488 M. L. Lorenz on the Reflewion of Light at 
If A’, for a given angle of incidence, is a small positive quan- 
tity, it gradually approaches = as the angle of incidence ap- 
proximates to the angle of polarization, and afterwards approaches 
givclf, on:-the contrary, A’ is a small negative quantity, on 
changing the angle of incidence A! approaches -3 and —7r. 
The retardation of the phase of the reflected ray R!, compared 
with the other polarized in the plane of mcidence R, may be ex- 
pressed by A’—A if the coefficients of cos kt have the same sign 
for both rays, that is to say, when the angle of incidence is 
greater than the angle of polarization. If, however, A’ and A 
be always taken in the first positive or negative quadrant, we can 
introduce any multiple we please of 27, and therefore express the 
retardation by A!—A + 2pzr, where p is a whole number. 
If now A is positive for this angle of incidence, it will increase 
as the angle of incidence diminishes ; and when the angle of in- 
cidence becomes less than the angle of polarization, and A! is 
taken in the first quadrant, the retardation of phase will be ex- 
pressed by 
A'—A+(2p+41)7r 
If, on the other hand, A! is negative for an angle of incidence 
greater than the angle of polarization, the retardation of phase 
will become A!—A + (2p—1)z7, if the angle of incidence is made 
less than that of polarization. These results agree with those of 
Jamin. In the first case Jamin puts y=—1, whereby the re- 
tardation of phase becomes 
A'—A—27 for a+B> =, 
A'—A—wa for atp<s; 
and bodies in which this is the case he calls “bodies of negative 
reflexion.” 
vm - 
In the second case (A! negative for «- ao 5) he puts p=1; 
and the retardation of phase of these sites which he calls 
“bodies of positive reflexion,” then becomes 
A'—A +20 for a+8> ZF; 
Al—A-+ @ for atB<s 
Jamin found, moreover, that most bodies whose index of re- 
fraction is less than a given amount (about 1°46) give negative 
