I have a Traditions Pennsylvania percussion rifle with a double set trigger. The pull is rather stiff without setting the set trigger. Then if I set the set trigger, it is like a hair trigger. Is their a way to adjust it so it meets in the middle?
Not really.
When the set triggers are unset, the front trigger must push up on the sear arm to release the lock. That means the front trigger must overcome the force of the sear spring and any residual friction between the nose of the sear and the full **** in the tumbler before the sear will move.
You can do like Phil suggests and polish all of the movable surfaces in the lock but that requires taking the lock apart, something that is best not done unless you have a "mainspring clamp". You can polish the bottom of the sear arm that sticks out away from the inside of the lock and the top of the front trigger blade. That's an easy thing to do but it usually doesn't improve things much.
As for that little screw between the triggers, it controls the amount of engagement between the front trigger and the rear trigger. Screwing it in reduces the amount of engagement. Screwing it out increases the amount of engagement. This really doesn't change the force that is needed to move the front trigger but it does change how far the front trigger needs to move before the rear trigger releases.
In order to properly adjust this screw screw it almost all the way out. Then, **** the gun to full ****. Slowly screw the little screw in until the rear trigger releases and the hammer falls. Now, unscrew the screw 1 (one) full turn.
That is the recommended setup for a set trigger but if you want to adjust it so the front trigger needs to move more, unscrew the screw further. Actually, the triggers will work even if that screw is totally removed.