1. The drift of our treatise now turns to a useful invention of the greatest ingenuity, transmitted by our predecessors, which enables us, while sitting in a carriage on the road or sailing by sea, to know how many miles of a journey we have accomplished. This will be possible as follows. Let the wheels of the carriage be each four feet in diameter, so that if a wheel has a mark made upon it, and begins to move forward from that mark in making its revolution on the surface of the road, it will have covered the definite distance of twelve and a half feet on reaching that mark at which it began to revolve.

2. Having provided such wheels, let a drum with a single tooth projecting beyond the face of its circumference be firmly fastened to the inner side of the hub of the wheel. Then, above this, let a case be firmly fastened to the body of the carriage, containing a revolving drum set on edge and mounted on an axle; on the face of the drum there are four hundred teeth, placed at equal intervals, and engaging the tooth of the drum below. The upper drum has, moreover, one tooth fixed to its side and standing out farther than the other teeth.

3. Then, above, let there be a horizontal drum, similarly toothed and contained in another case, with its teeth engaging the tooth fixed to the side of the second drum, and let as many holes be made in this (third) drum as will correspond to the number of miles—more or less, it does not matter—that a carriage can go in a day's journey. Let a small round stone be placed in every one of these holes, and in the receptacle or case containing that drum let one hole be made, with a small pipe attached, through which, when they reach that point, the stones placed in the drum may fall one by one into a bronze vessel set underneath in the body, of the carriage.

4. Thus, as the wheel in going forward carries with it the lowest drum, and as the tooth of this at every revolution strikes against the teeth of the upper drum, and makes it move along, the result will be that the upper drum is carried round once for every four hundred revolutions of the lowest, and that the tooth fixed to its side pushes forward one tooth of the horizontal drum. Since, therefore, with four hundred revolutions of the lowest drum, the upper will revolve once, the progress made will be a distance of five thousand feet or one mile. Hence, every stone, making a ringing sound as it falls, will give warning that we have gone one mile. The number of stones gathered from beneath and counted, will show the number of miles in the day's journey.

5. On board ship, also, the same principles may be employed with a few changes. An axle is passed through the sides of the ship, with its ends projecting, and wheels are mounted on them, four feet in diameter, with projecting floatboards fastened round their faces and striking the water. The middle of the axle in the middle of the ship carries a drum with one tooth projecting beyond its circumference. Here a case is placed containing a drum with four hundred teeth at regular intervals, engaging the tooth of the drum that is mounted on the axle, and having also one other tooth fixed to its side and projecting beyond its circumference.

6. Above, in another case fastened to the former, is a horizontal drum toothed in the same way, and with its teeth engaging the tooth fixed to the side of the drum that is set on edge, so that one of the teeth of the horizontal drum is struck at each revolution of that tooth, and the horizontal drum is thus made to revolve in a circle. Let holes be made in the horizontal drum, in which holes small round stones are to be placed. In the receptacle or case containing that drum, let one hole be opened with a small pipe attached, through which a stone, as soon as the obstruction is removed, falls with a ringing sound into a bronze vessel.

7. So, when a ship is making headway, whether under oars or under a gale of wind, the floatboards on the wheels will strike against the water and be driven violently back, thus turning the wheels; and they, revolving, will move the axle, and the axle the drum, the tooth of which, as it goes round, strikes one of the teeth of the second drum at each revolution, and makes it turn a little. So, when the floatboards have caused the wheels to revolve four hundred times, this drum, having turned round once, will strike a tooth of the horizontal drum with the tooth that is fixed to its side. Hence, every time the turning of the horizontal drum brings a stone to a hole, it will let the stone out through the pipe. Thus by the sound and the number, the length of the voyage will be shown in miles.

I have described how to make things that may be provided for use and amusement in times that are peaceful and without fear.