1<J18] 



on Studies on Liquid Films 



387 



A hexagonal prism is an interesting case illustrating the impossi- 

 bility of getting more than three films to meet at one point. A wire 

 ])risni of indifferent dimensions — say, with its hexagonal edge of the 

 same order of length as its height — wdll give six triangular vertical 

 lilms directed from each vertical edge towards the centre, where 

 their apices are linked by a horizontal hexagon (Fig. 26). There 

 are in addition six pairs of truncated triangular films linking top and 

 bottom opposite hexagonal prism edges to the parallel central film 

 hexagon, Fig. 26 (a, b, c). If the prism height is increased and 



Fig. 26. 



this configuration preserved, then the central hexagon will decrease 

 in dimensions and should vanish when the height of the prism is 

 three time its hexagonal side, all the eighteen films then meeting 

 at the centre. What happens during tbe process is shown in 

 Fig. 26 (d) : the central hexagon is preserved, the vertical planes are 

 no longer triangles but have sides concave towards the apex, while 

 the twelve remaining surfaces springing from the top and bottom 

 edges are curved and look like a sort of hexagonal hour-glass — seen in 

 profile (d). The condition governing all these arrangements is the 

 equal inclinations of the tangent planes at the lines of intersection. 



