ders of China, which Tartars have the said inhabitants of Chili for their Antipodes.

This will become evident, by placing the globe in the position of a right sphere, and bringing those nations to the edge of the broad paper circle.

PROBLEM XXIII. The day of the month being given, to find all those places on the globe, over whose zenith the sun will pass on that day.

Rectify the terrestrial globe, by bringing the given day of the month on the back side of the strong brass meridian, to coincide with the plane of the broad circle: observe the number of degrees of the brass meridian, which

paper

given day of the month.

corresponds to the

This number of degrees, counted from the equator on the strong brass meridian, towards the elevated pole, is the point over which the sun is vertical; and all those places, which pass under this point, have the sun directly vertical on the given day.

Example. Bring the 11th of May to coincide with the plane of the broad paper circle, and the said plane will cut eighteen degrees for the elevation of the pole, which is equal to the sun's declination for that day, which being counted on the strong brass meridian towards the elevated pole, is the point over which the sun will be vertical; and all places that are under this degree, will have the sun on their zenith on the 11th of May,

Hence, when the sun's declination is equal to the latitude of any place in the torrid zone, the sun will be vertical to those inhabitants that day; which furnishes us with another method of solving this problem.

OF PROBLEMS PECULIAR TO THE SUN.

PROBLEM XXIV, To find the sun's place on the broad

paper circle.

Consider whether the year in which

you seek the sun's place is bissextile, or whether it is the first, second or third year after.

If it be the first year after bissextile, those divisions to which the numbers for the days of the months are affixed, are the divisions which are to be taken for the respective days of each month of that year at moon; opposite to which, in the circle of twelve signs, is the sun's place.

If it be the second year after bissextile, the first quarter of a day backwards or towards the left-hand, is the day of the month for that year, against which, as before, is the sun's place.

If it be the third year after bissextile, then three quarters of a day backwards is the day of the month for that year, opposite to which is the sun's place.

If the year in which you seek the sun's place be bissextile, then three quarters of a day backwards is the day of the month from the 1st of January to

the 28th of February inclusive. The intercalary, or 29th 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.

Upon my father's globes there are twenty-three 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 23 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

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

PROBLEM XXVI. To find 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 XXVII. The day and hour at any place in the torrid zone being given, to find 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,