16 Lord Rayleigh on Bells. 



From these, by elimination of Sr, 



dSz^drd,/ d$<l> \_~ 

 ~dz "dzdzV dcfr J ' 



dSz 2 dfy__ dr<P84> 

 d<j> +r dz T dz d$ 2 



from which again, by elimination of 8z, 



IzV dz ) dJ di? ~ U - 



(4) 

 (5) 



(6) 



For the purposes of the present problem we may assume 

 that d(f> varies as cos scj), or as sin scj); thus, 



d§cj> 



d 2 r 



dz\ dz I dz 2 



. . . (7) 



is the equation by which the form of B(p as d Ainction of z is 

 to be determined. 



When application is made to the hyperboloid of one sheet 



: - = 1 



a 2 U 2 



(8) 



we find, since 



dr _ a 2 z 

 V dz~W 



d d 2 r __a 4 



r Tz 2 ~h 2 ' 



4z(^y4^- 



(9) 



The solution of this equation is expressed by an auxiliary 

 variable %, such that 



in the form 



2 = 6 tan ^, ^ = asec% .... (10) 

 <£ = A coss% + Bsin s% (11) 



In order to verify this it is only necessary to observe that 

 by (10) 



9 d a? d 

 dz o a% 



We will now apply this solution to an inextensible surface 



