Just a couple of pictures of an internal taper I made using the compound slide on my SB Heavy 10 lathe. The workpiece in the photos is the underside of a shop-made turret-type tool post for the same lathe. For scale, this is a 4" square tool post that takes 1/2" square tool bits, and the clamping screws are 7/16".
The reason for the taper was an experiment based on the idea that the taper presents more surface area per unit of length, and therefor better grip when the indexing lever is tightened. I forget the included angle of the taper (I made this last year) but it is obvious that it is a self-releasing type.
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I post pictures of this because I'm particularly proud of the fine finish I was able to achieve with just the (hand-fed) compound slide.
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The mating post (what would that be called?) has a similar finish (no pictures available).
Thanks for indulging me!