The remarkable history of James Ferguson, a self-educated man who achieved a prominent place in astronomical circles during the middle of the last century, affords an incident which will be of interest to many readers of this magazine. While engaged one evening in a religious controversy, and to prove his contention, he volunteered to construct a mechanical device which seemingly was contrary to all mechanical laws and declared as impossible by those with him, He appeared by appointment a week later, however, with the arrangement of gears given in the following description, which greatly mystified his associates, who were unable to solve the reason why the gears moved contrary to recognized laws. The original model made by Ferguson was of wood, and similar ones can easily be made if the directions are carefully followed, which will be a good puzzle for the unitiated to study over and show the extent of their knowledge of gears.

Ferguson s Mechanical Paradox 152

We will first have a description of the device, which the illustration shows to be a train of gears mounted on a frame and which may be turned in either direction by the handle. The gear D is a fixed gear, the others turn on their shafts. If the frame be revolved, any number of times, the several gears will presumably be found to mesh at the same places when the frame is brought to the same vertical position, but this is just what does not take place.

Of the three gears, F, G and H, one will remain in the same place, another will be found several teeth to the right, and the other several teeth to the left of the position from which it started. This will be made evident if, before the frame is turned a chalk mark is drawn on the top of these three gears, the location of the chalk marks after several turns of the frame showing the movement of two of the gears mentioned above.

The solution of the mystery lies in the fact that the gear G has one tooth less, and the gear H one tooth more than the others, the teeth on G being thickened slightly and on II thinned, to run on E without binding. That the difference in pitch be as inconspicuous as possible, the gears should have quite a number of teeth. Gears 4 in. in diameter make a good size, and 100 teeth are easily laid out on this size.

To make a wooden model, a supporting board, A, is first prepared. This may be 12 in. long. 3 in. wide and J in. thick. The piece B is 14 in. long, 1 1/2 in. wide and 3/4 in. thick. To avoid excessive wear, the shafts can best be made of brass rod 3/8 in. diameter; that for gear being 3 in. long, and for the others 2 in. long. The shaft for D is driven with a tight fit into a hole bored 2 1/4 in. from the top of and in the center of the board, A. A hole is bored in B, the center of which is 1 in. from the upper end and is an easy fit for the shaft, so that B may freely turn on it. The gear D is a tight fit on this shaft and does not turn. A small piece of wood 1/2 in. thick is placed on the shaft A and B, to keep the latter away from the former. The shaft for E is driven with a tight fit into a hole bored in E and centering about 3 7/8 in. from the hole for D. The locating of the holes for the shafts should be done after the gears are made, that they may be so spaced as to prevent binding or looseness. The shaft for the three gears, F, G and H, is also spaced about 3 7/8 in. from that for E, and tightly driven in a hole in B.

The gear, D, should be about 1/2 in. thick, and the three gears, F, G and II, each 1/4 in. thick. They should be made of well seasoned maple or birch of even grain, which should run parallel with the shafts. They should also be well soaked in oil, after the teeth are cut, to avoid splitting or change of shape. The gears, D, E and F, have 100 teeth, G has 99 teeth, and H 101 It will also be necessary to make the teeth on E rather thinner than that pitch would ordinarily allow. The shaft for the three lower gears should have a small hole drilled near the outer end, into which a stay pin can be placed, holding the gears in position when turning, yet allowing of their easy removal to adjust so that there will be a straight row of teeth at the top of these gears before commencing to turn and upon which a chalk mark can be made, when showing the device to visitors.

The handle is attached to the lower end of B. It is evident that, if the frame be turned, the gear G, having one tooth less than F, will turn on its axis faster than .F and in the direction it moves on its axis, while H, having one tooth more than , will turn slower than F and in the opposite direction from which it turns on its axis.

This device offers an excellent study in wood working, as well as an interesting example of the action of a train of gears and will prove of much interest to anyone making it, as well as to visiting friends interested in mechanical novelties.