<p>A roller (40) with grooves (43a) for a wire saw around which a cutting wire is wrapped comprises a hollow core member (42) having its inside divided into two with a boundary (40a) at the centre in the longitudinal direction. Each of the internal halves has a passage (60) for circulation of a coolant and the inlet (45a) and outlet (45b) of each passage (60) are provided in the vicinity of the outer end of the half including the passage (60). <MATH></p>
