2l6 WILLIAMSON: STRAINS IN OPTICAL GLASS 



ah 



p. = - - -+ "^"^ 



4K(e-f) "^ 4'c(e-f) V° a=^ V 

 ahr^ 

 i6K(e — f) """ 4f 



ctiii- ahai" / i\ Ci C2 



P2 =--^-7 ^+ . \. (inr— ) + -^ + -^ 



- l-K(e-f) \ 2/ 2 r- 



where Ci and C2 are evaluated by equating the right hand ex- 

 pression to zero for r = a and r = ai. 



SccT^' _L «hai^ / ^ i\ ^ Ci C2 



^' -~i6K(e-f) + 4«(e-f)\ "^ 2/ + 2 "r^ 



where Ci and C2 have the values found for the preceding equation. 



(III6). For a small-bored tube. Linear heating, on outside only. 



ah(a2-2r-) 

 Pi = 



P2 = 



P3 = 



8K(e-f) 



ah(a^-r^-^) 



i6/c(e-f) 



o;h^a2-3r2 + -^J 



i6K(e-f) 



(IV). 5o/i(i cylinder. Linear heating, on outside only. 



de _ hr 

 dr 2k 



ahCa^ — 2r2) 



Pi = 

 P2 = 



Pa = 



8K(e-f) 

 Qfh(a'^-r ^) 

 i6K(e-f) 

 Q;h(a^ — 3r^). 



i6/c(e-f) 



(V). Slab. Linear heating, on outside only. 



d^ hr 

 dr K 



~ 2K(e-f)\3 ^ / 



