be so adjusted, because the interval between the successive returns of the sun to the meridian is continually varying, on account of the unequal motion of the sun in its orbit, and of the obliquity of the ecliptic; each of these varying intervals is called a true solar day, and it is the mean of these during the year which is measured by the 24 hours of a well regulated clock, this period of time being a mean solar day; hence, at certain periods of the year, the sun will arrive at the meridian before the clock points to 12, and at other periods the clock will precede the sun; the small interval between the arrival of the index of the clock at 12 and of the sun to the meridian, is called the equation of time, and it is given on pages I. and II. of each month of the Nautical Almanac for every day in the month; this correction, therefore, must always be applied to the apparent time determined by trigonometrical calculation to obtain the mean time or that shown by a well regulated clock or chronometer, or vice versâ, and the Nautical Almanac always indicates whether this correction is additive or subtractive.*

A third kind of time is called siderial time. A siderial day is the period of revolution of the earth upon its axis with reference to the fixed stars, or it is the time which elapses after a fixed star passes the meridian of any place until the same star comes to that meridian again. Owing to the apparent motion of the sun from west to east along the stars about 360°

365

daily, occasioned by the real motion of the earth in its annular orbit,

the solar day is a little longer than the siderial, because when the meridian of a place has revolved with the earth on its axis from west to east to come under a certain star, the sun which the day before may have been on the meridian with the star having moved a little to the east, the meridian has a little farther to revolve towards the east to come under the sun again, and thus complete the solar day. The difference between the siderial and solar day is about 3 57. The same fixed stars cross the meridian, rise and set about this much later every day. The siderial day is divided into 24 siderial hours, the hour into 60 siderial minutes, and these each into 60 siderial seconds. At pages 584, 585, 586, 587 of the

To solve the above problem very accurately it would be necessary to compute the sun's declination at the time of sunrise as deduced approximately above, and then to go over the calculation again. The Nautical Almanac gives the declination of the sun at noon for every day in the year, and of the process for determining its declination at any other time of the day we shall have numerous examples in Part. V.

+ The Nos. of these pages change a little every year.

Greenwich Nautical Almanac are what are called tables of time equivalents. On pages 584, 585 will be found for any given interval of mean solar hours, or minutes, or seconds, the equivalent interval in siderial time. And similarly on pages 586, 587, for any given siderial interval will be found the equivalent mean solar interval.

EXAMPLE.

Required the equivalent of an interval of 7 28 30′ of mean solar time in siderial time. From page 584 the equivalent

7 is found to be 71′′

of

8.99

Required the solar equivalent of 22 id. A 30m 27' (page 586 N. A.)

224 = 21 56 2375

An astronomical clock is one which keeps siderial time. A common clock may be made to do this by shortening a little the pendulum. The weight attached to the pendulum is usually furnished with a screw by which it may be lengthened and shortened at pleasure, and this should be done till the clock goes just 24 hours from the time a star makes its transit over the meridian till the same star makes its meridian transit again. The exact instant of a star's crossing

the meridian is observed with a "Transit Instrument."

This instrument consists of a telescope a b supported by a horizontal axis, each half of which c and d is a hollow cone of brass, at the outer ends of which are short solid cylindrical pivots which rest upon stone pillars e and f, called piers, the latter being imbedded in a mass of masonry extending a few feet below the surface of the

e

ground, in order that the vibrations occasioned by passing vehicles or the tread of the observers may not be felt. The pivots of the axis do not rest immediately upon the piers, but upon flat pieces of brass about 4 inches square, and an inch in thickness, which are screwed to the top of the stone. These brass pieces have a notch technically called a y or v from its shape, in which the pivot of the axis rests. The part of the piece of brass having the notch or v is detached and movable, by means of a screw arranged differently at the opposite ends of the horizontal axis c d, so that one end may be moved horizontally, and the other vertically.

The exact line of vision directed to a distant object is marked by two threads of spider's web, technically called wires, crossing each other at right angles, at a point in or near the optical axis of the telescope. They are stretched across a ring or diaphragm to which they are fastened with wax, and this ring, which is smaller in diameter than the tube of the telescope, is held in its place by screws passing through the tube, having their heads outside. By loosening the screw on one side of the tube and tightening the other, the diaphragm, and consequently the point in which the wires cross, receives a lateral motion. The diaphragm is placed at the focus of the object glass near the eye end b.f

The whole instrument just described has to be so placed that as it turns on the pivots of the horizontal axis the line of vision along the optical axis of the telescope shall describe the plane of the meridian; narrow trap doors in the roof and sides of the transit room serve to expose the meridian to view. As this plane is vertical, if the line of vision above mentioned be exactly perpendicular to the axis cd, whilst at the same time the axis is exactly horizontal, and finally the telescope point due north and south, then will the required position be attained. For this, therefore, three adjustments are requisite. 1. The adjustment of the line of collimation in a perpendicular to the supporting axis c d. 2. The adjustment of the supporting axis to a horizontal position. 3. The adjustment of the line of collimation to the meridian.

*

The method of making these several adjustments we shall describe in their order.

1. To collimate the instrument.-Bring the intersection of the wires upon a well defined point of some distant terrestrial object; take the instrument out of the y and reverse the supporting axis end for end; bring the telescope upon the same distant point, and if the intersection of the wires covers it exactly, the instrument is collimated; if not, move

i. e. the line of vision determined by the intersection of the wires.
For the illumination of the wires see p. 363.

the diaphragm containing the wires by means of the screws at the side of the tube, till the intersection of the wires is brought half way back to cover the distant* point; bring the cross wire on the same or some other point again, by means of the screw in the y, which gives a horizontal motion to the whole instrument, and repeat the process already described; after a few trials the point will be found to be exactly covered by the intersection of the wires in both positions of the telescope. This indicates that the line of collimation, or line determined by the intersection of the cross wires, and the distant point, is exactly perpendicular to the axis on which the instrument turns as the object end of the telescope is elevated or depressed.

2. To render the supporting axis horizontal.-This is done by means of a spirit level, of which there are two kinds for the purpose, the hanging level, and the riding or striding level.

The former is suspended by hooks from the pivots of the supporting axis, so as to hang parallel to it underneath. The latter is sustained above the supporting axis by two long feet with notches at their bottoms, by means of which it stands upon the pivots of the axis.

First, to adjust the spirit level itself, place it on the pivots, and by means of the screw in the y at that extremity of the axis which gives it a vertical motion, bring the long air bubble of the level to reach exactly the same distance on either side of the centre marked with a zero on the level scale above the tube; for which purpose the divisions of this scale are numbered in precisely the same manner on the right and left of the zero. Then reverse the level on the pivots, turning it end for end, and if the bubble still reaches the same distance on both sides of the zero, the level requires no adjustment. If not, make half the correction by filing away the notch in one of the feet, or by means of a screw sometimes added for shortening the foot, and the other half by the screw in the y. Repeat this process till the adjustment is complete. When the level itself is once

This may be exhibited with the error of collimation exaggerated in the annexed diagram, in which a b represents the supporting axis, c d the true line of collimation, co the erroneous position of the line of collimation in the first position of the instrument in the direction c o of the object, and c e the position of the line of collimation in the reversed position.

adjusted, the supporting axis is made horizontal by placing the level upon it, and turning the screw in the y till the centre of the air bubble is opposite the zero of the scale.

3. To adjust the instrument to the meridian.-Observe the instant that some circumpolar* star (the pole star is the best, from the slowness of its motion) crosses the vertical wire of the transit instrument both at its superior and inferior transit, that is above and below the pole. If the interval of time between the superior and inferior transit be the same with that between the latter and the next superior transit of the same star again, the instrument is in the meridian. If not, it is on that side of the meridian on which the arc described by the star between the two transits is shortest, and must be moved a little by means of the screw in the y, which gives horizontal motion, and the same observations repeated. When the instrument is once fixed in the meridian, a meridian mark about half a mile distant may be made upon some object, set up if necessary, upon which the vertical wire is to be brought whenever afterwards an observation is to be made.

Method of observing the meridian transit of a star.-Before describing this we shall observe that for diminishing the error of observation there are inserted on each side of the vertical middle wire, one, two, or three others, making three, five, or seven in all. There is also attached to the supporting axis near one of the pivots a graduated circle, the plane of which is perpendicular to that axis, and consequently vertical. This circle is graduated so that the index points to zero when the telescope points to the zenith, or else when the telescope is horizontal, so that when the telescope is directed to a star, the index will mark the zenith distance of the star in the former case, and its altitude in the latter. The star's declination being known from the Nautical Almanac, or from a catalogue, and the latitude of the place of observation being also known, the instrument may be easily set so that when the star makes its meridian transit it will pass through the middle of the field of view of the telescope. For it is only necessary to bear, in mind that the declination is the distance of the star from the equator and the latitude is the distance of the zenith from the equator, so that by simple addition or subtraction of these quanti

A circumpolar star is one which never sets, but describes daily a circle round the pole of the heavens, the whole of which is visible above the horizon.

† A method of determining the exact deviation from the meridian, and the consequent error in the time of meridian transit, will be presently given.

These measures are all made on the same great circle of the heavens, viz. the meridian of the place of observation, upon which the star is supposed to be at the instant of transit.