Polarization in perfectly transparent Media. 467 
where A’, B’, C’, EH’, F’, G’ are constant, and ® a quadratic 
function of L, M, and N, for a given medium and light of a 
given 
12. Equating the statical and kinetic energies, we have 
5, +8,=T zs t+ 2 
that is, by equations (6), (9), (10), (11), and (12), 
$(Aa’*+BA?+Cy?+EZf,y,+Fy,a,+Ga,f,) 
+3(Aa,?+B6+Cy2+Ef,y +Fy,a,+Ga,f,) 
p 
+> [L(4.y.—-7,A;) + M(y,¢,—4,7,) + N(a,f,—f,a,) 
Yk 
=F (a: +B ty! tast+ pity, 
2x7 : 
- 3 (A'a,? +Bi624+C0'y{+E'By,+F'y,a,+G'a,f) 
27" ; 
te (A'a,’ + BiB2+C'y?+E'f,y,+F'y,a,+G af.) 
$a tL (By — yf) +M(y,a- apt N(a spay. Os) 
pl 
If we set 
A SrA’ ; B 2zB' 
= ri we Pe etc., (14) 
PDP Iz’ 
and ?~ Sap Pp ’ (15) 
the equation reduces to 
aa, +bB'+cy,"+eB,y,+fy,a,+9a,f, 
+aa,'+bB? +ey, +eB.y.+SV,4, +942, 
2 3 
+FPL(By.—-7,A,) * M(y,a,—a,y,) + N (a, f,—f,a,)] 
P pay 
Sgt Ae ees +h ey, (16) 
13. Now this palit which expresses a relation between 
the constants of the equations of wave-motion (1), will apply, 
with those Saree not Sea = such vibrations as actually — 
take place, but also to such as we may imagine to take place 
under the influence hasan determining the type of 
¥ 
vibration. The free or unconstrained vibrations, with which 
alone we are concerned, are characterized by this, that infin- 
‘itesimal variations (by constraint) of the type of Vesdenege 
