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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.
(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 versa, 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 C A Z 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 distance will be Z A S; whereas, if seen from the centre, it will appear in the direction C S, with an angular distance from the zenith of A equal to Z C S; so that ZAS—ZCS or
since by trigonometry C S
Z A S : sin A S C, it follows that the sine of the parallax _ Radius of earth . 740 - Distance of body
(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 x sine of apparent zenith distance, and since A C S is always less than Z A S 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, «'. 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 se. The former are real, the latter technical corrections. The real corrections are refraction, aberration and parallax. The technical are 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.
* This account of the law of heliocentric parallax is in anticipation of what follows in a subsequent chapter, and will be better understood bj the student when somewhat farther advanced.
(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 6ine 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.
OF THE SUN'S MOTION.
APPARENT MOTION OP THE 8UN NOT UNIFORM. — ITS APPARENT DIAMETER ALSO VARIABLE VARIATION OF ITS DISTANCE CONCLUDED. — ITS APPARENT ORBIT AN ELLIPSE ABOUT THE FOCCS.
LAW OF THE ANGULAR VELOCITY. — EQUABLE DESCRIPTION
OF AREAS PARALLAX OF THE SUN. — ITS DISTANCE AND MAGNITUDE. — COPERNICAN EXPLANATION OF THE SUN's APPARENT MOTION. — PARALLELISM OF THE EARTH'S AXIS. — THE SEASONS.
— HEAT RECEIVED FROM THE SUN IN DIFFERENT PARTS OF THE ORBIT. — MEAN AND TRUE LONGITUDES OF THE SUN. — EQUATION OF THE CENTRE.—SIDEREAL, TROPICAL, AND ANOMALISTIC YEARS.
— PHYSICAL CONSTITUTION OF THE SUN — ITS SPOTS.—FACUL*.
— PROBABLE NATURE AND CAUSE OF THE SPOTS ATMOSPHERE
OF THE SUN — ITS SUPPOSED CLOUDS — TEMPERATURE AT ITS SURFACE — ITS EXPENDITURE OF HEAT.— TERRESTRIAL EFFECTS OF SOLAR RADIATION.
(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 wo observe the place of the Bun 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 path, its apparent angular motion is far from uniform. The change of longitude in twenty-four mean solar hours average* 0° 59' 8"*33; but about the 31st of December it amounts to 1° 1' 9"*9, and about the 1st of July is only 0° 57' 11"*5. Such are the extreme limits, and such the mean value of the sun's apparent angular velocity in its annual orbit
(348.) This variation of its angular velocity is accompanied with a corresponding change of its distance from us. The change of distance is recognized by a variation observed to take place in its apparent diameter, when measured at different seasons of the year, with an instrument adapted for that purpose, called the heliometer*, or, by calculating from the time which its disc takes to traverse the meridian in the transit instrument. The greatest apparent diameter corresponds to the 1st of December, or to the greatest angular velocity, and measures 32' 35"-6, the least is 31' 31"-0 ; and corresponds to the 1st of July; at which epochs, as we have seen, the angular motion is also at its extreme limit either way. Now, as we cannot suppose the sun to alter its real size periodically, the observed change, of its apparent size can only arise from an actual change of distance. And the sines or tangents of such small arcs being proportional to the arcs themselves, its distances from us, at the above-named epoch, must be in the inverse proportion of the apparent diameters. It appears, therefore, that the greatest, the mean, and the least distances of the sun from us arc in the respective proportions of the numbers 1*01679, 100000, and 0*98321; and that its apparent angular velocity diminishes as the. distance increases, and vice versa.
(349.) It follows from this, that the real orbit of the sun, as referred to the earth supposed at rest, is not a circle with the earth in the centre. The situation of the earth within it is excentric, the excentricity amounting to 0*01679 of the mean distance, which may be regarded as our unit of measure in this inquiry. But besides this, the form of the orbit is not circular, but elliptic If from any point O, taken to represent the earth, we draw a line, O A, in some fixed
* HAios thr wo, and furpiir to measure.