1884.] of a thin homogeneous and isotropic elastic shell. 



69 



Let the shell be bounded by the surfaces 



a 2 c 2 



a 2 + e c 2 + e 



where e is a very small quantity compared with a 2 and c 2 . 



Take the orthogonal system of curvilinear coordinates £, rj, f, 

 where + £ and — n are the roots of the quadratic 



z 2 



+ 



and 



x 2 + y* 

 of + \ ' 



£= tan" 



= 1 



-'(9 



The unstrained surfaces of the shell are then given by 



£=0, f=e. 



The limits of r) are + a 2 and + c 2 . 



During the motion of any point of the shell 77 and £ remain 

 constant, while £ is always a very small (positive or negative) 

 quantity, and a function of the time only. 



In the most general case of symmetrical motion 



It is easily shewn that 



(a 2 +Z)(a 2 - V )\ 



x' + y< = 



a —c 

 2 _ (o 2 +g)0?-o 8 ) 



a 2 -c 9 





J 



Also, if p t , p 2 be the principal radii of curvature of the strained 

 shell at time t, the formulae in §§ 242, 181 of Salmon's Conies 

 become 



5i= \4 



(Z + vf 



(g + a 2 )(g + c 2 ) 



% + c 2 



.(1). 



9£V 



(jte) + (4) + ®) ' and similarly for ** A » 



