CHAP. V. EQUATION OF THE CENTRE. 203 culation of the equation of the centre is performed by a table constructed for that purpose, to be found in all "Solar Tables." (322.) The maximum value of the equation of the centre depends only on the ellipticity of the orbit, and may be expressed in terms of the excentricity. Vice versâ, therefore, if the former quantity can be ascertained by observation, the latter may be derived from it; because, whenever the law, or numerical connection, between two quantities is known, the one can always be determined from the other. Now, by assiduous observation of the sun's transits over the meridian, we can ascertain, for every day, its exact right ascension, and thence conclude its longitude (art. 260.). After this, it is easy to assign the angle by which this observed longitude exceeds or falls short of the mean; and the greatest amount of this excess or defect which occurs in the whole year, is the maximum equation of the centre. This, as a means of ascertaining the excentricity of the orbit, is a far more easy and accurate method than that of concluding its distance by measuring its apparent diameter. The results of the two methods coincide, however, perfectly. (323.) If the ecliptic coincided with the equinoctial, the effect of the equation of the centre, by disturbing the uniformity of the sun's apparent motion in longitude, would cause an inequality in its time of coming on the meridian on successive days. When the sun's centre comes to the meridian, it is apparent noon, and if its motion in longitude were uniform, and the ecliptic coincident with the equinoctial, this would always coincide with mean noon, or the stroke of 12 on a well-regulated solar clock. But, independent of the want of uniformity in its motion, the obliquity of the ecliptic gives rise to another inequality in this respect; in consequence of which, the sun, even supposing its motion in the ecliptic uniform, would yet alternately, in its time of attaining the meridian, anticipate and fall short of the mean noon as shown by the clock. For the right ascension of a celestial object, forming a side of a right-angled spherical triangle, of which its longitude is the hypothenuse, it is clear that the uniform increase of the latter must necessitate a deviation from uniformity in the increase of the former. (324.) These two causes, then, acting conjointly, produce, in fact, a very considerable fluctuation in the time as shown per clock, when the sun really attains the meridian. It amounts, in fact, to upwards of half an hour; apparent noon sometimes taking place as much as 161 min. before mean noon, and at others as much as 14 min. after. This difference between apparent and mean noon is called the equation of time, and is calculated and inserted in ephemerides for every day of the year, under that title; or else, which comes to the same thing, the moment, in mean time, of the sun's culmination for each day, is set down as an astronomical phenomenon to be observed. (325.) As the sun, in its apparent annual course, is carried along the ecliptic, its declination is continually varying between the extreme limits of 23° 28′ 40′′ north, and as much south, which it attains at the solstices. It is consequently always vertical over some part or other of that zone or belt of the earth's surface which lies between the north and south parallels of 23° 28′ 40′′. These parallels are called in geography the tropics; the northern one that of Cancer, and the southern of Capricorn; because the sun, at the respective solstices, is situated in the division, or signs of the ecliptic so denominated. Of these signs there are twelve, each occupying 30° of its circumference. They commence at the vernal equinox, and are named in order-Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. They are denoted also by the following symbols:-Y, 8, II, , n, m,, m, ↑, vs, ~~, . The ecliptic itself is also divided into signs, degrees, and minutes, &c. thus, 5$ 27° 0′ corresponds to 177° 0′; but this is beginning to be disused. CHAP. V. TROPICAL AND ANOMALISTIC YEARS. 205 (326.) When the sun is in either tropic, it enlightens, as we have seen, the pole on that side the equator, and shines over or beyond it to the extent of 23° 28′ 40′′. The parallels of latitude, at this distance from either pole, are called the polar circles, and are distinguished from each other by the names arctic and antarctic. The regions within these circles are sometimes termed frigid zones, while the belt between the tropics is called the torrid zone, and the immediate belts temperate zones. These last, however, are merely names given for the sake naming; as, in fact, owing to the different distribution of land and sea in the two hemispheres, zones of climate are not co-terminal with zones of latitude. (327.) Our seasons are determined by the apparent passages of the sun across the equinoctial, and its alternate arrival in the northern and southern hemisphere. Were the equinox invariable, this would happen at intervals precisely equal to the duration of the sidereal year; but, in fact, owing to the slow conical motion of the earth's axis described in art. 264, the equinox retreats on the ecliptic, and meets the advancing sun somewhat before the whole sidereal circuit is completed. The annual retreat of the equinox is 50"-1, and this arc is described by the sun in the ecliptic in 20' 19'9. By so much shorter, then, is the periodical return of our seasons than the true sidereal revolution of the earth round the sun. As the latter period, or sidereal year, is equal to 365d 6h 9m 9s 6, it follows, then, that the former must be only 365d 5h 48m 49s 7; and this is what is meant by the tropical year. (328.) We have already mentioned that the longer axis of the ellipse described by the earth has a slow motion of 118 per annum in advance. From this it results, that when the earth, setting out from the perihelion, has completed one sidereal period, the perihelion will have moved forward by 11"-8, which arc must be described before it can again reach the perihelion. In so doing, it occupies 4' 39'7, and this must therefore be added to the sidereal period, to give the interval between This inter two consecutive returns to the perihelion. val, then, is 365d 6h 13m 49s 3*, and is what is called the anomalistic year. All these periods have their uses in astronomy; but that in which mankind in general are most interested is the tropical year, on which the return of the seasons depends, and which we thus perceive to be a compound phenomenon, depending chiefly and directly on the annual revolution of the earth round the sun, but subordinately also, and indirectly, on its rotation round its own axis, which is what occasions the precession of the equinoxes; thus affording an instructive example of the way in which a motion, once admitted in any part of our system, may be traced in its influence on others with which at first sight it could not possibly be supposed to have any thing to do. (329.) As a rough consideration of the appearance of the earth points out the general roundness of its form, and more exact enquiry has led us first to the discovery of its elliptic figure, and, in the further progress of refinement, to the perception of minuter local deviations from that figure; so, in investigating the solar motions, the first notion we obtain is that of an orbit, generally speaking, round, and not far from a circle, which, on more careful and exact examination, proves to be an ellipse of small excentricity, and described in conformity with certain laws, as above stated. Still minuter enquiry, however, detects yet smaller deviations again from this form and from these laws, of which we have a specimen in the slow motion of the axis of the orbit spoken of in art. 318.; and which are generally comprehended under the name of perturbations and secular inequalities. Of these deviations, and their causes, we shall speak hereafter at length. It is the triumph of physical astronomy to have rendered a complete account of them all, and to have left nothing unexplained, either in the motions of the sun or in those of any other of the bodies of our system. But the nature of this explanation cannot be These numbers, as well as all the other numerical data of our system, are taken from Mr. Baily's Astronomical Tables and Formulæ, unless the contrary is expressed. PHYSICAL CONSTITUTION OF THE SUN. 207 understood till we have developed the law of gravitation, and carried it into its more direct consequences. This will be the object of our three following chapters; in which we shall take advantage of the proximity of the moon, and its immediate connection with and dependence on the earth, to render it, as it were, a stepping-stone to the general explanation of the planetary movements. (330.) We shall conclude this by describing what is known of the physical constitution of the sun. When viewed through powerful telescopes, provided with coloured glasses, to take off the heat, which would otherwise injure our eyes, it is observed to have frequently large and perfectly black spots upon it, surrounded with a kind of border, less completely dark, called a penumbra. Some of these are represented at a, b, c, plate iii. fig. 21, in the plate at the end of this volume. They are, however, not permanent. When watched from day to day, or even from hour to hour, they appear to enlarge or contract, to change their forms, and at length to disappear altogether, or to break out anew in parts of the surface where none were before. In such cases of disappearance, the central dark spot always contracts into a point, and vanishes before the border. Occasionally they break up, or divide into two or more, and in those offer every evidence of that extreme mobility which belongs only to the fluid state, and of that excessively violent agitation which seems only compatible with the atmospheric or gaseous state of matter. The scale on which their movements take place is immense. A single second of angular measure, as seen from the earth, corresponds on the sun's disc to 465 miles; and a circle of this diameter (containing therefore nearly 220,000 square miles) is the least space which can be distinctly discerned on the sun as a visible area. Spots have been observed, however, whose linear diameter has been upwards of 45,000 miles*; * Mayer, Obs. Mar. 15. 1758. "Ingens macula in sole conspiciebatur, cujus diameter diam. solis." |