70 Mr Ibbetson, On the small free normal vibrations [Jan. 28, 



Then 



h= ^i^m±^ 



k 



= 2 / (a*-v)(y-c*) y 



1 _ / a 2 -c 2 

 3 V(f + a 2 )(a 2 -^)j 



Let square brackets [ ] denote that the quantity enclosed is to 

 have the value it assumes when £ = 0. 



Then if dS be the element of surface of the unstrained shell at 

 either of the two points (r), £) 



dr) . d£ 



dS= 



[W 



= ^\/ {a ^^\ v -or d71 ' d ^ 



(c 



Thus the integral, taken over the whole surface, of any function 

 U of 7] only is, if the shell be oblate, 



27ra ro? I j. 



and if it be prolate, 



zira re* I v 



.(3). 



The perpendicular from the centre on the tangent plane to the 

 unstrained shell at (rj, £) is \ [AJ. Hence if t be the thickness at 

 that point, 



_ 6 Y^K 



T " 2 L 9|. 



e 7) (a 2 + c 2 ) - aV 

 2ac ' t\\ 



The normal velocity at time t of the point (rj, £) will be, ap- 

 proximately, 



f 



= A VS 



[AJ 2ac 



