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independent constants deduced from experiments. One of these 

 constants is common to liquids and solids, and is called the modulus 

 of cubical elasticity. The other is peculiar to solids, and is here 

 called the modulus of linear elasticity. The equations of Navier, 

 Poisson, and Lame and Clapeyron, contain only one coefficient; and 

 Professor G. G. Stokes of Cambridge, seems to have formed the first 

 theory of elastic solids which recognised the independence of cubical 

 and linear elasticity, although M. Cauchy seems to have suggested 

 a modification of the old theories, which made the ratio of linear 

 to cubical elasticity the same for all substances. Professor Stokes 

 has deduced the theory of elastic solids from that of the motion of 

 fluids, and his equations are identical with those of this paper, which 

 are deduced from the two following assumptions. 



In an element of an elastic solid, acted on by three pressures at 

 right angles to one another, as long as the compressions do not pass 

 the limits of perfect elasticity — 



1st, The sum of the pressures, in three rectangular axes, is pro- 

 portional to the sum of the compressions in those axes. 



2d, The difference of the pressures in two axes at right angles to 

 one another, is proportional to the difference of the compressions in 

 those axes. 



Or, in symbols : — 



..(p,.P,.p.)=3,(4-%ii'.4o 



fji being the modulus of cubical, and m that of linear elasticity. 



These equations are found to be very convenient for the solution 

 of problems, some of which were given in the latter part of the paper. 



These particular cases were — 



That of an elastic hollow cylinder, the exterior surface of 

 which was fixed, while the inferior 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. 



