between Venus and the earth-that is to say, in the proportion of 72 to 28. Again, the angular diameter of the sum is known from instrumental measurement. It is clear, then, that if we knew the angular breadth of the zone included between the chords C Y D, F X H, or, in other words, if we knew the proportion which the angular breadth of the zone bears to the whole apparent diameter of the sun, we should be enabled to determine by a process of simple proportion the absolute diameter of the sun, and hence, knowing already the apparent diameter of that body, we should finally arrive at a knowledge of its distance, and consequently its horizontal parallax. The solution of the problem plainly depends, therefore, on the determination of the angular breadth of the zone included between the chords C Y D, F X H. Now the breadth of this zone may obviously be derived from the length of the chords C Y D, F X H, relatively to the apparent diameter of the sun. But the motion of the planet being known, the length of either of the chords will be indicated by the time which the planet occupies in passing from one extremity of the chord to the other. The problem is, therefore, finally reduced to the observation of the times occupied by the planet in traversing the chords C Y D, F X H, as seen from the two stations O and P.

In the explanation just given we have not taken account of the earth's orbital motion. It is to be borne in mind, however, that when Venus is in inferior conjunction, it is travelling in the same direction as the earth, but, being nearer the sun than the earth, its motion is quicker, and the result is that it apparently travels over the sun's disc with a velocity equal to the excess of its orbital motion over that of the earth. Hence the explanation of its transit will obviously be sufficient, if we suppose the earth to be at rest, and the planet to be travelling over the sun's disc merely with its relative motion. It may be remarked, further, that the time of the transit is materially influenced by the earth's rotation on its axis. We have not, however deemed it necessary to enter into all the niceties of this celebrated problem, but have endeavoured merely to give a general idea of the principle of the method of solution.

In 1761 and 1769 there occurred transits of Venus, on each of which occasions the principal Governments of Europe despatched observers to different parts of the world both in the northern and the southern hemispheres, who noted at their respective stations the time occupied by the planet in traversing the sun's disc. From the materials thus collected the late distinguished astronomer, Professor Encke, determined the horizontal parallax of the sun to be 8".57. This value, it will be seen, does not agree with that derived from observations of Mars. The researches of astronomers derived from other sources would seem to indicate that the latter value-namely, 8".95-is the more accurate of the two. The value 8".57 has been deduced chiefly from the transit of Venus, which occurred in 1769, the observations of which in the northern hemisphere have been considered defective. In the years 1874 and 1882 there will again occur transits of the planet, the observations of which, it may be expected, will lead to a definitive determination of the solar parallax. In the mean time, the result derived from recent researches namely, 8".95—has been adopted by astronomers as the most trustworthy value of that element. It is, accordingly, the value which has been employed in computing the various numerical results depending on the solar parallax which are given in this explanatory work.

CHAPTER X.

The Sun-Elements of its Orbit-Variation of Apparent Diameter-Distance from the Earth-Solar Spots-Rotation of the Sun-Periodicity of the Spots-Physical Constitution of the Sun.

The sun, which exercises so genial an influence on the animal and vegetable productions of the earth, must naturally have been an object of much interest to astronomers in all ages. The attention of the Greek astronomers was confined exclusively to an investigation of the facts relating to its apparent motion in the heavens. They did not fail to discover that the supposition of the sun revolving uniformly in a circular orbit round the earth in the centre was irreconcilable with the results of observation. Hence originated the epicyclical theory which placed the earth in a position a little excentric with respect to the orbit in which the sun revolved. The amount of this excentricity constituted one of the elements of the solar orbit. But the excentricity of the orbit implied a variation of the sun's distance from the earth, and suggested the determination of the direction of the line joining the points of least and greatest distance. This constituted the second element of the solar orbit. The other two elements, the length of the year and the mean longitude of the sun, corresponding to a given epoch, were also determined by the Greek astronomer Hipparchus with considerable precision, and upon the aggregate results thus obtained the earliest tables of the sun's motion were constructed.

In the Copernican system of the universe the orbit which the sun apparently describes in the heavens is merely an optical illusion due to the real motion of the earth round the sun. It has been further established by astronomical researches that the orbit, whether apparent or real, is an ellipse, the earth occupying the focus in the one case and the sun in the other. The variable distance of the sun as it revolves in its annual orbit is clearly indicated by observations of its apparent diameter. As the distance of the sun from the earth increases the apparent diameter necessarily diminishes, and vice versa. Now, it is found by actual measurement that the apparent diameter of the sun is perpetually varying throughout the year. It is greatest on the 31st of December, when it amounts to 32′ 36′′.4, and least on the 3d of July, when it measures only 31' 32". It follows, therefore, that the sun is nearest to the earth on the 31st of December, and most distant from it on the 3d of July. If we suppose the mean distance of the sun to be represented by 10,000, the greatest distance will be represented by 10,168, and the least distance by 9832.

It may naturally be asked, how does it happen that it is hottest when the sun is most distant from the earth, and coldest when it is nearest to our planet? The reason of this is simple enough. In summer the sun, although distant, rises high and remains long above the horizon; in winter, although nearer, its height is inconsiderable, and it remains only a short time above the horizon. It results, indeed, from the laws of the diffusion of heat and of the angular motion of the sun round the earth, that the variation of the sun's distance exercises only an inconsiderable influence on the heating of the earth's surface; for when the sun is nearest, and consequently most favourable for the diffusion of heat, its angular velocity is greatest; and on the other hand, when it is most distant and least favourable for the diffusion of heat, its angular velocity is least. The sun, therefore, dwells a shorter time in the half of its orbit which is more favourable to the heating of the earth's surface, and dwells longer in the half which is less favourable to that object, and a compensation is thus effected which almost entirely neutralises the influence due to the variation of the sun's distance.

The absolute distance of the sun from the earth is 91,200,000 miles. Its absolute diameter measures 850,000 miles, a result which, in round numbers, exceeds the earth's diameter in the proportion of 108 to 1. Consequently in volume the sun exceeds the earth in the proportion of 1,259,712 to 1.

When the sun is viewed with a telescope there appear numerous dark spots on its surface. These spots are very irregular both in form and magnitude. They generally consist of a dark central nucleus, surrounded by a less obscure region termed the penumbra. Their structure is subject to rapid and extensive fluctuations. Sometimes a large spot will be seen to break up into several detached spots. On other occasions several contiguous small spots will coalesce and form one great spot. An attentive observer of the spots will not fail to discover changes of this kind even in the course of a single day.

When a spot has been observed for several days in succession, it is found to be gradually travelling from left to right on the sun's disc, until it finally disappears at the western limb. A careful comparison of such observations has led to the important discovery that the sun has a motion of rotation on a fixed axis. According to the most recent researches, the inclination of the solar equator to the ecliptic is 7° 15', and the longitude of the ascending node is 73° 40′. These elements have been assigned by Mr Carrington, in his elaborate work on the solar spots as applicable to the year 1850. The time of rotation has been determined to be 25 days, 7 hours, 48 minutes. These results are all liable to a considerable degree of uncertainty in consequence of the solar spots being affected with a proper motion independent of the sun's rotation.

If the plane of the solar equator coincided with the plane of the ecliptic, the apparent path of a spot across the sun's disc would invariably be a straight line. Since, however, the two planes are inclined to each other at an angle of more than 7°, it results that the apparent path of a solar spot is generally of an elliptical form. In June the plane of the solar equator passes through the earth, and the apparent path of the spot is then a straight line. During the next six months, however, the north pole of the sun is turned towards the earth, and the paths of the spots are ellipses with the convexity turned downwards, the minor axis being greatest in September, when the north pole is turned the greatest possible towards the earth. In December the plane of the solar equator again passes through the earth, and the apparent paths of the spots become straight lines. Henceforward till June the same succession of changes ensues in a reverse order. The south pole is now turned towards the earth, and the apparent paths of the spots are ellipses with their convexity turned upwards, the minor axis being greatest in March, when the south pole is turned towards the earth as much as possible. The various forms which the apparent path of a solar spot thus presents in the course of a year are exhibited in Plate 3.

The spots generally appear in groups, and are confined to a region extending about 35° on each side of the solar equator. It has been already remarked that they fluctuate very much in form and magnitude. The same is true with respect to their paucity or abundance. On some occasions not one spot is visible on the solar disc. At other times the whole of the region in which they usually appear is thickly strewed with them.

Schwabe, a German astronomer, has found that the number of spots visible on the sun's disc recur in periods of somewhat more than ten years. It has since been discovered that the variations of terrestrial magnetism are characterised by a period of equal duration.

Many of the solar spots are of great magnitude. Frequently they have a diameter of two or three minutes, and when seen through a hazy atmosphere have been visible to the naked eye. Besides the spots, there are patches of light on the sun's disc which are more luminous

than the general surface. These have been termed facula. They generally are seen in the vicinity of extensive groups of spots.

In recent years the observations of the luminous surface of the sun have revealed a curious phenomenon in the existence of a number of objects of determinate form and magnitude spread over the entire surface, and suggesting in the outlines of their structure a resemblance to willow leaves. Observers are not yet agreed on the question whether such phenomena are distinct entities now discovered for the first time, or whether they are merely modifications of some of the ordinary phenomena exhibited by the solar photosphere.

The spots are cavities in the sun's surface. This has been established beyond all doubt by the observations made by Dr Wilson of Glasgow towards the close of the last century. Nothing definite beyond this has heretofore been made out respecting them. That the nuclei of the spots are portions of the dark body of the sun revealed to us by rents in the photosphere seems highly probable, but how the spots are generated, and what is the origin of the characteristics which they exhibit, are questions involved in profound mystery.

In recent years photography has been applied with great success at the Observatory of Kew to the delineation of the solar spots. An instrument has been expressly fitted up in connection with this object, and every day on which the sun is visible a picture of its surface is taken by the agency of its own light. Important results may hereafter be expected from a discussion of the accumulated results of such observations.

In Plate 3, the solar disc is represented as seen under a low magnifying power. In the same Plate are seen, on a portion of the disc, several solar spots as viewed with a high magnifying power, accompanied by numerous faculæ.

The recent researches in spectral analysis have thrown some important light on the question of the physical structure of the sun. According to the conclusions arrived at, the sun is to be regarded as an incandescent body, surrounded by an atmosphere of a somewhat lower temperature, in which are contained vapours of sodium, iron, magnesium, and certain other substances (see Chapter XVIII.) Of the existence of an atmosphere about the sun, the phenomena seen during total eclipses of that body afford very strong proof. We shall have occasion hereafter to refer to this subject.

The question with respect to the source of the solar heat is involved in profound mystery. It has been supposed in recent times, by Sir William Thomson and others, that it may have originated from the friction occasioned by a zone of meteors circulating in the solar atmosphere round the sun, and falling gradually in upon its surface.

In Plate 3 we have a representation of the apparent magnitude of the sun as viewed from the different planets. To an observer on Mercury the sun would present an apparent diameter of not less than a degree and a half; as the distance of each planet increases, the apparent diameter of the sun diminishes, until at length, to an observer on the surface of Neptune, the apparent diameter of the sun would not exceed 1'; in other words, the sun would exhibit merely the apparent magnitude which the planet Venus presents to an observer on the earth at the time when it is approaching the position of inferior conjunction.

CHAPTER XI.

The Moon-Its Distance and Magnitude—Sidereal and Synodic Revolutions—Variation of apparent Diameter - Motion of the Nodes and Apsides - Explanation of its Phases-Origin of the Lumière cendrée, or ashy Light-Mountains of the MoonPhysical Constitution.

The moon stands in the relation of a satellite to the earth, accompanying it in its annual motion round the sun, and at the same time revolving round it in a monthly orbit. The mean distance of the moon from the earth amounts to 238,750 miles. Its linear diameter measures 2150 miles. In considering the revolution of the moon round the earth, there exists the same distinction between the sidereal and synodic revolutions as holds in the case of the planets. The moon travels in the heavens from west to east; that is to say, in the same direction as the sun and planets, accomplishing a complete revolution round the earth with respect to the stars in 27 days, 7 hours, 43 minutes, 11 seconds. This is accordingly denominated the time of a sidereal revolution of the moon. But while the moon has thus been revolving in its monthly orbit, the sun has been travelling in the same direction in its apparent annual orbit. The result, consequently, is, that when the moon has completed its sidereal revolution round the earth, the sun has advanced in its orbit a certain angular distance to the eastward of the position which it occupied at the commencement of the moon's revolution; and in order that the two bodies should again occupy the same relative position which they originally did, it is necessary that the moon should advance somewhat further in its orbit; hence originates the idea of a synodic revolution of the moon, which represents the time included between two consecutive returns of the sun and moon to the same relative position. The time of a synodic revolution of the moon amounts to 29 days, 12 hours, 44 minutes, 3 seconds.

The orbit in which the moon revolves round the earth is an ellipse, having the earth in one of the foci. It has been found by observation that the major axis of this ellipse is not stationary. According to the researches of astronomers, its extremities, or the points of least and greatest distance from the earth, in other words, the perigee and apogee, are continually advancing in the direction of the moon's motion, effecting a complete circuit of the heavens in 3222 days, 13 hours, 56 minutes, 16.8 seconds, or somewhat less than 9 years.

The excentricity of the solar orbit is small, and sensibly invariable. The excentricity of the lunar orbit, on the other hand, is considerable, and is subject to extensive variations from the disturbing influence of the sun's attraction. It happens, in consequence, that the least and greatest distances of the moon from the earth vary relatively to each other much more extensively than do the corresponding distances of the sun from the earth. Thus, while the least and greatest distances of the sun from the earth are only in the proportion of 30 to 31, the least and greatest distances of the moon are in the proportion of 7 to 8. Hence also the least and greatest apparent diameters of the moon are in the same proportion, with this difference only, that when the distance is greatest the apparent diameter is least, and vice versâ. Thus, when the moon is at her least perigean distance, her apparent diameter amounts to 33′ 31′′; on the other hand, when she is at her greatest apogean distance, her apparent diameter measures only 29′ 22".

The orbit of the moon is inclined to the ecliptic at an angle of 5° 8'. While the moon revolves in the direction of the signs of the zodiac, the points of intersection of its orbit and the ecliptic, in other words, the nodes of the lunar orbit, retreat in the opposite direction. In