AND DEFORMATION OP A THIN KLASTIC SHKI.I. 



519 











3/3 * 



m + n J f c") /, 9A 



m 13-3/3 3> U 3. 



3 /, 3AA1 1 

 " 8. \A, 3/3 / J J 



2m 



/oo\ 



(32) 



The first terms in these equations reduce to those in CLEBSCH'S equations 

 (' Elasticitat,' pp. 306-307) in case the shell becomes a plane plate. 



The second terms (in ph?) arise from the " rotatory inertia." 



The third terms (in h?n) arise from the term W, in the potential energy, and depend 

 on the bending ; the fourth terms (in 2A) arise from the term W 2 , and depend on the 

 stretching. 



11. The boundary-conditions are 



.!:. ..'. ft 



V 



- 



p 



ro 1 



X 



m + n 



TO-H \ i-fn 

 -f 2 2- put|1 

 m 



(33) 



