vernier, together with a part of the graduated circle.

vernier is a double one, for convenience 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 vernier, 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 another 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.

4. TO READ AN ANGLE.

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

20

20

10

ΟΙ

30

25

The

10

10

towards the left, until a "minute" mark is found exactly in

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 the 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.

CASSIOPEIA

Polaris, or the North Star, being not exactly at the pole, revolves around it through a small circle. It is therefore due north of an observer only when vertically above or below the pole. To observe it at either of these points, reference is had to certain bright stars which are in vertical range with it near the time of culmination. Its vertical range with either of the reference stars being observed, the true meridian may be set out by means of a direct observation of Polaris at an interval of time thereafter derived from the accompanying table.

The stars thus used are, first, the middle star of the three composing the handle of the Dipper, called Ursa Majoris; second, the star called 8, at the foot of the first stroke of the W in the constellation Cassiopeia, which lies opposite the Dipper, at about an

POLE STAR

POLE

DIPPER

equal distance from the pole. Of course, when one of these stars is in upper, the other is in lower culmination; and the approximate time for observation may be found in Table I., giving the culminations of Polaris. At present, Jan. 1, 1890, the Pole Star culminates not quite one minute earlier than it comes to the same vertical with Ursa Majoris—a fact indicated by the negative sign in the annexed table. The two

The following table gives, with sufficient accuracy for any latitude in the United States south of Alaska, and for either the upper or the lower culminations of these bright stars, the value of the time interval, and the annual increase thereof in minutes, between the moment of vertical coincidence, and the moment of the culmination of Polaris.

To establish the meridian, choose still weather, hang a plumb-bob from some high fixed object into a bucket of water, that it may be both free and steadfast, and select a place of observation so far southward that the plumb-line shall cover the breadth of sky between the reference star and the pole,—the farther the better. The point of observation may be an upright bodkin or compass-sight, fastened to a block movable horizontally eastward and westward. Watch for the moment when, from the point of observation, the plumb-line covers Polaris and the reference star. On the lapse of the tabular interval thereafter bring the plumb-line in range with Polaris by shifting the observation point laterally. That range will be the true meridian. Stakes may be set on it forthwith by means of candles.

If the star in Cassiopeia be used within the coming two and a half years, attention is directed to the negative time interval. Its treatment hardly needs exposition.

With a transit the plumb-line is not necessary, but special care should be taken to adjust the vertical thread of the telescope, and the horizontality of its transverse axis. This is best done by sighting up and down a fine cord or wire suspending a plummet in water. When making observations at night the cross hairs may be illuminated 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. Multi

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 westward. If both the eastern and western elongations be observed, the true meridian will pass through the point of observation, bisecting the angle between the northern range marks.

With a vernier instrument, the azimuth can be laid off directly, in degrees and minutes.