Venus, the second planet in order of distance from the sun. According to the estimate of the sun's distance used throughout this work (91,430,000 m.), Venus travels at a mean distance from the sun of about 66,134,000 m. The eccentricity of her orbit is small, not exceeding 0.00686, so that her greatest distance, 66,586,000 m., does not exceed her least distance, 65,682,000 m., by more than about 900,000 m. In estimating her greatest and least distances from the earth, accordingly, it is more important to notice the effect of the earth's variation of distance, which amounts (see Earth) to about 3,000,000 m. The actual point of nearest approach between the two orbits lies in longitude about 70°, and here the orbits are about 24,150,000 m. apart; this then is the nearest approach Venus can ever make to the earth. The orbits are furthest apart in about longitude 250°, where they are separated by about 26,500,000 m.; and adding to this the diameter of Venus's orbit, about 132,300,000 m., we find the greatest distance separating the two planets to be about 158,800,000 m. The mean inclination of Venus's orbit to the ecliptic is about 3° 23' 31"; but her path is not so largely inclined to the mean plane of the solar system.

Her mean sidereal revolution is completed in 224.700787 days, and her mean synodical revolution in 583.920 days. Her diameter is about 7,510 m.; her volume 855 thousandths of the earth's, her mass about 885 thousandths (her density exceeding the earth's in the proportion of 103 to 100). Venus, travelling on a path within the earth's, is never seen in opposition, passing between the earth and sun when at her nearest. At this time she is of course invisible, her dark hemisphere being turned toward the earth. On the other hand, when she turns her fully illuminated hemisphere toward the earth, she is not only at her furthest, but lies almost directly on the prolongation of a line directed toward the sun, and is therefore lost in his superior lustre. Between these phases she exhibits all the figures shown by the moon, passing from a nearly full disk to the finest crescent (as an evening star), and from finest crescent, after her disappearance in inferior conjunction, to nearly a full disk (as a morning star), when she again disappears in superior conjunction.

But as her distance from the earth, unlike the moon's, undergoes great variations, she varies in apparent size as well as in phase, having the least diameter when nearest to a full orb, and the greatest when her crescent of light is finest. She lies furthest from the sun in the heavens when her disk is about half illuminated, the distance (her elongation, as it is called) varying in different synodical revolutions from about 45° to about 47° 12'. - Although this planet approaches the earth so much more closely than her rival in beauty, Jupiter, it has not been found possible to examine her surface with the telescope to any very useful purpose. Her great brightness introduces a difficulty which does not exist in the case of Jupiter, closely though he resembles her in appearance when both are seen under like conditions with the unaided eye; for the illumination of Venus exceeds that of Jupiter (mile for mile of surface) fully 48 times, though the intrinsic brilliancy of Venus does not surpass Jupiter's much more than 20 times. It is singular that, notwithstanding this difficulty, the first observers with the telescope achieved considerable success in recognizing and watching spots on her surface.

In fact, the best telescopes of modern times fail to show spots which Cassini, Bianchini, and others of the early observers agree in describing. If the earlier observers had deduced different rotation periods, we should be led to conclude that the spots they saw had no real existence; and this indeed has been the general conclusion to which modern astronomers have been led. Yet it should be noted that in presence of the close agreement between the rotation periods deduced by Cassini, Schroter, and De Vico, it is difficult to reject altogether the evidence which led to such closely accordant results. Domenico Cassini, after long seeking in vain for recognizable marks, noted in 1667 a bright spot not very far from the southern horn of the planet; and from observations of this spot he deduced a rotation period of about 23 hours. In 1726 Bianchini made observations whence he deduced the monstrous period of 24 days 8 hours. (It was on this rotation period that Ferguson based his remarkable account of the diurnal phenomena of Venus.) The younger Cassini, having carefully compared his father's observations with Bianchini's, found that both series could be explained by a rotation period of 23 hours and between 21 and 22 minutes, whereas a period of 24 days 8 hours could not be reconciled with D. Cassini's observations.

This explanation was received, because it was known that Bianchini's observations were not continuous, but interrupted for want of sky room, a neighboring building interfering with his view of the planet. Schfoter's observations led to the rotation period 23 h. 21 min. 19.2 sec. They were made on a mountain (or what he took to be such) near the southern horn of Venus. He remarked that while the northern horn always preserved its proper pointed figure, the southern sometimes appeared rounded, which circumstance he considered due to the presence of a mountain whose shadow fell on the place where the horn should have been. Beyond this place he observed a luminous point which he regarded as the summit of another mountain, illuminated by the sun. The proper position for showing these appearances cannot be long maintained, as the planet rotates, and thus their recurrence affords a means of determining the rate of its rotation. By taking as many as 160 rotations, Schroter deduced the rotation period mentioned above. De Vico at Rome, in 1839'41, made a series of observations, confirming Bianchini's drawings in a remarkable degree.

He deduced the rotation period 23 h. 21 min.

22 sec. Accepting this result, we find for the three planets Venus, the earth, and Mars, in this order (the order of their distances), the rotation periods 23 h. 21 min. 22 sec, 23 h. 56 min. 4 sec, and 24 h. 37 min. 23 sec, increasing with distance from the sun in a nearly uniform manner. - While, as we have said, it seems impossible to reject the evidence afforded by the observations of Schröter, De Vico, and others, in favor of the existence of recognizable marks on Venus, yet as many of the ablest observers, using the finest telescopes of our day, have failed to recognize such spots, we must adopt Sir John Herschel's explanation, who says that "the most natural conclusion from the very rare appearance and want of permanence of the spots is, that we do not see, as in the moon, the real surface of the planet, but only its atmosphere, much loaded with clouds, serving to mitigate the otherwise intense glare of the sunshine." It is clear from other circumstances that Venus has an atmosphere. During her transits over the sun's disk in 1761 and 1769 a sort of penumbral light was observed round her disk. Wargentin observed that the part of the disk off the sun could be recognized by a faint light bordering it, during almost the whole time of emersion.

Bergman, who observed the transit of 1761 at Upsal, states that at ingress the part of Venus still off the sun could be seen, being bounded by a crescent of light. At the egress this appearance was even more remarkable. As more of the planet's disk passed off the sun's, the part of the crescent of light furthest from the sun grew fainter and ultimately vanished, so that at last only the horns could be seen. Many other accounts of these two transits contain similar statements, and during the recent transits the same appearances were seen by many observers. It is readily perceived that such appearances might be expected in the case of a planet surrounded by an atmospheric envelop'e. The sun would be raised by atmospheric refraction precisely as our own sun is raised above the horizon after he has really passed below it. When we look at the part of Venus furthest from the sun, before immersion or after emersion (at a transit), we are looking in the same direction as an observer of Venus at that part who should direct his gaze sunward.

As he would see the sun raised above the horizon by atmospheric refraction, though really below, so we see the sun doubly raised because the line of sight passes through the hither half as well as the further half of the atmosphere above that part of Venus. In other words, though the outline of the sun's disk is really (that is, in a geometrical sense) behind the disk of Venus, we receive actual sunlight round even the part of Venus's disk remotest from the sun; a fortiori then is sunlight received round the remaining part of Venus's disk which lies outside the sun's. Hence an arc of light, brightest near the cusps of Venus, but visible (soon after immersion begins and again till near the end of emersion) at the part of Venus remotest from the sun. Prof. Lyman of Yale college has even seen this light at the part remotest from the sun, when the whole disk of Venus has been off the sun's, as at inferior conjunctions where there has been no transit. From such an observation it may be inferred that the atmosphere of Venus is deeper than our own. For we can infer from Bergman's observations a horizontal refraction scarcely less than that of our own atmosphere; and Lyman's observation would imply an atmospheric refraction nearly twice as effective.

The atmosphere of Venus has been analyzed with the spectroscope by Huggins, Vogel, and others, and the presence of aqueous vapor is held to have been demonstrated by the observations; yet it was not until the transit of 1874 that this point was in reality established. On that occasion Tacchini's observations seemed to demonstrate the fact that there is water on Venus. - A curious question is raised by the apparently strong evidence obtained during the 18th century to show that Venus is accompanied by a satellite. It is quite certain now that no such satellite exists, yet several skilful observers not only imagined that they perceived such a satellite, but even assigned to it a definite period of revolution around its primary. During the transits of 1761, 1769, and 1874, it was conclusively shown that no such body exists, but the difficulty of accounting for the apocryphal observations remains as great as ever. - Thirteen sidereal revolutions of Venus are completed in a period very nearly equal to eight sidereal years. Hence at every fifth conjunction the planets return nearly to the same longitude. Accordingly the perturbing effects taking place at one conjunction are repeated at the fifth conjunction thereafter, and so on.

Consequently there is an accumulation of perturbations, resembling the great inequality of Saturn and Jupiter, though far less remarkable in amount. It has for its period about 240 years. The greatest acceleration and retardation of either planet amounts only to a few seconds of arc. (For transits of Venus, see Transit).