of  Loaded  and  Unloaded  Bars.  365 
For  x  <  a, 
-EI^=M^+(M1-M0)f  +Pco'^  [\x-z)yzdz 
OCJX  'if a  Cl        -.  ..  bx 
*-— -  '  yx  dx  —  mi)  -r. 
2    !/aJoJ  Ja  I 
If  x > a,  add  mya (x—a). 
By  putting  x  =  a,  as  in  previous  cases,  we  find 
M„=^,f  + -00357143  "f^ 
M1=»y.^  +  -00357143^; 
and  hence  for  x  <  a, 
-EIy=po^;(^Y(2-V-2-38095.^  +  '59524  ~  -2*72V 
+  1-  78572  ZVV 0~3  +  «!#,  -^  (3«^  -  Pa?  -  abx  +  a2x)  ; 
and  for  x  >a  the  latter  portion  of  the  expression  is  changed  to 
my a  -T73  (3l%2  —  2ax?y  —  6l2x2  +  3a?#2  +  3/3t#— a/3) . 
When  #  =  a,  either  of  the  above  gives 
-£*  =EI.P, 
where 
P"1  =  ^  10-3(l'78572Z6-2-7aZ5  +  2;7a*Z2-2-38095a5/ 
+  -o9524a6)4-^(jj. 
§  19.  In  the  next  approximation,  for  x< a: 
EI^=M0+(M1-M<))f  +pm  fb  f  (.t-%^,-  ^£*  fV(l-*)<to 
I     t/a      Jo  ' 
«9  «10\ 
-  V38ZV  +  '.49603a?8  --33068  j  +  -06614  -^- ) 
m     f  /  3     „,       /3       a3  \    ,   .    /a/3       <r^2    .   a3l\   . 
+  6?  {  (26^-20"  io)*  +  U  ~    2    +  4  f 
/3    .„-,      7    ,     ,  a4?      a'V-'\    ")  -1        ..  ?).c 
