Magic, Stage Illusions and Scientific Diversions, Including Trick Photography

by Albert A. Hopkins

Let us imagine an apparatus in the form of a box ([Fig. 1]) in which is contained the entire machine that we are to describe. Upon the bottom of the box rests a copper face wheel, Α Β, having, say, eight teeth. In the bottom there is an opening in which a rod, fixed to the hub of one of the wheels of the vehicle and engaging at every revolution, pushes forward one of the teeth, which is replaced by the following one, and so on indefinitely. Whence it results that when the wheel of the vehicle has made eight revolutions, the face wheel will have made one. Now, to the center of the latter there is fixed perpendicularly, by one of its extremities, a screw which, by its other extremity, engages with a crosspiece fixed to the sides of the box. This screw gears with the teeth of a wheel whose plane is perpendicular to the bottom of the box. This wheel is provided with an axle whose extremities pivot against the sides of the box. A portion of this axle is provided with spirals formed in its surface, so that it becomes a screw. With this screw there gears a toothed wheel parallel with the bottom of the box. To this wheel is fixed an axle, one of the extremities of which pivots upon the bottom, while the other enters the crosspiece fixed to the sides; and this axle likewise carries a screw that gears with the teeth of another wheel placed perpendicular to the bottom. This arrangement may be continued as long as may be desired, or as long as there is space in the box; for the more numerous are the wheels and screws, the longer will be the route that one will be able to measure.

In fact, every screw, in making one revolution, causes the motion of one tooth of the wheel with which it gears; so that the screw carried by the face wheel, in revolving once, indicates eight revolutions of the wheel of the vehicle, while it moves only one tooth of the wheel upon which it acts. So, too, the said toothed wheel, in making one revolution, will cause the screw fixed to its plane to make one revolution, and a single one of the teeth of the succeeding wheel will be thrust forward. Consequently, if this new wheel has again thirty teeth (and this is a reasonable number), it will, in making one revolution, indicate 7,200 revolutions of the wheel of the vehicle. Let us suppose that the latter is ten cubits in circumference, and this would be 72,000 cubits, that is to say, 180 furlongs. This applies to the second toothed wheel. If there are others, and if the number of teeth likewise increases, the length of the journey that it will be possible to measure will increase proportionally. But it is well to make use of an apparatus so constructed that the distance which it will be able to indicate does not much exceed that which it is possible to make in one day with the vehicle, since one can, after measuring the day’s route, begin anew for the following route.

This is not all. As one revolution of each screw does not correspond with mathematical accuracy and precision to the escapement of one tooth, we shall in an express experiment cause the first screw to revolve until the wheel that gears with it has made one revolution, and shall count the number of times that the wheel will have revolved. Let us suppose, for example, that it has revolved twenty times while the adjacent wheel has made a single revolution. This wheel has thirty teeth; therefore, twenty revolutions of the face wheel correspond to thirty teeth of the toothed wheel moved by the screw. On the other hand, the twenty revolutions allow 160 teeth of the face wheel to escape, and this makes a like number of revolutions of the wheel of the vehicle, that is to say, 1,600 cubits; consequently, a single tooth of the preceding wheel indicates 53¹⁄₃ cubits. Thus, for example, when, in starting from the origin of the motion, the toothed wheel will have revolved by fifteen teeth, this will indicate 800 cubits, say two furlongs; upon this same wheel we shall therefore write 53¹⁄₃ cubits. Making a similar calculation for the other toothed wheels, we shall write upon each one of them the number that corresponds to it. In this way, after we ascertain how many teeth each has moved forward, we shall know by the same the distance that we have traveled.

Now, in order to be able to determine the distance traveled without having to open the box in order to see the teeth of each wheel, we are going to show how it is possible to estimate the length of the route by means of an index placed upon the external faces. Let us admit that the toothed wheels of which we have spoken are so arranged as not to touch the sides of the box, but that their axles project externally and are squared so as to receive indexes. In this way the wheel, in revolving, will cause its axle with its index to turn, and the latter will describe upon the exterior a circle that we shall divide into a number of parts equal to that of the teeth of the interior wheel. The index should have a length sufficient to describe a circumference greater than that of the wheel, so that such circumference may be divided into parts wider than the interval that separates the teeth. This circle should carry the number already marked upon the interval wheel. By this means we shall see upon the external surface of the box the length of the trip made. Were it impossible to prevent the friction of the wheels against the sides of the box, for one reason or another, it would then be necessary to file them off sufficiently to prevent the apparatus from being impeded in its operation in any way.

Moreover, as some of the toothed wheels are perpendicular to and others parallel with the bottom of the box, so, too, the circles described by the indexes will be some of them upon the sides of the box and others upon the top. Consequently, it will be necessary to so manage that the side that carries no circle shall serve as a cover; or, in other words, that the box shall be closed laterally.

Another engineer, probably Græco-Latin, since he expresses distances sometimes in miles and sometimes in stadia, has pointed out an arrangement of a different system for measuring the progress of a ship.

We shall describe this apparatus, which we illustrate in [Fig. 2].

Let Α Β be a screw revolving in its supports. Let us suppose that its thread moves a wheel, Δ, of 81 teeth, to which is fixed another and parallel wheel, Ε (a pinion), of nine teeth. Let us suppose that this pinion gears with another wheel, Ζ, of 100 teeth, and that to the latter is fixed a pinion, Η, of 18 teeth. Then let us suppose that this pinion gears with a third wheel, Θ, of 72 teeth, which likewise is provided with a pinion, Κ, of 18 teeth, and again that this pinion engages with a wheel, Λ, of 100 teeth, and so on; so that finally the last wheel carries an index so arranged as to indicate the number of stadia traveled.

On the other hand, let us construct a star wheel, Μ, whose perimeter is five paces. Let us suppose it perfectly circular and affixed to the side of a vessel in such a way as to have, upon the surface of the water, a velocity equal to that of the vessel. Let us suppose, besides, that, at every revolution of the wheel, Μ, there advances, if possible, one tooth of Δ. It is clear, then, that at every distance of 100 miles made by the vessel the wheel, Δ, will make one revolution; so that, if a circle concentric with the wheel, Λ, is divided into 100 parts, the index fixed to Λ will, in revolving upon this circle, mark the number of miles made by the number of the degrees.

Odometers, like so many other things, have been reinvented several times, notably in 1662 by a member of the Royal Society of London, and in 1724 by Abbot Meynier.