Switch on the hot plate (40°-50°C). Carefully pour some sulfuric acid into a small beaker. Into another small beaker, dissolve the potassium (or ammonium) dichromate (warning: chromates are carcinogenic!) in about 5 mL water. Put the watch glass on the hot plate and pour a few mL water onto it, such that about half the surface of the glass is covered. Then, with the tweezers, put a piece of gallium in the middle. Wait until the gallium has melted.

Execution:

Using a pipette, add a drop of concentrated sulfuric acid. The gallium will form a round shiny sphere. Add a few more drops of sulfuric acid.
Then, using a pipette, add a few drops of the dichromate solution. The gallium will relax and run, then contract again, relax, et cetera, like the beating heart of a metal robot. The frequency rises with some more sulfuric acid. When the beating stops, one may add some dichromate.

Explanation:

The metal gallium melts at 29,77° so it forms a liquid sheet.
In a strongly acid environment, gallium is losing electrons to hydrogen ions. Uncharged hydrogen is formed: The gallium³⁺-ions enter the solution rather slowly, so the gallium as a whole grows positively charged as long as acid is still available. The charge causes contraction: by repulsion, all charged bodies try to form a sphere. Charges try to displace from each other as much as possible. A flat puddle has, at the edges, a very curved shape and therefore the charges are very near. In a sphere, they are at equal distances, as far as possible. Gravation and other forces may work oppositely.
Why do some Ga³⁺ions remain in the drop? A small layer of hydrogen remains adsorbed at the surface, similar to the working of platinum as a catalyst. This jacket of hydrogen will break down by dichromate acting as an oxididant while hydrogen is the reductor. Then the gallium ions can escape into the solution, the gallium is discharged, and the gallium relaxes to a puddle. But the hydrogen layer is repaired by the reaction between H⁺ and gallium, just as the charge and the contraction. Et cetera. This goes on until the orange chromate(VI) has been used up and has been converted to green chrome(III).

Remark: Some authors write that puffing up of gallium by sulfuric acid happens because of the creation of gallium sulfate. This is wrong. In fact, the gallium has been charged positively when hydrogen is created by the reaction of gallium and sulfuric acid.

Afterwards: 

Using rubber gloves, put the watch glass into a bowl or pan containing ice water. The remaining gallium will solidify and can be removed with the tweezers for later use. Now, add soda until foaming stops. The solution has been neutralized, then be poured into a bottle, labeled: Inorganic waste containing chrome. Bring the bottle to the municipal place where chemical waste is collected.

Click here for a movie .WMV or here .MP4    (4'25").

At YOUTUBE a movie can be found, made at Nottingham University. Many websites refer to this movie. It speaks about more properties of gallium than the beating heart only. However, the explanation given in this movie (i.e. gallium sulfate as cause of the contraction and beating), is false. On the contrary: it is hydrogen (causing a lack of sulfate). Click here:

For Dutch version: click the flag