the surface tension of soap films 289 
The points C, D should be at equal distances from the corre- 
sponding ends of the rod. The distance AC should be three or 
four times the distance AB. 
If the whole system be dipped into soap solution and be then 
withdrawn, a film will be formed in the area bounded by the 
thread and the lower rod CD. The threads now take the form 
of curves AGC, BHD, which we shall show are arcs of circles. 
The vertical part PQ of the bent rod is fixed in a clamp and 
a horizontal scale S is placetl close to the film, and the distance 
GH between the two points on the threads where the tangents 
are vertical is determined from the scale readings of the threads. 
The film is then broken and the scale readings of the threads are 
again taken. Before the first pair of readings is taken as much 
as possible of the solution adhering to the lower rod is removed 
by filter paper so that the supported mass may be as nearly as 
possible the rod alone. 
Let the distance HF (Fig. 3) between the threads when they 
are vertical be a cm. and let the distance between the points 
GH when the threads are curved be b cm. Let the mass of 
the rod CD be m grms.; the mass of the threads and of the film 
may be neglected. Let the tension of the threads at Gand H 
be WV dynes. 
The weight of the part of the system below a_ horizontal 
plane through G, H is mg dynes, and this is supported by the 
stresses which act across the plane. The force due to the film 
is 27'b dynes, since there are two faces to the film, and the force 
due to the threads is 2 dynes. Hence the equation of equi- 
librium is 
DUD SSDI or TilOpn tte race eee feta. ae Ores (2). 
Since the weight of the threads is negligible and since the 
furce exerted by the film on any element of either thread is at 
right angles to the element, it follows that the tension of each 
thread is constant and equal to NV dynes. 
Fig. 4, 
Let P,Q (Fig. 4) be two neighbouring points on the thread, 
and let the radius of curvature of the arc PQ be pcm. Let PQ 
