34 -Ml;. L. N. G. FILOX OX AX Ari’KOXlMATE SOLUTIOX FOK IJEXDIXG A 
(.) 
irh 
L 
, , L f* 7 / sblll // - Vlj . Ii.r , 
(».)=:-7 . -. cosh Sill — (Of 
irlj Jn Sllili 2 u + ' 111 - h 
+ 
'0 siiih 2;/ + 2 ii 
a cosh a 
irh Jo 2ii — 'In 
L// r“ ‘u cosh n . . iiij . U-j: , 
Jo siiih 2ii + 2ii h h 
siiih — Sin - dll 
h h 
sinh -u 
L // p u s 
7 r?7"Jy siuli 2^6 
Lp p" a eosli a 
h// 
— cosh ~ sill dll, 
111 it 0 
S = , I . ” cosh ' f cos ' " dll 
'irlr Jo smh 2 u 2 ii h 
+ 
+ 
ii sink ii 
irlr Jo sink 2v, — 'In 
h p cosk ii — n sink n 
nrh J 0 
smli - COS - dll 
h h 
sink '2a + 2u 
■ 1 >'!! 1 
sinh , cos — 1 O .7 
h I) 
. L f* sink It — « cosk y( , a if ux 
+ rtj„ si,.h 2„ - 2« ' 1, “"T 
I 
(106). 
34 . E.qinssioiir'i for the Disi>lacements and Stresae.s in Series of Poiuers oj the 
Rudkis Vector from a Point. 
'J’he exj)i‘essions given aliove for U, V, P, Q, S may be ti'ansformed exactly as in 
.10, 17, and ive obtain expansions about the point (0, h) A\ here the shear is applied. 
Kx’entnally, r', (f)' liaving the same meaning as on p. 02, ive find : 
Ui= - 
L I 1 
27r ' x' + yU, ^ /x J 
+ - ) log ( 7 ) — ^ , cos (j)' 
IX / ^ V) I 27rix r ^ 
IT + IX ' /X 
TT \ IX ' (1 ' tl 
, /x r<is(2i7 + 2 ) P 
^ + r A 
(2i7+ 2 ); 
/■' cos (277 + 1 ) {^' jj 
^(277 + 1 )’ 
(ir,.-, - n,,) 
-f - )i.„+ p' - i sr 11.,.), 
TTll IX 0 ' II / (2i7) . Till IX 0 \ll j \2v + 1 ) . 
n 0 
Lp 
h // . .7 
- sill (jj 
(107), 
27r (\' + ix) 2'ivix /■' 
2h / 1 . 1 \ ® fr'p^^ sin (277 -(■ !)()>' ,, 
TT W + II IX ' 0 \t> / 
(2v + 1)! 
+ 
2L , 1 \ V / 2v(j)' 
77 ' X' + ixj ) {'2v) ! 
/pr — H ) 
(2771! 
pdf S ' (11=,:, - ir.) + s d ffkf 11 . 
irii/x I, ii { 2 i' + 1 ) ^ 777777. I II {xi'} . 
