252 / FRESNEL. 
hesitate to say, if we admit no dependence between the 
motions of the different luminous molecules (and I know 
plane, thus differing essentially from the former. See Professor Mac- 
cullagh’s paper ‘On the Laws of Crystalline Refraction,” Transac- 
tions of the Irish Academy, vol. xviii.; and Dr. Lloyd’s Lectures on 
the Wave Theory, part ii. p. 80. The whole subject has been fully 
discussed by the Translator in three papers in the Philosophical Mag- 
azine for July, August, and October, 1856. 
The demonstration in either case is grounded on the assumption of 
the law of vis viva; viz: 
m (h2 — hi2) = m, hj. 
And Fresnel’s formulas would be directly deduced if we had also 
the relations 
h+W/ =h, for vibrations perpendicular to the plane of incidence, 
and h—W = hj —— 
Cos 4 
The difficulty is, that these formulas are not both deducible from 
the principle of equivalent vibrations as laid down by Professor ? 
Maccullagh. Another mode of deduction, on a different assumption, 
is pointed out in the Philosophical Magazine for Oct. 1855, by means 
of the geometrical construction above given. 
The theory of Fresnel, it will be easily seen, is equivalent to the 
assertion that “the plane of vibration is perpendicular to the plane of 
polarization,’ whereas in that of Maccullagh they are coincident. 
Several classes of experiments have been now shown to necessitate 
the adoption of the former view: for an account of which the reader 
is referred to the Philosophical Magazine for Aug. 1856, before cited. 
To proceed to the applications of these formulas: we may consider } 
common light as consisting of two portions of equal intensity, polar- 
ized at right angles to each other. If the intensity of the incident 
light be 1, that of each of these components will be#. At reflexion 
each component gives a reflected and a refracted ray polarized re- 
spectively at right angles. In the reflected ray the intensity of the 
portion polarized in the plane of incidence (1) will be = #2/2. That 
in the plane perpendicular to (K) will be = 4 k/2, and it is easily seen, 
from the nature of the fractions, that of these quantities the first will 
always be the greater; and thus in their sum or the total intensity 
there will be an excess of light polarized in the plane of incidence, or 
the light is at all incidences partially polarized in the plane of inci- 
dence. The difference of the two expressions gives the quantity of 
light so polarized. 
. » + - parallel to the plane of incidence. 
ny bate gael Zager 
~ 
