being very nearly that in which a fixed star appears to revolve about the earth. The dial of the clock having its circumference divided into twenty-four equal parts, the hourhand is made to indicate xxiv, or 0 hours at the instant that the first point of Aries is in the meridian; and if the clock were duly adjusted, it is evident that the hour, minute, and second which it might express at any moment would be equivalent to the angle, at that moment, between the plane of the meridian and a plane passing the earth's axis and the equinoctial point above-mentioned. Thus, the clock would show the right ascension of the mid-heaven, or meridian, at that instant, right ascensions being generally expressed in time.

It follows, therefore, that if a telescope were accurately placed in the plane of the meridian, and a star were to appear to be bisected by a vertical wire in the middle of the field of view, the time shown by the sidereal clock at that instant would express the apparent right ascension of the star. On the other hand, if it were required to make the clock express sidereal time, it would be only necessary, at the moment that a fixed star whose apparent right ascension is given in the Nautical Almanac is observed to be bisected by the wire of the telescope, to set the hands to the hour, minute, &c. so given; for then, the clock being supposed to be duly regulated, O hours will be indicated by it when the first point of Aries is on the meridian.

The different species of time, and the processes which are to be used in reducing one species to another, will be explained further on. (Chap. XIV.)

74. The Micrometer is an instrument by which small angles are measured; and it is employed for the purpose of ascertaining the angle subtended at the observer's eye by the diameter of the sun, the moon, or a planet, or by the distance between a fixed star and the moon or a comet when they are very near each other, or for any like purpose in practical astronomy.

C

E

D

It consists of a brass tube with lenses, constituting the eye-piece of a telescope and carrying a frame, AB, containing two perforated plates: to one of these is attached a very fine wire, or spider thread, Pq, and to the other a similar wire st,

A

m

a

t

b

n

B

F

the two wires being parallel to one another. There is besides, usually fixed to one of the plates, a fine wire mn at right angles to both pq and st. The plates are capable of a rectilinear motion in the direction AB, perpendicular to the axis of the telescope, by means of screws at A and B, and thus the wires may be made to approach to, or recede from, one another, retaining always their parallelism. When they have been moved till the object, or the space between two objects, is comprehended between them, the angle subtended at the eye by such object or space is ascertained by a scale ab in the field of the telescope: one revolution of each screw carries its wires through an extent equal to one of the graduations on the scale ab, and this extent is subdivided by the graduations on the circular heads C and D of the screws. The angular value of each graduation depends on the magnifying power of the telescope to which the micrometer is applied, and it must always be determined by observation: this may easily be effected, when the micrometer is attached to the telescope of a circle revolving in azimuth like the horizontal limb of a theodolite, by means of a small and well-defined terrestrial object.

75. Having made one of the wires bisect the object, move the other by causing its screw to make any number of revolutions; then the azimuth circle being turned till this last wire appears to bisect the object, the difference between the two readings on the circle when the object was bisected, being divided by the number of revolutions, will give the value of an angle subtended at the eye by the positions of the micrometer wire at the commencement and end of one revolution of the screw: and as one revolution of a screw carries its wire over a space equal to one of the intervals between two divisions on the scale, the angular value of a revolution is, of course, the equivalent of such interval.

76. The value of a revolution may be obtained by measuring between the wires the apparent diameter of the sun, if the field of view is sufficiently extensive; in this case the micrometer screw must be turned till the two wires are tangents to the upper and lower edges of the sun's disk. Then, the angle subtended by that diameter being given in the Nautical Almanac, on dividing this angle by the number of revolutions, the result is the angle corresponding to one revolution. It may be found, also, by observing the transit of the pole-star upon one of the wires when the star is on, or very near the meridian, and again after having displaced the wire by several revolutions of the screw; now t (in seconds) being the time in which the pole-star passes from the

wire in the first, to the same wire in the second position, 15 t (since by the rotation of the earth on its axis in 24 hours every point in the heavens appears to describe about that axis an angle or arc equal to 15 degrees in an hour, 15 minutes in one minute of time, &c.) will express in seconds of a degree the angle subtended at the centre of the star's parallel of declination by the interval between the two places of the wire, and being multiplied by the cosine of the star's declination (art. 70.) it will express the angle subtended at the centre of the equator by an equal interval on that great circle. But, as will be hereafter explained, this as well as the other stars has constantly a movement in right ascension, that is, in the same direction as the earth revolves on its axis, the amount of which, during the time t, may be found from the Nautical Almanac; and, whether the star be above or below the pole, an increase of right ascension will increase the time in which, by the diurnal rotation, it appears to pass between the two positions of the wire: therefore that change of right ascension (in arc) must be subtracted from the above product in order to express the angle corresponding to the number of the screw's revolutions.

77. If the micrometrical apparatus be placed in a frame which is capable of being turned about the optical axis of the telescope, and be provided with a graduated circle, as EF, whose centre is in that axis, so that the position of the micrometer wires with respect to the plane of any vertical, or horary circle, may be known at the time that the micrometrical angle is observed, the instrument is called a Position Micrometer. It is usually attached to an equatorial instrument or to a telescope having an equatorial movement. manner of using a micrometer for the measurement of small angles will be explained in the description of the equatorial (art. 119.).

The

78. The micrometer microscope, which is attached to the rim of an astronomical circle, consists of a system of lenses similar to those of an ordinary microscope, and the image of the graduations of the circle is by the disposition of the lenses made to fall at the place of a wire or of a pair of wires crossing each other at an acute angle near the eye-end of the tube. Now the smaller kind of astronomical circles are divided into spaces each equal to 15 minutes of a degree, but those of a larger kind into spaces equal to 10 minutes or 5 minutes; and across the field of view in the microscope is a scale or a plate divided into spaces, each of which is equal to one minute. The micrometer screw, by one complete revolution, moves the wire through one of the spaces on the plate, and its cir

cular head being divided into 60 parts (for example) a portion of a revolution, which carries one of these parts under the fixed index, evidently causes the wire to move through a space equal to one second of a degree. The object glass of the microscope has a small motion in the direction of the axis, in order that the magnifying power may be varied; and that by such motion the image of one of the intervals on the circle (suppose it to be one-twelfth of a degree), or of the number of parts on the scale, into which it is divided, may be increased or diminished till so many revolutions of the micrometer screw will cause the wire to move exactly through the extent of that interval; the tube containing the eye-glasses being adjusted so as to afford distinct vision.

79. As it is difficult to adjust the microscopes so that five revolutions of the micrometer screw shall carry the wire over exactly one of the five-minute spaces on the circle (if the latter be so graduated), it is preferred to observe the number of revolutions and the part of a revolution made by the screw while the wire passes over the space; then if, for example, the number of revolutions, instead of five, be 54, the value

5'

5.4'

of one revolution will be or 0.926 nearly, and the whole number of minutes and parts of a minute which are indicated by the revolutions of the screw being multiplied by that value will give the correct value of the reading. The number of revolutions of the screw, which in this case are 5·4, made while the wire moves along one of the divisions on the circle, is called a run of the micrometer screw.

80. In using the micrometer microscope, after the object has been put in contact with the wire in the field of the telescope, the number of whole degrees, and of the quarter, sixth, or twelfth parts of a degree are read on the circle; and if a division-line should exactly coincide with the wire in the microscope when that wire is at the zero point of the micrometer scale, the reading is complete: but if a division do not so coincide the wire must, by the micrometer screw, be moved up along the scale till it coincides with the next division-line on the circle; then the number of revolutions, and the part of a revolution which the screw has made must, when reduced as above, be added to, or subtracted from the degrees, &c. which are read on the circle, according to the direction in which the latter has been turned in taking the angle.

81. The transit instrument is a telescope whose tube consists of two cylindrical parts united near the middle of its length to the opposite sides of a portion which is either cubical or globular. At right angles to the tube is an axis of brass

consisting of two conical arms which, at their larger extremities, are joined on opposite sides to the cubical or globular portion just mentioned: the smaller extremities of the cones are made cylindrical, and equal to one another; and when the telescope is mounted for service, each of these extremities lies in a notch cut at the top of a moveable vertical plate of brass, (corresponding to what in a common theodolite is called a Y,) which enters into a fixed plate of the like metal. The latter either rests on a stone pier or forms the head of the stand supporting the telescope; and each notch has the form of two inclined planes whose surfaces are tangents to the cylindrical pivot: one of the notched plates is capable, by means of a screw, of being elevated or depressed for the purpose of rendering the axis of motion horizontal; and the other may, in like manner, be moved a small way in azimuth, in order that the optical axis of the telescope, (the line joining the centres of all the lenses,) may be brought accurately into the plane of the meridian.

82. At the focus of the object glass are fixed three, five, or seven parallel wires, besides one which crosses them at

right angles: the latter is intended to be always in a horizontal position; and the others, when the telescope lies horizontally between its supports, are in vertical positions. The diaphragm, or perforated plate to which the wires are attached, is capable of a small movement by means of screws which pass through the sides of the telescope, in order that the intersection of the horizontal with the central wire at right angles to it may be made to fall exactly in the optical axis or line of collimation, as it is called, of the telescope. One of the arms of the axis of motion is hollow, and a lamp being attached to the pier, or side of the stand on which that arm

F