great circle passing through the poles of another is called its secondary. That vertical circle, which has its plane perpendicular to the plane of the meridian, is called the prime vertical. The meridian and prime vertical, by their intersections with the horizon, divide it into four equal parts: the points of their intersection are called the cardinal points. The meridian cuts the horizon at right angles in the north and south points, and the prime vertical cuts it at right angles in the east and west points. Lesser circles of the sphere parallel to the horizon are called parallels of altitude or almacantar.

The armillary sphere was a machine formerly in use, which represented the principal circles above described, the poles of the earth, &c.; but since globes which contain all those circles have been more general, this machine is become exploded.

The degrees of longitude are not equal like those of latitude, but diminish in proportion as the meridians incline, or their distance contracts as they approach the pole. Thus in 60° of latitude, a degree of longitude is but half the length of a degree of the equator. We therefore here add

A Table, showing the Number of Miles contained in a Degree of Longitude in each Parallel of Latitude from the Equator.

For the methods of calculating the latitude and longitude, see LATITUDE and LONGITUDE. SECT. III. OF THE DIFFERENT POSITIONS OF

THE SPHERE, THE ZONES, CLIMATES, &C.

If we suppose an inhabitant of the earth living at either of the poles, he will there have one of the celestial poles always in his zenith and the other in his nadir, the equator coinciding with the horizon. Hence all the celestial parallels are also parallel to the horizon; and hence a person, or people, are said to live in a parallel sphere, or to have a parallel horizon.

Those who live under the equator have both poles in the horizon, all the celestial parallels cutting the horizon at right angles; whence they are said to live in a right sphere, or to have a right horizon.

Those who live between either of the poles and the equator are said to live in an oblique sphere, or to have an oblique horizon; because the celestial equator cuts their horizon obliquely, and all the parallels in the celestial sphere have their planes oblique to that of the horizon. In this sphere some of the parallels intersect the horizon at oblique angles, some are entirely above it, and some entirely below it; all of them, however, so situated, that they would obliquely intersect the plane of the horizon extended.

The largest parallel which appears entire above the horizon of any place, in north latitude, is called by ancient astronomers the arctic circle of that place. Within this circle, i. e. between it and the arctic pole, are comprehended all the stars which never set in that place, but are carried perpetually round the horizon, in circles parallel to the equator.

The largest parallel which is hid entirely below the horizon of any place, in north latitude, was called the antarctic circle of that place by the ancients. This circle comprehends all the stars which never rise in that place, but are carried perpetually round below the horizon, in circles parallel to the equator.

In a parallel sphere, however, the equator may be considered as both arctic and antarctic circles; for, being coincident with the horizon, all the parallels on one side are entirely above it, and those on the other entirely below it. In an oblique sphere, the nearer any place is to either of the poles the larger are the arctic and antarctic circles, as being nearer to the celestial In a right equator, which is a great circle. sphere, the arctic and antarctic circles have no place, because no parallel appears either entirely above or below it.

By the ancients the arctic circle was called maximus semper apparentium, and circulus perpetuæ apparationis; the antarctic circle, on the other hand, being named maximus semper occultorum, and circulus perpetuæ occultationis.

By the arctic and antarctic circles, however, modern geographers in general understand two fixed circles, at the distance of 23° 30′ from the poles. These mark out the space all round the globe where the sun appears to touch the horizon at midnight in mid-summer, and to be entirely sunk below it in winter.

According to the different positions of the

globe, with regard to the sun, the celestial bodies exhibit different phenomena to the inhabitants. Thus, in a parallel sphere, they appear to move in circles round the horizon; in a right sphere they appear to rise and set as at present, but always in circles cutting the horizon at right angles; but, in an oblique sphere, the angle varies according to the degree of obliquity, and the position of the axis of the sphere with regard to the sun. The phenomena thence arising will be sufficiently understood from what is said under the article ASTRONOMY.

The space between the two tropics, called the torrid zone, extends 47° of latitude all round the globe; and throughout the whole of that space the sun is vertical to some of the inhabitants twice a year, but to those who live directly under the tropics only once. Throughout the whole torrid zone also there is little difference between the length of the days and nights. The ancient geographers found themselves considerably embarrassed in their attempts to fix the northern tropic; for though they took a very proper method, namely, to observe the most northerly place where objects had no shadow on a certain day, yet they found that on the same day no shadow was cast for a space of no less than 300 stadia. The reason of this was, the apparent diameter of the sun; which, being about half a degree, seemed to extend himself over as much of the surface of the earth, and to be vertical every where within that space.

The division of the earth into zones has arisen from the various appearances of the sun, and the effects of his light and heat upon different parts of it. These are five in number: 1. The torrid zone lying between the two tropics for a space of 470 of latitude. This is divided into two equal parts by the equator; and the inhabitants have the sun vertical to them twice a year, excepting only those who dwell under the tropics, to whom he is vertical only once. 2. The two temperate zones lie between the polar circles and the tropics, containing a space of 43° of latitude. And, 3, The two frigid zones lie between the polar circles and the poles. In these last the longest day is never below twenty-four hours; in the temperate zones it is never quite so much, and in the torrid zone it is never above fourteen. The zones are named from the degree of heat they were supposed to be subjected to. The torrid zone was supposed by the ancients to be uninhabitable by reason of its heat; but this is now found to be a mistake, and many parts of the temperate zones are more intolerable in this respect than the torrid zone itself. Towards the polar circles, also, these zones are intolerably cold during winter. Only a small part of the northern frigid zone, and none of the southern, is inhabited. Some geographers reckoned six zones, dividing the torrid zone into two by the equator.

From the difference in the length and positions of the shadows of terrestrial substances, ancient geographers have given different names to the inhabitants of certain places of the earth; the reason of which will be easily understood from the following considerations:-1. As the sun in

his apparent annual revolution never removes farther from the equator than 23° 30′, none of those who live without that space, or beyond the tropics, can have that luminary vertical to them at any season of the year. 2. All who live between the tropics have the sun vertical twice a year, though not all at the same time. Thus, to those who live directly under the equator, he is directly vertical in March and September at the equinox. If a place is in 10° north latitude, the sun is vertical when he has 10° north declination; and so of every other place. 3. All who live between the tropics have the sun at noon sometimes north and sometimes south of them. Thus, they who live in a place situated in 20° north latitude, have the sun at uoon to the northward when he has more than 20° north declination, and to the southward when he has less. 4. Such of the inhabitants of the earth as live without the tropics, if in the northern hemisphere, have the sun at noon to the south of them; but to the north, if in the southern hemisphere. 5. When the sun is in the zenith of any place, the shadow of a man or any upright object, falls directly upon the place where they stand, and consequently is invisible; whence the inhabitants of such places were called Ascii, or without shadows. Those who live between the tropics, and have the sun sometimes to the north and sometimes to the south of them, have of consequence their shadows projecting north at some seasons of the year and south at others; whence they were called Amphiscii, or having two kinds of shadows. They who live without the tropics have their noon shadows always the same way; and are therefore called Heteroscii, that is, having only one kind of shadow. If they are in north latitude the shadows are always turned towards the north, and, if in the southern hemisphere, towards the south. When a place is so far distant from the equator that the days are twenty-four hours long or longer, the inhabitants were called Periscii, because their shadows turn round them.

Names have likewise been given the inhabitants of different parts of the earth, from the parallels of latitude under which they live, and their situation with regard to one another. Thus, when two places are so near each other that the inhabitants have only one horizon, or at least that there is no perceptible difference between them, the inhabitants were called Synoeci, that is, near neighbours; the seasons, days, nights, &c., in both places being perfectly alike. Those who lived at distant places, but under the same parallel, were called Periceci, that is, living in the same circle. Those who are on the same side of the equator have the seasons of the year at the same time; but, if on different sides, the summer season of the one is the winter of the other; as explained under ASTRONOMY. Some writers, however, by the name of Percici, distinguish those who live under opposite points of the same parallel, where the noon of the one is the midnight of the other. When two places lie under parallels equally distant from the ecuator, but in opposite hemispheres, the inha

bitants were called Anteci. These have a similar increase of days and nights, and similar seasons, but in opposite months. According to some, the Antoci were such as lived under the same geographical meridian, and had day and night at the same time. If two places are in parallels equally distant from the equator, and in opposite meridians, the inhabitants are called Antichthones with respect to one another, that is, living on opposite sides of the earth; or Antipodes, having their feet opposite to one another. When two persons are Antipodes, the zenith of the one is the nadir of the other. They have a like elevation of the pole, but it is of different poles: they have also days and nights alike, and similar seasons of the year; but they have opposite hours of the day and night, as well as seasons of the year. Thus, when it is mid-day with us, it is midnight with our Antipodes; when it is summer, with us, it is winter with them, &c.

From observing the diversity in the length of the days and nights, the rising and setting of the sun, with the other phenomena already mentioned, ancient geographers divided the surface of the earth into certain districts which they called CLIMATES (see our article of that title); and instead of the method of describing the situation of places by their latitude and longitude, as we do now, they contented themselves with mentioning the climate in which they were situated. When more accuracy was required they mentioned also the beginning, middle, and ending of the cli

mates.

This distinction, however, was vague and inaccurate for the only method they had of determining the difference was by the length of the day; and a climate, according to them, was such a space as had the day in its most northerly part half an hour longer than in the most southerly. For the beginning of their first climate they took that paral'el under which the day is twelve hours and three-quarters long: those parts of the world which lie nearer the equator not being supposed to be in any climate, either because in a loose sense they may be considered as in a right sphere, or because they were unknown, or thought to be uninhabitable by reason of the heat. The principal ancient climates are mentioned in the article above referred to.

A parallel was said to pass through the middle of a climate when the day under that parallel is a quarter of an hour longer than that which passes through the most southerly part. Hence it does not divide the space into two equal parts, but that part next the equator will always be the larger of the two; because, the farther we recede from that circle, the less increase of latitude will be sufficient to lengthen the day a quarter of an hour. Thus, in every climate there are three parallels; one marking the beginning, the second the middle, and the third the ending of the climate; the ending of one being always the beginning of another. Some of the ancients divided the earth by these parallels; others by a parallel did not mean a mere line, but a space of some breadth and hence the parallel may he understood as the same with half a cli

mate.

Let PZES of the diagram represent the celestial meridian of any place, P and S being the poles of the sphere; let EQ be the equator and HOR the horizon, stereographically projected upon the plane of the meridian; let PCS represent the six o'clock hour circle, and mOn the parallel of declination described by the sun or a star at any given day of the year; the point O being that in which it cuts the horizon; then n O represents half the arch described by the sun when above the horizon, and Om the half of the arch described when below the horizon. Let P OS represent an hour circle passing through the sun or star when in the horizon, and meeting the equator EQ in A; the arch EA of the equator intercepted between the meridian and hour circle, being found, and converted into time (allowing fifteen degrees to an hour), will evidently give half the time that the sun or star remains above the horizon, as the arch A Q will give half the time it remains below the horizon. As the arch EC contains ninety degrees, and corresponds to six hours, it is only necessary to find the arch CA, which is called the sun's ascensional difference, it being the difference between his right ascension and his oblique ascension; and, having converted it into time, to add it to or subtract it from six hours, according as the latitude of the place and sun's declination are of the same or of contrary names, that is both north or both south, or the one north and the other south, and the sum or difference shall be half the length of the day as required.

In the spherical triangle CAO, right angled at A, we have AO the complement of the sun's declination, to be found from astronomical tables, and the angle ACO, the complement of the latitude of the place, in order to find AC the right ascension. Hence, from the principles of spherics, we have the following proportion :

As radius to the tangent of the latitude, so is the tangent of the sun's declination to the sire of the sun's ascensional difference required.

When the sun is in the same hemisphere with any place, and his declination is equal to the complement of its latitude, which can only happen to places in the polar circles, then mn, the

parallel of declination, will not cut the horizon, and consequently the sun will not set in those places during the time his declination exceeds the co-latitude; but when the sun and place are in opposite hemispheres, then he will never rise at that place so long as his declination exceeds the co-latitude; and hence it is easy to see how to find the time when the sun begins to shine constantly upon any given place within the polar circle; and also the time when that place begins to be wholly in the dark for a considerable time together.

R.

It has been observed, in our article ASTRONOMY, that the twilight commences in the morning and ends in the evening when the sun is eighteen degrees below the horizon. The time of its commencement, or ending, may be found by spherical trigonometry as follows:-Let Z be the zenith, P the pole of the sphere, and T the place of the sun, eighteen degrees below the horizon H In the spherical triangle, PZT, we have P Z the distance of the pole from the zenith, which is equal to the co-latitude of the place, and PT the complement of the sun's declination; also ZT the distance of the sun from the zenith, which, in this case, is always 90°+18° or 108°. From these we are to find the hour angle Z PT, which may be had by the following proportion. Let V the perimeter of the triangle. Then, as sine Z Px sine PT to the square of the radius, so is sine (V-ZP) x sine (V-PT) to the square of the sine of half Z PT. The angle ZPT being turned into time will give the time from noon of the beginning or ending of the twilight. SECT. V. OF THE CONSTRUCTION AND USE OF

MAPS.

A map is a representation of the earth, or a part of it. A map of the world is a delineation in perspective of the globe, as it would appear to an eye placed in a particular point. The circles bounding such a map represent the brass meridian; and the curve lines running across, at every ten degrees, show the latitude north or south of the equator. The top and bottom are the north and south poles; and the curve lines uniting them are other meridians passing through every tenth degree of the equator, and showing the longitude east or west from the first meridian. The straight line intersecting these meridians, and passing through the centre, is the equator or equinoctial; at proper distances from which, on each side, are curve lines representing the tropics and polar circles.

Maps and charts, especially the latter, are sometimes drawn on what is called Mercator's projection, so called from the inventor, Gerard Mercator, an eminent geographer in Flanders, who, about the middle of the sixteenth century, published a map of the world on this construction. In these maps the meridians and parallels are

straight, and the former equidistant from each other. The degrees of longitude in every parallel are the same; while the degrees of latitude are all unequal, being lengthened towards the poles. Charts drawn on this construction are particularly of use to navigators, because the rhumbs, which point out the bearings of places, and consequently the courses to be steered to art rive at them, are all straight lines. See our charof the world on this projection.

In maps of particular countries the top is generally considered as the north, the bottom as the South; and the east is consequently on the right hand, and the west on the left. Where this rule is not followed a fleur-de-lis is usually placed on some part of the map, pointing towards the north, by which the other points may be easily known. From the top to the bottom of the map are drawn meridians, or lines of longitude; and from side to side parallels of latitude. The outermost of the meridians and parallels are marked with degrees of latitude and longitude, by means of which, and the scale of miles commonly placed in the corner of the map, the situation, distance, &c., of places may be found. Thus, to find the distance of two places, suppose London and Paris, by the map, we have only to measure the space between them with the compasses, and to apply this distance to the scale of miles, which shows that London is 210 miles distant from Paris. If the places lie directly north or south, east or west, from each other, we have only to observe the degrees on the meridians and parallels; and by turning these into miles we obtain the distance without measuring. Rivers are described in maps by black lines, and are wider towards the mouth than towards the head or spring. Mountains are sketched on maps as on a picture. Forests and woods are represented by a kind of shrub; bogs and morasses by shades; sands and shallows are described by small dots; and roads usually by double lines. Near harbours the depth of the water is expressed by figures denoting fathoms.

Having discovered by maps, or any other way, the true situation of the different places of the earth with regard to each other, we may easily know many other particulars relative to them; as, their distance from us, the hour of the day, the season of the year, &c., at any particular place. As each of these problems, however, would require a particular and sometimes troublesome calculation, machines have been invented, by which all the calculations may be saved, and every problem in geography may be solved mechanically, and in the most easy and expeditious manner. These machines are the celestial and terrestrial globes, for the use of which see GLOBE.

For the mechanical details of the construction of maps, see MAPPING.