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The sun's declination is north from March 21st to September 23rd, and south the remainder of the year. Its greatest declination, either north or south, is 23° 28'.
The sun's altitude, or height above the horizon, will be increasing to any place, whilst the days are increasing at that place; and its altitude on the same day will be different to places that have different latitudes : hence the sun's meridian altitude furnishes an easy method of determining the latitude of a place.
Of the length of the Days and Nights. The sun shining upon the earth illuminates that half of it which is turned towards it; the enlightened part intercepts the sun's rays from the other half.
The horizon represents, on the globe, the boundary line between light and darkness.
In the problems respecting day and night, the sun is supposed to be in the zenith ; his rays, therefore, which extend to the horizon, will spread exactly 90° in every direction.
As the earth turns round on its axis from W. to E., once in 24 hrs., every meridian will, in that time, successively enjoy the light of the sun, and be deprived of it.
Suppose a patch to be put upon a globe to represent any place, and the globe to be turned round from west to east ; when the place comes to the western side of the horizon, the sun appears to the inhabitants of that place to be rising in the east; but it is more properly the inhabitants of that place rising in the west. Continue to turn the globe round, and the place will ascend higher towards the meridian, which causes the sun to appear to ascend in a contrary direction.
When the place has arrived at the meridian, it will then be noon there, and the sun will be at his greatest altitude for that day.
As you continue to turn the globe, the place will gradually recede from the meridian, and descend towards the eastern horizon, which will cause the appearance of the sun descending towards the west. When the place has arrived at the eastern horizon, as it is then going below the terminator, or boundary of light and darkness, the sun will appear to be setting in the west.
The place having gone below the horizon, and being now at a greater
distance than 90° from that point where the sun is vertical, is deprived of his light, and continues in darkness till, by the revolution of the earth, it arrive again at the western horizon,—when the sun will appear to rise as before.
It is evident that the sun will be rising at the same instant of time to all places that are on the western side of the horizon, and that it will be setting at the same time to all places that are on the eastern side.
Twice a year the days and nights are of the same length to all places upon the earth : these two days are when the sun is in the first of aries and libra, or March 21st, and September 23rd. These are called the equinoxes,—March 21st the vernal, and September 23rd the autumnal equinox.
On these days the sun's place is on the equator. Let the equator be placed in the zenith, and the poles be made to coincide with the horizon. Fix upon any number of places situated upon the same meridian of longitude, say the first, distinguish them by patches, bring them to the brass meridian, and set the index to 12 o'clock. Turn the globe till they come to the western horizon, and the index will then be six o'clock a.m., which will be the hour of the sun's rising; continue to turn the globe from west to east till the places have arrived at the eastern horizon, and the index will now point to six o'clock p.m., the time of the sun's setting. Hence, the length of the day to all these places is twelve hours. Now if the same thing happens with any other places on any other meridian, say the opposite, it is evident that the days and the nights must be twelve hours to every place, or that they are equal all over the globe.
At all places under the equator the days and nights are always equal.
In proof of this it may be observed, that in whatever situation the equator may be placed, provided it be not parallel with the horizon, it is always cut by the horizon into two equal parts. The equator dips beneath the horizon on the one side exactly where it is marked east, and on the other where it is marked west ; which two points are half a circle from each other.
In all places between the equator and the north pole the day is longest when the sun is in the first degree of cancer, June 21st,—and shortest when in the first of ca.. pricorn, Dec. 21st; but in those places between the
equator and the south pole the contrary happens,-the day is shortest when the sun is in the first of cancer, and longest when in the first of capricorn. June 21st is called the summer solstice, it being then summer to all places in the northern hemisphere ; and Dec. 21st, the winter solstice, it being then winter to the same places.
On the 21st of June the sun is 23° 28 to the north of the equator; his rays, which still extend 90° on all sides of him, will penetrate 23° 28 further north than they did when he was on the equator, and be withdrawn to the same extent from the south. To put the globe in the position which the earth will occupy with respect to the sun on the 21st June, raise the north pole 23° 28' above the horizon. Then fix upon some places having the same longitude, taking care that one shall be in the south and another in the north frigid zone. On turning the globe from west to east it will be seen that the place in the north frigid zone never goes below the horizon, and that the one in the south frigid never rises above it, while of the other places, that will appear first upon the horizon whose latitude north is greatest. If the elevation of the north pole be diminished, it will be found that the length of the days to the places north of the equator lessens, and if the south pole be elevated, those parts possessing a southern latitude will have the same length of day which those of a northern latitude formerly enjoyed.
PROBLEM XIV. . To find the Sun's place in the Ecliptic. 1. Seek the given day in the calendar on the horizon, and against it, in the adjoining circle, will be found the sign and degree in which the sun is for that day.
2. Find the same sign and degree in the ecliptic, and this is the sun's place for that day at noon.
EXAMPLES. What is the sun's place on the following days? 1. March 10th Answ. * 20° 7'. 2. June 4th
Answ. I 13° 57'. 3. January 1st
6. April 4th 4. February 2nd
7. May 5th 5. March 3rd
8. June 6th
9. July 7th
14. December 12th 10. August 8th
15. March 22nd 11. September 9th
16. June 22nd 12. October 10th
17. September 23rd 13. November 11th
18. December 22nd. PROBLEM XV.
To find the Sun's Declination. Bring the sun's place for the given day to the brass meridian, and the degree over it will be the declination sought; or bring the day of the month marked on the analemma to the brass meridian, and the degree over it will be the declination, as before.
The sun's declination is given in several of the almanacks, and also in Table I. at the end of this work.
1. The declination of the sun being its distance N. or S. from the equator, this problem is the same as that for finding the latitude of a place.
2. The greatest north declination, 23° 28', is when the sun enters cancer, June 21st,--that being the greatest distance of the ecliptic north of the equator. The greatest south declination, 23° 28', is when it enters capricorn, December 21st,—that being the greatest distance of the ecliptic south of the equator.
EXAMPLES. What is the sun's declination for the following days? 1. March 10th
Answ. 3° 54' S.
6. March 5th
7. July 23rd 5. August 1st
8. October 19th 9. On what days has the sun no declination ? 10. When has the sun the greatest declination north? 11. When has the sun the greatest declination south? 12.What is the sun's declination for to-day ?
PROBLEM XVI. To rectify the Globe for the Sun's place on any day. 1. Find the sun's declination for the given day.
2. Elevate the pole, which is of the same name as the declination, as many degrees as are equal to it.
When the globe is rectified for the sun's place, and the sun brought to the zenith, the horizon will be the terminator, or boundary circle of light and darkness; it will therefore be day with those places that are above the horizon, and night with all that are below it.
EXAMPLES. 1. Rectify the globe for the sun's place on June 4th.
Answ. On June 4th the sun's decl. is 22° N.; the north pole must therefore be raised 22." above the horizon.
2. Elevate the globe for the sun's place on October 6th.
Answ. The sun's decl. on Oct. 6th is 5o S.; hence the south pole must be elevated 5° above the horizon.
PROBLEM XVII. To find the Rising and Setting of the Sun, and the Length
of the Day and Night. 1. Elevate the globe for the sun's declination, bring the given place to the meridian, and set the index to 12.
2. Turn the globe till the given place come to the eastern edge of the horizon, and the index will show the time of the sun's rising.
3. Bring the place to the western edge of the horizon, and the index will show the time of its setting.
4. Double the time of the sun's setting for the length of the day, and of the sun's rising for the night.
If the hour circle have a double row of figures, make use of that which increases towards the east; the sun's rising and setting may then be found at once, by bringing the place only to the eastern edge of the horizon, for the index will point in one row to the hour of rising, and in the other (that which increases towards the west) to the hour of setting.
This problem may also be performed thus. 1. Elevate the globe for the latitude of the place, bring the sun's place to the meridian, and set the index to 12.
2. Bring the sun's place to the eastern horizon, and