Hardinge gave this attachment the rather ponderous name of "Model D Straight and Taper Turning Slide", but its function is basically the same as the front compound. Especially helpful in softer materials like aluminum, it allows a short distance (up to 1.75") to be traversed by means of the lever at right. It is quite useful for making large bevels and tapers without tying up the front toolholder. When used on the back of the cross slide as shown, you can use tools mounted either right side up or upside down - whichever geometry works best.
Like the normal compound, it can be used for general work. Suprisingly enough, it is fairly easy to get a nice finish in most metals with a bit of practice, despite the deceptive appearance of being a bit loosey-goosey.