386 Professor Sir James Dewar [Jan. 18, 



gniphs, but in the laboratory a beam of parallel rays throwing the 

 shadows on a sheet of tissne"^ paper fixed on the side of the cubical 

 glass chamber (containing the film-cluster), opposite to the source of 

 light, gave means of making accurate measurements both of lines 

 and inclinations of planes, as well as careful tracings for further 

 study. Fig. 16 shows the shadow picture given by the quadruple 

 column shown in Figs. 14 and 15. 



Wire Models of Bubble Clusters axd Plateau 

 Frames. 



The wire frames already mentioned can be used to build up the 

 corresponding clusters. When they are dipped in soap solution 

 linked films are formed on every plane outlined by the wires, because 

 these are in the same stable relation that exists in the associated 

 bubble group. It is then possible to iusert bubble segments into the 

 spaces between the planes and thus build up the actual cluster on a 

 wire frame. 



These form an interesting comparison Avith the well-known 

 Plateau film groups, which were formed on wire frames made in the 

 shape of geometrical solids — cube, tetrahedron, triangular prisms,. 

 etc. When such frames were dipped in soap solution linked film 

 planes were obtained in beautiful regular formation, though not 

 necessarily lying in the planes of the solid figure represented in 

 skeleton by the wire, because these planes are not the stable planes 

 of liquid films in contact. The film figures finally obtained were 

 enclosed within the space of the skeleton figure. Thus the films 

 initially obtained on the six faces of a skeleton cube are pulled 

 inwards until they meet at an angle of l^O'^ instead of the original 

 right-angle. As a result a small vertical or horizontal square is 

 formed at the centre with a pair of equally inclined truncated 

 triangles radiating from each of its edges to the parallel edges of the 

 cube ; this gives eight equal truncated triangles linked by the cenrral 

 square. If a small bubble is included, this is drawn into a cuboid at 

 the centre with the remaining planes as before. So with a tetra- 

 hedron, six planes are seen to be drawn inward one from each edge,, 

 to the four lines joining the apices to the centroid. This point 

 is therefore common to the six planes which thus divide the 

 space inside the tetrahedron into four equal and similar parts, like 

 the conventional model of the four affinities of a carbon atom. 

 A double tetrahedron has this appearance repeated at each end. 

 Using an octahedron frame, we obtain six kite-shaped figures, in 

 three perpendicular pairs, linking the three pairs of opposite vertices^ 

 and having their obtuse ends fitting alternately at the centre, while 

 the acute ends stretch out to the apices. These six kites are con- 

 nected to the twelve edges of the frame by twelve triangular planes,, 

 making eighteen films altogether. 



