314 Mr Ibbetson, On an elastic shell. [May 25, 1885. 



A % = | + ( 1 - 2/*) a 2 - ( V - 3/0 / + ££ + 2/,) a 6 



+ 



, 1 + ^1 - a 2 



2(l+2/ i )a 4 -(l + 5/ i )a 6 +^-a 8 



yi - a 2 



The times of vibration are 



= 87m j p (1 - /c 2 ) a 3 (3 + 4a 2 + 8a*) ] 



1 /3 2 V 5? * " A 1 | ( 



t = Sira /p (1 -/r) a 6 (8 + 4a*+-3/j f ' 



To the first power of the ellipticity e (= 1— a) of the meridional 

 section, 



t = *™JfJ5I$. (1 -e) ! 



0" V 2 * q 



^ ! V2' ? 



whence it appears that, in a series of shells of the same material, 

 whose inner and outer surfaces have the same major axes (a and 

 a Jl + ft 2 ), the sphere is the form of maximum period for the 

 class of vibrations considered. 



