Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/833

from b, c, d, <kc.), let us draw a vertical line downwards from a to C, that is, towards the nadir, and let us draw Ca at right angles to aC, meeting the circle EaE , of which dg is an arc, in a. Through C. the centre of this circle, draw TCP parallel to aP a . Then we suppose throughout that the pole of the celestial sphere is so far off compared with the dimensions of the circle EaE , that the apparent direction of the polar axis at all points of the arc dg is the same, and therefore parallel to CP. Thus the polar axis at b is represented by the line bP b , at c by the line cP c , and so on. Draw the vertical lines bC, cC, dC, etc., and at right angles to them, through C, draw Cb, Cc, Cd, cfec. ; then clearly the angular elevation of the pole at a, or the angle P tt ae, is equal to the angle PCa; at b the elevation of the pole, or the angle P b ba, is equal to the angle PC6; at c to PCc, and at d to PCd But these angles PCa, PC6, PCc, PCcZ, diminish uniformly. In other words, to an observer travelling uniformly along an arc abed towards the south, the angular elevation of the pole would diminish uniformly, as it is observed to do, if (1) the arc da is circular, and (2) the pole of the heavens so far from the observer that lines drawn to it are appreciably parallel. Similarly the uniform increase of the polar elevation, to an observer travelling northwards along the arc ag, is explained, since the elevation of the pole, as he passes to the stations e, f, and g, changes through the values PCe, PC/, PQ/, increasing therefore uniformly.

Continuing this voyage beyond ad, southwards, the observer linds the pole continues to sink, until at length when he has arrived at a station E, the north pole of the heavens is on the horizon due north, or in direction EP E . All the phenomena of cslestial rotation continue unchanged, excspt that towards the south many new stars have come into view. Moreover, the south pole of the heavens has now risen to the horizon, and lies due south, or in direction EP E . If the observer were now to retrace his course, he would, of course, find the north pole of the heavens rising uniformly again. But if instead of this he continue his journey southwards, he finds the south pole of the heavens rising uniformly. As he travels onwards to the successive stations d , c , b , a , &c., so placed that Ed=Ed, Ec=EC, &c., the phenomena presented maybe described exactly as for the northern stations d, c, b, a, tfcc., respectively, except that for northern must be written southern, and for southern northern, throughout.

The difference in the position of observers on the northern and southern sides of E, fig. 6, may be con veniently illustrated as in fig. 7, where G represents the place of an observer near Greenwich, and C the place of an observer near Cape Town, but due south of the former, and HZh, H Z /i , are supposed to represent the apparent hemispherical .dome of the heavens above and around these respective observers. (These hemispherical domes should, of course, be very much larger in proportion, each being here represented with a radius of about 3500 miles, whereas the nearest of the celestial bodies, our moon, is nearly 240,000 from us.) G/> represents the apparent direction of the northern celestial pole as seen from Greenwich, raised about 514- above the north point of the horizon at h, and Ge is the direction of the southern or culminating point of the celestial equator, about 3S above the south point H of the Greenwich horizon. (The east and west points of the horizon-circle are projected at the point G.) At C, Cp is the direction of the southern celestial pole, about 34 above the southern horizon at H ; Ce is the direction of the culminating or north point of the celestial equator, about 55^ D above the northern horizon at h.

Fig. 7.—Domes of Heavens near Greenwich and near Cape Town.

We see that journeys taken in a north-and-south direction lead to apparent changes of the dome of the heavens, only explicable on the assumption that the path traversed is a circular arc, or nearly so. It is clear also that the radius of this circular arc is determinable if the observer notes how much the elevation of the pole is changed for any given distance traversed by him in a north- and-south direction. Suppose, for instance, that in travel ling from a to b (fig. 6) he finds the elevation of the pole diminished by 7, and that he has travelled about 480 miles, then (as already shown) he knows that ab=ab=change in polar elevation=an arc of 7 of the circumference of the circle along which he is travelling. Hence the whole circumference=-^- x 480 miles=24,686 miles; whence the diameter of the circle=(roughly) 24,686 x=7855 Sz miles. This is not the true diameter of the earth s globe, being supposed to be the result of only a rough observation; but the method serves sufficiently to show how in very early times astronomers obtained a measure of the earth. For from whatever station the observer starts on north- and-south journeys, the same uniform elevation or depres sion of the visible pole as he travels towards or from it is observed ; and the inference, therefore, is that the earth is a globe, since all the lines drawn on it in a north-and-south direction are circular arcs of equal radius. The points corresponding to E, where the poles are both on the horizon, mark the place of the terrestrial equator ; and the points on the earth, P and P (which have never yet been reached), where the north and south celestial poles are respectively vertical, are the terrestrial or geograjihical poles.

Thus far we have considered only journeys made along Earth s

a north-and-south course. Journeys pursued due east or surface due west, that is, always towards the point of the hori- cur . ve . zon which is 90 to the right or to the left of the north west point, show equally that the observer is travelling on the surface of a globe, though they produce no apparent change either in the elevation of the pole or in the posi tion of the points at which known stars rise, culminate, and set. "We have seen that the observer who remains always at one station can determine the absolute time when any given star will culminate. Let us suppose that when journeying eastward or westward he can carry with him his sidereal time-measurer, and that this continues throughout to show the true sidereal time of his original station. Then if he is travelling eastward he will find that any given star, instead of culminating at the time noted for that star as observed at his original station, will cul minate earlier. The right ascension of the star will remain

unchanged, for this is the difference between its time of