named, together with the north and south poles. z. is the Zenith of London, N the Nadir, H the south point of the Horizon, o the north point, c the east and west points, s the summer solstice, w the winter solstice, a the ecliptic's north pole, e the ecliptic's south pole. The two equinoctial points are represented by c, supposing one to be on this side, the other on the opposite side of the globe. If you would have the two colures represented here in this figure, you must suppose the meridian to be the solsticial colure, and the axis of the world to represent the equinoctial colure. Note, This representation or projection of the sphere in strait lines is usually called the analemma. See how to project it or to erect this scheme, Sect. XX. Probl. XV. Fig. xxiii. SECT, V.-Of Longitude and Latitude on the Earthly Globe, and of different Climates. THE various parts of the earth and heavens bear various relations both to one another, and to these several points and circles, which have been described. First, The earth shall be considered here. Every part of the earth is supposed to have a meridian line passing over its zenith from north to south through the poles of the world. It is called the meridian line of that place, because the sun is on it at noon. That meridian line which passes through Ferro, one of the Canary Islands, has been usually agreed upon by geographers as a first meridian, from which the rest are counted by the number of degrees on the equator. Others have placed their first meridian in Teneriff, another of the Canary Islands, which is two degrees more to the east, but this is matter of choice and custom, not of necessity. The longitude of a place is its distance from the first meridian toward the east measured by the degrees upon the equator. So the longitude of London is about 20 degrees, counting the first meridian at Ferro. Note, In English globes or maps sometimes the longitude is computed from the meridian of London, in French maps from Paris, &c. for it being purely arbitrary where to fix a first meridian, mariners and map-makers determine this according to their inclination. When only the word longitude is mentioned in general, it always means the distance eastward; but sometimes we mention the longitude westward as well as eastward, i. e. from London to Paris, &c. especially in maps of particular countries. By the meridian circles on a map or globe the eye is directed to the true longitude of any place according to the degrees marked on the equator: and upon this account the meridians are sometimes called lines of longitude. The latitude of a place is its distance from the equator toward the north or south pole measured by the degrees on the meridian. So the latitude of London is 51 degrees 32 minutes, that is, about 51. A place is said to have north latitude or south latitude according as it lies toward the north pole or south pole in its distance from the equator. So London has 51 degrees of north latitude. The elevation of the pole in any particular place is the distance of the pole above the horizon of that place measured by the degrees on the meridian, and is exactly equal to the latitude of that place for the pole of the world or of the equator is just so far distant from the horizon as the zenith of the place (which is the pole of the horizon) is distant from the equator. For which reason the latitude of the place or the elevation of the pole are used promiscuously for the same thing. The truth of this observation, (viz.) that the latitude of the place and the poles elevation are equal, may be proved several ways; I will mention but these two. See figure iv. Let Hc o be the horizon, z the zenith, or the point over London, E z the latitude of London 514, P o the elevation of the north pole above the horizon. Now that E z is equal to P o is proved, thus. Demonstration I. The arch z P added to E z makes a quadrant, (for the pole is always at 90 degrees distance from the equator.) And the arch z p added to P o makes a quadrant, (for the zenith is always at 90 degrees distance from the horizon.) Now if the arch z P added either to E z or to P o completes a quadrant, then Ez must be equal to P o. Demonstration II. The latitude E z must be the same with the poles elevation ro: For the complement of the latitude, or the heighth of the equator above the horizon E H is equal to the complement of the poles elevation P z. I prove it thus: The equator and the pole standing at right angles as E C P, they complete a quadrant, or include 90 degrees: Then if you take the quadrant E C P out of the semicircle, there remains ro the elevated pole, and E н the complement of the latitude, which complete another quadrant. Now if the complement of the latitude added to the elevation of the pole, will make a quadrant, then the complement of the latitude is equal to the complement of the poles elevation, and therefore the latitude is equal to the poles eleva *Note, The complement of any arch or angle under 90 degrees denotes such a number of degrees as is sufficient to make up 90; as the complement of 50 degrees is 40 degrees, and the complement of 51 is 38 degrees. And so the complement of the sine or tangent of any arch is called the co-sine or co-tangent: So also in Astronomy and Geography we use the words co-latitude, co-altitude, co-declination, &c. for the complement of the latitude, altitude, or declination, of which words there will be more frequent use among the problems. tion; for where the complements of any too arches are equal, the arches themselves must also be equal. As every place is supposed to have its proper meridian or line of longitude, so every place has its proper line of latitude which is a parallel to the equator. By these parallels the eye is directed to the degree of the latitude of the place marked on the meridian, either on globes or maps. By the longitude and latitude being given you may find where to fix any place, or where to find it in any globe or map: For where those two supposed lines (viz.) the line of longitude and parallel of latitude cross each other, is the place enquired. So if you seek the longitude from Ferro, 20 degrees, and the Jatitude 51 degrees, they will shew the point where London stands. Those parallels of latitude which are drawn at such distances from each other near and nearer to the poles, as determine the longest days and longest nights of the inhabitants to be half au hour longer or shorter, include so many distinct climates, which are proportionally hotter or colder according to their distance from the equator. Though it must be owned that we generally use the word climate in a more indeterminate sense, to signify a country lying nearer or farther from the equator, and consequently hotter or colder, without the precise idea of its longest day deing just half an hour shorter or longer than in the next country to it. The latitude is never counted beyond 90 degrees, because that is the distance from the equator to the pole: The longitude arises to any number of degrees under 360, because it is counted all round the globe. If you travel never so far directly towards east or west your latitude is still the same, but longitude alters. If directly toward north or south, your longitude is the same, but latitude alters. If you go obliquely, then you change both your longitude and Latitude. The latitude of a place, or the elevation of the pole above the horizon of that place, regards only the distance northward or southward, and is very easy to be determined by the sun or stars with certainty, as Sect. XX. Prob. VII, and IX. because, when they are upon the meridian they keep a regular and known distance from the horizon, as well as observe their certain and regu lar distances from the equator, and from the two poles, as shall be shewn hereafter: So that either by the sun or stars (when you travel northward or southward) it may be found precisely how much your latitude alters. But it is exceeding difficult to determine what is the longitude of a place, or the distance of any two places from each other eastward or westward by the sun or stars, because they are always moving round from east to west. The longitude of a place has been therefore usually found out and determined by measuring the distance travelled on the earth or sea, from the west toward the east, supposing you know the longitude of the place whence you set out. SECT. VI.-Of Right Ascension, Declination, and Hour Circles. HAVING considered what respect the parts of th earth bear to these artificial lines on the globe, we come, secondly, to survey the several relations that the parts of the heavens, the sun or the stars, bear to these several imaginary points and artificial lines or circles. The right ascension of the sun or any star is its distance from that meridian which passes through the point aries, counted toward the east, and measured on the equator; it is the same thing with longitude on the earthly globe. The hour of the sun or any star is reckoned also by the divisions of the equator; but the hour differs from the right ascension chiefly in this, (viz.) The right ascension is reckoned from that meridian which passes through arises; the hour is reckoned on the earthly globe, from that meridian which passes through the town or city required; or it is reckoned on the heavenly globe from that meridian which passes through the sun's place in the ecliptic, and which, when it is brought to the brazen meridian, represents noon that day. There is also this difference. The right ascension is often computed by single degrees all round the equator, and proceeds to 360: The hour is counted by every 15 degrees from the meridian of noon, or of midnight, and proceeds in number to 12, and then begins again: Though sometimes the right ascension is computed by hours also instead of degrees, but proceeds to 24. So the sun's right ascension the 10th of May is 59 degrees, or as sometimes it is called 3 hours and 56 minutes. The same lines which are called lines of longitude or meridians on the earth are called hour circles on the heavenly globe, if they be drawn through the poles of the world at every 15 degrees on the equator, for then they will divide the 360 parts or degrees into 24 hours. Note, As 15 degrees make one hour so 15 minutes of a degree make one minute in time, and one whole degree makes four minutes in time. Note, degrees are marked sometimes with (d) or with a small circle (°), minutes of degrees with a dash () seconds of minutes with a double dash ( ́ ́), hours with (b), minutes of hours sometimes with (m) and sometimes a dash, seconds with a double dash. By these meridians or hour-lines crossing the equator on the heavenly globe, the eye is directed to the true hour, or the degree |