By counting the number of meridians (supposing them to be drawn through every fifteen degrees of the equator) between the horizon and the brass meridian, on any parallel of latitude, half the length of the day will be determined in that latitude, the double of which is the length of the day.

1. In the parallel of 20 degrees north latitude, there are six meridians and two thirds more; hence, the longest day is 13 hours and 20 minutes; and, in the parallel of 20 degrees south latitude, there are five meridi ans and one third; hence, the shortest day in that latitude is ten hours and forty minutes.

2. In the parallel of 30 degrees north latitude, there are seven meridians between the horizon and the brass meridian; hence, the longest day is 14 hours; and in the same degree of south latitude, there are only five meridians; hence, the shortest day in that latitude is ten hours.

3. In the parallel of 50 degrees north latitude, there are eight meridians between the horizon and the brass meridian; the longest day is, therefore, sixteen hours; and in the same degree of south latitude, there are only four meridians; hence, the shortest day is eight hours.

4. In the parallel of 60 degrees north latitude, there are 91 meridians from the horizon to the brass meridian; hence, the longest day is 18 hours; and, in the same degree of south latitude there are only 23 meridians; the length of the shortest day is, therefore, 51 hours.

By turning the globe gently round on its axis from west to east, we shall readily perceive that the sun will be vertical to all the inhabitants under the tropic of Cancer, as the places successively pass the brass meridian.

If any place be brought to the brass meridian, the number of degrees between that place and the horizon (reckoning the nearest way) will shew the sun's meridian altitude. Thus, at London, the sun's meridian altitude will be found to be about 62 degrees, at Petersburg 54 degrees, at Madrid 73 degrees, &c. To the inhabitants of these places, the sun ppears due south at noon. At Madras, the sun's meri iian altitude

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will be 79 degrees; at the Cape of Good Hope, 32 degrees; at Cape Horn, 101 degrees, &c. The sun will appear due north to the inhabitants of these places at noon. If the southern extremity of Spitzbergen, in latitude 7610 north, be brought to that part of the brass meridian which is numbered from the equator towards the poles, the sun's meridian altitude will be 37 degrees, which is its greatest altitude; and if the globe be turned eastward twelve hours, or till Spitzbergen comes to that part of the brass meridian which is numbered from the pole towards the equator, the sun's altitude will be 10 degrees, which is its least altitude for the day given in the problem. It was shewn, in the foregoing part of the problem, that, when the sun is vertically over the equator in the vernal epuinox, the north pole begins to be enlightened; consequently, the farther the sun apparently proceeds in its course northward, the more daylight is diffused over the north polar regions, and the sun will appear gradually to increase in altitude at the north pole, till the 1st of June, when his greatest height is 23 degrees; he will then gradually diminish in height till the 23d of September, the time of the autumnal equinox, when he will leave the north pole and proceed towards the south; consequently, the sun has been visible at the north pole for six months.

3. For the Winter Solstice.-The winter solstice, to the inhabitants of north latitude, happens on the 21st of December, when the sun enters Capricorn, at which time his declination is 23° 28′ south. Elevate the south pole 23 degrees above the southern point of the horizon, bring the sign of Capricorn in the ecliptic to the brass meridian, and over that degree of the brass meridian under which this sign stands, let the sun be supposed to be fixed, at a considerable distance from the globe.

Here, as at the summer solstice, the days at the equator will be twelve hours long, but the equinoctial point Aries will be in the eastern part of the horizon, and Libra in the western. From the equator southward, as far as the Antarctic circle, the diurnal arches will exceed the nocturnal arches. All the parallels of latitude within the Antarctic circle will be wholly above the horizon. From the equator northward, the noctur

nal arches will exceed the diurnal arches. All the parallels of latitude within the Arctic circle will be wholly below the horizon. The inhabitants south of the equator will now have their longest day, while those on the north of the equator will have their shortest day.

As the globe turns on its axis from west to east, the sun will be vertical successively to all the inhabitants under the tropic of Capricorn. By bringing any place to the brass meridian, and finding the sun's meridian altitude (as in the foregoing part of the problem), the greatest altitudes will be in south latitude, and the least in the north; contrary to what they were before. Thus, at London, the sun's greatest altitude will be only 15 degrees, instead of 62; and his greatest altitude at Cape Horn will now be 571 degrees, instead of 102, as at the summer solstice: hence it appears, that the difference between the sun's greatest and least meridian altitude at any place in the temperate zones, is equal to the breadth of the torrid zone, viz. 47 degrees, or more correctly, 46° 56'. On the 23d of September, when the sun enters Libra, that is, at the time of the autumnal equinox, the south pole begins to be enlightened, and as the sun's declination increases southward, he will shine farther over the south pole, and gradually increase in altitude at the pole; for, at all times, his altitude at either pole is equal to his declination. On the 21st of December the sun will have the greatest south declination, after which his altitude at the south pole will gradually diminish as his declination diminishes; and on the 21st of March, when the sun's declination is nothing, he will appear to skim along the horizon at the south pole, and likewise at the north pole; the sun has therefore been visible at the south pole for six months.

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PROBLEM XXII.

To place the globe in the same situation, with respect to the Polar Star in the heavens, as our earth is to the inhabitants of the equator, &c. viz. to illustrate the three positions of the sphere, right, parallel and oblique, so as to shew the comparative length of the longest and shortest days.*

1. For the Right Sphere.-The inhabitants who live upon the equator have a right sphere, and the north

* In this problem, and in all others where the pole is elevated to the latitude of a given place, the earth is supposed to be fixed, and he sun to move round it from east to west. When the given place is brought to the brass meridian, the wooden horizon is the true rational horizon of that place, but it does not separate the enlight ened part of the globe from the dark part, as in the preceding prob lem. Mr Adam Walker, lecturer in philosophy, in his "Easy introduction to Geography," disapproves of this method of elevating the pole. He says: "Simplicity and perspicuity should ever be studied by those who cultivate the young mind; and jarring, opposing, or equivocal ideas, should be avoided almost as much as error or falsehood. Our globes, till of late years, were equipt with an hour circle, which prevented the poles from sliding through the horizon; hence their rectification was generally for the place on the earth, instead of the sun's place in the ecliptic which put the globe in so unnatural and absurd a position respecting the sun, that young people were confounded when they compared it with the earth's position during its annual rotation round that luminary, and considering the horizon as the boundary of day and night Being, therefore, sometimes obliged to rectify for the place on the earth, and sometimes for the sun's place in the ecliptic, the two rules clash so unhappily in the pupil's mind, that few remember a single problem a twelvemonth after the end of their tuition." It will certainly be admitted that jarring, opposing, or equivocal ideas, should be avoided, and that perspicuity should be the study of every tutor; but there is nothing either absurd or unnatural in elevating the pole to the latitude of the place on the earth; for this is placing the globe in its true situation respecting the heavens and the fixed stars besides, in explaining the principles of dialling, and other problems where the globe is exposed to the sun's rays, the pole must be elevated to the latitude of the place, as will be shewn in some of the succeeding problems. The pupil who wishes to make himself completely master of the globes, must endeavour to comprehend, why he sometimes elevates the pole to the latitude of the place, and at others to the sun's declination. A little perseverance will soon remove all jarring and equivocal ideas from his mind, and, instead of forgetting the problems in a twelvemonth, he will remember them

polar star appears always in (or very near) the horizon. Place the two poles of the globe in the horizon, then the north pole will correspond with the north polar star, and all the heavenly bodies will appear to revolve round the earth from east to west, in circles parallel to the equinoctial, according to their different declinations: One half the starry heavens will be constantly above the horizon, and the other half below, so that the stars will be visible for twelve hours, and invisible for the same space of time; and, in the course of a year, an inhabitant upon the equator may see all the stars in the heavens. The ecliptic being drawn on the terrestrial globe, young students are often led to imagine that the sun apparently moves daily round the earth in the same oblique manner. To correct this false idea, we must suppose the ecliptic to be transferred to the heavens, where it properly points out the sun's apparent annual path amongst the fixed stars. The sun's

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diurnal path is either over the equator, as at the time of the equinoxes, or in lines nearly parallel to the equator: this may correctly be illustrated by fastening one end of a piece of packthread upon the point Aries on the equator, and winding the packthread round the globe towards the right hand, so that one fold touch ano ther, till you come to the tropic of Cancer; thus you will have a correct view of the sun's apparent diurnal path from the vernal equinox to the summer solstice ; for, after a diurnal revolution, the sun does not come to the same point of the parallel whence it departed, but, according as it approaches to or recedes from the tropic, is a little above or below that point. When the sun is in the equinoctial, he will be vertical to all the inhabitants upon the equator, and his apparent diurnal path will be over that line: when the sun has ten degrees of north declination, his apparent diurnal path will be from east to west nearly along that parallel. When the sun has arrived at the tropic of Cancer, his

as long as ne retains his faculties: "What we acquire with difficulty we remember with ease;" and nothing but a superficial knowledge of any subject can be obtained without close application and attention.