364  Mr.  J,  Morrow  on  the  Lateral  Vibration 
and  the  equations  of  the  central  line 
-•8433/V6'5  +  -1984/V-<)276/^9+'0030^n---0005(v12) 
_/^_17^7      ^_^Z4      W>\    -|")l 
V30      420        60       45 "  + 315y,/'J  j  J' 
y  =E1  L"6/(      l')(a  —2/./'  +  ^)-^  {  ,™l0-*(-l-0386P*  +  l-7085JV 
-'8433/7.t'5  +  -1984/-V--0276/8lr9  +  -0030/.^11--0005^12) 
™A  r  a^7  a/./-6  __  /a-  Z2 \av>  aHx*  __  nr  a2l2  2Z*W 
6/  L  840  T  120  U  3/  20  24  \20  +  "3  "  15 /T 
aHos2/ 17     7      a5/2   t  a3/4      4aZ6\  17     .,1)1 
+  -4^+(420a-60  +  45-;U5J*r-420^/J}J- 
Putting  ,r  =  rt  in  either  or  these,  we  get  the  following  rela- 
tion between  ya  and  ya  : 
~~  (f|)  '  =  SI  PlJT  +  0&)P  I  C-1'0386P«  +  1-7085/V--8433/V 
+  ■1984Z5a7- -0276/V-f  '0030/a11  - -QOOSfl12)^10"* 
A 
711  a 
+  MC3392857rf6  +  -5178572a5Z.-l-3a^  +  -6a^--1904762/6)  [1 
§  17.  In  particular,  if  a=  -  , 
A=jgi*,     and     P-1=-~-_-0i03051/Oa>/4; 
hence 
_  Ha  _  -ft  P1^8  3,306/oct)Z  + 7-436^  ~[  - 2 
y«  L  ±8~  +  322'U38/oa>/  +  65P042m  ^  J      ' 
and  further,  if  the  masses  of  the  load  and  bar  be  equal, 
ya      31-375  EI 
§  18.   Clamped- Clamped  Massive  Bar,  Load  in  any  position. 
The  end  conditions  lead  to  the  preliminary  assumption 
