EQUILIBRIUM OF AN ISOTROPIC ELASTIC ROD OF CIRCULAR SECTION. 919 

 where 



. (0) _ 3v-20 1_ (v-2)(7v-64) 

 •t"^~ 8-v ^3 (8-v)2 



,(2) _ 8(2-r) 



"^^-i- 8-v ' 



^(2) _ 8(2-v)(v-l) p^(o) _ 2 2v^- - 5v - 46 J_ (v - l)(v - 2)(7v- 64) 



Vi- 8-v ' *'i~3 8-v ^3 (8-v)2 



(2) 8(2-v)(3-v) p(0) 2 -V--2 + 7V+14 1 (3 - v)(v- 2)(7v- 64) 





8-v 



C 



+ ^ 



(8-v)2 



and, for 7n>l, 



A<r^ = 



v-2m-l j^(o) _ v2 -(?);. + 2)v -2??i2 ^(o) v^ - (m + 2)v - 2?»^ 



Solution for souo'ce 9 = T)zS' ^. Permanent terms, p^-p'. z>z'. 



2p'2a-2_^(z-.'), 



O — V 





with 



(l} = a-^p' 



Al:\ { 4(2 - ^'fp - \(^ - ^y ) + Al°\(^ - 2>a2] cos (co - 0,' 



a~'ip'^A^g^\(z - z')p cos (o) - to'), 



= p'{z - 2')p ^ cos (oj - «)') 



+ a V 



Kf 1 { |(^ - ^Tp - \{^ - ^')P' ] + B?\(^ - ^')pa2 



cos (o) - O)') 



- —a- V^Bf \(z - z')p cos ((o - o)'), 



(// = rt -ip' 



C?\ I |(2 - ^')V - 1(2 - ^')P' } + C?\(^ - z}pa^ sin (o. - CO') 



and 



1 



- g-" ^p'^Cf\{z - z')p sin (w - 0)'), 



t(7H + l) 



a~-'"-~-p "'+-Ag (2 - z )p cos m{iM - o) _ 



cos?re(a) — w') 



4(m+l) 



= —p'"\z — z)p~""' COS m(a) - w') 

 ■ni 



+ a~''"'~-p'"' 



1 



b:;,. { |(^-^')V"-47^/2-^v'^^} +B:;'„,(.-.vv]cosm(co-co') 



4(m + l) 



4(m + l) 



-2«-2p'm+2g(2 /^ - Z')/0'"C0S ?«(u) - O)'), 



1 



c". { i<- ^')V" - jhVt/^ - ^'v } + o - ^y-r 



sin »i((o — 0)') 



4(m+ 1) ' 



W 



here 



a(2) _ 



32 



A?\ = 



16 1 4 7v-64 



.-. "■! 3 8-V 3 (8-v)2- 



-P,(2) _ 8( 3v + 4) ^(0) _ 1 7v + 64 1_ (3v + 4)(7v - 64) 



^«,i- "8"^-^' ''^-"3 8-v 3 (8-v)2 



(-(0) 



(8-v)2 

 (2) 16(v + 2) p(o) 4 v + 4 , 2 (v + 2)(7v-64) 



^6,1 = 



+ -7r 



-V ■- 3 8-v 3 (8-v) 



TRANS. ROY. SOC. EDIN., VOL. XLIX PART IV. (NO. 17). 



126 



(4) 



(5) 



(6) 



(7) 



(«) 



(9) 



