THE EQUILIBRIUM OF ELASTIC SOLIDS. 31 



ence between elastic solids and fluids. Both tend to recover their volume, but 

 fluids do not tend to recover their shape. 



Now, since there are in nature bodies which are in every intermediate state 

 from perfect solidity to perfect liquidity, these two elastic powers cannot exist 

 in every body in the same proportion, and therefore all theories which assign to 

 them an invariable ratio must be erroneous. 



I have therefore substituted for the assumption of Navier the following 

 axioms as the results of experiments. 



If three pressures in three rectangular axes be applied at a point in an 

 elastic solid, 



1. The sum of the three pressures is proportional to the sum of the com- 

 pressions which they produce. 



2. The difference between two of the pressures is proportional to the differ- 

 ence of the compressions which they produce. 



The equations deduced from these axioms contain two coefficients, and differ 

 from those of Navier only in not assuming any invariable ratio between the 

 cubical and linear elasticity. They are the same as those obtained by Professor 

 Stokes from his equations of fluid motion, and they agree with all the laws of 

 elasticity which have been deduced from experiments. 



In this paper 2 )ressures are expressed by the number of units of weight to 

 the unit of surface ; if in English measure, in pounds to the square inch, or 

 in atmospheres of 15 pounds to the square inch. 



Compression is the proportional change of any dimension of the solid caused 

 by pressure, and is expressed by the quotient of the change of dimension divided 

 by the dimension compressed "*. 



Pressure will be understood to include tension, and compression dilatation ; 

 pressure and compression being reckoned positive. 



Elasticity is the force which opposes pressure, and the equations of elasticity 

 are those which express the relation of pressure to compression f. 



Of those who have treated of elastic solids, some have confined themselves 

 to the investigation of the laws of the bending and twisting of rods, without 



* The laws of pressure and compression may be found in the Memoir of Lam<j and Clapeyrou. See 

 note A. 



t See note B. 



