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Let a few others have a guess then put us out our misery. Well done by the way!

On a mainspring you should use OIL not grease :) you should use some grease on some point but never in a mainspring barrel .

I use 8200 breaking grease on the barrel walls (in two places) and then 8141 on the spring and barrel floor

If you are buying and installing a new main spring it should come ready coiled inside a washer to a small enough diameter to fit into the barrel. You just place the spring/washer onto the barrel so that the wall of the barrel is supporting the washer and then carefully and evenly push the spring through the washer and into the barrel. Push the outside coils of the spring not the middle and it should just pop into place. Make that you place the washer the right way up so that the spring coils up in the right direction (clockwise or anti-clockwise) as you only get one shot at this the easy way.

Here is the pic