# James Clerk Maxwell (1831-1879)

## On the equilibrium of elastic solids

88

MR JAMES CLERK MAXWELL ON THE

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

spheres 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.†

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 con-

sidering the relation of the coefficients which occur in these two cases; while

others have treated of the general problem of a solid body exposed to any forces.

The investigations of LEIBNITZ, BERNOULLI, EULER, VARIGNON, YOUNG, LA

HIRE, and LAGRANGE, are confined to the equilibrium of bent rods; but those of

NAVIER, POISSON, LAMÉ and CLAPEYRON, CAUCHY, STOKES, and WERTHEIM, are

principally directed to the formation and application of the general equations.

The investigations of NAVIER are contained in the seventh volume of the

*Memoirs of the Institute*, page 373; and in the *Annales de Chimie et de Physique,
2 ^{e} Série,* x.v., 264, and xxxviii., 435;

*L'Application de la Mécanique*, tom. i.

Those of POISSON in *Mém. de l' Institut*, viii., 429; *Annales de Chimie, 2e Série,*

xxxvi., 334; xxxvii., 337; xxxviii., 338; xlii. *Journal de l'École Polytechnique,*

cahier xx., with an abstract in *Annates de Chimie* for 1829.

The memoir of MM. .LAMÉ and CLAPEYRON is contained in CRELLE'S *Mathe-
matical Journal*, vol. vii.; and some observations on elasticity are to be found

in LAMÉ'S

*Cours de Physique.*

M. CAUCHY'S investigations are contained in his *Exercises de Analyse*, vol. iii.,

p. 180, published in 1828.

Instead of supposing each pressure proportional to the linear compression

which it produces, he supposes it to consist of two parts, one of which is propor–

* The laws of pressure and compression may be found in the Memoir of Lamé and Clapeyron.

See note A.

† See note B.