170 REPORT— 1885. 
According to both Green and Cauchy they depend on a function ¢, 
where 
d = goe (arty + eo ’ , ‘ . (22) 
And in both theories ? Wye, oh, 
c 
a’? + 0? = = : z : x . (28) 
Green puts A/p very large, so that a’?+?=0, and 
= e+’"{K sin (by + ct) + Los(by + ct)} . - (24) 
while Cauchy, without any dynamical justification, writes A/p=—c?/k?, 
k being a large quantity, so that Ais a small negative quantity. Hence 
a/?24+52= —f?, 
The assumption of a negative value for A leads to the conclusion that 
the modulus of compression is negative—that is, that the medium is such 
that pressure causes it to expand and tension to contract, and this alone 
is fatal to the theory. 
§ 5. We come, then, to the conclusion that the phenomena of reflexion 
and refraction cannot be explained, any more than the phenomena of 
double refraction, on a purely elastic solid theory involving a sudden 
change of properties on crossing the interface. Green’s theory is the 
only possible consistent one, and it, in its original form, leads to results 
differing from experiment. 
Part IJ.—Moprern Drvetorments or THE ExAstic Sorin THeory. 
We now come to the consideration of rather more modern investiga- 
tion on this subject. The limits of space will confine us to the theoretical 
work which has been done. The great experimental researches of Fizeau, 
Jamin, Quincke, Cornu, and others, will only be occasionally referred to. 
A complete account of these must be left for some future time. 
Chapter I.—Gurnrrat Properties oF THE HrHER ON THE ELASTIC 
Som THeEory. 
The elastic solid theory of the propagation of light and double refrac- 
tion has been discussed in various papers by Haughton, Lamé, St. Venant, 
Boussinesq, Von Lang, Sarrau, Lorenz, Rankine, Lord Rayleigh, Kirch- 
hoff, and others. 
§ 1. Haughton considered the problem of the general equations of an 
elastic solid in a paper read before the Irish Academy in 1846, in which 
he adopts Canchy’s views as to the constitution of the medium. These 
views are modified in a second paper,! read in 1849, in which the general 
equations are formed, and the correct expression found for the potential 
energy. 
In this paper Haughton shows how to calculate the strain in any 
direction produced by a given elongation in the same direction. This 
strain is proved to be inversely proportional to the fourth power of the 
radius of a certain surface, called by Rankine the tasimonic surface. A 
form is found for the equation to the surface of wave slowness, which is 
said to reduce to MacCullagh’s if the vibrations be strictly transversal ; 
but, in making the reduction, the dilatation 0 is equated to zero, its co- 
1 Haughton, ‘ On a Classification of Elastic Media and the Law of the Propaga- 
tion of Plane Waves through them,’ Zvish Trans. vol. xxii. p. 97. 
