- 486 M. L. Lorenz on the Reflexion of Light at 
A wave which is reflected by the layer whose angle of refrac- 
tion is 2, Or 2), Y,-.., and afterwards interferes with the wave 
reflected by the first layer, will be retarded relatively to the latter ; 
and we may indicate the successive retardations of phase by the 
letters 6, 5,, 6,,.... These quantities are functions of a, 2, 
X_q.-.3 but may also be regarded as functions of wu, wu, Ug)... - 
We ‘may therefore represent the amplitude of the ray reflected 
once at the layer whose angle of refraction is 2, by ; 
A cos (At—96) du, 
where ¢ is the time, and £ a constant. 
For reasons analogous to those stated above, it is easy to see. 
that the amplitude of all the reflected rays may be expressed by | 
“8 “B 
A \ du cos (kt—8) — ( inf du, 
Uy ”~ Uy 
This series is the real part of 
* (kt—8) V1 
af du «€ Tu); 
Uy 
Pi, inthe 5 28 — 92) +.. J. 08) 
“where 
FL =f ay dug €6:-5:)¥=1 f(g). 
Uy Uy 
From this last equation we may deduce the differential equation 
d | -wai |= aS ea a 8; | 
<p) | =e) 
from which we obtain another expression for series (15), since it 
is the real part of 
(kt—6)V—1 dis ; 
Ale fw | 
or since for u=u,, we have f'!(ug)=0 and 5=0, the real part of 
AA Mag”. 
If in the above differential equation we substitute 
Ast 
ola ee Ug—Uy 
» will be determined as a function of wu by the following eqnse 
tion : 
aN tee d(Qa—8) | dd dA—8) 
"Spt 2 SP ag du dus du 
A=0 for U=Uny and wath, for u=Ug. 
du 
