MERCURY VENUS .] 



ASTRONOMY. 



945 



period in which Saturn would perform a complete revo- 

 lution would be nine and a-half years. It is apparenl 

 that the periodic times do not, however, increase accord- 

 ing as the squares of the distances, as in that case the 

 periodic time of Saturn would be upwards of ninety 

 years, whilst in reality it is about thirty. After nume- 

 rous and laborious trials, Kepler at length found out the 

 remarkable analogy that the squares of the numbers repre- 

 senting the periodic times were exactly proportional to the 

 cubes of their mean distances from the sun. Comparing 

 the earth and Mars, for example, we find that (305 -2oC4) 2 : 

 (686-9796P : : 100000 3 : 152369 3 . All of those remark- 

 able laws were afterwards found by Sir Isaac Newton to 

 be necessary consequences of the laws of gravitation ; and 

 thus what was deduced by Kepler from observations on 

 one particular planet, and at one particular point of its 

 orbit, was verified, and found to be universally applicable 

 to the whole solar system, and to form a connecting link 

 between all its members. 



From the third law of Kepler the mean distance of a 

 planet from the sun can be readily calculated, and with 

 much less difficulty and more accuracy than by direct 

 observations. The periodic time may be found by 

 observing the time of the planet's passage through the 

 nodes, and by observing the intervals between the 

 ascending and descending nodes, and the descending and 

 ascending (which, if the orbit be an ellipse, will not be 

 exactly alike) ; a value of the eccentricity may be 

 obtained from the greatest difference, the true and mean 

 anomalies, or the equation of the centre. To deter- 

 mine the mean distance supposing t to be the periodic 

 time of the earth, and T that of the planet, D being the 

 mean distance of the earth, and A that of the planet, 

 we have 



r 2 : : D s : A s , whence 



D X 



(i) 



I 



The longitude of the planet in the nodes, or the longi- 

 tude of the node, may be determined from two helio- 

 centric latitudes and longitudes. 



TELESCOPIC APPEARANCE OP THE PLANETS. The planet 

 Mercury appears under all the phases of the moon and 

 Venus, but is seldom visible in our latitudes to the naked 

 eye, as, when most favourable for that purpose, there is 

 always a strong twilight, and it is situated too near the 

 mists of the horizon. At its nearest approach to the 

 earth, or at the time of inferior conjunction, its apparent 

 diameter amounts to 12", and at its superior conjunction 

 this decreases to 4'; at its mean distance from the earth 

 its apparent diameter is 6"' 7. Its diameter is upwards 

 of 3,000 English miles ; but observers differ considerably 

 as to its apparent diameter as measured by the micro- 

 meter. In such a small body as this, it is almost impos- 

 sible to perceive anytliing beyond the mere form of the 

 disc by means of the most perfect and powerful tele- 

 scopes ; and even these are sometimes rendered useless 

 by the scintillation and bad definition of the planet. 

 The only observer who has followed this planet with the 

 requisite attention, is Schroeter, who, by means of 

 powerful reflecting telescopes, was able to perceive that 

 the crescent was not always regular, but that sometimes 

 one horn was blunter than another. This, he naturally 

 considered, was due to their irregularities on the surface 

 of the planet a mountain, or chain of mountains, 

 situated in the southern hemisphere, intercepting the 

 rays of the sun from proceeding onwards. Schroeter 

 endeavoured to make use of this appearance in deter- 

 mining the time of rotation of the planet. He atten- 

 tively observed the form of the disc, and the degree of 

 bluutness of the southern horn at one particular time ; 

 and the changes which it underwent in a few hours were 

 found to be plainly perceptible. When the planet re- 

 appeared on the following day, or any number of days 

 afterwards, the time at which its disc presented the same 

 form was again recorded, and so on for any length of 

 time. Schroeter concluded, from these observations, that 

 the time of rotation of the planet on its axis must be 

 24h. 5m. ; and by taking the extreme times of observa- 

 tion, and dividing the interval by the number of ruvolu- 



Vol. I. 



tions, he concluded it must have one rotation on its axis 

 in the space of 24h. His assistant, M. Harding, on one 

 occasion, perceived a faint spot on the disc, and, by 

 following it attentively, he arrived at the same conclusion 

 as Schroeter. The latter attempted to arrive at a know- 

 ledge of the height of the mountains by measuring the 

 deficient part of the horn ; and his observations go to 

 prove that some of those were upwards of twelve miles 

 in altitude, which is three times that of any on the earth, 

 and, compared with the actual size of the two planets, is 

 out of all proportion. During the passage of Mercury 

 over the sun's disc on November 9, 1802, Sir W. Herschel 

 could not perceive any indications of an atmosphere, nor 

 the least departure from the circular shape in its form. 

 Even if it were as much compressed at the poles as the 

 earth, the ellipticity of its outline would not, however, 

 be visible in such a small body. Many observers have 

 perceived a dusky ring of considerable extent surround- 

 ing the planet at those times, and others have noticed a 

 bright spot on its disc on the same occasions ; but this 

 has been explained on optical grounds. During the 

 passage, Mercury appeared as a very dark spot, and 

 considerably more so than any of the spots which 

 appeared on the sun at the time. The transits of 

 Mercury over the sun's disc, which will occur during 

 the remainder of the present century, are as follows : 

 18G8, November 4, 1891, May 9. 



1870, May 6. 1894, November 10. 



1881, November 7. 



Those in 1881, November 7, and 1891, May 9, are in- 

 visible in the northern parts of Europe. 



VENUS. The phases which Mercury undergoes are 

 seen in a much more perceptible manner in those of 

 Venus, from the great size and brilliancy of the planet 

 at those times. The same appearance of the different 

 sharpness of the horns has likewise been noticed ; and 

 from these circumstances Schroeter endeavoured to de- 

 termine the period of rotation in the same manner as 

 pursued by him in Mercury, and apparently with more 

 chance of success. Not only was the southern horn no- 

 ticed to be very blunt, but a detached point of light was 

 perceived by him, which he concluded to be the summit 

 of a mountain illumined by the setting rays of the sun. 

 By numerous consecutive observations on this planet 

 (continued for many years), Schroeter came to the con- 

 clusion that it performed a rotation on its axis in the 

 space of 23h. 20m. 59 -04s., or, in round numbers, 23h. 

 21m. Previous to this time, Cassini had perceived, in 

 the clear sky of Italy, a small bright spot on the surface 

 of the planet ; by the observation of which, on several 

 consecutive mornings, in the summer of the year 1667, 

 lie arrived at the conclusion that its period of rotation 

 was 23h. L'l in. or 22m. A far more extensive series of 

 observations on several dusky spots was made during 

 1726-'27by Bianchini, at Rome, with excellent telescopes. 

 The period of rotation, as determined by this observer, 

 from those numerous spots, was very different from those 

 of Cassini and Schroeter, amounting to 24h. 8m. It 

 lad been suspected, by recent observers, that a mistake 

 arose from the spots so closely resembling each other ; 

 and as they were only observed during the evenings, it 

 was impossible to recognise them by their appearance 

 alone. The late De Vico has reobserved all the effects 

 perceived by Bianchini (from which it is certain that 

 ;hey were not of the fleeting, cloudy nature, suspected 

 jy Herschel nd Schroeter) ; and from some thousands of 

 micrometrical observations, made botli during the day 

 and evening, he concluded that it performs its rotation on 

 ~.ts axis in 23h. 21m. 21 9s. The axis of rotation was 

 jupposed by Cassiui, Schroeter, and Bianchini to be in- 

 clined as much as 70" to the pole of the ecliptic. The 

 atter determination of De Vico, although it does not 

 show an inclination so considerable as this would prove 

 to be, shows one nearly twice as great as that of the 

 earth viz., 53 11'. Sir W. Herschel, on one or two 

 occasions, perceived spots, but they were too faint and 

 uncertain to give any idea of the time of rotation. He 

 was never, however, able to perceive the bluntness of the 

 southern horn observed by Scliroeter ; which is the more 



