but it is now usual to connect that circle with a clock-work movement by which, when the telescope has been directed to a star, it may be made to revolve about the polar axis with a velocity equal to that of the earth's diurnal rotation; and thus the celestial body will remain in the field of the telescope during the time of making the observation. The hands of the observer are, therefore, left at liberty to turn the micrometer screw at the eye-piece of the telescope when it is required to ascertain, for example, the distances of two stars from each other.

The framework MN consists of four bars, or tubes, two on each side of the circle EF, to whose plane they are parallel; and those which are on opposite sides of the circle are at such a distance from it that the circle with the telescope can turn freely between them in its own plane. The upper extremities of the four bars which form the frame MN are let into a ring at N, and from this ring rise three arms which terminate in the conical pivot at B. The whole apparatus is supported at A and B in conical cups or sockets which receive the pivots; the lower socket being capable of a small movement in the plane of the meridian, and at right angles to that plane, for the purpose of allowing any derangement of the polar axis AB to be corrected.

111. An instrument like that which is above represented, being supported at the two extremities A and B, is only fit for a fixed observatory, but the following figure represents one in which the polar axis can be placed at any angle with the horizon, and consequently it may be set up in any part of the world.

The part MN represents the circular base of the whole instrument, and at each of the opposite extremities of one of its diameters is a pillar or stand BQ; the upper parts of these two pillars support a bar which turns

on

a horizontal axis, passing through B in an east and west direction; and, in the diagram, it is supposed to be perpendicular to the paper.

At right angles to this bar is fixed a tube in the direction AB, which, turning on the axis just mentioned, and carrying a graduated semicircle ab, its axis A B may be placed at any angle with

A

M

H

E

N

F

K

a vertical line passing through it; consequently, at any station whose latitude is known, on bringing that vertical line and the axis AB in the plane of the meridian, the latter axis may be made parallel to that of the earth's rotation. Within this tube is a solid cylinder to the top of which is attached a rectangular brass plate at CD, perpendicular to the axis of the cylinder and tube, and capable of being turned upon that axis. The length of the plate, of which CD is one extremity, is about equal to the diameter of the circle MN; and the direction of the length is in the diagram supposed to be perpendicular to the paper.

per

At each of the opposite extremities of this plate, and pendicularly to its plane, rises an arm, one of which appears from B to G, and the upper parts of these arms receive the extremities of a bar whose axis is parallel to the length of the plate at CD, or perpendicular to the polar axis AB (in the diagram the axis of the bar is also supposed to be perpendicular to the paper). The bar, near one of its extremities, as G, carries the declination circle EF, and, at the opposite extremity, the telescope HK: the circle and the telescope turn together on the axis passing through G; and at the same time the circle, telescope, and axis turn upon the polar axis AB: thus the circle with its telescope is constantly in a plane parallel to that of some horary circle, and the telescope may have any movement in declination.

112. If it be supposed that the polar axis of an equatorial instrument is already nearly parallel to the axis of the earth's rotation, its position with respect to the latter axis may be determined by the following processes. Direct the telescope to any one of the circum-polar stars whose apparent places are given in the Nautical Almanac, when the star is on, or nearly on the plane of the meridian, and (the index of the declination circle being at or near zero when the telescope is directed to the pole of the equator) observe by that circle the star's distance from the zero point; then turn the instrument half round on the polar axis, and having again directed the telescope to the star, read the distance of the index from zero. Take the mean of these distances, and find the refraction due to the star's altitude: the sum of these values is the corrected instrumental distance of the star from the pole; and, being compared with the polar distance of the star in the Nautical Almanac, the difference will be the error of the polar axis in altitude. This error, in an instrument constructed like that which is represented in the figure to art. 110., may be corrected by two of the screws at the foot of the axis (the angular movement of the axis depending on a

revolution of the screw having been previously found). Half the difference between the two polar distances read on the declination circle is the index error of that circle: and the index may, by its proper screws, be moved through a space equal to that half difference in order to render the readings equal, in the two positions of the circle.

The instrument must now be turned on the polar axis till the plane of the declination circle is at right angles to that of the meridian; and in this state the telescope must be directed to a star on the eastern or western side. The instrumental polar distance of the star must then be read, and corrected for the effects of refraction in polar distance (which may be computed by a formula proper for this purpose); and if the result should not agree with the north polar distance in the Nautical Almanac, the polar axis deviates from its true position, towards the east or west. This deviation must be corrected by means of the other two screws at the foot of the axis. In portable equatorials, like that which is represented in the figure to the preceding article, the adjustment of the polar axis is made by the vertical semicircle ab, and by a screw acting on the horizontal axis passing through B: the base MN having been previously levelled by means of the foot screws at M and N.

113. The position of the meridian wire in the telescope with respect to the optical axis is found by bringing the declination circle in, or near the plane of the meridian, and observing the transit of a star near the equator. Let both the time of the transit, by the sidereal clock, and the graduation at the index of the equatorial circle be read (it being supposed that this circle is divided into hours, &c. like the dial of the clock); then, turning the instrument half round on the polar axis in order that the meridional wire, if not correctly placed, may be on the opposite side of the optical axis, observe the transit of the same star: read the time by the clock, and the graduation on the equatorial circle as before. The difference between the times shown by the clock, and the difference between the readings on the circle (which would be equal if the wire passed through the optical axis), being supposed to disagree, the wires must be moved through a space equal to half the error by means of their proper screw at one side of the eye-piece. In order that this adjustment may be complete, several successive trials will probably be neces

sary.

114. The axis of the declination circle in the first of the two preceding figures may be made perpendicular to the polar axis by means of a spirit level: thus, bring the declination

circle in, or near the plane of the meridian, and having made its axis horizontal by means of the level (the latter having been previously adjusted by trying it in direct and in reversed positions), read the graduation at the index of the equatorial circle; then turn the instrument half round on the polar axis, and having again made the axis of the declination circle horizontal by the level, read the equatorial circle. If these readings should differ by exactly twelve hours, the last-mentioned axis is correct: if not, move the declination circle till the index stands half way between its actual place and that which it ought to occupy in order that the readings may so differ, and make the axis horizontal by means of its proper screws; this axis will then be perpendicular

to AB.

115. Lastly, the index of the vernier belonging to the equatorial circle should be exactly at the zero of the hours when the plane of the declination circle is in the meridian. Or, when one of the stars whose apparent places are given in the Nautical Almanac appears to be bisected by the middle horary wire in the telescope (the latter being directed to the star), the index of the equatorial circle should show the hour, &c. corresponding to the star's horary angle, that is, the angle between the meridian and a horary circle passing through the star. The star observed for this purpose should be near the equator; and if its horary angle be computed for the instant at which it appears to be bisected by the middle wire, the index of the equatorial circle should point to that angle, or it must be made to do so by its proper screw.

116. In order to use the equatorial instrument for the purpose of obtaining differences of right ascension, and of declination; turn the telescope to one of the objects, suppose a comet: then the clamp screws being fastened, mark the times by the sidereal clock when the comet appears to be bisected by the horary wires, as in a transit telescope, and take a mean of those times; also bisect the comet by the wire which is perpendicular to those wires. If shortly afterwards a known star should enter the field of the telescope, the whole instrument remaining clamped, the time of its transit at the middle wire may be observed on the sidereal clock, and it may be bisected by the perpendicular wire, which, for this purpose, must be moved in polar distance by the screw of the micrometer in the telescope. The difference between the times of the transits at the middle wire will be the difference between the right ascensions of the comet and star, and the scale of the micrometer will give the difference between their declinations. Should there be no star in the immediate vici

nity of the comet, the telescope may be moved in declination till any star is found above or below the comet, and the difference of declination must then be read on the circle; the difference of right ascension being obtained as before from the times of the transits. If the transit and the declination of the star be afterwards observed on the meridian, the star's place, and consequently that of the comet, may be very correctly determined. But if, with the equatorial instrument, a star be observed above, and another below the parallel of the comet's declination; also, if, after having made the observations on the comet and star, the instrument be turned half round on the polar axis, and similar observations be again made, the mean results will give the place of the comet still more accurately.

117. An equatorial instrument enables an observer readily to find a star in the heavens during the day. For this purpose, the right ascension and declination being known, for a given time, by computation, or from the Nautical Almanac, the telescope is clamped in the position which it assumes when the indices of the equatorial and declination circles are set to the computed right ascension and declination respectively: then, at the given time, the star will be seen in the field of the telescope.

K

118. A telescope is frequently mounted on a stand having at its top a cylindrical block of wood, which is cut through obliquely to its mathematical axis, so that the plane of section makes angles with the upper and lower surfaces equal to half the colatitude of the place in which it is to be used; the upper portion being capable of turning upon that plane about a pin fixed in the lower portion perpendicularly to the same plane. Thus, let AED, ABD represent the two portions of the block, and let a plane passing through AD perpendicularly to the paper be the plane of separation: then, if the upper portion be placed in the position which it has in the figure, the superior surface of the block will be inclined to the inferior surface in an angle equal to the colatitude of the place. If the upper portion be turned till the point A comes

D

B

G

H

to D, those surfaces will be parallel to one another, and both of them may be made parallel to the horizon.

To the upper surface is attached, perpendicularly, a brass