Clearly, the “lightmill” rotates faster if more light hits it. Light bulbs behave like point sources in the sense that energy is propagated uniformly in all directions. So the intensity of light should roughly decrease with the square of the distance. This is why there was such a big difference in the rotating speed among the three lightmills. When both light bulbs were switched on, the resulting intensity profile is reminiscent of the electric potential between two positive charges.
So why do the radiometers rotate at all? There are two popular (but wrong) explanations.
Many people think that the light hitting on the vanes impart a momentum on them. Photons have no mass but they do possess (de Brogile’s) momentum. However, the problem with this explanation is, the photons bouncing off the bright surfaces should impart more momentum (through elastic collisions) to the bright surfaces. The photons being absorbed by the dark surfaces should impart less momentum (through inelastic collisions) to the dark surfaces. This explanation predicts the radiometer rotating with the dark surfaces leading, which is the opposite of the observed behavior of the radiometer!
Another equally popular but wrong explanation goes like this. The dark surfaces are warmer than the bright surfaces, causing the air to be hotter near the dark surfaces than bright surfaces. The higher pressure on the dark side (compared to the bright side) rotates the radiometer with the bright surfaces leading. Unfortunately, this explanation is flawed because higher temperature need not always result in higher pressure. In fact, we expect the air to be cooler but denser on the bright side. So even though the air molecules are less energetic individually, there are more of them, making the pressure as high as the dark side, which have more energytic but less number of molecules. In fact, the pressure in the radiometer should be uniform throughout even though there is a temperature gradient between a dark and bright surface.
The currently accepted explanation is based on something called thermal transpiration. Since I have no idea what it is, I will not write about it.
Further reading: http://en.wikipedia.org/wiki/Crookes_radiometer