I want an accurate division plate with, for example, 14 divisions. Not a problem - just whip out the dividing head and .... But wait! The dividing head doesn't have a 14 hole plate (we'll pretend). What to do? I need a 14 hole plate to make a 14 hole plate. The proverbial chicken-egg problem.
Well, they didn't have a dividing head when they made the first plate. There must be some way to do it that doesn't require a dividing head. It's either that or I have to admit to myself that the dividing head plate sitting in front of me doesn't really exist.
The technique described here requires only a lathe and a bit of mathematics. I can't provide an historical reference that proves this was how the first accurate plate was made but, nevertheless, it's a fascinating technique and may serve you in good stead some day.
Imagine you've turned yourself a top-hat shaped piece of steel. Now imagine you've turned 14 circular disks. When you paste these disks on the brim of the hat, touching (what I'll call) the 'crown' of the hat, they all just fit, simultaneously touching the adjacent disks and the crown. Voila, a '14 hole' dividing plate. All that's required is to make a suitable detent to locate between adjacent disks and you've got a dividing plate. With such a contrivance it would be easy to use it as a locator to drill a more conventional dividing head plate.
If the diameter of the crown of the hat is known, it's only a bit of elementary trigonometry to compute the required disk diameter for any number of divisions. After turning a piece of stock to that diameter on the lathe it's simple to slice off 14 disks. The attached .jpg file illustrates the arrangement and the math that must be done. While straightforward, a small program makes things easier. After all, the program will never transpose a digit, forget a term, take a cosine instead of a sine or make any of those other idiotic mistakes we're all so prone to make. Moreover, you'll probably want to experiment a bit to get a combination of crown diameter and disk diameter that fits your available stock. That means solving the same equation several times. So much easier with a program than a calculator. The program is available on my page; see sig for URL.