ON SOME ANALOGIES BETWEEN THE EQUATIONS OF 
ELASTICITY AND ELECTRO-MAGNETISM. 
By JOHN E. DAVIES, 
Professor of Physics in the University of Wisconsin. 
The whole tendency of experimental work in electricity and magnet¬ 
ism since Clerk Maxwell’s celebrated working-out of the stresses and 
strains in a dielectric medium subjected to electric or magnetic forces, 
has been to confirm the reality of the existence of such states of stress. 
The work of Hertz, Lodge, Thompson, Tesla and many others, points 
certainly in this direction. One cannot take up a modern treatise on 
elasticity in which the lines of stress of a strained elastic medium are 
shown without being struck with the resemblance of these lines to those 
of electro-static or electro-magnetic induction across dielectrics con¬ 
necting conductors or magnetized bodies. 
To the mathematican the analogies presented by the analytical for¬ 
mulae are numerous and striking. Especially is this true of some of the 
differential equations which present themselves in the theories of 
elasticity and of electro-statics. But it is also true of many of the equa¬ 
tions peculiar to electro-magnetism. Some of these formal analogies 
have already been alluded to by Sir Wm. Thomson* and Oliver Heavi¬ 
side — especially the latter. 
* From a remark of Sir William Thomson in his presidential address 
before the Institution of Electrical Engineers, January 10th, 1889, en¬ 
titled, “ Ether Electricity and Ponderable Matter,” it would appear that 
Faraday had set forth a theory of electro-statical induction, which sug¬ 
gests the idea that there may be a problem in the theory of elastic 
solids corresponding to every problem connected with the distribution 
of electricity on conductors, or with the forces of attraction and repul¬ 
sion exercised by electrified bodies. Sir William adds “ the clue to a 
similar representation of magnetic and galvanic forces is afforded by 
Mr. Faraday’s recent discovery of the affection with reference to polar¬ 
ized light of transparent solids subjected to magnetic or electro-magnetic 
forces. I have thus been led to find three distinct particular solutions 
of the equations of equilibrium of an elastic solid, of which one ex¬ 
presses a state of distortion, such that the absolute displacement of a 
particle in any part of the solid represents the resultant attraction at 
this point produced by an electrified body. Another gives a state of the 
