290 Dr Searle, Some methods of measuring 
subtend an angle @ radians at O, the centre of curvature. 
Theay2Q = pe! 
The force which the other parts of the thread exert upon PQ 
is 2M sin 30 in the direction KO, where K is the point of inter- 
section of the tangents at P and Q. The force which the film 
exerts on PQ is in the direction OK and lies between 27’. PQ and 
27. PQ cos 46 dynes or between 27'p0 and 276 cos 40 dynes. 
Since the force due to the thread balances the force due to the 
film, we see that N lies between 
and 2T/p | ay aintg cos 40. 
When 0 approaches zero, the limit of ite 40 is unity and the 
limit of cos 4@ is also unity. Hence 
N = 27 p dynes .....01.. 32 eeeeeeee (3). 
Since N and 7 are constant, p also is constant and hence the 
threads form arcs of circles. 
The equilibrium equation now becomes 
T(2b + 4p) = mg, 
Ty 29 
P sin 40 
i ee) 
or = 3B ap 1 ee (4). 
Fig. 5, 
The radius of curvature, p, of the threads must now be found. 
Let e=4(a—D) so that (Figs. 4,5) c= HF= HG. Then, from 
Fig. 5, if BD=hem. 
x (2p — x) = th, 
(ew 
or p= on + 9 a:'n \0°6iie'vo.ra)-eior wl Gvetenevenete teeter ckenetenerere (3): 
The vertical distance h= BD is measured while the film is wn- 
broken. 
