Part 2

14. _Declination and Right Ascension._--The _declination_ of a heavenly body is its distance north or south of the celestial equator. The _polar distance_ of a heavenly body is its distance from the nearer pole. Declination and polar distance are measured on hour circles, and for the same heavenly body they are complements of each other.

The _right ascension_ of a heavenly body is its distance eastward from the first point of Aries, measured from the equinoctial colure. It is equal to the arc of the celestial equator included between the first point of Aries and the hour circle which passes through the heavenly body. As right ascension is measured eastward entirely around the celestial sphere, it may have any value from 0° up to 360°. Right ascension corresponds to longitude on the earth, and declination to latitude.

15. _The Meridian Circle._--The right ascension and declination of a heavenly body are ascertained by means of an instrument called the _meridian circle_, or _transit instrument_. A side-view of this instrument is shown in Fig. 20.

It consists essentially of a telescope mounted between two piers, so as to turn in the plane of the meridian, and carrying a graduated circle. The readings of this circle are ascertained by means of fixed microscopes, under which it turns. A heavenly body can be observed with this instrument, only when it is crossing the meridian. For this reason it is often called the _transit circle_.

To find the declination of a star with this instrument, we first ascertain the reading of the circle when the telescope is pointed to the pole, and then the reading of the circle when pointed to the star on its passage across the meridian. The difference between these two readings will be the polar distance of the star, and the complement of them the declination of the star.

To ascertain the reading of the circle when the telescope is pointed to the pole, we must select one of the circumpolar stars near the pole, and then point the telescope to it when it crosses the meridian, both above and below the pole, and note the reading of the circle in each case. The mean of these two readings will be the reading of the circle when the telescope is pointed to the pole.

16. _Astronomical Clock._--An _astronomical clock_, or _sidereal clock_ as it is often called, is a clock arranged so as to mark hours from 1 to 24, instead of from 1 to 12, as in the case of an ordinary clock, and so adjusted as to mark 0 when the vernal equinox, or first point of Aries, is on the meridian.

As the first point of Aries makes a complete circuit of the heavens in twenty-four hours, it must move at the rate of 15° an hour, or of 1° in four minutes: hence, when the astronomical clock marks 1, the first point of Aries must be 15° west of the meridian, and when it marks 2, 30° west of the meridian, etc. That is to say, by observing an accurate astronomical clock, one can always tell how far the meridian at any time is from the first point of Aries.

17. _How to find Right Ascension with the Meridian Circle._--To find the right ascension of a heavenly body, we have merely to ascertain the exact time, by the astronomical clock, at which the body crosses the meridian. If a star crosses the meridian at 1 hour 20 minutes by the astronomical clock, its right ascension must be 19°; if at 20 hours, its right ascension must be 300°.

To enable the observer to ascertain with great exactness the time at which a star crosses the meridian, a number of equidistant and parallel spider-lines are stretched across the focus of the telescope, as shown in Fig. 21. The observer notes the time when the star crosses each spider-line; and the mean of all of these times will be the time when the star crosses the meridian. The mean of several observations is likely to be more nearly exact than any single observation.

18. _The Equatorial Telescope._--The _equatorial_ telescope is mounted on two axes,--one parallel with the axis of the earth, and the other at right angles to this, and therefore parallel with the plane of the earth's equator. The former is called the _polar axis_, and the latter the _declination axis_. Each axis carries a graduated circle. These circles are called respectively the _hour circle_ and the _declination circle_. The telescope is attached directly to the declination axis. When the telescope is fixed in any declination, and then turned on its polar axis, the line of sight will describe a diurnal circle; so that, when the tube is once directed to a star, it can be made to follow the star by simply turning the telescope on its polar axis.

In the case of large instruments of this class, the polar axis is usually turned by clock-work at the rate at which the heavens rotate; so that, when the telescope has once been pointed to a planet or other heavenly body, it will continue to follow the body and keep it steadily in the field of view without further trouble on the part of the observer.

The great Washington Equatorial is shown in Fig. 22. Its object-glass is 26 inches in diameter, and its focal length is 32-1/2 feet. It was constructed by Alvan Clark & Sons of Cambridge, Mass. It is one of the three largest refracting telescopes at present in use. The Newall refractor at Gateshead, Eng., has an objective 25 inches in diameter, and a focal length of 29 feet. The great refractor at Vienna has an objective 27 inches in diameter. There are several large refractors now in process of construction.

19. _The Wire Micrometer._--Large arcs in the heavens are measured by means of the graduated circles attached to the axes of the telescopes; but small arcs within the field of view of the telescope are measured by means of instruments called _micrometers_, mounted in the focus of the telescope. One of the most convenient of these micrometers is that known as the _wire micrometer_, and shown in Fig. 23.

The frame _AA_ covers two slides, _C_ and _D_. These slides are moved by the screws _F_ and _G_. The wires _E_ and _B_ are stretched across the ends of the slides so as to be parallel to each other. On turning the screws _F_ and _G_ one way, these wires are carried apart; and on turning them the other way they are brought together again. Sometimes two parallel wires, _x_ and _y_, shown in the diagram at the right, are stretched across the frame at right angles to the wires _E_, _B_. We may call the wires _x_ and _y_ the _longitudinal_ wires of the micrometer, and _E_ and _B_ the _transverse_ wires. Many instruments have only one longitudinal wire, which is stretched across the middle of the focus. The longitudinal wires are just in front of the transverse wires, but do not touch them.

To find the distance between any two points in the field of view with a micrometer, with a single longitudinal wire, turn the frame till the longitudinal wire passes through the two points; then set the wires _E_ and _B_ one on each point, turn one of the screws, known as the _micrometer screw_, till the two wires are brought together, and note the number of times the screw is turned. Having previously ascertained over what arc one turn of the screw will move the wire, the number of turns will enable us to find the length of the arc between the two points.

The threads of the micrometer screw are cut with great accuracy; and the screw is provided with a large head, which is divided into a hundred or more equal parts.

These divisions, by means of a fixed pointer, enable us to ascertain what fraction of a turn the screw has made over and above its complete revolutions.

20. _Reflecting Telescopes._--It is possible to construct mirrors of much larger size than lenses: hence reflecting telescopes have an advantage over refracting telescopes as regards size of aperture and of light-gathering power. They are, however, inferior as regards definition; and, in order to prevent flexure, it is necessary to give the speculum, or mirror, a massiveness which makes the telescope unwieldy. It is also necessary frequently to repolish the speculum; and this is an operation of great delicacy, as the slightest change in the form of the surface impairs the definition of the image. These defects have been remedied, to a certain extent, by the introduction of silver-on-glass mirrors; that is, glass mirrors covered in front with a thin coating of silver. Glass is only one-third as heavy as speculum-metal, and silver is much superior to that metal in reflecting power; and when the silver becomes tarnished, it can be removed and renewed without danger of changing the form of the glass.

_The Herschelian Reflector._--In this form of telescope the mirror is slightly tipped, so that the image, instead of being formed in the centre of the tube, is formed near one side of it, as in Fig. 24. The observer can then view it without putting his head inside the tube, and therefore without cutting off any material portion of the light. In observation, he must stand at the upper or outer end of the tube, and look into it, his back being turned towards the object. From his looking directly into the mirror, it is also sometimes called the _front-view_ telescope. The great disadvantage of this arrangement is, that the rays cannot be brought to an exact focus when they are thrown so far to one side of the axis, and the injury to the definition is so great that the front-view plan is now entirely abandoned.

_The Newtonian Reflector._--The plan proposed by Sir Isaac Newton was to place a small plane mirror just inside the focus, inclined to the telescope at an angle of 45°, so as to throw the rays to the side of the tube, where they come to a focus, and form the image. An opening is made in the side of the tube, just below where the image is formed; and in this opening the eye-piece is inserted. The small mirror cuts off some of the light, but not enough to be a serious defect. An improvement which lessens this defect has been made by Professor Henry Draper. The inclined mirror is replaced by a small rectangular prism (Fig. 25), by reflection from which the image is formed very near the prism. A pair of lenses are then inserted in the course of the rays, by which a second image is formed at the opening in the side of the tube; and this second image is viewed by an ordinary eye-piece.

_The Gregorian Reflector._--This is a form proposed by James Gregory, who probably preceded Newton as an inventor of the reflecting telescope. Behind the focus, _F_ (Fig. 26), a small concave mirror, _R_, is placed, by which the light is reflected back again down the tube. The larger mirror, _M_, has an opening through its centre; and the small mirror, _R_, is so adjusted as to form a second image of the object in this opening. This image is then viewed by an eye-piece which is screwed into the opening.

_The Cassegrainian Reflector._--In principle this is the same with the Gregorian; but the small mirror, _R_, is convex, and is placed inside the focus, _F_, so that the rays are reflected from it before reaching the focus, and no image is formed until they reach the opening in the large mirror. This form has an advantage over the Gregorian, in that the telescope may be made shorter, and the small mirror can be more easily shaped to the required figure. It has, therefore, entirely superseded the original Gregorian form.

Optically these forms of telescope are inferior to the Newtonian; but the latter is subject to the inconvenience, that the observer must be stationed at the upper end of the telescope, where he looks into an eye-piece screwed into the side of the tube.

On the other hand, the Cassegrainian Telescope is pointed directly at the object to be viewed, like a refractor; and the observer stands at the lower end, and looks in at the opening through the large mirror. This is, therefore, the most convenient form of all in management.

The largest reflecting telescope yet constructed is that of Lord Rosse, at Parsonstown, Ireland. Its speculum is 6 feet in diameter, and its focal length 55 feet. It is commonly used as a Newtonian. This telescope is shown in Fig. 27.

The great telescope of the Melbourne Observatory, Australia, is a Cassegranian reflector. Its speculum is 4 feet in diameter, and its focal length is 32 feet. It is shown in Fig. 28.

The great reflector of the Paris Observatory is a Newtonian reflector. Its mirror of silvered glass is 4 feet in diameter, and its focal length is 23 feet. This telescope is shown in Fig. 29.

21. _The Sun's Motion among the Stars._--If we notice the stars at the same hour night after night, we shall find that the constellations are steadily advancing towards the west. New constellations are continually appearing in the east, and old ones disappearing in the west. This continual advancing of the heavens towards the west is due to the fact that the sun's place among the stars is _continually moving towards the east_. The sun completes the circuit of the heavens in a year, and is therefore moving eastward at the rate of about a degree a day.

This motion of the sun's place among the stars is due to the revolution of the earth around the sun, and not to any real motion of the sun. In Fig. 30 suppose the inner circle to represent the orbit of the earth around the sun, and the outer circle to represent the celestial sphere. When the earth is at _E_, the sun's place on the celestial sphere is at _S'_. As the earth moves in the direction _EF_, the sun's place on the celestial sphere must move in the direction _S'T_: hence the revolution of the earth around the sun would cause the sun's place among the stars to move around the heavens in the same direction that the earth is moving around the sun.

22. _The Ecliptic._--The circle described by the sun in its apparent motion around the heavens is called the _ecliptic_. The plane of this circle passes through the centre of the earth, and therefore through the centre of the celestial sphere; the earth being so small, compared with the celestial sphere, that it practically makes no difference whether we consider a point on its surface, or one at its centre, as the centre of the celestial sphere. The ecliptic is, therefore, a great circle.

The earth's orbit lies in the plane of the ecliptic; but it extends only an inappreciable distance from the sun towards the celestial sphere.

23. _The Obliquity of the Ecliptic._--The ecliptic is inclined to the celestial equator by an angle of about 23-1/2°. This inclination is called the _obliquity of the ecliptic_. The obliquity of the ecliptic is due to the deviation of the earth's axis from a perpendicular to the plane of its orbit. The axis of a rotating body tends to maintain the same direction; and, as the earth revolves around the sun, its axis points all the time in nearly the same direction. The earth's axis deviates about 23-1/2° from the perpendicular to its orbit; and, as the earth's equator is at right angles to its axis, it will deviate about 23-1/2° from the plane of the ecliptic. The celestial equator has the same direction as the terrestrial equator, since the axis of the heavens has the same direction as the axis of the earth.

Suppose the globe at the centre of the tub (Fig. 31) to represent the sun, and the smaller globes to represent the earth in various positions in its orbit. The surface of the water will then represent the plane of the ecliptic, and the rod projecting from the top of the earth will represent the earth's axis, which is seen to point all the time in the same direction, or to lean the same way. The leaning of the axis from the perpendicular to the surface of the water would cause the earth's equator to be inclined the same amount to the surface of the water, half of the equator being above, and half of it below, the surface. Were the axis of the earth perpendicular to the surface of the water, the earth's equator would coincide with the surface, as is evident from Fig. 32.

24. _The Equinoxes and Solstices._--The ecliptic and celestial equator, being great circles, bisect each other. Half of the ecliptic is north, and half of it is south, of the equator. The points at which the two circles cross are called the _equinoxes_. The one at which the sun crosses the equator from south to north is called the _vernal_ equinox, and the one at which it crosses from north to south the _autumnal_ equinox. The points on the ecliptic midway between the equinoxes are called the _solstices_. The one north of the equator is called the _summer_ solstice, and the one south of the equator the _winter_ solstice. In Fig. 33, _EQ_ is the celestial equator, _EcE'c'_ the ecliptic, _V_ the vernal equinox, A the autumnal equinox, Ec the winter solstice, and _E'c'_ the summer solstice.

25. _The Inclination of the Ecliptic to the Horizon._--Since the celestial equator is perpendicular to the axis of the heavens, it makes the same angle with it on every side: hence, at any place, the equator makes always the same angle with the horizon, whatever part of it is above the horizon. But, as the ecliptic is oblique to the equator, it makes different angles with the celestial axis on different sides; and hence, at any place, the angle which the ecliptic makes with the horizon varies according to the part which is above the horizon. The two extreme angles for a place more than 23-1/2° north of the equator are shown in Figs. 34 and 35.

The least angle is formed when the vernal equinox is on the eastern horizon, the autumnal on the western horizon, and the winter solstice on the meridian, as in Fig. 34. The angle which the ecliptic then makes with the horizon is equal to the elevation of the equinoctial _minus_ 23-1/2°. In the latitude of New York this angle = 49° - 23-1/2° = 25-1/2°.

The greatest angle is formed when the autumnal equinox is on the eastern horizon, the vernal on the western horizon, and the summer solstice is on the meridian (Fig. 35). The angle between the ecliptic and the horizon is then equal to the elevation of the equinoctial _plus_ 23-1/2°. In the latitude of New York this angle = 49° + 23-1/2° = 72-1/2°.

Of course the equinoxes, the solstices, and all other points on the ecliptic, describe diurnal circles, like every other point in the heavens: hence, in our latitude, these points rise and set every day.

26. _Celestial Latitude and Longitude._--_Celestial latitude_ is distance measured north or south from the ecliptic; and _celestial longitude_ is distance measured on the ecliptic eastward from the vernal equinox, or the first point of Aries. Great circles perpendicular to the ecliptic are called _celestial meridians_. These circles all pass through the poles of the ecliptic, which are some 23-1/2° from the poles of the equinoctial. The latitude of a heavenly body is measured by the arc of a celestial meridian included between the body and the ecliptic. The longitude of a heavenly body is measured by the arc of the ecliptic included between the first point of Aries and the meridian which passes through the body. There are, of course, always two arcs included between the first point of Aries and the meridian,--one on the east, and the other on the west, of the first point of Aries. The one on the _east_ is always taken as the measure of the longitude.

27. _The Precession of the Equinoxes._--The equinoctial points have a slow westward motion along the ecliptic. This motion is at the rate of about 50'' a year, and would cause the equinoxes to make a complete circuit of the heavens in a period of about twenty-six thousand years. It is called the _precession of the equinoxes_. This westward motion of the equinoxes is due to the fact that the axis of the earth has a slow gyratory motion, like the handle of a spinning-top which has begun to wabble a little. This gyratory motion causes the axis of the heavens to describe a cone in about twenty-six thousand years, and the pole of the heavens to describe a circle about the pole of the ecliptic in the same time. The radius of this circle is 23-1/2°.

28. _Illustration of Precession._--The precession of the equinoxes may be illustrated by means of the apparatus shown in Fig. 36. The horizontal and stationary ring _EC_ represents the ecliptic; the oblique ring _E'Q_ represents the equator; _V_ and _A_ represent the equinoctial point, and _E_ and _C_ the solstitial points; _B_ represents the pole of the ecliptic, _P_ the pole of the equator, and _PO_ the celestial axis. The ring _E'Q_ is supported on a pivot at _O_; and the rod _BP_, which connects _B_ and _P_, is jointed at each end so as to admit of the movement of _P_ and _B_.

On carrying _P_ around _B_, we shall see that _E'Q_ will always preserve the same obliquity to _EC_, and that the points _V_ and _A_ will move around the circle _EC_. The same will also be true of the points _E_ and _C_.

29. _Effects of Precession._--One effect of precession, as has already been stated, is the revolution of the pole of the heavens around the pole of the ecliptic in a period of about twenty-six thousand years. The circle described by the pole of the heavens, and the position of the pole at various dates, are shown in Fig. 37, where o indicates the position of the pole at the birth of Christ. The numbers round the circle to the left of o are dates A.D., and those to the right of o are dates B.C. It will be seen that the star at the end of the Little Bear's tail, which is now near the north pole, will be exactly at the pole about the year 2000. It will then recede farther and farther from the pole till the year 15000 A.D., when it will be about forty-seven degrees away from the pole. It will be noticed that one of the stars of the Dragon was the pole star about 2800 years B.C. There are reasons to suppose that this was about the time of the building of the Great Pyramid.

A second effect of precession is the shifting of the signs along the zodiac. The _zodiac_ is a belt of the heavens along the ecliptic, extending eight degrees from it on each side. This belt is occupied by twelve constellations, known as the _zodiacal constellations_. They are _Aries_, _Taurus_, _Gemini_, _Cancer_, _Leo_, _Virgo_, _Libra_, _Scorpio_, _Sagittarius_, _Capricornus_, _Aquarius_, and _Pisces_. The zodiac is also divided into twelve equal parts of thirty degrees each, called _signs_. These signs have the same names as the twelve zodiacal constellations, and when they were first named, each sign occupied the same part of the zodiac as the corresponding constellation; that is to say, the sign Aries was in the constellation Aries, and the sign Taurus in the constellation Taurus, etc. Now the signs are always reckoned as beginning at the vernal equinox, which is continually shifting along the ecliptic; so that the signs are continually moving along the zodiac, while the constellations remain stationary: hence it has come about that the _first point of Aries_ (the _sign_) is no longer in the _constellation_ Aries, but in Pisces.

Fig. 38 shows the position of the vernal equinox 2170 B.C. It was then in Taurus, just south of the Pleiades. It has since moved from Taurus, through Aries, and into Pisces, as shown in Fig. 39.