_!_' Ml; K. V. SOITTHWKLL ON THE GENERAL THEORY OF ELASTIC STABILITY. 



where 



A= - 



4C 



B = 



and 



<T = ; 



(55) 



We may assume a solution for equations (52-54) of the form* 

 u' = 2 T U*. , sin k (6 + 6,) sin 2 ( z + Zg ) J 



= 2 W 4 . sin i- 



cos 



2 ( 2 + Zq ) ] 





where Jt must be integral, and U M , V M , W ti , are functions of r only, which satisfy 

 the differential equations 



A 



f/ w A\l d /3m- 4 A\ l"l v 

 A "L\m-2 2/rdr Vm-2 " 2/f*J fc 



2.\^ Afi + ^r\ + iid w 



aLm-2 4 \ r*/ 4_Ur 



(57) 



and 



(68) 



aLlm-2 4\ i ) 4 J dr \rn-2 4 



r A / 2\ TJ ~n i 



aLm-2~T\ "^) + T\r k - q 



L A 

 4 * 



r 



m-2 



r 2 / 4 J \r dr rV 



^< . = 0. 



(59) 



It is easy to show that the phase-relations assumed in equations (56) are necessary. 





