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one-quarter with the tangent screw. Repeat until the adjustment is effected. An experienced transitman will generally prefer to make this adjustment without aid, points in range being readily found.

5. Having thus brought the cross-hair to revolve in a plane, it is next to be seen whether the plane in which it revolves is truly vertical. To do so, set the instrument near the base of some lofty point, as a church spire or chimney, on which point direct the cross-hair, and then, tilting the object end of the telescope downwards, set a pin, or make a pencil dot in line. Unclamp the spindle; turn the instrument horizontally halfway round; clamp fast; fix the cross-hair again on the lower point, and try it on the upper one. If it misses, correct half the error by means of the adjusting screws now usually provided, at one of the bearings of the cross-bar; or, if these be lacking, by filing off the feet of the standard which supports the higher end of the cross-bar.

6. TO ADJUST THE NEEDLE. Having removed the cap, and placed the instrument conveniently in a still room, push one end of the needle a little aside from the point where it tends to settle, and exactly to some figured division line on the graduated circle. There gently stay it in position by means of a small wooden block, an ivory die, or the like. Observe where the opposite end strikes. If between graduation lines, mark the precise spot with a sharp pencil. Turn the needle end for end, and stay the reverse point at the division line first observed. Again spot with the pencil where the opposite end stakes. Midway of these two pencil spots make another. Take the needle off the pivot, and bend it this way or that, until, by repeated trials, when replaced with one end stayed at the division line first observed, the other shall cut the midway pencil spot.

7. The needle being thus straightened, proceed to rectify the position of the centre pin, if necessary, by bending it with nippers so that the needle shall cut opposite degrees at the quarter points of the circle.

XV.

4

MISCELLANEOUS,

THE VERNIER.

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1. The vernier in the transit a short graduated arc, movable around the graduated circle of the instrument, by means of which subdivisions of the circle graduation can be read. There are many varieties of the vernier; but a knowledge of the principle upon which one is made introduces the student to an easy acquaintance with all.

2. Suppose the tenth part of a foot to be marked off on a straight edge into ten equal parts, and that on another straight edge a space equal in length to nine of these parts is divided also into ten equal parts. The subdivisions of the latter scale will then each be nine-tenths as large as the subdivisions of the former; and if the graduated edges are placed together, with the zero marks in both exactly lined, the first mark of the latter, or vernier, scale will fall short of the first mark of the former, or limb, so to speak, by one-tenth part of the first space on the limb; that is to say, by one-tenth part of one-hundredth of a foot, or one-thousandth of a foot. The second mark of the vernier will fall short of the second mark of the limb hy two-thousandths of a foot, and so on. If, therefore, the vernier scale be moved slowly forward, the successive oppositions of the scale marks will indicate successive advances of the vernier, each equal to the one-thousandth part of a foot. The marginal example reads 6.217=six feet, two-tenths, one-hundredths, and seventhousandthis

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vernier, together with a part of the graduated circle.
vernier is a double one, for con-
venience in reading angles right
or left. It will be observed that
a space, equal to twenty-nine half
degrees on the limb, is laid off
from zero each way on the ver-
nier, and there subdivided, on
both sides of zero, into thirty
equal parts. If now the zeros
are brought into line, the first
marks of the vernier right and
left will fall one-thirtieth part of
a half degree short of the first, or
half-degree marks on the limb;
that is to say, one minute short.
The vernier, therefore, is scaled
to read minutes; and, if its zero
mark be moved slowly half a
degree on the limb, its several
subdivision marks, one after an-
other in arithmetical succession,
will be seen to line with marks
of the limb until the thirtieth is
reached, when zero will be found
to have traversed the half degree
space.

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4. TO READ AN ANGLE.

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First note whether the vernier has been moved right or left; then observe on the limb the number of full degrees, and the half-degree, if any, which zero of the vernier has passed; next, look along the vernier from its zero towards the right, if the movement has been towards the right, and from zero towards the left, if the movement has been towards the left, uutil a “minute” inark is found exactly in

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minute mark on the vernier to the angle already ascertained within half a degree from the limb: the sum will be the angle sought. The vernier in the figure reads 1° 20' L.

5. In some respects a vernier graduated decimally would be more convenient on railroad locations, where the 100-feet chain is used; the calculation of engineers’ tables to sixtieths of a degree has prevented its adoption.

6. TO RE-MAGNETIZE A NEEDLE.

Lay the north half flat on a smooth, hard surface, and with gentle pressure draw the south pole of a common magnet over it, from the centre outwards, withdrawing the magnet from it six or eight inches after each pass. Repeat ten or a dozen times. Treat the south half of the needle in the same manner with the north pole of the magnet. Replace the balancing wire. If the needle yet proves to be sluggish, take out the centre pin, and newly point and polish it.

7. If the needle, by reason of electricity, clings to the covering glass in the field, a touch of the moist finger to the top of the cover will release it.

8. Do not suffer idlers to play it about with knives, keys, and the like.

9. When the instrument is out of use, leave the needle free.

10. TO REPLACE CROSS-HAIRS.

Take out the eye-glass tube. Remove the small lateral capstan head screws which hold the cross-hair ring athwart the barrel. Loosen the vertical screws, and, taking care throughout to observe the position of the ring, in order that it may be got back again right side up and right face forward, turn it lengthwise of the barrel. Insert the end of a pine sliver into one of the side holes, take out the vertical screws, and withdraw the ring. Stretch across new hairs, in the scores traced for them, of the finest clean spider-line; secure them with a touch of gum or wax, and put the ring in by a reverse process.

11. TO FIX A TRUE MERIDIAN.

By equal shadows of the sun.

before noon, mark the extremity of its shadow. With radius reaching to that mark, from a centre on the surface vertically below the top of pole, strike an arc eastward. Two or three, hours after noon, watch for the moment when the extremity of the shadow touches thic arc. There make another mark. The true meridian will pass from the centre midway between the two marks, if the observations be made about the period of the solstice, in June or December. The method gives a fair approximation at any time of year.

12. By observation of the North Star in meridian.

Find the time of passage in Table I. Choosing still weather, hang a plumb-bob from some high place into a bucket of water, and establish a point of observation so far southward that the suspending line shall cover the breadth of sky between the Dipper and the North Star. The point of observation may be an upright bodkin, or compass-sight, fixed on a block movable horizontally east and west. Watch for the moment when, from the point of observation, the plumb-line covers the North Star and the first star in the handle of the Dipper; that is to say, the star nearest to the four which make the Dipper bowl. Exactly seventeen minutes afterwards, bring the plumb-line in range with the North Star, by shifting the observation point laterally. That range will be the true meridian. Stakes may be set in it forthwith by means of candles.

With a transit in good adjustment, the plumb-line is not necessary. Illuminate the cross hairs by reflecting light on the object glass from white paper.

13. By observation of the North Star at its extreme elongation.

Find the time in Table II., and make the preparations above directed. Keep the plumb-line in range with the star until the star apparently ceases to move. Mark that range. Multiply the natural tangent of the azimuth, given in Table III., by the distance in feet from the point of observation to the mark in the northern range just set. The product will be the distance from said northern range mark, square right or left, to a point in the true meridian passing through the point of observation. If the western elongation was observed, set off the calculated distance eastward from the northern range mark; if the eastern elongation was observed, set the distance off

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