[Hardcase]

I can think of a pretty easy way to locate any arbitrary number of equidistant points on the end of a cylinder.

Draw a circle of a given circumference, then divide that circumference by the number of points. That gives you the distance along the arc between each point. Plot the points and draw a line from each point to the center of the circle. Now all you have to do is pick points on those radius lines and you'll have perfectly spaced chambers.

So, for a seven chamber cylinder, I'd pick, say, 7 inch circle. Then every inch along the circle, mark a point. Locating the center of a circle with a compass and a straight edge is trivial, so having done that, draw the radius lines. Then locate the chambers along each of those lines.

I'll bet that they didn't really care about the angles. Just the radius and spacing. There are a gazillion practical tricks like that to get the job done.