492 Royal Irish Academy. 
to a metal body not connected with the sheathing, and therefore that 
the system adopted by that gentleman is the best which human pru- 
dence could suggest. The memoir contains numerous extracts from 
all authentic sources in illustration of the several positions very 
briefly noticed in this report. 
ROYAL IRISH ACADEMY. 
[Prof. MacCullagh’s Note continued from p. 413.] 
I].—On Fresnel’s Formula for the Intensity of Reflected Light, with 
Remarks on Metallic Reflexion. 
When Mr. Potter discovered, by experiment, that more light is 
reflected by a metal at a perpendicular incidence than at any oblique 
incidence (at least as far as 70°), the fact was looked upon, by him- 
self and others, as contrary to all received theories; and certainly 
the universal opinion, up to that time, was, that the intensity of 
reflexion always increases with the incidence. It may therefore be 
worth while to remark, that the formula given by Fresnel for re- 
flexion at the surface of a transparent body, though not of course 
applicable, except in a very rude way, to the case of metals, would 
yet lead us to expect, for highly refracting bodies as the metals are 
supposed to be, precisely such a result as that obtained by Mr. Potter. 
For when the index of refraction exceeds the number 2 + 3, or 
the tangent of 75°, the expression for the intensity of reflected light 
will be found to have a minimum value at a certain angle of inci- 
dence ; while for all less values of the refractive index the intensity 
will be least at the perpendicular incidence. 
Let 7 and i! be the angles of incidence and refraction, and put 
_ sin _cosé 
~snd? = Cosi? 
then if I be the intensity of the reflected light, when common light 
is incident, Fresnel’s expression 
pee sin? (i—?’) _ tan® (¢—7’) 
2 *| sin?(i+7') * tan? (@+7) f’ 
in which the intensity of the incident light is taken for unity, may 
be put under the form 
2 2 
o(are V+ Gee) 
— (< 8 tet)” 
ORD 
which has a minimum value when 
i 
: ity eel 
° + i 
. 
> 
the value of I being in that case 
M— x7) —4 Ma). 
(M— af Ge eee 
—[— 
— = > 
1 1\? 
M— zi) Yuga 
( x) 2 (M+ xr) ‘ 
