I have a 3 1/2 ton 1988 carrier air conditioner. It will run for 2 or 3 hours then blow one the 40 amp fuses. What would cause this?

Actually many items could cause this type of problem

Dirty outcoor coils
Intermittent condenser fan motor
Loose or defective wiring
Bad capacitor
Over charge of refrigerant

These are just a few items to have checked. Many times the outdoor disconnect has been overheated from years of abuse and the fuse holder is loose or the copper contact area has been anealed allowing for a loose fit of the fuse which creates a hot spot. The wiring from the panel inside to the outdoor disconnect and from the disconnect to the unit have terminals or wire landing areas. These areas can also become loose causing a hot spot on on leg of the 220/240 volts which will eventually cause a time delay or temp limiting fuse to go out.

This list could go on and on so I suggest that you contact a qualified HVAC contractor so they can do a ON SITE inspection of your system and get it fixed before more damage is done. If you know how to deal with electric you can check the ideas I posted above but be careful.

This is a long shot, but possible,, if you have an old mercury style thermostat, it may be worn out cuasing stat to "short cycle" in which case the compressor would shut down and then try to start up again right away in turn drawing high amps and blowing the fuse.. The only way this could happen is if you don't have a compressor time delay in condensing unit.