362  Mr.  J.  Morrow  on  the  Lateral  Vibration 
the  equation 
drii  [ x 
"EIsf2=pft)J0  yix-z)dz+mxyi 
gives 
-EIy=/o«?/1(-08194Z4~-1126984lZ3^  +  -0416tv4---0iy 
+  -00019841 5i)+wiy1('16^^-5P*+-3?) 
,Vi  _  EI 
yi      -08194/)«/4+-3m/3" 
The  next  approximation  gives 
_EI«  = pa)^llQ"3. (pft)f6-63084/8-9-12718^ 
17      •08194/W4  +  -3rf  I      \ 
+  3-41435Z4^--93915/V  + -02480^8--00367 - 
#12  \ 
+  •00002-^  Um(26-1905/7-36-i^+13-8>^ 
-446/V  +  '1984^7)\+my1(-3Z3---5Z2tu  +  -16>). 
Whence 
!/i  \  '081Mpa>l  +  -3m  J 
§  15.  Supported  Massive  Bar,  Load  in  any  position. — Let 
the  load  divide  the  bar  into  segments  a  and  b.     At  each  end 
dor 
and  when  #  =  a,  y=ya- 
Hence,  for  the  first  approximation 
ya 
y  — 
where,  for  brevity 
y=*£(P*-2&»+**): 
A~Z3a-2k3-fa4. 
For  #<a, 
When   ei' > a  we   must  add  —mya(x — a)  to   the  above  ex- 
pression.     Determining    the    constants    of    integration   by 
