CHAPTER VI. OF THE SUN'S MOTION. ITS APPARENT ELLIPSE ABOUT THE FOCUS. APPARENT MOTION OF THE SUN NOT UNIFORM. MOTION. THE SEASONS. - FACULE. 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. 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 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 fouud 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 averages 0° 59' 8"-33; but about the 31st of Decem ber 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 are in the respective proportions of the numbers 1.01679, 1.00000, and 0-98321; and that its apparent angular velocity diminishes as the distance increases, and vice versâ. (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 direction, from which we then Fig. 51. set off a series of angles, A O B, A O C, &c. equal to the observed longitudes of the sun throughout the year, and in these respective directions 1 Ήλιος the sun, and μετρειν to measure. measure off from O the distances O A, O B, O C, &c. representing the distances deduced from the observed diameter, and then connect all the extremities A, B, C, &c. of these lines by a continuous curve, it is evident this will be a correct representation of the relative orbit of the sun about the earth. Now, when this is done, a deviation from the circular figure in the resulting curve becomes apparent; it is found to be evidently longer than it is broad - that is to say, elliptic, and the point O to occupy, not the centre, but one of the foci of the ellipse. The graphical process here described is sufficient to point out the general figure of the curve in question; but for the purposes of exact verification, it is necessary to recur to the properties of the ellipse,' and to express the distance of any one of its points in terms of the angular situation of that point with respect to the longer axis, or diameter of the ellipse. This, however, is readily done; and when numerically calculated, on the supposition of the excentricity, being such as above stated, a perfect coincidence is found to subsist between the distances thus computed, and those derived from the measurement of the apparent diameter. (350.) The mean distance of the earth and sun being taken for unity, the extremes are 1.01679 and 0.98321. But if we compare, in like manner, the mean or average angular velocity with the extremes, greatest and least, we shall find these to be in the proportions of 1-03386, 1.00000, and 0.96670. The variation of the sun's angular velocity, then, is much greater in proportion than that of its distance - fully twice as great; and if we examine its numerical expressions at different periods, comparing them with the mean value, and also with the corresponding distances, it will be found, that, by whatever fraction of its mean value the distance exceeds the mean, the angular velocity will fall short of its mean or average quantity by very nearly twice as great a fraction of the latter, and vice versa. Hence we are led to conclude that the angular velocity is in the inverse proportion, not of the distance simply, but of its square; so that, to compare the daily motion in longitude of the sun, at one point, A, of its path, with that at B, we must state the proportion thus: O B2 : 0 A3 :: daily motion at A: daily motion at B. And this is found to be exactly verified in every part of the orbit. (351.) Hence we deduce another remarkable conclusion — viz. that if the sun be supposed really to move around the circumference of this ellipse, its actual speed cannot be uniform, but must be greatest at its least distance and less at its greatest. For, were it uniform, the apparent 1 See Conic Sections, by the Rev. H. P. Hamilton, or any other of the very numerous works on this subject. angular velocity would be, of course, inversely proportional to the distance; simply because the same linear change of place, being produced in the same time at different distances from the eye, must, by the laws of perspective, correspond to apparent angular displacements inversely as those distances. Since, then, observation indicates a more rapid law of variation in the angular velocities, it is evident that mere change of distance, unaccompanied with a change of actual speed, is insufficient to account for it; and that the increased proximity of the sun to the earth must be accompanied with an actual increase of its real velocity of motion along its path. (352.) This elliptic form of the sun's path, the excentric position of the earth within it, and the unequal speed with which it is actually traversed by the sun itself, all tend to render the calculation of its longitude from theory (i. e. from a knowledge of the causes and nature of its motion) difficult; and indeed impossible, so long as the law of its actual velocity continues unknown. This law, however, is not immediately apparent. It does not come forward, as it were, and present itself at once, like the elliptic form of the orbit, by a direct comparison of angles and distances, but requires an attentive consideration of the whole series of observations registered during an entire period. It was not, therefore, without much painful and laborious calculation, that it was discovered by Kepler (who was also the first to ascertain the elliptic form of the orbit), and announced in the following terms: Let a line be always supposed to connect the sun, supposed in motion, with the earth, supposed at rest; then, as the sun moves along its ellipse, this line (which is called in astronomy the radius vector) will describe or sweep over that portion of the whole area or surface of the ellipse which is included between its consecutive positions: and the motion of the sun will be such that equal areas are thus swept over by the revolving radius vector in equal times, in whatever part of the circumference of the ellipse the sun may be moving. - (353.) From this it necessarily follows, that in unequal times, the areas described must be proportional to the times. Thus, in the figure of art. 349, the time in which the sun moves from A to B, is to the time in which it moves from C to D, as the area of the elliptic sector AOB is to the area of the sector DO C. (354.) The circumstances of the sun's apparent annual motion may, therefore, be summed up as follows:-It is performed in an orbit lying in one plane passing through the earth's centre, called the plane of the ecliptic, and whose projection on the heavens is the great circle so called. In this plane, however, the actual path is not circular, but elliptical; having the earth, not in its centre, but in one focus. The excentricity of this ellipse is 0.01679, in parts of a unit equal to the mean distance, or half the longer diameter of the ellipse; i. e. about one sixtieth part of that semidiameter; and the motion of the sun in its circumference is so regulated, that equal areas of the ellipse are passed over by the radius vector in equal times. (355.) What we have here stated supposes no knowledge of the sun's actual distance from the earth, nor, consequently, of the actual dimensions of its orbit, nor of the body of the sun itself. To come to any conclusions on these points, we must first consider by what means we can arrive at any knowledge of the distance of an object to which we have no access. Now, it is obvious, that its parallax alone can afford us any information on this subject. Suppose PABQ to represent the earth, C its centre, and S the sun, and A, B two situations of a spectator, or, which comes to the same thing, the stations of two spectators, both observing the sun S at the same instant. The spectator A will see it in the direction A Sa, and will refer it to a point a in the infinitely distant sphere of the stars, while the spectator B will see it in the direction B Sb, and refer it to b. The angle included between these directions, or the measure of the celestial arc ab, by which it is displaced, is equal to the angle ASB; and if this angle be known, and the local situations of A and B, with the part of the earth's surface A B included between them, it is evident that the distance C S may be calculated. Now, since ASC (art. 339) is the parallax of the sun as seen from A, and BSC as seen from B, the angle ASB, or the total apparent displacement is the sum of the two parallaxes. Suppose, then, two observers -one in the northern, the other in the southern hemisphere at stations on the same meridian, to observe on the same day the meridian altitudes of the sun's centre. Having thence derived the apparent zenith distances, and cleared them of the effects of refraction, if the distance of the sun were equal to that of the fixed stars, the sum of the zenith distances thus found would be precisely equal to the sum of the latitudes north and south of the places of observation. For the sum in question would then be equal |