globe, as well as the largest circle of declination on the celestial, that appears entire above the horizon of any place in north latitude, was called by the ancients the arctic circle, or circle of perpetual apparition.

Between the arctic circle and the north pole in the celestial sphere, are contained all those stars which never set at that place, and seem to us, by the rotative motion of the earth, to be perpetually carried round above our horizon in circles parallel to the equator.

The largest parallel of latitude on the terrestrial, and the largest parallel of declination to the celestial globe, which is entirely hid below the horizon of any place, was by the ancients called the antarctic circle, or circle of perpetual occultation.

This circle includes all the stars which never rise in that place to an inhabitant of the northern hemisphere, but are perpetually below the horizon.

All arctic circles touch their horizons in the north point, and all antarctic circles touch their horizons in the south point; which point, in the terrestrial and celestial spheres, is the intersection of the meridian and horizon.

If the elevation of the pole be 45 degrees, the most elevated part either of the arctic or antarctic circle will be the zenith of the place.

If the pole's elevation be less than 45 degrees, the zenith point of those places will fall without its arctic or antarctic circle; if greater, it will fall

within.

Therefore, the nearer any place is to the equator, the less will its arctic and antarctic circles be; and on the contrary, the farther any place is from the equator, the greater they are. So that,

At the poles, the equator may be considered as both an arctic and antarctic circle, because its plane is coincident with that of the horizon.

But at the equator (that is, in a right sphere) there. is neither arctic nor antarctic circle.

They who live under the northern polar circle, have the tropic of Cancer for their arctic, and that of Capricorn for their antarctic circle.

And they who live on either tropic, have one of the polar circles for their arctic, and the other for their antarctic circles.

Hence, whether these circles fall within or without the tropics, their distance from the zenith of any place is ever equal to the difference between the pole's elevation and that of the equator above the horizon of that place.

From what has been said, it is plain there may be as many arctic and antarctic circles, as there are individual points upon any one meridian between the north and south poles of the earth.

Many authors have mistaken these mutable circles, and have given their names to the immutable polar circles, which last are arctic and antarctic circles, in one particular case only, as has been shewn.

PROBLEM XIX. To find the circle or parallel of perpetual apparition, or occultation of a fixed star, in a given latitude.

By rectifying the globe to the latitude of the place, and turning it round on its axis, it will be immediately evident, that the circle of perpetual apparition is that parallel of declination which is equal to the complement of the given latitude northward; and for the perpetual occultation, it is the same parallel southward; that is to say, in other words, all those stars whose declinations exceed the co-latitude, will always be visible, or above the horizon; and all those in the opposite hemisphere, whose declination exceeds the co-lat tude, never rise above the horizon.

For instance,he latitude of London 51 deg. 30 min. whose cc-litude is 38 deg. 30 min. gives the parallels desired; for all those stars which are within the circle, towards the north pole, never descend below our horizon; and all those stars which are within the same circle, about the south pole, can never be seen in the latitude of London, as they never ascend above its horizon.

OF PROBLEMS RELATING TO THE AZIMUTH, &c. OF

THE SUN AND STARS.

PROBLEM XX. The latitude of the place and the sun's place being given, to find the sun's amplitude.

That degree from east to west in the horizon, wherein any object rises or sets, is called the amplitude.

Rectify the globe, and bring the sun's place to the eastern side of the meridian, and the arch of the horizon intercepted between that point and the eastern point will be the sun's amplitude at rising.

If the same point be brought to the western side of the horizon, the arch of the horizon intercepted between that point and the western point, will be the sun's amplitude at setting.

Thus, on the 24th of May the sun rises at four, with 36 degrees of eastern amplitude, that is, 36 degrees from the east towards the north, and sets at eight, with 36 degrees of western amplitude.

The amplitude of the sun at rising and setting increases with the latitude of the place; and in very high northern latitudes, the sun scarce sets before he rises again. Homer had heard though it is not true of the Læ applies it:

omething of this,

ones, to whom he

Six days and nights a doubtful course we steer;
The next, proud LAMOS' lofty towers appear,
And Læstrygonia's gates arise distinct in air.
The shepherd quitting here at night the plain,
Calls, to succeed his cares, the watchful swain.
But he that scorns the chains of sleep to wear,
And adds the herdsman's to the shepherd's care,
So near the pastures and so short the way,
His double toils may claim a double pay,
And join the labours of the night and day.

PROBLEM XXI. To find the sun's altitude at any given time of the day.

Set the centre of the artificial sun to his place in

the ecliptic upon the globe, and rectify it to the latitude and zenith; bring the centre of the artificial sun under the strong brass meridian, and set the hour index to that XII which is most elevated; turn the globe to the given hour, and move the graduated edge of the quadrant to the centre of the artificial sun; and that degree on the quadrant, which is cut by the sun's centre, is the sun's height at that time.

The artificial sun being brought under the strong brass meridian, and the quadrant laid upon its centre, will shew its meridian, or greatest altitude for that day.

If the sun be in the equator, his greatest or meridian altitude is equal to the elevation of the equator, which is always equal to the co-latitude of the place.

Thus, on the 24th of May, at nine o'clock, the sun has 44 deg. altitude, and at six in the afternoon 20 degrees.

OF THE AZIMUTHAL OR VERTICAL CIRCLES.

The vertical point, that is, the uppermost point of the celestial globe, represents a point in the heavens, directly over our heads, which is called our zenith.

From this point circular lines may be conceived crossing the horizon at right angles.

These are called azimuth or vertical circles. That one which crosses the horizon at 10 degrees distance from the meridian on either side is called an azimuth circle of 10 deg.; that which crosses at 20 is called an azimuth of 20 degrees.

The azimuth of 90 deg. is called the prime verti