Uniform and Varying Sectional Area. 123 



.-. -y=^/-098,928,57Z 4 --143 ? 537,41/ 3 ,r + 083a' 1 

 and - '04 j + -001,275,51^, 



-•^ =10-1083^. 

 For the second approximation 

 -fl= 1 4^^ r r r 2 (.r-^)(-09892857r--14353741^ 



+ -083 z' - -04 -' + -001,275,51 ? ^dz 

 = ' U nl& ( 8-24405 /V- 7-17687 ZV + 1-48809 * - 



— 5y + •00966^°), 

 -. -y=^|^-Y-75074/ 8 - 1-09782/^+ -68700 ZV 



r 9 r 12 \ 



- -35884 /V + -02657 x" - -00772 ~ + -00007 y j 



-^ = 10-9812^. 



This gives 3-313 dU 



2tt I* ' 



For a third approximation the differential equation re- 

 duces to 



-f¥ i 5 ^^V"°62562 ZV— 054891 /V + '012268 ZV 

 rfar &dH \ 



- -004984 Z V + -000201 a? 10 - -000049 ~) , 



.-. -y = '^^^-5655/ 12 --8275r. y + -52135ZV 



-•27446 ZV+-02191 fr 8 — -00692 ZV 



+ -00015 x 12 - -00003^). 

 "Whence _ £ _ 1 1 .Qgo Ec?2 



3/i f^ 



AT 3-326 dV 



and JN = -= ts- . 



2-7T r 



This is again independent of the breadth o£ the bar. 



