An adaptor and a connection device are provided. The adaptor and the connection device fix a tool to an arbor of a hollow spindle machine. The adaptor has an inlet opening at a first part of the adaptor, the inlet opening being connectable to the central passage way of the arbor. The adaptor has an outlet opening at a second part of the adaptor, the second part radially protruding over the first part and being adapted for holding the tool. The adaptor has a connection device for fixing the adaptor to the arbor and a fluid distribution passage way connecting the inlet opening with the outlet opening so that the coolant is supplied to the tool via the outlet opening of the adaptor.