Is there a fusible link between the starter solenoid & battery?  Look for
melted/charred wire.  Or the solenoid itself created the smoke.  Check for
voltage on the solenoid contacts - voltage means the wiring is good, no
volts means the wiring is not good.

That usually means you have blown a fuse link wire.  They are about 8"
long and have a loop at the bolt where they hook up to the positive
cable and a rubber tube crimp connector where they hook to the wiring
harness.

You can buy the wire in bulk at the dealer usually and crimp a
replacement in.  They are usually color coded for size, but most are 14
ga. protecting the starter circuit.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
88 Cherokee 235 BFG AT's
Canadian Off Road Trips Photos:  Non members can still view!
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You probably melted a fusible link wire.  An easy way to check is to
pull on the various wires branching off from the battery.  Fusible
link wire is made with insulation that will not burn easily and may
appear fine.  If the wire stretches when you pull on it there is your
problem.  I doubt that you destroyed your alternator or anything else.

Now please relax about the backwards battery -- many have done it
before you and many will do it after you!  This includes automotive
service professionals who suffer a momentary attack of
absent-mindedness.  

Don
www.donsautomotive.com

Mike,

Quit beating yourself up.  I receive hundreds of questions per year
from people who have connected jumper cables backwards and to a lesson
extent the battery cables backwards.

Several others have already recommend that checking and replacing your
fusible link.  A couple of additional points.  Often the heat will
damage the insulation of the positive of the positive cable(s).  Most
electrical tape can not withstand the high underhood temperatures
found with today's cars, so you might want to find a good substitute.
The second point is that you might want to carefully test all the
electronic devices that were on when the battery was reversed.
Examples are emission computer, clock, memory presets, security
alarms, etc.