7'J THE EQUILIBRIUM OF ELASTIC SOLIDS, 



NOTE C. 



As the coefficient o>, which determines the optical effect of .pressure on a substance, 

 varies from one substance to another, and is probably a function of the linear elasticity, a 

 determination of its value in different substances might lead to some explanation of tli<- 

 action of media on light 



This paper commenced by pointing out the insufficiency of all theories of elastic solids, 

 in which the equations do not contain two 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. Piofessor 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 proportional to the sum 

 of the compressions in those axes. 



2nd. 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: 



.. 



2. 



p 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. 



