36 ROUGH WAYS MADE SMOOTH. 



to discover the disturbing planet. I believe, however, that 

 no one who examines the evidence will deny the accuracy of 

 this statement. It was manifest, from the nature of the 

 perturbations experienced by Uranus, that between 1820 and 

 1825 Uranus and the unknown body had been in conjunction. 

 From this it followed that the disturber must be behind 

 Uranus in 1840-1845 by about one-eighth of a revolution 

 round the sun. With the assumptions made by Adams and 

 Leverrier, indeed, the position of the stranger in this respect 

 could have been more closely determined. There could be 

 little doubt that the disturbing planet must be near the eclip- 

 tic. It followed that the planet must lie somewhere on a 

 strip of the heavens, certainly not more than ten degrees 

 long and about three degrees broad, but the probable posi- 

 tion of the planet would be indicated as within a strip four 

 degrees long and two broad. 1 Such a strip could be 

 searched over effectually in the time I have named above, 

 and the planet would have been found in it. The larger 

 region (ten degrees long and three broad) could have been 

 searched over in the same time by two observers. If indeed 

 the single observer used a telescope powerful enough to 



1 Let the student make the following construction if he entertains 

 any doubt as to the statements made above. Having traced the orbits 

 of the earth and Uranus from my chart illustrating the article ' Astro- 

 nomy' in the Encyc. Brit., let him describe a circle nearly twice as 

 large to represent the orbit of Neptune as Bode's law would give it. 

 Let him first suppose Neptune in conjunction with Uranus in 1820, 

 mark the place of the earth on any given day in 1842, and the place of 

 the fictitious Neptune ; a line joining these points will indicate the direc- 

 tion of Neptune on the assumptions made. Let him next make a 

 similar construction on the assumption that conjunction took place in 

 1825. (From the way in which the perturbation of Uranus reached a 

 maximum between 1820 and 1825, it was practically certain that the 

 disturber was in conjunction with Uranus between those years.) These 

 two constructions will give limiting directions for Neptune as viewed 

 from the earth, on the assumption that his orbit has the dimensions 

 named. He will find that the lines include an angle of a few degrees 

 only, and that the direction line of the true Neptune is included 

 between them. 



