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If it did penetrate you would struggle to use water on it in the future. As the water would bead off. And it might have a long term effect on the glue of a backed coticule. You may also find the hone...

Instead of oil why not try Glycerine first. It'll thicken up water a touch but unlike oil it's not going to impregnate the stone and change it's characteristics if the stone is porous.

You should...