847 



z = z,JJa;\/k), (10') 



z^ being the ordinate ( — CO) at the top ( ^» = -, — )• As was to be 



expected, the course of this function corresponds to the curve of 

 fig. 4'). The maximum B is found at ,4/^ =i 3.83 ') and its oidinate 

 is :b = 0.4028 z^. hence the total height of the drop is given by 



£r= 1,4028 ^,= 1,4028 X-— (37) 



independently of the width (at least as long as R^ is large). 



At a large distance from the axis of rotation the curve approach- 

 es to 



^' sinx[/k'^ ' (38) 



y^ii.^x 



§ 12. Although the capillary constant has sometimes been calculated 

 from observations on large di-ops (lying on a surface) or gas-bubbles 

 and although methods are known which are based on tliat principle *), 

 a really practical importance cannot be ascribed to them. It is only 

 for the sake of completeness tliat we shall refer to these methods 

 here in a few words and supplement them, whei-e necessary. 



In our discussion of the different ways in which surface-tension 

 may be determined by means of very small drops and bubbles'), 

 the methods were divided under three groups which might be called : 

 the piessure-melhods, the weight-methods^ and the geometrical methods. 

 In the methods of (he first group the surface-tension is derived 

 from the measurement of tlie pressure in a drop or bubble of given 

 radius; in those of the second the force is measured which makes 

 equilibrium with the surface-tension along a special line (in other 

 words: the weight is measured of the liquid carried by the surface- 



1) See for instance Jahnke und Emde, Funktionentafeln. 

 ») For water (with k = 13) therefore Xb = 1-06 cm. 



>) Cf. Nielsen, Ioc. cit. For large values of x the general solution of (9") is 

 as follows 



am {x \/lc' ^ b) (38') 



The other portions of the meridional curve, such as BDEFG (fig. 4) do not seem 

 to be possible. If a horizontal ring is moistened with liquid, one or more drops 

 will remain suspended, but they do not unite into a ring of liquid. 



*) See for instance Winkelmann, p. 1155. 



•^) Leiden. Gomm. Suppi. N». iM (1918); these Proc. XXI (1) p. 366. 



55* 



