PURPOSE: To determine the feed for cutting a fragmentary material by setting a reference level at the top end of the sensing probe of an apparatus for detecting the displacement amount of the ingot end face, and reading the displacement amount of the ingot end face position from the reference point.

CONSTITUTION: A calibrated detecting unit 10 is attached to a reference shaft 2 of the slicing machine side. An ingot W is lowered till its end face abuts on the top end of a sensing probe 12. Then, the sensing probe 12 is sequentially put in contact with several appropriate points of the end face of the ingot W, and the displacement amounts at that time are read with a dial gauge 14. From the respective readings, the farthest size (a) relative to the reference line (numerically, in this case, the zero point of the dial gauge) is determined. With this, the original cutting position of the ingot W is obtained by the height value L of a level line W plus the size (a), so the ingot W is lowered by the height value L plus the size (a) from its measuring point and cut with a blade.