required the places to which the sun is rising and setting: also where it is noon and midnight.

Answ. Rising-Greenland, the Azores, Cape Verd Isles, Ascension Isle. Setting-Aleutian Islands, Queen Charlotte's Islands, eastern coast of New Holland. Noon-Middle of Siberia, middle of the western Peninsula of India. Midnight-Middle of N. America, Mexico.

3. To what places is the sun rising and setting July 27, when it is 2 hrs. a.m. at Pico (Azores); and where is it noon and midnight at the same time?

4. May 24, 8 p.m. at Newcastle, where is the sun rising and setting, and where is it noon and midnight?

5. At what places is the sun rising and setting, and where is it noon and midnight, when it is 10 p.m. at Botany Bay on August 15th?

6. April 4th, 6 a.m. at Edinburgh, where it is noon, midnight, sun-rise, and sun-set?

7. June 9th, 3 a.m. at Glasgow, where is it noon and midnight, and where is the sun rising and setting?

8. Midnight at Singapore Sept. 15, where is the sun vertical, and where is it rising and setting?

PROBLEM XXVI.

A place being given in the North Frigid Zone, to find when the Sun begins to appear, and when to disappear; also the Length of the longest Day and Night.

BY THE GLOBE.-1. Elevate the globe for the latitude, and bring the ascending signs to the south point of the horizon observe what degree of the ecliptic is cut by that point, and find, on the calendar, the day of the month answering to that degree; this will be the time of the sun's beginning to appear above the horizon at the given place; which is the end of the longest night.

2. Bring the descending signs to the south point of the horizon, and the day answering to the degree of the

ecliptic cut by it, will be that on which the sun disappears, which is the beginning of the longest night.

3. Bring the ascending signs to the north point of the horizon; and the degree of the ecliptic, noted as above, will show when the sun begins to shine continually; which is the beginning of the longest day.

4. Bring the descending signs to the same point, and in the same manner it will be found when the sun ceases to shine continually, or the end of the longest day.

5. From the end of the longest night to the beginning of the longest day, and conversely, the sun rises and sets daily.

BY THE ANALEMMA.-1. Elevate the globe for the latitude, and bring the analemma to the south point of the horizon, then the two days of the month on the analemma cut by the horizon, will be the beginning and end of the longest night.

2. Bring the analemma to the north point of the horizon, and you will find in the same manner the beginning and end of the longest day.

WITHOUT THE GLOBE.-1. Subtract the latitude from 90°; the remainder is called the co-latitude.

2. The sun being in the ascending signs, find, by the table, on what day its declination is equal to the colatitude, but of a contrary name; this will be the day on which the sun first appears above the horizon: find the same when the sun is in one of the descending signs: this will be the day on which it entirely disappears.

3. Find, in the same manner, the two days when the sun's declination is equal to the co-latitude, and of the same name with it: the one will be the beginning, and the other the end, of the longest day.

EXAMPLES.

1. Whale Island, discovered by Mackenzie, lies in lat. 69° 14' N.; required the time when the sun first appears

above the horizon, and when it disappears; also the lengt of the longest day and night there.

Here 69° 14' being taken from 90°, leaves 20° 46′ for the co-latitude. The two days on which the sun's declination is 20° 46′ S. (of a contrary name to the latitude) are Jan. 17th and Nov. 25th; the former is the day on which the sun first appears above the horizon, the latter that on which it disappears.

The two days on which the sun's declination is 20° 46′ N. (of the same name with the latitude) are May 24th and July 20th; the former is the beginning, and the latter the end, of the longest day.

Hence, at Whale Island, the sun first appears Jan. 17th, and rises and sets daily till May 24th,-a space of 127 days: it continues above the horizon from May 24th to July 20th; therefore the longest day there is equal to 57 natural days. From July 20th it rises and sets daily to Nov. 25th, 128 days, and never rises again till Jan. 17th; so its longest night is equal to 53 days.

2. When does the sun begin to appear above the horizon at North Cape, in Lapland, lat. 71° 10′ N.; when does it disappear; and how many days are the inhabitants without seeing the sun?

Ans. The sun appears Jan. 26, and rises and sets daily till May 15; after which time it continues above the horizon till July 29; then it rises and sets daily till Nov. 16, when it disappears till Jan. 26; the length of the longest night is therefore equal to 71 days.

3. When does the sun begin to appear at South Cape, in Spitzbergen, lat. 76° N.; when to disappear; and what is the length of the longest day there?

4. The most northerly land discovered are seven islands, called the Seven Sisters, that lie to the north of Spitzbergen, in lat. 81° N. Captain Phipps, in his voyage towards the North Pole, was so completely surrounded with ice at this place, that he and all the ship's company were for some time under the dreadful apprehension of being obliged to pass the winter here. How long would they have been without seeing the sun?

5. How long is the longest day at the North Pole? 6. In 1819-20, Captain Parry wintered at Melville Island, in the Polar Sea, lat. 75°; how many days were he and his men deprived of the light of the sun?

7. In 1827, Captain Parry, in his attempt to reach the North Pole, advanced as far as 82° 45′ North; required the length of the longest day there?

PROBLEM XXVII.

To find in what Latitude, in the North Frigid Zone, the Sun begins to shine, without setting, on any given day.

Find the sun's declination on the given day, subtract it from 90o, and the remainder will be the latitude required. The given day must be between March 21st and June 21st.

In the same manner it may be found in what latitude, in the south frigid zone, the sun begins to shine, without setting, on any given day between Sept. 23d and Dec. 21st.

EXAMPLES.

1. In what latitude does the sun begin to shine without setting on April 23? Ans. 77° 31′ N.

Having the length of the longest Day in any place, to find the Latitude of that Place.

By the Globe.-1. Bring the first of cancer to the meridian, and set the index to 12.

2. Turn the globe westward till the index point to the hour of setting, which is equal to half the length of the day.

3. Raise or depress the pole, till the sun's place be observed to be exactly in the western horizon; the elevation of the pole will give the latitude of the place.

By this problem it may be found in what latitude any day is of a given length, by bringing the sun's place for the given day to the meridian, and proceeding as above.

The examples in this problem may be proved by Problem XVII.

EXAMPLES.

1. In what latitude is June 21st 16 hours long?

Ans. Lat. 49o N.

2. Where 18 hours long? Ans. Lat. 5810 N. 3. Where is Dec. 1st 14 hrs. long? Ans. Lat. 32o 46'S. 4. In what latitudes is January 21st

6. In what latitudes is May 15th, or July 29th

6 hours long?

9 hours? 14 hours?

18 hours?

PROBLEM XXIX.

To find the Latitudes of those places in the Frigid Zone where the Sun does not set for a given number of Days.

1. Take half the number of the days, and count as many degrees from the first of cancer towards the equinoctial point.

2. Bring the point thus arrived at to the brass meridian, and observe the degree cut by it.

3. Subtract this from 90°, and the remainder will be the latitude of the place.

The above method is not perfectly correct, because the sun does not advance one degree in the ecliptic every day, but takes 365 days to move through the whole 360 degrees in the ecliptic.

EXAMPLES.

1. In what latitude does the sun shine continually for 50 days? Ans. 69o.

2. In what latitude does it shine for 76 days? Ans. 71°30′. 3. In what latitude does the sun shine continually for 1 month; for 2, 3, 4, 5, and for 6 months?

QUESTIONS FOR EXAMINATION IN SECTION V.

Into how many zones is the earth divided? What are the boundaries of the torrid zone? What is its breadth? How are the two temperate zones situated? What is the breadth of each? What lines are the boundaries of the frigid zones? In which of the zones does the sun rise and set daily? In which does it not set for a certain number of days in summer, or rise for a certain number of days in winter? What is meant by the sun's being vertical? In which of the zones is the sun