PROBLEM XXXV.

To find the beginning, end, and duration of twilight at any place, on any given day.

Rule. Find the sun's declination for the given day (by Problem XX.) and elevate the north or south pole, according as the declination is north or south, so many degrees above the norizon as are equal to the sun's declination; screw the quadrant of altitude on the brass meridian, over the degree of the sun's declina tion; bring the given place to the brass meridian, and set the index of the hour circle to twelve: turn the globe eastward till the given place comes to the horizon, and the hours passed over by the index will shew the time of the sun's setting, or the beginning of evening twilight: continue the motion of the globe eastward, till the given place coincides with 18° on the quadrant of altitude below* the horizon, the time past over by the index of the hour circle, from the time of the sun's setting, will be the duration of evening twilight. The morning twilight is the same length.

OR, THUS :

Elevate the north or south pole, according as the latitude of the given place is north or south, so many degrees above the horizon as are equal to the latitude; find the sun's place in the eciiptic, bring it to the brass meridian, set the index of the hour circle to twelve, and screw the quadrant of altitude to the brass meridian over the given latitude; turn the globe westward on its axis till the sun's place comes to the western edge of the horizon, and the hours passed over by the index will shew the time of the sun's setting, or the beginning of evening twilight; continue the motion of the globe westward till the sun's place coincides with 18° on the quadrant of altitude below the horizon, the time passed over by the index of the hour circle, from the time of the sun's setting, will be the duration of evening twilight.

誓

*The quadrant of altitude belonging to our modern globes is always graduated to 18 degrees below the horizon.

OR, BY THE ANALEMMA.

Elevate the pole to the latitude of the place, as above, and screw the quadrant of altitude upon the brass meridian over the degree of latitude; bring the middle of the analemma to the brass meridian, and set the index of the hour circle to twelve; turn the globe westward till the given day of the month, on the analemma, comes to the western edge of the horizon, and the hours passed over by the index will show the time of the sun's setting, or the beginning of evening twilight: continue the motion of the globe westward till the given day of the month coincides with 18° on the quadrant below the horizon; the time passed over by the index, from the time of the sun's setting, will be the duration of evening twilight.

Examples. 1. Required the beginning, end, and duration of morning and evening twilight at London, on the 19th of April.

Answer. The sun sets at two minutes past seven, and rises at fifty-eight minutes past four: the duration of twilight is two hours and seventeen minutes; consequently, evening twilight ends at nineteen minutes past nine, and morning twilight begins, or day breaks, at forty-one minutes past two.

2. What is the duration of twilight at London on the 23d of September? what time does dark night begin? and at what time does day break in the morning?

Answer. The sun sets at six o'clock, and the duration of twilight is two hours; consequently, the evening twilight ends at eight 'clock, and the morning twilight begins at four.

3. Required the beginning, end, and duration of morning and evening twilight at London, on the 25th of August.

4. Required the beginning, end, and duration of morning and evening twilight at Edinburgh, on the 20th of February.

5. Required the beginning, end, and duration of morning and evening twilight at Cape Horn, on the 20th of February.

6. Required the beginning, end, and duration of morning and evening twilight at Madras, on the 15th of June.

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PROBLEM XXXVI.

To find the beginning, end, and duration of constant day or twilight at any place.

Rule. Find the latitude of the given place, and add 18° to that latitude; count the number of degrees correspondent to the sun, on that part of the brass meridian which is numbered from the pole towards the equator, mark where the reckoning ends, and observe what two points of the ecliptic pass under the mark ;* that point wherein the sun's declination is increasing, will show on the horizon the beginning of constant twilight; and that point wherein the sun's declination is decreasing, will show the end of constant twilight.

Examples. . When do we begin to have constant day or twilight at London, and how long does it continue?

Answer. The latitude of London is 514 degrees north, to which add 18 degrees, the sum is 69, the wo points of the ecliptic which pass under 69 are two degrees in I, answering to the 22nd of May, and 29 degrees in, answering to the 21st of July ; so that, from the 22nd of May to the 21st of July, the sun never descends 18 degrees below the horizon of London.

2. When do the inhabitants of the Shetland islands cease to have constant day or twilight?

3. Can twilight ever continue from sun-set to sunrise at Madrid?

4. When does constant day or twilight begin at Spitzbergen?

5. What is the duration of constant day or twilight at the North Cape in Lapland, and on what day after their long winter's night, does the sun's rays first enter the atmosphere?

* If, after 18 degrees be added to the latitude, the distance from the pole will not reach the ecliptic, there will be no constant wilight at the given place: viz. to the given latitude add 18 degrees, and subtract the sum from 9, if the remainder exceed 23 degrees, there can be no constant twilight at the given place.

PROBLEM XXXVII.

To find the duration of twilight at the north pole.

Rule. Elevate the north pole so that the equator may coincide with the horizon; observe what point of the ecliptic, nearest to Libra, passes under 18° below the horizon, reckoned on the brass meridian, and find the day of the month correspondent thereto; the time elapsed from the 23d of September to this time will be the duration of evening twilight. Secondly, observe what point of the ecliptic, nearest to Aries, passes under 180 below the horizon, reckoned on the brass meridian, and find the day of the month correspondent thereto; the time elapsed from that day to the 21st of March will be the duration of morning twilight.

Example. What is the duration of twilight at the north pole, and what is the duration of dark night there?

Answer. The point of the ecliptic nearest to Libra which passes under 18 degrees below the horizon, is 22 degrees in m, answering to the 13th of November; hence the evening twilight continues from the 23d of September (the end of the longest day) to the 13th of November (the beginning of dark night) being 51 days. The point of the ecliptic nearest to Aries which passed under 18 degrees below the horizon is 9 degrees in, answering to the 29th of January; hence the morning twilight continues from the 29th of January to the 21st of March (the beginning of the long. est day) being fifty-one days. From the 23d of September to the 21st of March are 179 days, from which deduct 102 (= 51 × 2), the remainder is 77 days, the duration of total darkness at the north pole; but, even during this short period, the moon and the Aurora Borealis shine with uncommon splendour.

PROBLEM XXXVIII.

To find in what climate any given place on the globe is situated.

Rule. 1. If the place be not in the frigid zones, find the length of the longest day at that place (by Problem XXVIII. and subtract twelve hours therefrom; the number of half hours in the remainder will show the climate.

2. If the place be in the frigid zone,* find the length of the longest day at that place (by Problem XXX), and if that be less than thirty days, the place is in the twenty-fifth climate, or the first within the polar circle. If more than thirty and less than sixty, it is in the twentysixth climate, or the second within the polar circle: if more than sixty, and less than ninety, it is in the twenty-seventh climate, or the third within the polar circle, &c.

Examples. 1. In what climate is London, and what other remarkable places are situated in the same climate?

Answer. The longest day at London is 164 hours, if we deduct 12 therefrom, the remainder will be 44 hours, or nine half hours: hence London is the 9th climate north of the equator; and, as all places in or near the same latitude are in the same climate, we shall find Amsterdam, Dresden, Warsaw, Irkoutsk, the southern part of the peninsula of Kamtschatca, Nootka Sound, the south of Hudson's Bay, the north of Newfoundland, &c. to be in the same climate as London. The learner is requested to turn to the note to Definition 69th, at page 15 and 16.

2. In what climate is the North Cape in the island of Maggeroe, latitude 71° 30′ north.

Answer. The length of the longest day is 77 days; these days divided by 30, give two months for the quotient, and a remainder of 17 days; hence the place is in the third climate within the polar circle, or the 27th climatc reckoning from the equator. The southern part of Nova Zembla, the northern part of Siberia, James' island, Baffin's Bay, the northern part of Greenland, &c. are in the same climate.

3. In what climate is Edinburgh, and what other places are situated in the same climate?

* The climates between the polar circles and the poles were unknown to the ancient geographers; they reckoned only seven climates north of the equator. The middle of the first northern climate they made to pass through Meroe, a city of Ethiopia, built by Cambyses on an island in the Nile, nearly under the tropic of Cancer; the second through Syene, a city of Thebais in Upper Egypt, near the cataracts of the Nile; the third through Alexandria; the fourth through Rhodes; the fifth through Rome or the Hellespont; the sixth through the mouth of the Borysthenes or Dnieper, and the seventh through the Riphæan mountains, supposed to be situated near the source of the Tanais or Don river. The southern parts of the earth being in a great measure unknown, the climates received their names from the northern ones, and not from particular towns or places. Thus the climate which was supposed to be at the same distance from the equator southward, as Meroe was northward, was called Antidiameroes, or the opposite climate to Meroe; Antidiasyenes, was the opposite climate to Syenes, &c.