; and the state of cylinders acted on by centrifugal fqrce and by heat was 

 determined. 



The principle of the superposition of compressions and pressures was applied to the case of 

 a bent beam, and a formula was given to determine E from the deflection of a beam 

 supported at both ends and loaded at the middle. 



The paper concluded with a conjecture, that as the quantity to (which expresses the 

 relation of the inequality of pressure in a solid to the doubly-refracting force produced) is 

 probably a function of m, the determination of these quantities for different substances 

 might lead to a more complete theory of double refraction, and extend our knowledge of the 

 laws of optics. 



VOL. I. 10 



