200 suppose to be north, then the hemisphere gm(r=_f is in sunshine, while the hemisphere glulsf is in darkness. As the earth rotates, 7: :9 a point which is at a at midday is " carried from it towards b, which it reaches at midnight; It is reached at C 6 o’clock P..I. and Is at sunset. Now if qb be the latitude of the place and 8 the sm1's declination Izlc=sin qstan 8; this in the parallel whose radius is cosqs corresponds to an angle whose sine is tanqs tan3. Call this angle 1;; the time taken to rotate through it is T131]; hence the length of the daylight is 12"+~,'{—,—n, and the length of night 12“ — 1331;. Now 1; vanishes when either qb or 3 is zero; that is, at the equator the nights and days are equal in length throughout the year; and again when the sun is in the equator, that is, at the equinox, the nights and days are equal in all latitudes. When the sun’s declination is equal to the co—latitude, 1; is a right angle, and the sun does not actually set; this can only happen at places within the polar circle. The longest day at Gibraltar is 141‘ 27”‘, at Falmouth 16“ 11"‘, and in Shetland 18“ 14'“; while in Iceland it is 20“ on the south coast and 24“ on the north. At Washington the longest day is 14“ -14”‘, and at Quebec 151‘ 40'“. All this, however, is on the supposition that day ends with sunset; but the length of apparent day is increased by atmospheric refraction and reflection. When the disk of the setting sun first seems to touch the horizon it is in reality wholly below it and is only seen by refraction. After the sun has wholly set at any given place his light still continues to illuminate the upper portion of the atmosphere there, so that, instead of ending abruptly, day- light gradually fades away until the sun is 18° below the horizon. In a diagram (fig. similar to the last draw mi parallel to gf, and at a distance from it equal to the sine of 18°; then gbf being the hemisphere unenlightened by the direct rays of the sun, gnu)‘ will re- present the twilight zone. A point 0 in the latitude of a describing the parallel ab loses sight of the sun at I.-, and is in twilight until it reaches the small circle mi, when the sun’s zenith J’ z 8 distance is 108°. The duration of twi- FiS- 5- light corresponds then to the portion Id of ab, the angle rotated through being sin ’ 1 (kl :hb)— sin‘ 1(]lk zltb) ; this converted into time gives the duration of twilight. llere hk=sin ¢lZ3.Il5; kl=sin18° seefi. At any given latitude the twilight is shortest when the great circle passing through It and 1 passes also through the sun. Expressed algebraically, if 1- be the duration of the shortest twilight in angular measure and 3 the sun’s declination at the time, then ~— sin 8 = sin :1» tan 9° sin ; 1- = see ¢> sin 9'’. Suppose in the last diagram the sun to be at his greatest northern declination, then ng = 93;«°, gm 18°, and nag = 48._l°. Ilence a place whose latitude is 48{;° N. has, at midsummer, twilight lasting from sunset to midnight and continuing from midnight to sunrise, that is, for a few days there is no absolute darkness. A little further south this G E O G ll. A 1’ H Y the angle neg equal to the sun’s declination, which we ' Since is-=231,°— l8°= [lI.TllE)I.TI('.L. 5.1,-'’, we see from the diagram that the South Pole is at this time in total darkness, which ex- tends to all places within 5§° of it. When the sun’s declination is 9° south, the North Pole is in the centre of the twilight belt ; thus all places whose latitude is greater than 81° then move in continual twilight, alternating between clearness and dimness, never attaining either day- light or total darkness. The actual period during which either pole is in total darkness is about two and a half months. At the equator, the shortest twilight occurs at the equinox, when it is 1“ 12'“; the longest when the sun is in the tropics, being 1" 18'“. At London, in latitude 511;”, twilight continues all night from May 22 to July 21 ; it is shortest about three weeks after the autumnal and three weeks before the vernal equinox, when its duration is 1" 50‘“. At Vashington the shortest twilight (being 1" 33'“) occurs on the 6th of March and 7th October ; at Quebec the shortest is 1“ 46”, falling on the 3d March and 10th October. At page 205, fig. 19 is a perspective representation of the earth—of n1ore than a hemisphere, in fact-namely, the segment my/7za_fi in fig. 5. It exhibits all those regions of the earth which at Greenwich apparent noon at midsummer are in sunshine and twilight. It is very re- markable how Asia and America, but especially the former, just escape going into darkness. Construction of .-llaps. In the construction of maps, one has to consider how a portion of spherical surface, or a configuration traced on a sphere, can be represented on a plane. If the area to be represented bear a very small ratio to the whole surface of the sphere, the matter is easy: thus, for instance, there is no difficulty in making a map of a parish, for in such cases the curvature of the surface does not make itself evident. If the district is larger and reaches the size of a county, as Yorkshire for instance, then the curvature begins to be sensible, and one requires to consider how it is to be dealt with. The sphere not being a developable surface cannot be opened out into a plane like the cone or cylinder, con- sequently in a plane representation of configurations on a sphere it is impossible to retain the desired proportions of lines or areas or equality of angles. But though one cannot fulfil all the requirements of the case, we may fulfil some by sacrificing others; that is to say, we may, for instance, have in the representation exact similarity to all very small portions of the (riginal, but at the expense of the areas, which will be quite misrepresented. Or we may retain equality of areas if we give up the idea of similarity. It is therefore usual, excepting in special cases, to steer a middle course, and, by making compromises, endeavour to obtain a representation which shall not offend the eye. A globe gives a perfect representation of the surface of the earth ; but practically, the necessary limits to its size make it impossible to represent i11 this manner the details of countries. A globe of the ordinary dimensions serves scarcely any other purpose than to convey a clear conception of the earth’s surface as a whole, exhibiting the figure, extent, position, and general features of the continents and islands, with the intervening oceans and seas; and for this purpose it is indeed absolutely essential and cannot be re- placed by any kind of map. The construction of a n1ap virtually resolves itself into the drawing of two sets of lines, one set to represent meridians, the other to represent parallels. These being drawn, the filling in of the outlines of countries presents no difficulty. The first and most natural idea that occurs to one as to the manner of drawing the circles of latitude
twilight is interrupted b_',' a slnrt perirl of d .rk:‘.es:<. I and longitude is to draw them according to the laws of