Sherline’s 4 jaw chuck was designed to fit on the lathe spindle, but can also be used on the vertical mill. This is very handy; when I make end plates for raised pillar reels I frequently move the work between mill and lathe, and I don’t have to re-chuck.
But this adapter is not sufficient by itself. Because of the direction of mill spindle rotation, contact of the work with an end mill tends to unscrew the chuck from the table. This invariably ruins the work, and possibly tools as well.
What is needed is a clamp to prevent rotation of the chuck relative to the table. Standard Sherline hold-down clamps do not fit. This is my homemade clamp; you can see it assembled in the top photo. The dog on the brass part hangs over the edge of the table, helping orient the clamp.