Just for information, there are two other methods of producing balls, especially if there is no real need for dead accuracy.
One is to use a hand held hollow/hollowed end tool with a sharp, ie cutting, edge on the end to form the ball. In other words, a specialized form tool.
The other method, which I used very successfully recently, is to calculate the necessary co-ordinates to enable a ball shape to be roughed out using a , eg, a narrow parting off tool to create a ball with a series of ridges. These ridges are then smoothed with a file, or three depending on how smooth you want it, and finished off with as smooth a device as you wish, eg emery paper. The resultant ball may not be dead accurate, but may well be good enough for practical purposes.
I found these ideas by trawling through old editions of ME.
Regards,
Peter G. Shaw