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KIt will be observed, (fig. 2), that just as the peg is inclined, the button or plane of the equator is inclined; and, of course, the line which would mark out on the wall, or amongst the stars, the several parts or points in the same plane with our equatorial button edge, will be inclined also, and to the same angle, viz., 23° 28'. Hence, we see that the equinoctial and ecliptic intersect, and form distinct lines in the sky. That point in the heavens where these imaginary lines so intersect, is the point from which astronomers reckon in assigning places to the several heavenly bodies. There is, of course, another intersection, diametrically opposite to this; that is, on the wall behind the pupil who examines our figure; and, in common language, we speak of these two intersections, viz., r in front and behind us, together, as "the equinoxes."
↳ Before we quit the diagram to advance with our problems, we would call attention to the manner in which the constant daily change of "right ascension" and "declination" is effected. We have said that the first point of Aries (r) is the reckoning point. It is evident that when the earth is in the position G, (see figure), the apparent declination of S is south of the equinoctial plane, and the right ascension about 335; and that it will then have advanced about 3° in the sign Pisces (*). But let us follow it to A, and its inhabitants will then have the sun's R. A. about 18° only; its apparent place being about 20° in Aries (r), and its position above the equinoctial, and in about 8° of north declination.
RELATING TO THE ANNUAL REVOLUTION OF THE EARTH.
A day being given, to find the sun's longitude or place in the ecliptic and his consequent declination and right ascension.
Repeat the following:
Ecliptic, (def. 61); Obliquity of the Ecliptic, (def. 62); Equinoctial Points, (def. 63); Geocentric, (def. 99); Heliocentric, (def. 100).
RULE.-Look for the given day in the circle of months on the wooden horizon; and against it, in the circle of signs, will be found "the sun's place" for that day. Look for the sign and degree corresponding to this in the ecliptic line; bring this degree to the brass meridian, and over it will be found the sun's north or south declination: the right ascension will be cut by the brazen meridian on the equinoctial.
Our memorial lines ("On New-Year's-day, &c.") in the Appendix, will give, with very little trouble, the sun's place for any day in the year, without reference to the wooden horizon, to any who may prefer such a mode of assistance.
Examples.-What is the sun's longitude, or "place in the ecliptic," for the following days; what his declination and right ascension; and what stars would appear very near him, if it
were not for his beams, on the days we have marked thus* ?
March 13-*January 16 ()-*Feb 10-Sept 19-*May 23-December 21-*December 1-*August 20—*October 14—June 21—*June 30-September 23-March 21*November 5-April 25-*July 12 (†).
A certain day of the year being given, to find what other day of the year is of a length exactly corresponding to it; and where, on those two days, the sun appears in the zenith.
Repeat the following:
Solstitial Points, (def. 64); Tropics, (def. 65); Zones, (def. 71); Amphiscii, (def. 72); Ascii, (def. 73); Analemma, (def. 66).
RULE. Find the sun's place and his declination, either on the celestial globe by the proper ecliptic line, or on the terrestrial globe by means of the record of declination answering to the ecliptic. Turn the globe till some other portion of this line is under the same degree of the brazen meridian; then find the sign and degree answering to it on the wooden circle of the globe, and directly against them will be the day of the month required.* The places having latitude answering to the declination of the sun, will be those to which he will, on these two days, pass vertically.
(a) 16th January, a little to the south-west of a and B, the remarkable stars in the Goat's head.
(b) 12th July, nearly half way between two very remarkable stars. *If the analemma be used, the two dates will be found at once under the declination.
LATITUDE, AND THE AMPLITUDE OF THE SUN. 111
Examples. Find the days corresponding in length to the following days; and the places to which, on those days, the sun is vertical.
1. 6th February-5th May-10th July-20th January -18th August.
Answer-4th November, &c. &c.
2. The sun rises to Greenwich at half-past four on the 29th of April; it will rise earlier next day: how many days must elapse before it will again rise precisely at this time ?*
3. The sun sets to me in London, at three quarters past seven on the 2d of August; it will set earlier next day : how many days must elapse before he will again set precisely at that time?
4. If the sun be vertical at a certain place on the 15th of March, how many days must elapse before he is again vertical to that place, and to what other places will he then also be vertical?
Conversely. 5. Find the days on which the sun is within one degree of the zenith of Calcutta, or of the south point of California; and also how long he is daily within the same distance of the zenith of Quito, at each of two periods of the year.
Given the day of the month and the sun's amplitude, to find the latitude of the place of observation.
Learn Zodiac, (def. 69); and the Memorial verses "On March 21st," &c., in the Appendix.
RULE.-Find the sun's place, and bringing it either eastward or westward of the brass meridian, elevate or depress
# Any two days which correspond in length, are equally distant from the 21st of June and the 21st of December, the longest and shortest days.
the pole until that part of the ecliptic can be made to coincide with the given amplitude, as marked on the wooden circle of the globe; then the degrees of elevation of the pole, or the degree of declination in the zenith, will show the latitude.
The sun, on any day, sets so many degrees north or south of the west, as he rises north or south of the east.
1. In what latitude does the sun rise 25° north of the east, and set 25° north of west, on the 21st of June?
Here finding the first point of Cancer to be the sun's place, I elevate or depress the pole until that point of the ecliptic can be made to coincide with 25°, the given amplitude, and find that this can occur only in lat. 23° north or 23° south.
2. In how many different latitudes does the sun rise duly east and set duly west, on the 21st of March, and on the 23d of September?
3. What was the variation of the magnet, and in what direction from the true north, at a place where, on either of these two days, he appeared to be rising 244° to the south of the east point of my compass, and to set 24° to the north of its western point?
It will help the pupil to answer this question, if he consider whether the east point of the compass was too far north or too far south.
4. In what latitude north, and in what latitude south, does the sun rise north-east and set north-west on the 21st of June.
5. On what points of the compass does the sun of the 21st December rise and set in the latitudes last found?
6. In what latitude north on the 21st of June, did the sun rise with amplitude 80° north of east, having been a very little time below my horizon; and to the inhabitants of what latitude south, does the sun, on that day, rise with the same amplitude to give a very short day, having been very many of the twenty-four hours below their horizon?
7. In what latitudes (north and south) has the sun 22 of amplitude on the 5th of May or on the 7th of August, on both of which days he has 16° of north declination;