372  Mr.  J.  Morrow  on  the  Lateral  Vibration 
the  vibration  curve  in  §  7  can  be  written 
and  we  can  take 
Then,  since 
the  equation  of  motion 
becomes 
..       91'..    ,  3EI         n 
_  l±         3EI 
(-  m- 
§27.  The  same  problems  worked  by  the  methods  of  this 
paper  do  not  involve  Lagrange's  Equations  and  are  as 
follows  : — 
Taking  the  origin  at  the  free  end, 
Whence  ..  /3      T,u/2  \ 
-EI0=-ni'/1^  +vm  \ 
Putting  —  =  -  l  we  set 
2m-> 
6  \yi>         Kl     317     yx        l 
;;,    -mi,-     zv  ,     /77~3T     9TF\ 
-  -  =  W(  !+  — »  +  V  1+  -73  +  -SmJ- 
y,        17  \        (Hi2       V  mt-      m-l  J 
