fore, the diameter of the wheel, the corresponding odometer must be ordered from the maker, and the record may be in miles or some scale unit, the latter being obtained by the surveyor making a false dial to be pasted over that which is furnished. This instrument is attached to the axle of the wheel and records by a small lug on the hub striking a starshaped wheel connected with an endless screw within the odometer. The mode of counting revolutions of a wheel most satisfactory to expert traversemen is by tying a rag to one of the spokes and counting the revolutions as it comes in view each time. The traverseman soon becomes so expert that he does this counting without any apparent effort, and he intuitively catches through the corner of his eye the flash of the white cloth. Others fasten gongs with heavy pendulum clappers to the spokes of the wheel, so that each time the wheel revolves the clapper falls and strikes the bell. Others rig gongs to the axle and cause them to be struck by clappers attached to the revolving wheel or hub. The simplest counter is, however, the most certain, and of these is the cloth tied to the spoke and counted mentally, or, best of all, on a hand-recorder which is pressed at each flash of the cloth as it revolves, the recorder registering automatically the number of revolutions. (Fig. 75.) In using any form of odometer measurement it becomes necessary to accurately measure the outer circumference of the wheel and then, for convenience in plotting, to arrange a small table in accordance with the scale of the map, so that the number of revolutions multiplied into the circumference will give decimals of the map scale. This table would therefore show for each tenth or hundredth of a mile or other unit the number of revolutions corresponding to such distance. (Table VII.) 99. Chaining.-The chain is little used by topographers excepting in dense woods and where the odometer cannot be run nor the stadia-rod seen. Chains are made of two lengths. The surveyor's or Gunter's chain is 66 feet long and consists of 100 links, each 7.92 inches long. It is only used in determining the areas of land where the acre is the unit of measure. It is universally used in all of the United States public-land surveys. In all deeds of conveyance of property, where the word "chain" is used it refers to the 66-foot chain. The engineer's chain, that commonly used now, consists of 100 links of steel wire, each connected with the next by two or three rings. Each link with its rings is one foot in length, and the total length of the chain is 100 feet. At intervals of ten links brass tags are brazed on, having one to four points to indicate distances of 10, 20, 30 feet, etc. The chain is provided at either end with brass handles fastened with a swivel, and the length of the chain includes the handles. The chain is done up from the middle, two links at a time being drawn into the hand. In measuring with the chain the front chainman carries a bundle of ten pins with pieces of cloth tied to them to attract the attention of the rear chainman, and one of these pins is pressed into the ground at each chain-length. They are picked up and tallied by the rear chainman as he progresses. It is very easy to make mistakes. in chaining, because of the liability to drop a chain in counting or the tendency to measure on sloping ground without making the proper reductions to the horizontal. Moreover, the chain varies in length by tension, expansion, and contraction. In chaining on steep ground the endeavor should be to hold the chain level and to plumb down from one end, and where the slopes are very steep.half-chains of fifty feet only should be measured at a time in order that the chain may be held horizontally. The chainmen usually work ahead of the transitman towards the front flag, but they may be passed by him and follow him. The rear chainman is the more important of the two, as under ordinary methods of running he lines in the front chainman. The latter walks ahead, dragging the chain behind him, and moves to one side or the other according to the rear chainman's signaled directions. The rear chainman shakes the chain out to get rid of kinked links, holds the end of the handle against his pin, and when the front chainman is in line calls out "Down!" when the latter places the fore pin in the ground. The front chainman should be the more active of the two, as the speed of the party depends upon his movements. CHAPTER XII. STADIA TACHYMETRY. 100. Tachymetry.-Tachymetry, or, as it is sometimes called, tachyometry, is a method of rapid surveying which enables the operator, by a single observation upon a rod, to obtain the necessary horizontal and vertical data for the determination of the three elements of position of a point on the surface of the earth. Optical measurement of distances, azimuths, and heights by one observation is its essential principle, and is performed by means of stadia, telemeter, or special tachymetric attachment. Tachymetry furnishes at one operation all the controlling elements required in topographic surveying as distinguished from plane surveying, which for topographic requirements must be supplemented by hypsometric surveying. The instruments employed in tachymetric measurement consist of a good transit or plane-table and alidade (Arts. 85, 56 and 59), and of a well-made rod variously divided according to the method employed (Art. 112). The requirements of this method are rapidity and comparative accuracy of measurement accomplished with the least cost, rather than with extreme precision. Where it is necessary to measure distances and elevations at the same time, tachymetry gives as nearly accurate results, at much less cost of time and money, as are possible with chain and spirit-level. There are practically two systems of tachymetric meas. urement: 1. The angular or tangential system; and |