Assuming you mean the mandrel that carries horizontal milling cutters normal practice is to have a taper on the end matching that in the spindle with a threaded drawbar running through a hollow spindle to hold it tightly in place. Its quite likely that the drawbar would have also been used to close the collets that were used to hold cutters directly in the spindle nose.
The outside end of the mandrel is usually arranged as a simple plain bearing to support the mandrel with sufficient endwise clearance for all end thrusts to be dealt with by the spindle.
Hopefully you have at least one collet so the type can be identified and the spindle taper derived from it.
However looking at the early brochure pictures on the lathes.www.co site its not clear whether on not the spindle is actually bored through. Some picture might have a drawbar sticking out of the end but its a matter of interpretation. iIf the spindle is solid the collets would have been closed by a nut running down on the external thread on the end of the spindle. Rather after the manner of a modern ER collet. Som eo the lathes.www.co pictures appear to show such a closer nut. If the spindle is solid the mandrel will still have a taper matching the spindle nose but a captive nut fitting the exteranl thread will be required to to hold it in place.
Clive