M.-i'rHEMA'ricAL.] concentric small circles are drawn such that the sum of their radii is a right angle or 90°. Let the inner circle be that traced among the stars by the zenith of any given place, say Q, then the outer circle encloses all those stars Fig. 3. which are circuinpolar at Q, that is, whose entire course is performed above that horizon ,' for cleai'ly the zenith distance of none of these can exceed 90° at Q. Or if the outer circle be that described by the zenith of Q, then the inner circle encloses all those stars which are circuiiipolar at The second circle in the diagram shows the diurnal paths of stars with reference to the horizon. If we consider in the first circle the changes of distance between any one star and the zenith of Q as the latter traces out its path in the heavens, we see that the distance becomes alternatelya maximum and a minimum everytwelve hours, namely, when the meridian of Q passes through the star. This is called the star’s culmination or meridian transit. It will be clear from an inspection of the figure that, if for instance the star culminate to the south of the zenith, the star’s declination plus its zenith distance at ci1l- mination is equal to the latitude of the zenith, that is, of Q. corresponding rule is easily made for a northern transit. Thus the simplest iiiaimer of determining the latitude is to measure the zenith distance of a known star at its meridian transit. The position of the zenith at any moment may be deter- mined by simultaneous observation of the zenith distance of two known stars. For these distances clearly determine a point in the heavens (two points rather, which however need not be confounded) whose declination and right ascen- sion can be computed by spherical trigonometry. Thus, at the same time, are obtained both the time and the latitude. For the success of this method, which is suitable for travellers exploring an unknown country, it is desirable that the stars should differ in azimuth by about a right angle. If the path of the zenith, that is, the latitude, be known, then clearly a single observation of the zenith distance of a known star, which should be towards the east or west not towards the north or south, will fix the place or right ascension of the zenith, that is, the sidereal time, at the moment of observation. Here the pole, the zenith, and the star are the angular points of a spherical triangle of which the three sides are known: the angle at the pole, being computed, is the difference of right ascension of the star and the zenith. Thus the sidereal time is found. The determination of the difference of longitude of the two stations AB on the earth’s surface requires that the true time be kept at each. All that is necessary is a com- parison of these times at any instant. For instance, the time at B may, by the_transport of chronometers, be brought to_A, and thus ‘the difference of the local times be ascer- tained, or the indications of the clock at A may be con- ilucted by electro—telegraphy to The difference of the focal tfines at. A and B is the time a star takes to pass ilomt e meridian of the one to that of the other, and t is is the difference of longitude which may be converted into angle at the rate of 360° to 24“. . GEOGRAPHY 199 But the traveller in unknown lands, who seeks to fix astronomically his position, has no telegraph to count on and his expectations for longitude depend chiefly on obser- vations of the moon. In the Ncmtical Almanac are pub- lished the angular distances of the moon from certain stars in its path for every three hours of Greenwich time. Therefore, by actually observing the distance of the moon from one of these stars, one can infer the corresponding Greenwich time at the moment of observation. The coni- parison of this with the local time gives the longitude. Observations on the sun have shown that it traces out amongst the stars in the course of a year a great circle, inclined to the equator at an angle of 2351;’ 3 at midsummer it attains a maximum northern declination of 23%’, and at midwinter a maximum southern declination of the same amount. Hence it is inferred that the earth moves round the sun in a plane, completing one orbital revolution yearly, the axis of the earth’s diurnal rotation being inclined to this plane at an angle of 66;’. Upon this angle of inclina- tion depend the seasons, and in great measure the climates of the different portions of the earth’s surface. It is usual to draw on globes and in maps a circle or parallel at the distance of 23;-° from the equator on either side; of these circles the northern is called the Tropic of Cancer, the southern is the Tropic of Capricorn. A circle drawn with a radius of 23:? from the North Pole as centre is the Arctic Circle ; a similar and equal circle round the South Pole is the Antarctic Circle. When the sun is in the equator-—- which it crosses from north to south in September, and from south to north in lIarch—it is in the horizon of either pole. When the sun has northern declination, the North Pole is in constant day- light and the South Pole in darkness. When the sun has southern declination the North Pole on the contrary is in constant darkness while the South Pole is illuminated by sunshine. At inidsunmier in the northern hemisphere the whole region within the Arctic Circle is in constant day- light, and that within the Antarctic Circle is in darkness; at midwinter this state of things is exactly reversed. The portion of the globe lying between the Tropic of Cancer and the Arctic Circle is called the North Temperate Zone; that between the Tropic of Capricorn and the Antarctic Circle is the South Temperate Zone. In the former the sun is always to the south of the zenith; in the latter it is always to the north. In the Torrid Zone, which lies between the Tropics, the sun, at any given place, passes the meridian to the north of the zenith for part of the year, and to the south for the remainder. When the sun is to the north of the equator the days are longer than the nights in the northern hemisphere, while in the southern hemisphere the nights are longer than the days ; when the sun has southern declination this condition is reversed. As the sun increases his north declination from 0° to 23%°, not only do the days increase in length in the northern hemisphere, but the rays of the sun—in the Temperate and Arctic regions—impiiige more perpendi- cularly on the surface ; hence the warmth of summer. Even in summer the rays of the sun in the Arctic regions strike the surface very obliquely ; this, combined with the protracted season of darkness, produces excessive cold. Summer in the northern hemisphere is thus contemporane- ous with winter in the southern; while winter in the northern hemisphere is simultaneous with summer in the southern. The length of the day at any place at any season of the year is easily ascertained from the following considerations. Let us (fig. 4) be the axis of rotation, eq the equator orthographically projected on a meridian plane, ab the
parallel of the given place; draw the diameter fg making