38 ROUGH WAYS MADE SMOOTH. 



position of the earth's path, and these changes had been too 

 carefully determined to be readily regarded as erroneous. 

 'This result naturally filled me with inquietude,' said 

 Leverrier later. ' Had I not allowed some error in the 

 theory to escape me? New researches, in which every 

 circumstance was taken into account by different methods, 

 ended only in the conclusion that the theory was correct, 

 but that it did not agree with the observations.' At last, 

 after long and careful investigation of the matter, he found 

 that a certain slight change would bring observation and 

 theory into agreement. All that was necessary was to 

 assume that matter as yet undiscovered exists in the sun's 

 neighbourhood. 'Does it consist,' he asked, 'of one or 

 more planets, or other more minute asteroids, or only of 

 cosmical dust ? The theory tells us nothing on this point/ 

 Leverrier pointed out that a planet half the size of 

 Mercury between Mercury and the sun would account for 

 the discrepancy between observation and theory. But a 

 planet of that size would be a very conspicuous object at 

 certain times, even when the sun was not eclipsed ; and 

 when favourably placed during eclipses would be a 

 resplendent orb which would attract the notice of even the 

 most careless observer. For we must remember that the 

 brightness of a planet depends in part on its size and its 

 distance from the earth, and in part on its distance from the 

 sun. A planet half as large as Mercury would have a 

 diameter about four-fifths of Mercury's, and at equal distance 

 would present a disc about two-thirds of Mercury's in 

 apparent size. But supposing the planet to be half as far 

 from the sun as Mercury (and theory required that the planet 

 should be rather nearer the sun), its surface would be illu- 

 minated four times as brightly as that of Mercury. Hence, 

 with a disc two-thirds as large as Mercury's, but illuminated 

 four times as brightly, the planet would shine nearly three 

 times as brilliantly when seen under equally favourable 

 conditions during eclipse. In such an inquiry, the mean 

 distance of the two bodies need not be specially considered. 



