254 
MR. J. LARMOR OX A UTNAMTCAL THEORY OF 
current dldt [fj,, b, e), in analogy with the Amperean forcive arising from the 
magnetic held acting on the electric current. The addition of this forcive 
{hdhidt — gde/df, ...... , . to (X', Y', Z') and the omission of (— ydgjdt + I3dh/dt, 
from (X, Y, Z). permits both to he expressed eccplicidy in terms of stress. 
Maxwell’s Theorem of a Representative Stress. 
40. The mechanical forcive acting in a polarized medium thus corresponds in the 
main to the system of bodily force and interfacial traction wdiich is the result of 
Maxwell’s magnetic stress (‘ Treatise,’ § 640) considered as an extraneous system 
applied to the medium. The electric stress of Maxwell (‘Treatise,’ §105) is 
something wholly different, leading in the case of homogeneous media to interfacial 
tractions only, without bodily force ; it could thus have valid application onl}' to 
unpolarized media, as for example to the theory of gravitation which passes through 
material bodies just as through a vacuum. The proposition really established^ is 
that the mechanical forcive due to attraction at a distance, obeying the law of 
inverse squares, between material bodies, may be represented by a connexion in the 
form of an imposed extraneous stress symmetrical with respect to the lines of force, 
acting across the intervening medium, provided that medium is not in any way 
polarized by the force. A stress restricted by this relation of symmetiy involves 
only two variables, the principal tractions along and at right angles to the line of 
force ; and the essence of Maxwell’s theorem is that it is possible always to 
determine these two variables so as to satisfy the three equations of equilibrium of 
the element of volume of the medium. These principal tractions prove, as is well 
known, to be equal in magnitude but opposite in sign. The proposition is in itself 
so remarkable that it deserves to be formulated abstractly ■without reference to 
hypothetical applications. The representation of a given bodily forcive by a 
geometrical stress-system is in general a widely indeterminate problem, as the six 
.stress components have to satisfy only three equations : but the condition of 
symmetry with respect to lines of force restricts the stress so much that such a 
representation would only in special circumstances be possible. 
The regular local Molecular Forcive in an excited Dielectric: its Expression as a 
Stress-system: Exampjles of the Principle of the Mutual Compensation of local 
Molecular Forcives. 
41. In the above estimate of the mechanical forces acting on an element of a 
polarized medium, the influence of the general mass of the medium on the molecules 
in the element has been alone included ; it remains to consider the role of such terms 
as would arise from the special forcives of neighbouring molecules. The intensity of 
* ArAXWEiJ/, “ Qn physical lines of force,” Part I., ‘Phil. AFag.’ 21, 1861, es^iecially Pi’oii. TFl. 
