applied to Magnetic Phenomena. _ 163 
The mechanical conditions of a medium under magnetic in- 
fluence have been variously conceived of, as currents, undula- 
tions, or states of displacement or strain, or of pressure or stress. 
Currents, issuing from the north pole and entering the south 
pole of a magnet, or circulating round an electric current, have 
the advantage of representing correctly the geometrical arrange- 
ment of the lines of force, if we could account on mechanical 
principles for the phenomena of attraction, or for the currents 
themselves, or explain their continued existence. 
_ Undulations issuing from a centre would, according to the cal- 
culations of Professor Challis, produce an effect similar to attrac- 
tion in the direction of the centre; but admitting this to be true, 
we know that two series of undulations traversing the same space 
do not combine into one resultant as two attractions do, but pro- 
duce an effect depending on relations of phase as well as intensity, 
and if allowed to proceed, they diverge from each other without 
any mutual action. In fact the mathematica! laws of attractions 
are not analogous in any respect to those of undulations, while 
they have remarkable analogies with those of currents, of the 
conduction of heat and electricity, and of elastic bodies. 
In the Cambridge and Dublin Mathematical Journal for 
January 1847, Professor William Thomson has given a “ Mecha- 
nical Representation of Electric, Magnetic, and Galvanic Forces,” 
by means of the displacements of the particles of an elastic solid 
in a state of stram. In this representation we must make the 
angular displacement at every point of the solid proportional to 
the magnetic force at the corresponding point of the magnetic 
field, the direction of the axis of rotation of the displacement 
corresponding to the direction of the magnetic force. The abso- 
lute displacement of any particle will then correspond in magni- 
tude and direction to that which I have identified with the elec- 
trotonic state; and the relative displacement of any particle, 
considered with reference to the particle in its immediate neigh- 
bourhood, will correspond in magnitude and direction to the 
quantity of electric current passing through the corresponding 
point of the magneto-electric field. The author of this method 
of representation does not attempt to explain the origin of the 
observed forces by the effects due to these strains in the elastic 
solid, but makes use of the mathematical analogies of the twe 
problems to assist the imagination in the study of both. 
We come now to consider the magnetic influence as existing 
in the form of some kind of pressure or tension, or, more gene- 
rally, of stress in the medium. 
Stress is action and reaction between the consecutive parts of 
a body, and consists in general of pressures or tensions different 
in different directions at the same point of the medium. 
M2 
