Your Burman shaft splines are cut on a milling machine. The selection of 40 teeth is simple, because a dividing head, used in those days, needed 40 turns of the operating handle to rotate through one revolution. Different ways of doing this milling, depended on the operators preference. That operator had to be by , and turn the handle after every single cut.
The ones I make today are generated with a controlled head. So I have the luxury of walking away until the job is complete.