of a moving object. From the known laws of its motion and the earth's, calculate its apparent or relative angular motion in the time taken by light to traverse its distance from the earth. This is the total amount of its apparent misplacement. Its effect is to displace the body observed in a direction contrary to its apparent motion in the heavens. And it is a compound or aggregate effect consisting of two parts, one of which is the aberration, properly so called, resulting from the composition of the earth's motion with that of light, the other being what is not inaptly termed the Equation of light, being the allowance to be made for the time occupied by the light in traversing a variable space. (336.) The complete Reduction, as it is called, of an astronomical observation consists in applying to the place of the observed heavenly body as read off on the instruments (supposed perfect and in perfect adjustment) five distinct and independent corrections, viz. those for refraction, parallax, aberration, precession, and nutation. Of these the correction for refraction enables us to declare what would have been the observed place, were there no atmosphere to displace it. That for parallax enables us to say from its place observed at the surface of the earth, where it would have been seen if observed from the centre. That for aberration, where it would have been observed from a motionless, instead of a moving station: while the corrections for precession and nutation refer it to fixed and determinate instead of constantly varying celestial circles. The great importance of these corrections, which pervade all astronomy, and have to be applied to every observation before it can be employed for any practical or theoretical purpose, renders this recapitulation far from superfluous. (337.) Refraction has been already sufficiently explained, Art. 40. and it is only, therefore, necessary here to add that in its use as an astronomical correction its amount must be applied in a contrary sense to that in which it affects the observation; a remark equally applicable to all other corrections. (338.) The general nature of parallax or rather of paral lactic motion has also been explained in Art. 80. But parallax in the uranographical sense of the word has a more technical meaning. It is understood to express that optical displacement of a body observed which is due to its being observed, not from that point which we have fixed upon as a conventional central station (from which we conceive the apparent motion would be more simple in its laws), but from some other station remote from such conventional centre: not from the centre of the earth, for instance, but from its surface not from the centre of the sun (which, as we shall hereafter see, is for some purposes a preferable conventional station), but from that of the earth. In the former case this optical displacement is called the diurnal or geocentric parallax; in the latter the annual or heliocentric. In either case parallax is the correction to be applied to the apparent place of the heavenly body, as actually seen from the station of observation, to reduce it to its place as it would have been seen at that instant from the conventional station. S (339.) The diurnal or geocentric parallax at any place of the earth's surface is easily calculated if we know the distance of the body, and, vice versâ, if we know the diurnal parallax that distance may be calculated. For supposing S the object, C the centre of the earth, A the station of observation at its surface, and CAZ the direction of a perpendicular to the surface at A, then will the object be seen from A in the direction A S, and its apparent zenith dis- T tance will be ZAS; whereas, if seen from the centre, it will appear in the direction CS, with an an gular distance from the zenith of A equal to Z CS; so that ZAS-ZCS or ASC is the parallax. Now since by trigonometry CS: CA: sin CAS = sin ZAS: sin AS C, it follows that the sine of the parallax = x sin ZA S. (340.) The diurnal or geocentric parallax, therefore, at a given place, and for a given distance of the body observed, is proportional to the sine of its apparent zenith distance, and is, therefore, the greatest when the body is observed in the act of rising or setting, in which case its parallax is called its horizontal parallax, so that at any other zenith distance, parallax = horizontal parallax × sine of apparent zenith distance, and since A CS is always less than Z AS it appears that the application of the reduction or correction for parallax always acts in diminution of the apparent zenith distance or increase of the apparent altitude or distance from the Nadir, i. e. in a contrary sense to that for refraction. (341.) In precisely the same manner as the geocentric or diurnal parallax refers itself to the zenith of the observer for its direction and quantitative rule, so the heliocentric or annual parallax refers itself for its law to the point in the heavens diametrically opposite to the place of the sun as seen from the earth. Applied as a correction, its effect takes place in a plane passing through the sun, the earth, and the observed body. Its effect is always to decrease its observed distance from that point or to increase its angular distance from the sun. And its sine is given by the relation, Distance of the observed body from the sun distance of the earth from the sun sine of apparent angular distance of the body from the sun (or its apparent elongation): sine of heliocentric parallax.* (342.) On a summary view of the whole of the uranographical corrections, they divide themselves into two classes, those which do, and those which do not, alter the apparent configurations of the heavenly bodies inter sc. The former are real, the latter technical corrections. The real corrections are refraction, aberration and parallax. The technical are This account of the law of heliocentric parallax is in anticipation of what follows in a subsequent chapter, and will be better understood by the student when somewhat farther advanced. precession and nutation, unless, indeed, we choose to consider parallax as a technical correction introduced with a view to simplification by a better choice of our point of sight. (343.) The corrections of the first of these classes have one peculiarity in respect of their law, common to them all, which the student of practical astronomy will do well to fix in his memory. They all refer themselves to definite apexes or points of convergence in the sphere. Thus, refraction in its apparent effect causes all celestial objects to draw together or converge towards the zenith of the observer: geocentric parallax, towards his Nadir: heliocentric, towards the place of the sun in the heavens: aberration towards that point in the celestial sphere which is the vanishing point of all lines parallel to the direction of the earth's motion at the moment, or (as will be hereafter explained) towards a point in the great circle called the ecliptic, 90° behind the sun's place in that circle. When applied as corrections to an observation, these directions are of course to be reversed. (344.) In the quantitative law, too, which this class of corrections follow, a like agreement takes place, at least as regards the geocentric and heliocentric parallax and aberration, in all three of which the amount of the correction (or more strictly its sine) increases in the direct proportion of the sine of the apparent distance of the observed body from the apex appropriate to the particular correction in question. In the case of refraction the law is less simple, agreeing more nearly with the tangent than the sine of that distance, but agreeing with the others in placing the maximum at 90° from its apex. (345.) As respects the order in which these corrections are to be applied to any observation, it is as follows: 1. Refraction; 2. Aberration; 3. Geocentric Parallax; 4. Heliocentric Parallax; 5. Nutation; 6. Precession. Such, at least, is the order in theoretical strictness. But as the amount of aberration and nutation is in all cases a very minute quantity, it matters not in what order they are applied; so that for practical convenience they are always thrown together with the precession, and applied after the others. CHAPTER VI. OF THE SUN'S MOTION AND CONSTITUTION. NITUDE. APPARENT MOTION OF THE SUN NOT UNIFORM.—ITS APPARENT (346.) IN the foregoing chapters, it has been shown that the apparent path of the sun is a great circle of the sphere, which it performs in a period of one sidereal year. From this it follows, that the line joining the earth and sun lies constantly in one plane; and that, therefore, whatever be the real motion from which this apparent motion arises, it must be confined to one plane, which is called the plane of the ecliptic. (347.) We have already seen (art. 146.) that the sun's motion in right ascension among the stars is not uniform. This is partly accounted for by the obliquity of the ecliptic, in consequence of which equal variations in longitude do not correspond to equal changes of right ascension. But if we observe the place of the sun daily throughout the year, by the transit and circle, and from these calculate the longitude for each day, it will still be found that, even in its own proper |