Problem with ring-method of du Nouy for calculating surface tension

I need to calculate the surface tension of a liquid with the ring-method of du Nouy and the correct formula to use is:

$\gamma = \frac{F}{4\pi R}$

I understand that the surface tension is the force that acts on a certain length which, in this case, is the circumference of the ring. Since the circumference of the ring is $2\pi R$ where does this extra $\times2$ come from?

Thanks!

Answer

If you look at a cross section of the ring the geometry looks like:

Note that the ring raises a cylinder of the fluid with an inside and ouside surface, and both surfaces pull on the ring. The force from each surface is $\gamma 2\pi r$, so the total force is $\gamma 4\pi r$.