Recueil de travaux offerts par les auteurs à H. A. Lorentz à l'occassion du 25me anniversaire de son doctorat le 11 décembre 1900
The otlier principal stresses operative radiallv and tangeutially are /> = (>.+ 2 + («I»)
Q = y.'~ + (A + 2/Si) -—y 4 (-'51)
ar r
The equation of equilibrium, analogous to (5), is obtained by considcriucr the stresses operative upon the polar element of area. lt is
m-u m
dr
Substituting froni (30), (31), we get
d-tt 1 dn u y d6
dr rdr r- /. + 2/i dr'
so that
y + " = TxV + •*> ^
dr r 2 ,«4
wliere x is au arbitrarv constant. Integrating a secoud time we tind
ru= ?- -(''trdr+hxrt + 13, (34)
/. -f- ~y-' o
in which, however, ,3 must vanish, if the cylinder is complete through r = 0. Froni (31)
P = (;. +p) x - i f 0r dr, (35)
?. + r-J i)
2 wy 1 f' 'Hwyó . Q = {>. + ,,) x-^-2 f trdr- . + 2- • • ■ (36)
and
,■ «- (37)
lt is 011 {P—(i) that tlif! doublé refraction depends wlien light traverses tlie cylinder in a direction parallel to its axis.