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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.

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