BEAM OF BECTANC4ULAli CliOSS-SECTlON UNDER ANY SYSTEM OF LOAD. 137 
The .series for V in tlie neiglibonrliood of the load sIioavs a similar plienomeiioii, 
points to the right of x = 0 being depressed hy , and points to the left raised 
by the same amount. 
(V),.=o = - 
L 
2L / 1 
.*■>0 
, 1 '\ V / (— 1)" 
4 (A' + /i) TT U' + ^ fj, / '^[h ) (2u + 1) I 
Ho being negative and Ho being positive, as Ave go aAvay from the load, the effect 
of the series is to decrease tliis effect, the level of the points in front of and 
behind the load tending to equalize itself. If Ave Avork out the series for V in the 
neighbourhood of tlie origin and of the point (0, — b), Ave find (V) in the neighbonr- 
hood of orio’in 
o 
_ _ il V / il Y I Zi \ , L// ^ / r Y dll 
1 fo/ r! X' + /j, /Li J 27r?'/i h / vl 
Avhere the F’s and G’s have the values given on p. tfo, except that now 
r — Cf siiih•'* , 
~ J. Uhii, 2 « - 
fSimilarly (V) in neighbourhood of point (0, — h) 
2L/ 1 
TT \ A A /U. jx 
4. -L] V /Zf ^i n(2u + l)r . 
^ (2Z. + 1)! 
1 \ b J (2v) 
_ ^ /Z sin( 2 i/ + 1 )</)" 
irlfi ‘^\h j (2v + 1) ! 
2L//" * YZi'" 
+ 
irlfi I \ i / (2fo ' 
+ 1 ) 
HL., 
-J/ + 1 ) 
AAheie the H s luiAm tlie value giAmn on page 1U2. 
From tliese expressions Ave obtain the following values for the transverse dis¬ 
placements of points on the lines y = 0, y = _ h :_ 
L » /A’\“‘'+i (— ly / 1 1 
Y — — __ 
® 2-77‘l\hl (2i'+ 1)! ' A'+ ^ 
V_;, = - ZfvYZf"''' (- -L)" 
TT 
d- F;,^,.|_, ) 
A / 
f' 
+ (a' + ;.+ 
So that, approximately, putting in the values of the constants, 
YOL. CCI.—A. 
T 
