altitude when at its culmination. We have seen how the movement of the star-sphere determines the cardinal points of the horizon. Suppose now a telescope or pointer, so set as to turn upon a horizontal axis lying exactly east and west, as in fig. 4. We see that when the telescope is rotated on this axis, the line of sight, es, or the optical axis of the telescope, sweeps round in the plane of the meridian. It can be directed due south towards S, or to JE> (the culminating point of the celestial equa tor), or to s, a star on the meridian, or to the zenith Z, or to the pole P, or to the north point N, in fine, to any point on the celestial meridian. Now, if any contrivance be adopted to enable the observer to note the exact moment of sidereal time when a star crosses the middle of the field of view of such a tele scope, then the right ascension of that star is known at once. If also the angle ZOs can be determined, we learn the star s zenith distance. This added to ZP, the zenith distance of the pole, is the star s north polar distance, PZs ; and in this instance the complement of the zenith distance is the north declination. Such an instrument, if devised simply or mainly for noting the moment of culmination, is called a transit instrument. If arranged with circles so that angles as the zenith distance Zs can be determined, the instrument is called a transit circle. An arrangement, now little used, in which a meridional circle bearing a telescope works against a fixed plane surface or wall (necessarily standing in a north-and-south position) is called a mural circle. At present, however, we need not discuss these varieties of construction. The point to be specially noted in this plan is that, from observations of the star- sphere, we determine the cardinal points ; and then the position of any star in the heavens can be determined by an instrument contrived so as to swing in the plane of the meridian. This done, a clock, carefully rated to show sidereal time, enables the astronomer at a fixed station to turn his transit instrument to the point of culmination of a star at the exact time when the star will culminate, and
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Fig. 4.—Transit Instrument.
Chapter II.—The Earth shown to be a Globe within the Star-sphere.
But now let us suppose our observer to travel in a north-and-south direction, in order to determine what change, if any, will be produced by such voyages. The first effect noticed is that the pole of the heavens riser, higher and higher above the northern horizon, as he travels farther and farther north, whereas the pole sinks lower and lower down towards the northern horizon the farther the observer travels towards the south. Close observation shows that the change of the pole s elevation is either exactly propor tional to the observer s change of place in a north-and-south direction, or so nearly so that any discrepancy will require the closest and most exact scrutiny. The observer also notices that the stars retain their relative positions abso lutely unaltered, but that new stars are seen in the south when he travels southward. This shows that the star- sphere is either truly a spherical enclosure, all the stars lying at the same distance, or else that the distances of the stars are so enormous that the displacement of the observer on the earth, even by several hundred miles, is as nothing by comparison. The uniform change in the pole s elevation cannot be explained, however, by merely supposing the stars very far away compared with terrestrial distances. For let us suppose that A, B, C, D (fig. 5) represent four equidistant stations along a straight north-and-south line SN, and that AP is the direction in which the polar axis seems to lie, as seen from the station A, then from D it is seen at a greater elevation, or as in direction DP. Now, if we suppose P to be the actual pole of the heavens, then BP and CP should represent the polar axis as observed at B and C; but the angles PAN, PEN, PCN, PDN, do not increase uniformly, for this would imply that the angles APB, BPC, and CPD are equal, which we know from geometry not to be the case. Moreover, the star-sphere cannot rotate uniformly about two different axes, as PA and PD.
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Fig. 5.
It is manifest that we can only explain the observed Earth s facts by assuming that the course pursued by the supposed surface observer is not a straight line as SN (fig. 5), but curved, curve(1 and that it is curved uniformly, since the polar elevation sout ], changes uniformly when the observer travels at a uniform rate. It follows, therefore, that the path of the observer must be part of a circular arc such as d a g in fig. 6. Here suppose a the first position of the observer, and that when
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Fig. 6.—Diagram to show Curvature of Earth.
