Charging ciruit problems - can someone check my logic?

[Thud_Mcguffin]

I have been having problems with my 1999 Elise, 1.8L K series engine. Basically the previous alternator failed and when I replaced it with a new one, the alternator is running very hot to the point of smoking. The car has a -ve earth and the alternator is earthed via the engine casing.

My assumption is that there is a short circuit somewhere because of the following :
1. I disconnected both battery terminals
2. using an ohm meter I found there was continuity between the alternator positive output terminal and the alternator casing itself (earth).
3. When I disconnect the alternator cables the continuity goes away, so I assume the short if not internal to the alternator.

Before I spend a significant time trying to find the open circuit. Can someone confirm that I should not be seeing continuity between the alternator output and ground when the battery is disconnected?

[Thud_Mcguffin]

Thanks. The ohms readings are a bit variable but are usually from 0 to 5. I take your point about also shorting the battery out, I don't see anything unusual when the battery is connected.

Is there anything else I should be checking which could be causing a hot (new) alternator?