$ 7. VERNIERS. B First form. Let AB (Fig. 9) represent a portion of a rod for measuring heights (§ 32). The graduation to feet and hundredths of a foot begins at the lower end, which rests on the ground when the rod is in use. The line extending nearly across the rod at the bottom of the portion shown marks the beginning of the fourth foot. The face of the rod is divided into four columns: in the first is written the number of feet; in the second, the number of tenths; and in the third, the number of hundredths. It is evident that, with the arrangement just described, heights could be measured only to hundredths of a foot. To enable us to find the height more precisely, a contrivance called a Vernier is used. This is shown at the right of the rod. It consists of a piece of metal or wood, the graduated part of which is of a foot in length; and this is divided into ten equal parts. Hence, one division of the vernier of 10% = 1000 of a foot; and one division of the vernier exceeds one division of the rod by 100 = 101‰0 of a foot. ΙΟΟ 1 1 100 10 1 1 The vernier slides along the face or side of the rod. RE 4 3 1 の 60 3 9 8 7 0 6 1 5 4 3 4 5 1 To use the vernier, place the lower end of the rod upon the ground, and move the vernier until its index or zero mark is opposite the point whose distance from the ground is desired. In the figure, the height of the index of the vernier is evidently 4.16 feet, increased by the distance of the index above the next lower line (4.16) of the rod. We shall now determine this distance. Observe which line of the vernier is exactly opposite a line of the rod. In this case, the line of the vernier numbered 7 is opposite a line of the rod. Then, since each division of the vernier exceeds each division of the rod by Too of a foot, 1 000 1000 6 of the vernier is 1 of a foot above the next lower line of the rod. 5 of the vernier is 1 of a foot above the next lower line of the rod. 4 of the vernier is 2 1000 10 of a foot above the next lower line of the rod. 3 1000 4 3 of the vernier is of a foot above the next lower line of the rod. 2 of the vernier is 1 of a foot above the next lower line of the rod. 1000 1000 6 1000 7 1000 1 of the vernier is 10 of a foot above the next lower line of the rod. 0 of the vernier is 1 of a foot above the next lower line of the rod. Hence, the required reading is 4.16+0.007=4.167 feet. In general, the following rule is evident: Move the vernier until its zero line is at the required height; read the height to the nearest hundredth below the index, and write in the thousandths' place the number of the division line of the vernier which stands opposite any line of the rod. 9 100 Second form. In this form (Fig. 10) the graduated part of the vernier is 1% of a foot in length, and is divided into ten equal parts. Hence, one division of the vernier 9 100 To of 10 vernier is less than one division of the rod 9 by 100-1000 = 1ooo of a foot. 1000 The height of the index of the vernier in Fig. 10 is 4.16 feet, increased by the distance of the index from the next lower line (4.16) of the rod. We shall now determine this distance. We observe that the line of the vernier numbered 7 stands exactly opposite the line of the rod numbered 3. Hence, 6 of the vernier is 10 of a foot above the next lower line of the rod. 5 of the vernier is of a foot above the next lower line of the rod. 1 1000 2 1000 3 4 of the vernier is 1 of a foot above the next lower line of the rod. 3 of the vernier is 1 of a foot above the next lower line of the rod. 2 of the vernier is 1 of a foot above the next lower line of the rod. 1 of the vernier is 10‰ of a foot above the next lower line of the rod. 0 of the vernier is 10 of a foot above the next lower line of the rod. 1000 4 1000 5 1000 6 1000 7 1000 Hence, the required reading is 4.16+0.0074.167 feet; and the rule is evidently the same as for the first form. Compass Verniers. Let LL' (Fig. 11) represent the limb of the compass graduated to half-degrees, and VV' the vernier divided into thirty equal spaces, equal to twenty-nine spaces of the limb. Then one space of the vernier is less than one space of the limb by 1', and the reading may be obtained to single minutes. In Fig. 11 the index or zero of the vernier stands between 32° and 32° 30', and the line of the vernier marked 9 coincides with a line of the limb. Hence, the reading is 32° 9'. When the index moves from the zero line of the limb in a direction contrary to that in which the numbers of the limb run, the number of minutes obtained as above must be subtracted from 30' to obtain the minutes required. If, however, the vernier be made double, that is, if it have thirty spaces on each side of the zero line, it is always read directly. The usual form of the double vernier, shown in Fig. 12, has only fifteen spaces on each side of the zero line. When the vernier is turned to the right less than 15' past a division line of the limb, read the lower figures on the left of the zero line at any coincidence; if moved more than 15' past a division line of the limb, read the upper figures on the right of the zero line at any coincidence; and vice versa. Uses of the Compass Vernier. The most important use of the vernier of the vernier compass is in setting off the variation of the needle (§ 23). If the variation of the needle at any place is known, by means of the vernier screw the compass circle may be turned through an arc equal to the variation. If the observer stands at the south end of the instrument, the vernier is turned to the right or left according as the variation is west or east. The compass will now give the bearings of the lines with the true meridian. In order to retrace the lines of an old survey, turn the sights in the direction of a known line, and move the vernier until the needle indicates the old bearing. The arc moved over by the vernier will indicate the change of variation since the time of the old survey. If no line is definitely known, the change of variation from the time of the old survey will give the arc to be set off. § 8. THE SURVEYOR'S TRANSIT. This instrument is shown on page 17. The The compass circle is similar to that of the compass. vernier plate which carries the telescope has two verniers and moves entirely around the graduated limb of the main plate. The axis of the telescope carries a vertical circle which measures vertical angles to single minutes by means of a vernier. Under the telescope, and attached to it, is a spirit level by which horizontal lines may be run, or the difference of level between two stations found. The cross wires are two fine fibres of spider's web, or fine platinum wires, which extend across the tube of the telescope at right angles to each other; their intersection determines the optical axis or line of collimation of the telescope. The transit is levelled by four levelling screws which pass through a plate firmly fastened to the ball spindle, and rest in depressions on the upper side of the tripod plate. A quick centring head enables the surveyor to change the position of the vertical axis horizontally without moving the tripod; and a quick levelling head enables him to bring the transit quickly to an approximately level position by the pressure of the hands, after which the levelling screws are used; also, to change the position of the transit without changing the position of the tripod legs, so as to bring the plummet exactly over any point. To level the transit by the levelling screws. Turn the instrument until the spirit levels on the vernier plate are parallel to the vertical planes passing through opposite pairs of levelling screws. Take hold of opposite screw heads with the thumb and fore-finger of each hand, and turn both thumbs in or out as may be necessary to raise the lower side of the parallel plate and lower the other until the desired correction is made. To use the telescope. Both the eye-piece and the object glass may be moved in and out by a rack-and-pinion movement. The eye-piece must be moved until the cross wires are |