42 ROUGH WAYS MADE SMOOTH. 



26, 1859, at about four in the afternoon, a round black 

 spot entered on the sun's disc. It had a diameter les than 

 one-fourth that of Mercury (which he had seen in transit 

 with the same telescope and the same magnifying power 

 on May 8, 1845). The time occupied in the transit of 

 this spot was about one hour seventeen minutes, and, the 

 chord of transit being somewhat more than a quarter of the 

 sun's diameter in length, Lescarbault calculated that the 

 time necessary to describe the sun's diameter would have been 

 nearly four and a half hours. The inclination of the body's 

 path to the ecliptic seemed to be rather more than 6 degrees, 

 and was probably comprised between 5^ and 7^ degrees. 



From Leverrier's calculations, it appeared that the time 

 of revolution of the new planet would be 19 days 17 hours, 

 its distance from the sun about 147, the earth's being taken 

 as 1,000 ; giving for Mars, the earth, Venus, Mercury, and 

 Vulcan (as the new planet was named), the respective 

 distances i, 524, 1,000, 723, 387, and 147. Leverrier 

 assigned \2\ degrees as Vulcan's inclination, and the 

 places where it crosses the ecliptic he considered to be in 

 line with those occupied by the earth on or about April 3 

 and October 6. Judging from Lescarbault's statement 

 respecting the apparent size of the dark spot, Leverrier con- 

 cluded that the volume of the stranger must be about one- 

 seventeenth of Mercury's, the masses being presumably in 

 the same proportion. Hence he inferred that the new 

 planet would be quite incompetent to produce the observed 

 change in the orbit of Mercury. 



Leverrier further found that the brilliancy of Vulcan 

 when the planet was furthest from the sun on the sky (about 

 eight degrees) would be less than that of Mercury when 

 similarly placed in his orbit, and he hence inferred that 

 Vulcan might readily remain unseen, even during total 

 eclipse. Here, as it seems to me, Leverrier's reasoning was 

 erroneous. If Vulcan really has a volume equal to one- 

 seventeenth of Mercury's, the diameter of Vulcan would be 

 rather less than two-fifths of Mercury's and the disc of 



