Rotatory Inertia on the Vibrations of Bars. 57 



which may be expressed more compactly by 



becoming, when rotatory inertia is neglected, 



d* P ,_d_(ldf P \ 

 dp f *dk\f p a%)' 



XL Normal Function Relations applied to Special Cases. 



1. Formulas for y 1 and y 2 . — T ne following formulae con- 

 necting y Y and y 2 will De found useful in applying the terminal 

 conditions to the above. 



71 2 = 1[ V /X8 + 4X 4 + A, 4 ]; 



y/=l[ v / A?T4A?---X 4 ]. 



y 1 y 2 = \ 2 ; 



7i 2 ~72 2 = 7i 2 72 2 ; 





or 1 1 _, 





— ^ = J.. 





72 2 7i 





/«/ \ 2 





©= 1+ - 2; 





©--- 





dy 1 _2\* l + 7l 2 _ 



_ 2X- 3 7! 



c/X 7l y?-\-y 2 



2 "2 i 9 ? 



i7a 7i + 72 2 



dy 1 = 2)^l-y^_ 



_ 2\ 3 72 



d\ y 2 7i 2 + 7 2 2 



7i 2 7i" + 72 2 ' 



*3?*»&=*>» 









dyi ^ dy 2 2X 5 





72 dX 7l dX 7i 2 + 7 3 2 ' 





^fe+^^Ei + x*]; 





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