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the 28th of February inclusive. The intercalary, or 2pth day, is three-fourths of a day to the lefthand from the 1st of March, and the 1st of March itself one quarter of a day forward, from the division marked one; and so for every day in the remaining part of the leap year; and opposite to these divisions is the sun's place.

In this manner the intercalary day is very well introduced every fourth year into the calendar, and the sun's place very nearly obtained, according to the Julian reckoning.

Thus,

A. D.' Sun's place. Apr. 25.

1788 Bissextile - .'- 8 5° 35'

1789 First year after - - tf 5 21

1790 Second V - tf 5 fi

1791 Third - - - - tf 4 5&

Upon my father's globes there are twenty-thre.e parallels, drawn at the distance of one degree from each other on both sides the equator, which, with two other parallels at 23? degrees distance include the ecliptic circle.

The two outermost circles are called the tropics; that on the north side the equator is called the tropic of Cancer; that which is on the south side, the tropic of Capricorn.

Now as the ecliptic is inclined to the equator, in an angle of 234- degrees, and is included between the tropics, every parallel between these must cross the ecliptic in two points, which two points shew the sun's place when he is vertical to the inhabitants of that parallel; and the days of the month upon the broad paper circle answering to those points of the ecliptic, are the days on which the sun passes directly over their heads at noon, and which are sometimes called their two midsummer days.

It is usual to call the sun's diurnal paths parallels to the equator, which are therefore aptly represented by the above-mentioned parallel circles; though his path is properly a spiral line, which he is continually describing all the year, appearing to move daily about a degree on the ecliptic.

Problem Xxv. To find the sun's declination, and thence the parallel of latitude corresponding thereto.

Find the sun's place for the given day in the broad paper circle, by the preceding problem, and seek that place in the ecliptic line upon the globe; this will shew the parallel of the sun's declination among the above-mentioned dotted lines, which is also the corresponding parallel of latitude; therefore all those places, through which this parallel passes, have the sun in their zenith at noon on the given day.

Thus on the 23d of May the sun's declination will be about 20 deg. 10 min.; and upon the 23d of August it will be 11 deg. 13 min. What has been said

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in the first part of this problem, will lead the reader to the solution of the following.

Problem xxvi. To Jlnd the two days on which the sun is in the zenith of any given place that is situated between the two tropics.

That parallel of declination, which passes through the given place, will cut the ecliptic line upon the globe in two points, which denote the sun's place, against which, on the broad paper circle, are the days and months required. Thus the sun is vertical at Barbadoes April 24, and August 18.

Problem xxvu. Tlie day and hour at any place in the torrid zone being given, tojind where the sun is vertical at that time.

Rectify the globe to the day of the month, and you have the sun's declination; bring the given place to the meridian, and set the hour index to XII; turn the globe till the index points to the given hour on the equator; then will the place be under the degree of the declination previously found.

Let the given place be London, and time the 11th day of May, at four min. past five in the afternoon; bring the 11th of May to coincide with the broad paper circle, and opposite to it you will find 18 degrees of north declination; as London is the given place, you have only to turn the globe till 4 min. past V westward, if it is on the meridian, when you will find Port Royal, in Jamaica, under the 18th degree of the meridian, which is the place where the sun is vertical at that time.

Problem xxvur. The time of the day at any one place being given, to find all those places where at the same instant the sun is rising, setting, and on the meridian, and where lie is vertical; likewise those places where it is midnight, twilight,and dark night; as well as tho\e places in which the twilight is beginning and ending; and also tojind the sun's altitude at any hour in the illuminated, and his depression in the obscure, hemisphere.

Rectify the globe to the day of the month, on the back side of the strong brass meridian, and the sun's declination for that day; bring the given place to the strong brass meridian, and set the horary index to XII upon the equator; turn the globe from west to east, until the horary index points to the given time. Then,

All those places, which lie in the plane of the .western side of the broad paper circle, see the sun rising, and at the same time those on the eastern side of it see him setting.

It is noon to all the inhabitants of those places, under the upper half of the graduated side of the strong brass meridian, whilst at the same time those under the lower half have midnight. :

All those places which are between the upper surface of the broad paper circle, and the wire circle under it, are in the twilight, which begms to all those places on the western side that are immediately under the wire circle; it ends at all those which are in the plane of the paper circle. /

The contrary happens on the eastern side; the twilight is just beginning to those places in which the sun is setting, and its «*nd is at the place just under the wire circle.

And those places which are under the twilight wire circle have dark night, unless the moon is favourable to them.

All places in the illuminated hemisphere have the sun's altitude equal to their distance from the edge of the enlightened disc, which is known by fixing the quadrant of altitude to the zenith, and laying its graduated edge over any particular place.

The sun's depression is obtained in the same manner by fixing the centre of the quadrant at the padir.

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Problem xxix. To find all those places within the polar circles on which the sun begins to shine, the time he shines constantly, when he begins to disappear, the length of his absence, as well as the first and last day of his appearance to those inhabitants; the day of the month, or latitude of the place being given.

Bring the given day of the month on the back side of the strong brass meridian to the plane of the broad paper circle; the sun is just then beginning

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