The Ten Books on Architecture, 10.9

Vitruvius  translated by Joseph Gwilt

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Of Measuring a Journey

9Let us now consider an invention by no means useless, and delivered to us by the antients as of ingenuity, by means of which, when on a journey by land or sea, one may ascertain the distance travelled. It is as follows. The wheels of the chariot must be four feet diameter; so that, marking a certain point thereon, whence it begins its revolution on the ground, when it has completed that revolution, it will have gone on the road over a space equal to twelve feet and a half.

2This being adjusted on the inner side of the nave of the wheel, let a drum-wheel be securely fixed, having one small tooth projecting beyond the face of its circumference; and in the body of the chariot let a small box be fastened, with a drum-wheel placed to revolve perpendicularly, and fastened to an axle. The latter wheel is to be equally divided, on its edge, into four hundred teeth, corresponding with the teeth of the lower drum-wheel: besides the above, the upper drum-wheel has on its side one tooth projecting out before the others.

3Above, in another enclosure, is a third horizontal wheel toothed similarly, and so that the teeth correspond with that tooth which is fixed to the side of the second wheel. In the third wheel just described are as many holes as are equal to the number of miles in an usual day’s journey. It does not, however, signify, if they be more or less. In all the holes let small balls be placed, and in the box or lining let a hole be made, having a channel, through which each ball may fall into the box of the chariot, and the brazen vessel placed under it.

4Thus, as the wheel proceeds, it acts on the first drum-wheel, the tooth of which, in every revolution, striking the tooth of the upper wheel, causes it to move on; so that when the lower wheel has revolved four hundred times, the upper wheel has revolved only once, and its tooth, which is on the side, will have acted on only one tooth of the horizontal wheel. Now as in four hundred revolutions of the lower wheel, the upper wheel will only have turned round once, the length of the journey will be five thousand feet, or one thousand paces. Thus, by the dropping of the balls, and the noise they make, we know every mile passed over; and each day one may ascertain, by the number of balls collected in the bottom, the number of miles in the day’s journey.

5In navigation, with very little change in the machinery, the same thing may be done. An axis is fixed across the vessel, whose ends project beyond the sides, to which are attached wheels four feet diameter, with paddles to them touching the water. That part of the axis within the vessel has a wheel with a single tooth standing out beyond its face; at which place a box is fixed with a wheel inside it having four hundred teeth, equal and correspondent to the tooth of the first wheel fixed on the axis. On the side of this, also, projecting from its face, is another tooth.

6Above, in another box, is enclosed another horizontal wheel, also toothed, to correspond with the tooth that is fastened to the side of the vertical wheel, and which, in every revolution, working in the teeth of the horizontal wheel, and striking one each time, causes it to turn round. In this horizontal wheel holes are made, wherein the round balls are placed; and in the box of the wheel is a hole with a channel to it, through which the ball descending without obstruction, falls into the brazen vase, and makes it ring.

7Thus, when the vessel is on its way, whether impelled by oars or by the wind, the paddles of the wheels, driving back the water which comes against them with violence, cause the wheels to revolve, whereby the axle is also turned round, and consequently with it the drum-wheel, whose tooth, in every revolution, acts on the tooth in the second wheel, and produces moderate revolutions thereof. Wherefore, when the wheels are carried round by the paddles four hundred times, the horizontal wheel will only have made one revolution, by the striking of that tooth on the side of the vertical wheel, and thus, in the turning caused by the horizontal wheel every time it brings a ball to the hole it falls through the channel. In this way, by sound and number, the number of miles navigated will be ascertained. It appears to me, that I have completed the description in such a manner that it will be easy to comprehend the structure of the machine, which will afford both utility and amusement in times of peace and safety.

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