ON OPTICAL THEORIES. Land 
Report on Optical Theories. 
By R. T. Guazesrook, W.A., F.R.S. 
Ds. Luoyn’s well-known Report on Physical Optics was presented to the 
_ Association at its meeting in Dublin in 1834—fifty-one years ago. Since 
that time the question of double refraction has been treated of very fully 
by Professor Stokes in the Report for 1862, but unfortunately he con- 
fined himself to that one branch of the subject. The years immediately 
succeeding that in which Dr. Lloyd’s report was read were marked by 
work of great importance, which has formed the basis for much that has 
since been done, and it is necessary, before writing of recent progress in 
the subject, to consider somewhat carefully the researches of Green, 
MacCullagh, Cauchy, and F. Neumann. 
_ This I propose to do, in as brief a manner as possible, for that part of 
the subject which is not included in Professor Stokes’s report. I then 
propose to go on to the consideration of more modern work, treating sepa- 
rately (1) of the simple elastic solid theory, (2) of theories based on 
7 mutual reactions of matter and ether, (3) of the electro-magnetic 
theory. 
¢ 
k Part I.—Inrtropuction. 
‘ 
| THE WORK OF MACCULLAGH, NEUMANN, GREEN, AND CAUCHY. 
s Chapter I.—MacCuttaau. 
§ 1. Fresnel! himself had developed a theory of reflexion and re- 
fraction, and had arrived at formule giving the intensities of the reflected 
and refracted waves in terms of the incident. 
__ In obtaining these he relied on the two following principles :— 
_ The resolved parts of the displacements parallel to the face of inci- 
dence are the same in the two media. 
The total energy in the reflected and refracted waves is equal to that 
in the incident wave. 
He further supposed that the rigidity of the ether is the same in all 
transparent media, and hence that reflexion and refraction are produced 
by a change of density ; from this it follows that the refractive index of 
a medium is proportional to the square of the density of the ether in the 
medium. The direction of vibration is considered to be perpendicular to 
the plane of polarisation. According to this theory there is a discon- 
tinuity in the component of the vibration at right angles? to the surface. 
§ 2. An elegant geometrical expression of the laws to which these 
principles lead was given by MacCullagh. He defines as the trans- 
versal of a ray the line of intersection of the wave front and the 
plane of polarisation ; the length of this line being proportional to the 
, ' Fresnel, Ann. de Chim. et de Physique, t. xlvi. p. 225; Wuvres completes, 
ep. 107. 
*- For a further consideration of this point see p. 186. 
