To Determine the Latitude of A PLACE.-In the explanation of the Table of Refractions it was stated that the refractions were calculated for latitudes at intervals of 21 degrees, which is as near as required for finding the apparent declination to set off on the declination arc, but to use the instrument for determining the meridian it is necessary that the latitude of the place should be known accurately, in order to set off the co-latitude. If this is not known, it may generally be found from a map within the 24 degrees for determining the apparent declination to set off in preparing the tables. Having done this, set off on the declination arc the apparent declination for 12 o'clock apparent noon of the given day. A few minutes before apparent noon set up the instrument and level carefully; set the declination arm at 12 o'clock on the hour ring and revolve the alidade in azimuth until the declination arm points towards the sun (Fig. 170). Set off the co-latitude approximately on the vertical circle, and clamp; then by means of the tangent screw bring the sun's image between the equatorial lines. As the sun continues to rise towards the meridian his image will descend; follow it with the tangent screw, keeping it between the equatorial lines, and by either lower tangent screw keep his image between the hour lines. On reaching the meridian his image will cease to descend and begin to rise. When this instant occurs, cease to follow it, and read the vertical circle, which will be the co-latitude of the place. The co-latitude thus found may be used with the instrument without regard to whether the vertical circle has an index error or not; but if the true co-latitude

FIG.170.

Equator

Horizontal Plane

BINY

is used with it, any index error must be determined and properly applied in setting it off, as also in determining the true co-latitude by a meridian observation, as above.

By observations on circumpolar stars. The latitude of a place being equal to the altitude of the pole, measured at the

place, the operation consists in simply observing the altitude of a circumpolar star at culmination, and correcting this altitude for refraction and for the pole distance of the star.

From a table of culminations find the time Polaris, or some other circumpolar star, crosses the meridian. About 15 or 20 minutes before this time set up the transit and level carefully. Set the horizontal wire of the telescope upon the star and follow it with the tangent screws until it reaches its highest or lowest point. Read the vertical angle and from it subtract the refraction corresponding to the reading, and then subtract if upper culmination, or add if lower culmination, the polar distance, and the result should be the latitude of the place.

Errors of adjustment of line of collimation, of vertical circle, and of plate-bubbles may be eliminated by determining the altitude of the star with the telescope direct about 5 minutes before culmination, then plunging the telescope and revolving alidade 180°, releveling, and again determining altitude, telescope reversed, by two readings. Then plunge telescope back to normal position, revolve alidade 180°, again relevel, and make another determination, telescope direct. Correct the mean of the four readings for refraction and pole distance as before.*

If the vertical arc of the transit is only 180°, an artificial horizon, as used with the sextant, may be employed, and an observation made, first to the star direct, and then to its image in the artificial horizon. The sum of the two observations will be double the apparent altitude of the star. Or, the first observation may be taken on the star direct, then two on its image in the artificial horizon, then another on the star direct, their sum giving four times the apparent altitude of the star, from which its altitude, and then the altitude of the pole or the latitude, may be obtained. The error due to an index error of the vertical circle will thus be eliminated.

*Errors of adjustment of the plate-bubble perpendicular to the line of sight and of the standards are not eliminated.

By meridian altitude of the sun, without solar attachment. The latitude of a place is equal to 90°-the meridian altitude of the sun+his declination (provided north declinations be considered positive and south negative). Or, when the observer and sun are upon the same side of the equator, the latitude

90°-the meridian altitude or the sun+the declination. When the observer or the sun are on different sides of the equator, the latitude=90°-the meridian altitude of the sun-the declination.

Hence, to find the latitude by an observation on the sun, make an observation for the altitude of his upper or lower limb when on the meridian at apparent noon, subtract meridian refraction, subtract his semi-diameter if on upper, or add if on lower limb, for the true altitude of the center, which latter subtract from 90°, and add the declination with its proper sign.

TO DETERMINE THE MERIDIAN WITH SOLAR ATTACHMENT.-Having now all the necessary data for using the instrument, to determine the meridian, or true north-andsouth line at any time of the day, take from the table the apparent declination corresponding to the mean time when the observation will be made, and set it off on the declination arc; set off on the vertical circle the co-latitude of the place, clamp the horizontal plates at zero, revolve the whole head of the instrument until the telescope is approximately in the meridian, then with one hand turn the declination arm on the polar axis toward the sun, and with the other turn the whole head of the instrument until the image of the sun is brought between the equatorial and the hour lines; then clamp the head, and by means of lower tangent screw and movement about polar axis keep the image there until exact instant for which the declination is computed, when the telescope will be in the meridian.*

*Or another method is to set the hour circle at the hour for which the declination is computed, and clamp; set off the declination and co-latitude as before, and about ten minutes before the computed time bring the sun on the plate between the equatorial lines and keep it

When the instrument is accurately adjusted and leveled, and the corrected declination of the sun for the day and hour and the co-latitude of the place are set off on their respective arcs, the image of the sun cannot, at the given hour, be brought between the equatorial lines until the polar axis is placed in the plane of the meridian of the place, or in a position parallel to the axis of the earth, and the line of collimation of transit telescope is in the meridian. (See foot-note, p. 220.)

The slightest deviation from this position will cause the image to pass above or below the lines. Thus from the posi tion of the sun in the heavens is obtained the true meridian with an accuracy corresponding to the accuracy of the adjustments and observation.

If the revolving arm be turned a little to one side of its proper position, a false image may appear in nearly the same position as that occupied by the true one. It is caused by the reflection of the true image from the surface of the arm. It can be distinguished by being much less bright and less clearly defined.

SMITH'S MERIDIAN ATTACHMENT.-Description. This attachment, shown in the figure and used in connection with the transit, consists of a small solar telescope free to revolve in the collars K, K. The collars are rigidly attached to the transit telescope, and therefore the only motion independent of the transit telescope possessed by the solar telescope is that of revolution about its longitudinal axis.

The amount of this revolution is recorded on the hour circle by an index on the upper collar K, the hour circle being a silvered ring graduated to ten minutes of time and rigidly attached to the solar telescope just above this upper collar. The vertical limb of the transit is used as a latitude arc. The declination arm is shown in the figure. Attached to the pivot end of this arm, and moving with it, is the rebetween them by moving the head of the instrument in azimuth by the lower tangent screw until the image appears between both the hour and equatorial lines-at this instant the telescope is in the meridian.

SMITH'S MERIDIAN ATTACHMENT.-B, reflector; K, K, collars; V, vertical limb, latitude arc; D, declination arc; A, B, C, C', solar line of collimation; a, hour wire; b, b, b equatorial wires. The line A B is parallel to the polar axis; and, as regards latitude, declination, and hour angle, is practically identical with it.

flector, so arranged that when the declination venier, properly adjusted, reads zero, the angle between the reflector and the optical axis of the telescope is 45°.

THEORY.-If the instrument, properly adjusted, be set in the meridian, and the latitude of the place set off on the latitude arc, the polar axis of the instrument will be parallel to the earth's polar axis.

If the declination vernier be set at zero, the portion of