[From the Transactions of the Royal Society of Edinburgh, Vol. XX. Part I.] 



III. On the Equilibrium of Elastic Solids. 



THERE are few parts of mechanics in which theory has differed more from 

 experiment than in the theory of elastic solids. 



Mathematicians, setting out from very plausible assumptions with respect to 

 the constitution of bodies, and the laws of molecular action, came to conclusions 

 which were shewn to be erroneous by the observations of experimental philoso- 

 phers. The experiments of (Ersted proved to be at variance with the mathe- 

 matical theories of Navier, Poisson, and Lame and Clapeyron, and apparently 

 deprived this practically important branch of mechanics of all assistance from 

 mathematics. 



The assumption on which these theories were founded may be stated thus : 



Solid bodies are composed of distinct molecules, which are kept at a certain 

 i/'.ttance from each other by the opposing principles of attraction and heat. When 

 the distance between two molecules is changed, they act on each other with a force 

 whose direction is in the line joining the centres of the molecules, and whose 

 magnitude is equal to the change of distance multiplied into a function of the 

 distance which vanishes when that distance becomes sensible. 



The equations of elasticity deduced from this assumption contain only one 

 coefficient, which varies with the nature of the substance. 



The insufficiency of one coefficient may be proved from the existence of 

 bodies of different degrees of solidity. 



No effort is required to retain a liquid in any form, if its volume remain 

 unchanged ; but when the form of a solid is changed, a force is called into 

 action which tends to restore its former figure ; and this constitutes the differ- 



