366  Mr.  J.  Morrow  on  the  Lateral  Vibration 
Similarly  for  x>a: 
-EI0  =M0  +  (M1-M0)  f  +paH[(x-:),jz(h+  f  (*-%*'<fej 
=M0+(M1-M0)*  +PcoYya  [^  10"^ --33068/^ 
+  l'48809ZV-l-38Z3^5  +  -49603a?8--33068j+-06614^ 
m   f(  3    97      a3\    ,      (aH      a?l2\   t      a2lV      aW 
Integrating  and  equating  when  a?=a,  we  find 
M 
_11     „c.   a2/6 
210 
3o/ 
,      ..  ah2 
+mya-w- 
M^P*.  [-0000071145^  + " «(- ^  +  f  -£* 
O  x    — ;  07 
Whence  the  form  of  the  centre-line  is 
l\2. 
-El2/=/3a>P^[^(-6yi0-^3-5573/V-5-5113/v/- 
+  4•9603/V-3•3069/^7  +  ^5511<r^-•3006^V<>501^) 
+  J3{(3a2Z-Z3-2a3)^0  +  (aZB^2a2Z2  +  a3Z)^+(7a6^2a7 
-35«4/3  +  52«3Z4-22a2/5)-^  +  (3a7-14«6/2  +  21a5/3-22a3Z5 
+B<}H'{TrM??} 
