( 761 ) 



The smallest, value i2„ obtains for /■ = 0. Then s = 0, i„ :*Jl ; 

 the minimal surface consists only of the surface of the circles 3/ and 

 C' i)laced side by side in the A'F-plane. We have 



2;r 



So also the surface i2o keeps moving between rather narrow limits. 

 Although the value of i2„ depends again in rather an intricate way 

 on k we can put pretty accurately, if once the critical argument 

 ?ƒ„ or the amplitude (f^ has been calculated, 



2jr sn 7(^ 



This is evident from the following table, in which have been 



o 

 inserted for some values of k the corresponding values of " and 



1 

 of . 



sn «, 



As we have h=:cnif„, where h represents again the radius of the 

 mean section we can in any case put with great approximation 



2.-r 



() — 



and in this way we obtain for the greatest possible just stable part 

 of an arbitrary cyclic minimal surface that can be extended between 

 two circles with radius H = 1 the same expression as for the 

 catenoid, 



