840 



^ 5. It follows from (10)'), thai for large values of .<; differing little 

 from / (x ^ I -\- u) 



gjcyk Ji gl Vk guyk 



(H) 





On the other hand it follows from (4') and (5), that for infinitel.y 

 small values of 'p, but x still differing little from /, 



logz[/k = logif> = u\/k — {2--logi)-'^^. . . (12) 



\iy equating the values of z in (11) and (12), putting a.i =:rand 

 remembering, that i^^^k— lv^k = iiAV'' k (eq. 6), we tind 



h \/k — 0,924 |/27ir {/ke-^^^ ..... (13) 



This therefore is the relation between the radius ;■ of a wide 

 tube and the ascension k of the liquid in the tube (the angle of 

 oontaot being zero). 



\ 6. An examination of the further course of the meridional curve 

 at a larger distance from the axis than .r ^ / (branch DEF... etc.) 

 shows, that the curve consists of a series of U-shaped curves, as 

 represented diagram matically in Winkelmann's Handbuch der Physik, 

 I (2) p. J141, fig. 404; these curves, however, are very much 



Fig. 2. 



elongated as shown in fig. 399 on p. 1135. The width of the cur-ves 

 is small compared to /; they therefore still belong to the maiginal 

 part of the meridional curve and the equation to these curves is 



1) See for instance Nielsen, Handbuch der Theorie der Gyliiiderfunktionen, 1904, 

 p. 156. 



