22 SECTIONAL ADDRESSES 
tion of the propagation of waves of light in a crystalline medium. In 
addition to the limitation used in his previous investigations, that trans- 
verse waves can be propagated in the medium independently of normal 
waves, he introduces the further limitation in accordance with Fresnel’s 
theory, that the media satisfy the condition that the directions of the 
transverse vibrations are always in the front of the wave. With these 
limitations he proves that, if the direction of a disturbance is parallel to 
the plane of polarisation and the medium is free from the action of any 
external forces, the directions of polarisation and the velocities of propaga- 
tion are the same as in Fresnel’s theory. In his previous investigations 
he had proved that in order to satisfy Fresnel’s relations between the 
amplitudes of the incident, transmitted, and reflected waves at the surface 
separating two isotropic homogeneous media, the direction of a disturb- 
ance is perpendicular to the plane of polarisation. He then shows that 
in order to satisfy Fresnel’s results for crystalline media when the direction 
of a disturbance is perpendicular to the plane of polarisation it is necessary 
to assume the existence of extraneous forces, and that, with the appro- 
priate restrictions on these extraneous forces, the results agree with those 
of Fresnel’s theory. 
It thus appears that an elastic solid medium which is self-contained 
and free from external constraints will not account for the observed facts. 
Cauchy arrived at the same result almost simultaneously. 
Various modifications of Green’s elastic solid theory of light have been 
proposed, but none of them is satisfactory. Perhaps the most interesting 
is that proposed by Lord Kelvin in his Baltimore Lectures. ‘This theory 
assumes that normal waves in the elastic medium are propagated with 
zero velocity, and to get over the difficulty, pointed out by Green, that 
such a medium is not stable, the medium is supposed to be attached to 
a boundary. ‘Thus, although this theory gives results for the relations 
between the amplitudes of the incident, the transmitted, and the 
reflected waves at the boundary separating two isotropic media and 
also for the propagation of waves in crystalline media which agree 
with Fresnel’s results, it is open to the same objection as Green’s 
elastic solid theory which requires the intervention of extraneous 
forces, as the condition that the medium is attached to a boundary 
postulates the existence of some other medium which acts on and 
controls it. 
Although these different investigations did not succeed in establishing 
a satisfactory mechanical theory of light, they were instrumental in 
advancing the knowledge of the subject. One important result emerged, 
that any theory to be satisfactory must agree with Fresnel’s results, and 
some writers, e.g. Lorenz, based many of their investigations on Fresnel’s 
results. 
In Green’s treatment of the elastic solid theory the Lagrangian function 
used by him is of the type which is expressed as the difference of a 
kinetic energy function and a potential energy function. The kinetic 
energy function is the sum of the squares of the velocities of the medium 
multiplied by the density, and, if the rate of transfer of energy due to 
