Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/834

culmination and the tirie when the point T culminates. But instead of T :uiminating when the clock points to h. m. s. of sidereal time, it will culminate before, the clock so points; and each star will culminate as much before its sidereal time, that is, before the sidereal time corresponding to its right ascension. On the contrary, if the observer travels westwards from his original station, he finds that each star culminates later. Moreover, the observer finds that the amount of change in point of time corresponds to the distance he travels. Suppose a, fig. S, to be his original sta tion, and let aa be a small circle of aglobe, having P and F, as before determined {see fig. 6), for poles. Then the observer linds that the change in the time of a star s culmination corre sponds exactly to the length of arc tra versed by him round the circle aa, on the assumption that a complete circumference of this circle corresponds to 24 hours of sidereal time. Thus, if a is at Greenwich, the polar elevation is 51^, and, therefore, Ea (from what has been already shown in explaining fig. C), is an arc of 51^-; ao, the radius of aa,=EO sin. 51-|, and the observer finds that T, the change of time in the culmination of T, or any given star, for a given easterly or westerly distance d traversed from Greenwich, is such

that

T : a sidereal day : : d : ITT . EO. sin. 51 J.

Fig. 8.

This corresponds with the result of the former series of observations in showing that the earth is a globe, suspended, as it were, within the star-sphere ; and that either the star- sphere turns iniformly around this terrestrial globe from east to west once in 24 sidereal hours, or else the terrestrial globe turns uniformly round the axis PP (fig. 6) once in 24 sidereal hours from west to east.

Chapter III.—Of the Apparent Motions of the Sun.

The earth has now been shown to be a globe within the star-sphere, and whether the earth rotates within the star- sphere, or the star-sphere rotates round the earth, or both the earth and the star-sphere rotate, it is known that, relatively to the earth, the star-sphere rotates from east to west once in 24 sidereal hours. This rotation, whether apparent or real, takes place without any appreciable change in the relative position of the fixed stars. And the law of rotation having once been ascertained, it follows that the time of culmination of any star, and the position of the star at the time, are known, insomuch that a telescope or pointer can be directed to the place of the star at the moment of culmination with perfect exactness. Moreover, a star can be followed by an instrument properly devised, in such sort that a pointer shall continue directed upon the star all through the 24 sidereal hours. Suppose, for example, that Equatorial PP (fig. 9) is a rod turning on pivots P and P so placed that the axis of the rod points to the pole of the heavens; then if TT be a telescope so attached to an axis in or on PP (as at 0) that it can be turned in any angle to PP ; then if this telescope be placed so that es, its optical axis, is directed towards a star (in which case, necessarily, the angle POs will be equal to the star s north polar distance), it is clear that by rotating the axis PP uniformly once in 24 sidereal hours, and in the direction corresponding to the rotation of the heavens, the opti cal axis es will con tinue to be directed towards the star throughout the whole of those 24 hours, even when the star is below the horizo^. If a star s north polar distance be known, a telescope thus mounted can be placed so that POs is the proper angle, without seeing the star. If, further, we know the star s right ascension, and also the true sidereal time, we can not only set the telescope so that POs shall be the proper angle, but can rotate the axis PP in such sort that the tele scope shall be pointed directly towards the star. Suppose, for example, that the star s N.P.D.=75, and the R.A.=1 hour 26 rnin. (or 2l), (in other words, the star is close to 77 of the constellation Pisces); and let the time indicated by the sidereal clock be 3 hours 10 rnin. Then set TT (fig. 9) so that the angle POs=75, turn the axle PP so that TT or es lies in the meridian, in other words, let the telescope be directed due south, only with an elevation of 53, which is the supplement of 75 + the polar elevation at Greenwich, where the observation is made. Then, since the sidereal time is 3 hours 10 min., we know that the point T was on the meridian 3 hours 10 min. before the moment of observation; and since the star s K.A.=1 hour 26 miu., we know that the star was on the meridian 1 hour 26 min. after T ; hence the star was on the meridian 1 hour 44 min. (3 hours 10 min. 1 hour 26 min.) before the moment, of observation. We have then only to rotate the axis PP so as to follow the rotation of the star-sphere through an angle of 26 (the angle corresponding to 1 hour 44 min.. since 360 corresponds to 24 hours) to have the telescope directed upon the star. And as we can thus direct a tele scope, mounted as shown in fig. 9, towards a star at any hour (even when a star is below the horizon, in which case, of course, the telescope will be directed downwards), so con versely, it is clear that when the telescope is directed in any manner we can tell towards what point of the star-sphero the tube is turned. Thus, if the time shown by the sidereal clock is 3 hours 10 min., and the telescope be in such a position that, in order to bring it to the meridian, it would have to be turned round the polar axis backwards through an arc of 26, corresponding to the rotation of the heavens in 1 hour 44 min., then we know that it is directed to a point in the star-sphere whose right ascension is 3 hours 10 min. - 1 hour 44 min., or 1 hour 26 min. If, further, we note that the angle POs is one of 75, we know that the north polar distance of the point towards which the tele scope is directed is 75. The point, therefore, is known, and is close to the star rj Piscium.

Fig. 9.—Equatorial instrument.

We perceive, then, that if any celestial object is visible,

whether by day or night, then by simply directing towards it such a telescope as is shown in fig. 9, we can ascertain in what part of the stellar heavens that celestial object lies. And if the object is moving upon the stellar heavens, or, in other words, if it is other than one of these fixed stars with which we have hitherto been dealing, then by turning a telescope towards it from time to time we can determines its apparent path among the stars. So that in the case of

the sun, which is never seen in company with the stars.