The image shown to the left was scanned from Miller's article1. His description of the toy is as follows:
The toy is made of "a slender stick of some 6 or 8 inches long, of square or rectangular cross section, a quarter-inch or so on an edge, to the end of which a propeller is attached. The stick is notched with a rasp or file for 3 or 4 inches, the notches being one-eighth inch deep, more or less, across one face. The propeller is a sliver of wood, 2 inches long, roughly, one-half inch wide, and about one-sixteenth inch thick...This strip is drilled with a small hole and held to the notched end of the stick by a brad or nail. If, now, the notched stick is stroked back and forth along the notches with another stick the propeller is made to whirl. The "secret" of the device lies in two details—in the hole in the propeller and in the method of stroking. Regarding the stroking, this is best done along a corner...Regarding the hole, this can be a round hole drilled ever so slightly offcenter or a hole somewhat off-round, elliptical, say. Either provides an eccentric mounting...A very rapid whirling can be achieved by very rapid stroking."The propeller can be made to turn in either direction. While stroking, if the index finger is laid over the stick and allowed to touch the opposite side, the propeller will spin in one direction. If instead of the index finger touching the opposite side, the thumb is advanced to touch the closer side during stroking, the propeller will spin in the opposite direction.
References
1) Julius Sumner Miller, "The Notched Stick," American Journal of Physics, Vol 23, 1955, pg 176.
2) Elizabeth R. Laird, "A Notched Stick," American Journal of Physics, Vol 23, 1955, pg 472.
3) G. David Scott, "Control of the Rotor on the Notched Stick," American Journal of Physics, Vol 24, 1956, pg 464.
4) F.H. Pettit, How to Make Whirlgigs and Whimmy Diddles, Crowell, New York, 1972, pg 25.
5) Anthony and Judy Peduzzi, Making Action Toys in Wood, Sterling Publishing Co., Inc., Two Park Avenue, New York, 1985, pg 24.