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MR. J. LARMOR OR" A DA'RAMICAL THEORY OF 
of energy, taken in co 2 ijunction witli the hjyothesis of eftective density constant 
throughout space, lead immediately to Fresxel’s equations of reflexion for isotropic 
media, and in MacCullagh’s hands give a compact geometrical solution when the 
media are of the most general character. A medium of this kind, however hetero¬ 
geneous and eeolotropic as regards elasticity, is still adapted to transmit transverse 
undulations without any change into the longitudinal type ; and the conditions of 
propagation are all satisfied without setting up any normal tractions in the medium, 
which might if unbalanced produce motion of translation of its parts. Thus the 
incidence of light-waves on a body will not give rise to any mechanical forces. 
Alternative Optical Theories. 
18. The equations of propagation of Fresnel above-mentioned obviously agree with 
those which are derivable from the variational equation 
dt 
dlh Ah + — 2K 
dP 
df j 
o + dr 
= 0 , 
which belongs to a medium having aeolotroj^ic inertia of the kind first imagined by 
Eankine, and having isotropic purely rotational elasticity. The coefficient of elasti¬ 
city K may be in the first instance assumed to he different in different substances. 
The surface-conditions for the problem of reflexion which are derived from this equation 
are clearly, in the light of the above analysis, continuity of tangential displacement 
and of tangential stress. A compression of the medium now takes part in the propa¬ 
gation of transverse undulations, yet the compression does not appear in this isotropic 
potential energy-function ; hence the resistance to laminar compression must be null, 
the other alternative infinity being on the latter account inadmissible. The surface 
condition as to continuity of normal displacement need not therefore be explicitly 
satisfied; and the remaining surface condition of continuity of normal traction is non¬ 
existent, there being no normal traction owing to the purely rotational quality of the 
elasticity. Whether a medium of this type could be made to lead to the correct 
equations of reflexion we need not inquire. [See however § 21.] 
19. It has been shown by Lord Kelvin* that a medium of elastic-solid type is 
possible which shall oppose no resistance to laminar compression, viz. to compression 
in any direction without change of dimensions sideways, and that its potential energy 
if elastically isotropic is of the same form as the above, with the addition of some 
terms which, integrated over the volume, are equivalent to a surface integral. The 
remaining coefficient of elasticity, that is the rigidity, must then be the same in all 
* Lord Kelvin (Sir W. Thomson) “ On the reflcxiou and refraction of light,” ‘ Phil. Mag.,’ 1882 (2), 
1 ). 414 ; Gl.^zebkook, do., p. 521. 
