MACHINES FOR TIIE MEASUREMENT OF SPACE.
As no precise idea can he formed of the length of a line except by comparing it with another line of known length, the necessity of having recourse for the interchange of ideas to some definite measure of distance seems to have been perceived in the earliest ages. Such standards were easily derived from Nature, and were intelligible alike to all mankind; hence originated the hairbreadth, the span, the foot, the cubit, and other measures of extent taken front parts of the human body or from other natural objects which, though not of an absolute and invariable length, had a certain mean value sufficiently definite to answer all the require ments of a rude state of society. As civilization advanced, the necessity of adopting more precise standards became recognized; the inadequacy of such measures as the foot, the cubit, etc. to convey accurate ideas was rendered most apparent in their application to multiplied measures or to the estimation of great distances. To meet this inconvenience, other meth ods of reckoning were resorted to, but they amounted only to descriptions more or less vague and not to measures; thus in ancient authors we fre quently read of a day's journey, a day's sail, etc.; and in many parts of the Continent of Europe at the present time it is the custom of the peas antry to reckon itinerary distances by hours.
The English standard of lineal measure is the yard, which is divided into 3 feet, and the foot is subdivided into 12 units or inches. The mul tiples of the unit are the pole or perch, r9S inches; the chain, 792 inches; the furlong, 792o inches; and the mile, 63,36o inches; but for itinerary distances the pole and furlong are now scarcely employed, distances being generally computed in miles and yards. The French system of measures, introduced during the Revolution, has for its theoretical standard the length of a quadrant of the earth's meridian through Paris. The unit of measures of length is the metre, which is 0 0 0 part of the quadrant, and equiv alent to 39.37oo91 inches of the English yard.
A variety of appliances have been invented from time to time for mechanically determining quantities of length and area, and though these have found but a limited application in actual practice, a glance at their character and construction may properly be here included.
Odometers.—An odometer is a device attached to a wheel for measuring the distance passed over in travelling. Odometers may be attached to the wheel of a carriage or may be driven by hand; in the latter form they are called "perambulators." Various kinds of machines have been con structed for this purpose both in ancient and in modern times. An odom
eter described by Vitruvius (fV. r27, _figs. 7, 2) consisted of a narrow drum wheel (.11, jig. r) fixed to the inner side of the hub of the carriage-wheel A, and had one small projecting tooth (13, fig. 2), which at each revolution turned one tooth of a cog-wheel (C) having four hundred teeth. This cog-wheel also carried a single projecting tooth which engaged a horizon tal ratchet-wheel (D) having holes (e) equal in number to the number of miles in an ordinary day's journey. In each of these holes of the third wheel was placed a small stone ball, and each ball was brought consec utively to a channel (F) in the case, through which it dropped into a metallic vase (G), thus audibly indicating the transit of one mile by the sound of a dropping ball. By the numerical proportion of the gearing, every four-hundredth revolution of the drum-wheel B caused one com plete turn of the cog-wheel C, whose projecting tooth moved but one tooth of the ratchet-wheel D, whereby a ball dropped through the channel F into the vase G; at the end of the journey the number of balls in the vase indicated the number of miles travelled. The wheels of the carriage or chariot were made of such a diameter that every revolution would advance the vehicle feet; thus in four hundred revolutions they passed over 500o feet, or the ancient Roman mile. The diameter of the wheels was therefore 4 feet 2 inches. Among the effects of the emperor Commodes there were carriages which not only measured the road, but also pointed out the hours. Odometers are sometimes employed in modern hacks and carriages for casual hire. A recent French instrument invented by Bruet and called a " compteur mecanique," or calculating-machine, not only reckons the distance travelled, but also indicates the exact sum of money due the driver. Figure 3 shows a carriage odometer which is attached to the spokes of a carriage-wheel, whose revolutions actuate an endless screw in contact with a toothed wheel by which the distance travelled is indi cated on the dial. A similar apparatus is used on bicycles, and is called a " cyclometer." perambulator is a machine which may be drawn along by a person on foot, and is employed in mapping districts of coun try. In one form it consists of a wheel STA feet in circumference jour nailed in the end of a stock, so that it may be lifted from contact with the ground; on the axis of the wheel is a pinion which works another pinion on the end of a rod having at its upper part an endless screw which moves a train of gearing that gives motion to two hands of an index, reg istering the distance to miles, furlongs, rods, and yards. Two revolutions of the wheel measure one rod.