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before midnight; or so much before noon, as he sets after
2. Keep the globe from rotating. Affix the quadrant of altitude to the sun's declination (i. e. to the latitude in which it is vertical); then, the graduated edge of the quadrant brought to coincide with any proposed place, will show its elevation in sun-light, or the altitude* at which the sun is appearing to its inhabitants at that instant.
N.B.-If the place should be found coinciding with the brass meridian, that circle may be used instead of the quadrant; and the degrees counted on it the shortest way towards the terminator, will show the meridian altitude of the sun at that place.
1. What is the length of the 15th of April or the 27th of August, to us in London; and how high is the sun above the western horizon of the island of Bermuda when it is setting here?
Elevating the north pole 10°, and bringing London to coincide with the brass meridian, we find that the index will have passed over 6 hrs. 53m., when London is coinciding with the eastern edge of the terminator, or is setting out of sun-light. Hence the time of sun-set being 6h. 53m., I subtract those hours from 12, or midnight, and I getfor the time of sun-rise on these mornings, nearly. By affixing the quadrant, and passing its graduated edge over, Bermuda, I find that that island has the pivot or sun 41° from its zenith, or is yet elevated -degrees in his beams.
2. What is the length of the 25th of October at St. Helena; and how high has the sun risen above the eastern horizon of the east point of Owhyhee, when St. Helena is leaving sun-light?
3. When does the sun rise, and what, consequently, is the length of the night and of the day, at Clerke's Island
* The pupil will understand this, if he considers that the number of degrees between the place and the terminator, is the complement of its distance from where the quadrant is screwed; viz., the zenith of the place to which the sun is vertical. If the places are situated nearly north or south of the sun, the brazen meridian will show the zenith distance and altitude.
LATITUDE AND LENGTH OF DAY.
(south of Behring's Straits) on the 10th of July; and when the sun is setting there on that day, what is his altitude at Mocha, where he is nearly north; at Calcutta, where he is declining westward; and at the Cape of Good Hope, where he appears advancing towards noon, considerably to the north of their east?
4. Find the time of sun-set at Petersburgh on the 21st of December; and the altitudes at which the sun appears at that instant to the inhabitants of the following places :To the south, at St. Helena, Gibraltar, Land's End, and the Faroe Islands.
To the north of the west of the Cape of Good Hope and Kerguelen's Land.
To the north of the east of Cape Horn.
To the south of the east of Antigua.
5. Find the time of sunset at Petersburgh on the 21st of June, its longest day, and describe the positions with regard to sun-light, of the above-named places at that instant.
Remark. We attended in Problem IV. Sect. I., and the succeeding, to the terrestrial globe as a model of our earth revolving on its axis in star-light; and found the "diurnal arcs" of several stars; that is, what portions of the time occupied by one rotation of the earth, were spent by places of given latitude in passing through the beams of a star of given declination.
We have since seen (page 108) how a constant change of the declination of the sun, the source of our day, is effected; and have proceeded to view some of the consequences of his change of declination in different latitudes. Referring also to the annexed figure, we remark that, owing to the power of his beams, the, reflection of them upon "the vapours and minute solid particles which float in our atmosphere, and perhaps also, upon the actual material atoms of the air itself," is rendered so sensible to our eyes, as to be
the means of conferring the important blessing of twilight, which continues until the sun has descended 18°; or, more correctly, (as the proper use of our terrestrial globe explains to us,) until, by the rotation of the earth, we have been carried 18° beyond the reach of those of his beams which fall directly upon its surface.
From the same cause we enjoy twilight for a corresponding portion of time before the sun rises; that is, before, by the rotation of the earth, that portion of its surface on which we dwell reaches his direct beams in the morning, or it is "sun-rise."
Let the annexed figure represent our earth with N, its north pole, elevated, say, 21 degrees above T T', the terminator; then V will represent the spot at which the sun is vertical; and it is evident that, as the earth rotates in the direction shown by the arrows, a part of the surface will be deriving light from t', an illuminated portion of the atmosphere, long before it can receive W the direct beams of the sun by arriving at T'. In the same manner, after having lost them at T, the eastern edge of the terminator, it will continue to enjoy them for a similar length of time, as they are reflected by the similar portion of atmosphere, t.
The month, day, and hour at any place being given, to find that particular place on the earth where the sun is vertical, and all others that have noon; those places also which have morning twilight, and those to which the sun is rising; those places where the sun is setting; those which have evening twilight; and those places at which it is midnight.
Disc, (def. 57); Eclipse, (def. 58); Eclipse of the Sun, (def. 59); Eclipse of the Moon, (def. 60). Read the preceding remark, and describe the figure.
RULE.-Elevate the pole to the declination of the sun : the wooden circle of the globe will then represent the terminator" of his direct beams for the given day. Bring the place at which the time is given to the brass meridian, and set the index to 12. Give the globe its eastward rotation until the index have passed over so many hours as the given time is past the last noon. And, lastly, affix the quadrant of altitude to the sun's declination. All places coinciding with the upper semicircle of the brazen meridian have noon; whilst those coinciding with its under semicircle have midnight. That particular place under the sun's declination has the sun vertical. The inhabitants of all places along the western edge of the terminator, see the sun in their eastern horizon, and are rising into his direct beams, having had the benefit of his twilight from the time of their being within 18° of this terminator. Those places along the eastern edge of the terminator have the sun setting in their west, as they are leaving his light; and all those places have evening twilight which are yet not more than 18° depressed below the terminator.
*The degrees of depression below the terminator, are to be measured by the crepuscular graduation of the quadrant; and it will be well for the pupil to remark, that as each place is most depressed at midnight, there must be certain places, (differing according to their latitudes and the declination of the sun,) which are within the twilight limit at that hour, and therefore have no real night.
Examples.-Find where the sun is vertical, and where else it is noon; where it is morning twilight and where sun-rise ; where it is sun-set, where evening twilight, and where midnight, at the several instants of time given at the following places :
It is much better to disregard the very trifling difference of declination due, in some instances, to the next day, than to reverse the proper motion of the globe for the purpose of bringing back the time.
1. 17th of February or 23d of October. Lisbon past
Answer.-Vertical, Lima.-Noon, Port Royal, west part of Cuba, Cape "Look Out," Washington, Lake Ontario, Isle of Juan Fernandez, &c.-Midnight, Cambodia, Tonkin, Irkoutsk, &c., Bencoolen, (nearly).-Rising, Western of Sandwich Islands, Melville Island, Navigators' Isles, Friendly Isles, (nearly). Morning Twilight, Aleouskie Islands, the Fejees, New Zealand. &c.-Setting, North of Iceland, North of Ireland, South-west of England, Iviza, Loango, Cape of Good Hope, (nearly).-Evening Twilight, Norway, Germany, Italy, Greece, Coast of Natal, &c.
2. 19th of May or 24th of July. London, 24m. past
3. 21st of June, (our longest day, or "summer solstice”). Greenwich, 28m. past 4 A.M.
4. 21st of March or 23d of September, ("the Equinoxes.") St. Helena, or Gibraltar, or Land's End, 5 P.M.
5. On 21st of March or 23d of September, when midnight at London, or Havre, or Valencia, note a particular island which is about to have twilight at midnight.
6. 21st of December, (our shortest day, or " winter solstice.") Bombay, 20m. to 7 A.M.: where is the sun vertical, where rising, &c.
7. 2d of June or 10th of July. Blackheath, midnight, where is the sun rising, where setting, &c., and note particularly, where twilight at midnight.
8. Suppose that in a certain year, on the 5th of January, at the time when the sun is vertical at Osnaburgh Island, (south-east of Otaheite,) the full moon be exactly opposite to the sun, and therefore totally eclipsed by the shadow of our earth; at what remarkable place in Arabia is the moon* vertically thus eclipsed; what places, as the earth revolves, are leaving the sun-beams to behold her in this condition; and at what places can the inhabitants, at that instant looking northward, point with the right hand to the sun rising in their eastern horizon, and with the left to the moon, setting thus eclipsed near their west ?†
The moon, at the time of total eclipse, is not invisible, but appears of a tarnished copper colour.
+ In consequence of the refracting power of the atmosphere, the sun and moon may, in this case, be both of them just above the horizon.