The applet above (written by Anne M. Denton) shows a small circle inside of a large circle. Think of the large circle as Robert Brown's microscope lens. The smaller circle inside is one of the pollen grains being observed by Brown. The red line is the center of the circle. The pollen grain is being bombarded by water molecules, which causes it to move about erratically.
Actually, however, Brown couldn't see the water molecules, and it would not be until 1905 that it was accepted that the erratic movement was caused by molecular bombardment. So to really see what Brown saw, click on "flip view" above , and you will just see the red center moving erratically. That's what Brown and others saw. What kind of strange animal was this?
Using the buttons above, you can stop and start the applet, or reset it. You can also change the parameters, such as mu (which is the viscosity of the fluid). If you slide mu to the left, so that the fluid becomes more like water than like honey, the particle moves about more freely.
In 1905 Einstein showed that the distance r traveled by the particle was proportional to the square root of time T:
r = a T0.5.
So on a log r versus log T scale, we get a line with a slope of 0.5.