EQUILIBRIUM IN LIQUID FILMS. 509 



These phenomena were so unexpected, that I thought it probable that in- 

 teresting- results would be obtained by the following alterations of the system of 

 wires in Fig. 12. 



1st. By uniting the upper and lower ends of all the wires, as shown in Fig. 16. 



2d. By uniting only the upper ends, as shown in Figs. 19, 20. 



Zd. By uniting only the lower ends, as in Figs. 21, 22. 



4th. By uniting the middle of the wires, as in Figs. 23, 24. 



5th. By uniting the middle, and also the upper and lower ends of the wires, 

 as in Figs. 25, 26, 27, and 28. 



6th. By uniting the wires at various points successively from their lower ends, 

 till they reached the position in the second system, as in Figs. 29, 30, 31, and 32. 



1st. In the jirst system, Figs. 16 and 17, we have four vertical and equal rect- 

 angles, and eight horizontal and equal right angled triangles, each of which is 

 concerned in producing the complex figure of equilibrium, shown in Figs, 16, 17, 

 and 18, and consisting of twenty-one films. As the wires are bound together, we 

 cannot vary the angle of the rectangles from 90° to 180°, in order to see that the 

 same remarkable changes will take place, as by varying the angle in fig. 12 ; nor 

 can we show, that by diminishing the angle from 90° to 45°, the central film will 

 become a line, and then start into the angle of 135°, but we can prove it by 

 uniting the wires when the rectangles are variously inclined to each other. 



In the normal state of this system, and in its various conditions from 90° to 

 180°, two of the right-angled triangles, and two at the bottom in front of the plane 

 central film, contain a plane liquid film,as in Fig. 18,* and the other two ahollow 

 triangular pyramid of films. When the central film is reduced to a line, and at 

 45° should start into the angle of 1 35°, the law of equilibrium demands that the 

 four plane films should sink into triangular pyramids, and the four triangular 

 pyramids rise into plane films ! 



If we now introduce bubbles of different sizes into the different angles of this 

 system of wires, the figures of equilibrium are very various and beautiful, chang- 

 ing with the inclination of the rectangular wire planes, and the size of the bubble. 



2d. When the rectangles are united only at their upper ends. In this case, the 

 system shown in Figs. 19, 20 consists of thirteen films, the central one of which is 

 a semi- ellipse nearly, with an angular summit upon its minor axis. The four 

 films adhering to this film, and the vertical wires, are curved, and the remaining 

 eight are the same as those shown in Fig. 18. 



2>d. When the rectangles are united only at their lower end. In this case the 

 system shown in Figs. 21, 22 is the same as that in Figs. 19, 20, inverted. 



4th. When the middle of the rectangles only are united. In this case the 

 system shown in Figs. 23 and 24 consists of sixteen films — those in the upper half 

 being similar to those in the lower half. 



* Fig. 18 is an enlarged vertical view of the upper face of figs. 16, 17. 

 VOL. XXIV. PAET III. 6 Y 



