The present disclosure provides an attachment for machining a tapered cylindrical surface on a lathe machine by compound slide method. The attachment can comprise a set of gears having a first gear such as an annular worm wheel fixed with compound slide and a last gear such as a worm pivotally fixed to the cross slide and can work to magnify rotational movement of the cross slide. A Main Angle Indicating Instrument (MAI) operatively coupled to the last gear can indicate the rotation. The magnification obtained by the gears and the MAI together can achieve a least count of 1 second or less such as 0. 5 second, 0.1 second etc of cross slide rotation thus providing means to set cross slide angle very precisely. The attachment is cheap to produce, simple to install and use, requires no calculations and gives direct reading of angle value.
