what does that part do?

Could you maybe elaborate a little? Where is it?

its a dust cap and meant to keep dirt and moister away from the points and shaft.

Mario Vintage Werks resto

It goes around the shaft and covers the points so that only the rotor is initially visible when you take the cap off.

I guess it keeps dirt and the carbon from the sparks from falling into the works of the distributor and gumming up the grease on the shaft?

Oh I get it. Yes it keeps junk away from the points, and to some extent moisture too like Mario said. It's not critical, if you have one, use it. If you don't, don't worry about it. It makes very little difference in my opinion.

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Take off the distributor cap. Look inside. See that black button in the middle? It is made of graphite -- pure carbon. It wears as the rotor spins about, depositing a fine dusting of CONDUCTIVE carbon granules all over the inside of the distributor. This leads to premature failure of the contact points and accelerated wear of the distributor-cam lobes.

And newer ones DO have it... if they are worth a shit. (It's the El Cheepo ones that leave it off.)

-Bob Hoover

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That makes sense but I've never seen a cover like that in any other distributor... although that might explain why some Delco rotors are round.

Jeff DeWitt