the surface tension of soap films 295 
AUR: ; 
or 2 = — sin 0@=rsin 0, 
where r=4T7/p. But dy/da=tan @ and hence 
| ypc ae SiG! an 
| dx  /] —sin?6 V7? = a? 
‘Thus aN ee Ke 
| Choosing the constant K so that y=0 when «= 0, we have 
| (y—r)y+aear’, 
) which represents a circle of radius 7 whose centre lies on VO at 
a distance r below V. Hence the film is spherical and has the 
radius 
r =A4T/p. 
The surface tension is therefore given by 
As the height, h, of the vertex of the film above the rim of the 
ring is gradually increased from zero to c, the radius of the rim, 
the radius of the bubble diminishes from infinity until it reaches c, 
If h be further increased, the radius of the bubble increases also. 
Hence the pressure excess must not be greater than 477/c, for if 
the height of the bubble be made to exceed c, the pressure which 
it can resist will become smaller as the radius of the bubble 
increases, with the result that, if the bubble be supplied with air, 
it will swell until it bursts. 
§11. Practical example. The following results were obtained 
by G. F. C. Searle and A. J. Berry. Two tubes in series were used 
between the manometer and the bubble stand. 
Length of tube (1) or CD (Fig. 6)=/,=28°8 cm. 
Mass of mercury filling tube =81°8 grms. 
Density of mercury =13'55 grms. per C¢.c. 
81:8 
i = ght OOS ues Saray 2 
Square of radius of tube=a, = 15 x oxO88 0:06672 cm. 
Hence a,=0'2583 cm. and a,4=4°452 x 10-2 cm.! 
4 4-452 x 10-8 
Th pre: 
ne T, 28:8 
=1°546x 10-4 cm.? 
By similar measurements on tubes (2) and (3) 
2=120:0cm., a=01437cm., a '=4:259 x 10~4cm.* 
l,z=158:2cem., a3=0:1479cm., a3'=4°784 x 10-4cm.4 
