Suppose the ceiling, under these circumstances, to be raised to the height of the house; the circle so described in the ceiling by the pointing of the peg during its progress round the table, would now appear to be considerably less; although, of course, really retaining its size as well as its bearing. Now, suppose the ceiling could, by any possi bility, be raised a mile, whilst retaining the bearing of its position, viz. with the said circle exactly 23° 28' towards the side of the table: would not the circle vanish, or at least dwindle into a point ? why so ? only because of the greatness of its distance when compared with its dimensions; that is, with the dimensions of our table or orbit.

Suppose a tiny individual to be perched on the upper extremity, or north pole, of our peg: in the former instance, before the removal of the ceiling, his head would be directed to the several points of the circle in the ceiling (see A in the figure); and if we conceive the stars to be so near as that their distance, when compared with the size of his tee-totum world, or its orbitual groove, were in the unelevated ceiling, it is evident that each day in the year might have its separate "pole star." Now, so great is the distance of the circle thus elevated, that his head will appear, during each of his 366 daily rotations to be under the same distant point.*

We may thus understand that the orbit of our earth, the diameter of which averages 190 millions of miles, if viewed with such eyes as our's at a distance equal to that of the pole-star, would not appear greater than our distant dwindled circle, or than the pole-star appears to us,a glittering speck!

Now, if our change of station of 190 millions of miles thus produces no apparent change of place (or parallax) of the pole star; it is evident that if the other stars be as distant as this star, no apparent change of place from this cause can be observed in them: hence their designation, "fixed stars."

But another important circumstance remains to be referred to, and explained; and we think the pupil will now readily

* The polar point in the heavens is, however, not strictly invariable: we shall soon attempt very familiarly, to illustrate this.

CELESTIAL LATITUDE AND LONGITUDE.

153

receive it, when we refer to the point into which the circle similarly described in the ceiling, and immediately over the groove, or orbit, on the table, would dwindle if similarly elevated. It is "the pole of the ecliptic," (see T in the preceding figure,) and is consequently situated (as laid down on all our celestial globes) just 23° 28' distant from the former point, or pole of the equinoctial, to which our inclined peg or axis is directed.

Unluckily, the early astronomers have employed also the words latitude and longitude in their uranography, in speaking of arcs of circles not corresponding to those meant by the same words on the earth; but having reference to the motion of the sun and planets amongst the stars. It is too late now to remedy this confusion which is engrafted into every existing work on astronomy: we can only regret it and warn the reader of it." Sir J. W. Herschel's Astronomy, p. 58.

N. B. The terms celestial longitude and celestial latitude referred to and censured by the great authority quoted above, regard the ecliptic and its pole in the same manner that right ascension and declination refer to the equinoctial and the pole of the equinoctial; or, as the latitude and longitude of our earth's surface refer to its equator and the pole of its equator. Accordingly, the circles parallel to the ecliptic on the celestial globe, are "parallels of celestial latitude;" and the lines drawn perpendicularly to the ecliptic (generally through every fifteen of its degrees) and centering in "the poles of the ecliptic," are lines of "celestial longitude," which is reckoned in signs and degrees, eastward only, from the first point of Aries. Declination and right ascension are, however, in most cases more convenient, and most employed.

A star may thus be north of the equinoctial, and yet have south latitude; or it may be south of the equinoctial, and, notwithstanding, have north latitude; that part of the heavens which is north of the ecliptic being called the northern hemisphere, and that south of the ecliptic the southern hemisphere.

PROBLEM XVII.

CELESTIAL GLOBE.

To find the latitude and longitude of a star or planet. Conversely. The latitude and longitude of a star, &c. being given, to find that star, &c.

Read p. p. 151-3. Learn Memorial Verses, "The Ram and Bull, we'll keep in view," &c. (Appendix.)

RULE.-Bring that pole of the ecliptic which is of the same hemisphere with the star's latitude, to the upper semicircle of the brazen meridian, and elevate the pole of the equinoctial 660: the ecliptic will now coincide with the horizon, and its pole with the zenith. Affix the quadrant of altitude to the zenith; and, keeping the globe steady, make the quadrant coincide with the given star; thus the graduation of the quadrant will show the star's latitude, and its longitude will be seen where the quadrant cuts the ecliptic in the horizon.

Conversely. The latitude and longitude being given to find the star-Place the O of the graduated edge of the quadrant on the given longitude in the ecliptic, and its 90th degree (or pivot) on the ecliptic pole of the star's hemisphere; then, underneath the degree which corresponds to the given latitude the star will be found.

1. What are the latitude and longitude of Vega (a Lyræ)? Ans. North latitude 62°, longitude 12° w, or 9 signs, 12o. 2. What are the latitude and longitude of a of Crux? Ans. S. L. 53°, longitude 100 m, or 7 signs, 1010.

3. What are the latitudes and longitudes of the following stars?

N. B. The sun being in the ecliptic, has no latitude; the moon (a) never has more than 5 of geocentric latitude: the apparent motions of the planets, with the exception of those of three of the asteroids, (b) are always within 8° of the ecliptic; and for the purpose of marking their ever shifting positions, lines of latitude and longitude are drawn (on most celestial globes) through every degree of this range, forming an appearance of checker-work.

4. Find, on the globe, from the five right-hand columns of the 13th page of White's Ephemeris, given on our page 51, the places of Saturn, Jupiter, Mars, and Venus, on the 1st June, and the place of Mercury on the 25th June; and record the stars, (large or small) near to which they were then appearing.*

Conversely.

5. What stars have the following latitudes and longitudes?

2010 S. L.....Long. O signs 19°

39 N. L...

Having the longitudes and latitudes of the planets, to find their times of rising and setting; their amplitudes, azimuths, &c., at any given place.

Repeat p. 25 (def. 1): also def. 7.

(a) On account of the nearness of the moon her place is much affected by parallax to those who are far from where she is vertical. (Note G. p. 18.)

(b) The inclination of the orbit of Pallas to our ecliptic plane is as much as 43° 35'.

* Thus, Saturn, just half a degree south of the small star - of Serpentarius; Mercury - south of Pollux.

RULE.-Elevate the pole for the latitude: find the places of the planets, as in the last problem, from an Ephemeris, and stick a very small piece of paper, * inscribed with the symbol of its planet, upon each place. Bring the sun's longitude to the meridian, and the index to 12.

Then, whilst the sun is so placed, if Venus or Jupiter (whether above or below the horizon) lie to the east of the plane of the meridian, it is an evening star; if it lie to the west of that plane, it is a morning star. Cause the globe to rotate westward. As these several symbols of the planets arrive at the eastern horizon, the upper meridian, and the west, their times of rising, their amplitudes, azimuths, culminations, and setting, may be noted as in Probs. IX. & XIV.

1. On the 13th October, 1834, the longitudes and latitudes of the planets were as follows: were Jupiter and Venus morning or evening stars; and at what hours did they and the other planets rise and set at Greenwich?

h 14° 31' lat. 2° N. 14'

2. On 1st February, 1836, the longitudes and latitudes of the planets were as follows:

h

5° m 9' lat. 2° N. 31'

24

7

14

0 N. 7

Were Venus, Jupiter, and Mercury, morning or evening stars; what were their times of rising and setting at Edin

* If the paper be cut of a triangular form, a corner may be put very exactly on the place of the planet: common writing paper, if wetted, will often adhere sufficiently; but a little piece of medallion wafer, such as those now so much used, will be better.