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plate werc kept at lixed temperatures, is compensated 1>y bfutihnj and cntails no stress. In sncli cases before calcnlating tlie stress by (11) wc must tlirow out tlie mean value of' ') so as to niake / Pdz = 0, and also siieli a term proportional to tlie distance froin tlie middle surfaee as sliall ensure tliat /'Pzdz = lI. Otlierwise tlie edges of tlie plate eould not be re gard cd as free froin imposed stress in tlie form of a foree or couple.

Tlie assumption in (1), (2) tliat « = /' = 0 is now replaced In

" = (x + ,5") i', i' — (x "t- i3-)//> (' ~)

and

w=w'—\ f), (12')

wliere va' is a functioii of : onlv. We find

/,' = (>. + 2*(« + /3r)—ytf, (13)

/' = « = >.+ (2;. + 2,*) (x + 0z) II.)

d:

s=r=u=» (!•">)

Since H is supposed lo vanisli, we get

p=u= 'Y'7, r ~— *1 (1,!)

/. ~f- 2 'j. L y. J

In (l<>) ^ and ,ü are to be deterinined by tlie eonditions

fp,h = 0, J'Pzdz = <l';

(ir. wliieh eoines In the saine, we are to reject froin 'i sueh linear ternis as will leave

j'0dz = tl, fózdz = 0 (17)

Since ir' and r) are independent ol x and //, the equations ol equilibriuin (5) are satisfied.

It is of interest to tracé the inlluence of time upon the doublé refraction of the lieated plate wlien light passes through it edgewavs, ?. </.

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