506 Sir W. Thomson on the Division of Space 



librium, and it is clear that the equilibrium is stable without 

 them*. 



* The corresponding two-dimensional problem is much more easily 

 imagined; and may probably be realized by aid of moderately simple 

 appliances. 



Between a level surface of soap-solution and a horizontal plate of glass 

 fixed at a centimetre or two above it, imagine vertical film-partitions to 

 be placed along the sides of the squares indicated in the drawing (fig. 2) : 



Fig. 2. 



these will rest in stable equilibrium if thick enough wires are fixed ver- 

 tically through the corners of the squares. Now draw away these wires 

 downwards into the liquid: the equilibrium in the square formation 

 becomes unstable, and the films instantly run into the hexagonal forma- 

 tion shown in the diagram ; provided the square of glass is provided with 

 vertical walls (for which slips of wood are convenient), as shown in plan 

 by the black border of the diagram. These walls are necessary to main- 

 tain the inequality of pull in different directions which the inequality of 

 the sides of the hexagons implies. By inspection of the diagram we see 

 that the pull is T/a per unit area on either of the pair of vertical walls 

 which are perpendicular to the short sides of the hexagons ; and on either 

 of the other pair of walls 2 cos 30° X T/a ; where T denotes the pull of the 

 film per unit breadth, and a the side of a square in the original formation. 

 Hence the ratio of the pulls per unit of area in the two principal directions 

 is as 1 to 1-732. 



