This section is from the book "The Boy Mechanic Vol. 2 1000 Things for Boys to Do", by Popular Mechanics Co.. Also available from Amazon: The Boy Mechanic, Vol2: 1000 Things for Boys to Do.
The centering gauge consists of a piece of celluloid on which several circles are drawn having different diameters, but all drawn from the same center. A small hole is made at the center to admit the point of a center punch. Two sets of circles may be drawn on one piece as shown, but the lines should be spaced far enough apart to allow the metal to be clearly seen through the celluloid. The sheet is placed on the end of a shaft and adjusted so that a ring will match the circumference of the shaft, then the center punch is set in the center hole and struck with a hammer. The center punch for marking is shown in the sketch. - Contributed by Harry Hoist, San Francisco, Cal.
Ill: Circles Drawn on Celluloid to Adjust It on the End of a Shaft in Finding the Center