Note 4 — Front matter

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 'Astronomy' 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 direction 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.