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by doubling the time of sun-rising and setting, as before.
PROBLEM VII. To find the length of the longest and shortest days in any latitude that does not exceed 66 degrees.
Elevate the globe according to the latitude, and place the centre of the artificial sun for the longest day upon the first point of Cancer; but for the shortest day upon the first point of Capricorn: then proceed as in the last problem..
But if the place hath south latitude, the sun is in the first point of Capricorn on their longest day, and in the first point of Cancer on their shortest day.
PROBLEM VIII. To find the latitude of a place, in which its longest day may be of any given length between twelve and twenty-four hours,
Set the artificial sun to the first point of Cancer, bring its centre to the strong brass meridian, and set the horary index to XII ; turn the globe till it points to half the number of the given hours and minutes ; then elevate or depress the pole till the artificial şun coincides with the horizon, and that elevation of the pole is the latitude required,
PROBLEM IX. To find the time of the sun's rising and setting, the length of the day and night, on any place whose latitude lies between the polar circles ; and also the length of the shortest day in any of those latitudes, and in what climate they are,
Rectify the globe to the latitude of the given place, and bring the artificial sun to his place in the ecliptic for the given day of the month ; and then bring its centre under the strong brass meridian, and set the horary index to that XII which is most elevated.
Then bring the centre of the artificial sun to the eastern part of the broad paper circle, which in this case represents the horizon, and the horary index shews the time of the sun-rising ; turn the artificial sun to the western side, and the horary index will shew the time of the sun-setting.
Double the time of sun-rising is the length of the night, and the double of that of sun-setting, is the length of the day.
Thus, on the 5th day of June, the sun rises at 3h. 40m. and sets at 8h. 20m.; by doubling each number it will appear, that the length of this day is 16h, 40m. and that of the night 7h, 20m.
The longest day at all places in north latitude, is when the sun is in the first point of Cancer : And,
The longest day to those in south latitude, is when the sun is in the first point of Capricorn.
Wherefore, the globe being rectified as above, and the artificial sun placed to the first point of Cancer,
and brought to the eastern edge of the broad paper circle, and the horary index being set to that XII which is most elevated, on turning the globe from east to west, until the artificial sun coincides with the western edge, the number of hours counted, which are passed over by the horary index, is the length of the longest day; their complement to 24 hours, gives the length of the shortest night.
If twelve hours be subtracted from the length of the longest day, and the remaining hours doubled, you obtain the climate mentioned by ancient historians; and if you take half the climate, and add thereto twelve hours, you obtain the length of the longest day in that climate. This holds good for every climate between the polar circles.
A climate is a space upon the surface of the earth, contained between two parallels of latitude, so far distant from each other, that the longest day in one, differs half an hour from the longest day in the other parallel.
PROBLEM X. The latitude of a place being given in one of the polar circles, (suppose the northern) to find what number of days (of 24 hours each) the sun doth constantly shine upon the same, how long he is absent, and also the
first and last day of his appear
Having rectified the globe according to the latitude, turn it about until some point in the first quadrant of the ecliptic (because the latitude is north)
intersects the meridian in the north point of the horizon : and right against that point of the ecliptic, on the horizon, stands the day of the month when the longest day begins.
And if the globe be turned about till some point in the second quadrant of the ecliptic cuts the meridian in the same point of the horizon, it will shew the sun's place when the longest day ends, whence the day of the month may be found, as before ; then the number of natural days contained between the times the longest day begins and ends, is the length of the longest day required.
Again, turn the globe about, until some point in the third quadrant of the ecliptic cuts the meridian in the south part of the horizon ; that point of the ecliptic will give the time when the longest night begins.
Lastly, turn the globe about, until some point in the fourth quadrant of the ecliptic cuts the meridian in the south point of the horizon ; and that point of the ecliptic will be the place of the sun when the longest night ends.
Or, the time when the longest day or night begins being known, their end may be found by counting the number of days from that time to the succeeding solstice; then counting the same number of days from the solstitialday, will givethe time when it ends,
It is not possible, in a treatise of this kind, to enter into a disquisition of the nature of time. It is sufficient to observe, that if we would with exactness estimate the quantity of any portion of infinite duration, or convey an idea of the same to others, we make use of such known measures as have been originally borrowed from the motions of the heavenly bodies. It is true, none of these motions are exactly equal and uniform, but are subject to some small irregularities, which, though of no consequence in the affairs of civil life, must be taken into the account in astronomical calculations.
There are other irregularities of more importance, one of which is in the inequality of the natural day.
It is a consideration that cannot be reflected upon without surprize, that wherever we look for commensurabilities and equalities in nature, we are always disappointed. The earth is spherical, but not perfectly so; the summer is unequal, when compared with the winter ; the ecliptic disagrees with the equator, and never cuts it twice in the same equinoctial point. The orbit of the earth has an eccentricity more than double in proportion to the spheroidity of its globe; no number of the revolutions of the moon coincide with any number of the revolutions of the earth in its orbit; no two of the planets measure one another: and thus it is, wherever we turn our thoughts, so different are the views