Attaching eiffel to eames wire chair  

Wire seats
The original mounting holes should be threaded so that nuts are not needed to secure. Since the mounting holes on the base are not threaded, you would insert the screw from the bottom up. Alternatively, if the screws are too long, you could try from the top down and use nuts on the base end. Or you could just get shorter screws.

Thank you
I screwed the base from the bottom. Unfortunately (for now), there are four lock washers on each screw helping to hold the base in place due to the length of the screws. One of these days, I'm going to cut the screw lengths down using my Dremel.
Nuts were not needed to hold the screws in place, except where the threads (2 holes) were pretty much stripped.
So far, it's holding up well. Not perfect. But, then again, it's an old chair.
David

Just buy new screws and be done with it
Why not just take the screws to the hardware store, have them find screws with matching thread and get yourself a new screws? Way less hassle than using a dremel to shorten the screws and it'll cost you less than a dollar. Or is there something special about these screws that I'm missing?
fm

Re screw replacements
I was at my local hardware store and could not find shorter replacement screws. Cutting the screw with a Dremel is simple.

cutting screws
Be careful when cutting screws : if they are just plated but not stainless steel, they will tend to rust. Not very important depending where these screws are located, but it might be a problem on Eames wire chairs...