Bode's Law did good service in the quest for a trans-Uranian planet by affording ground for a probable assumption as to its distance. A starting-point for approximation was provided by it; but it was soon found to be considerably at fault. Even Uranus is about 36 millions of miles nearer to the sun than the order of progression requires; and Neptune's vast distance of 2,800 million should be increased by no less than 800 million miles, and its period of 165 lengthened out to 225 years,[223] in order to bring it into conformity with the curious and unexplained rule which planetary discoveries have alternately tended to confirm and to invalidate. Within seventeen days of its identification with the Berlin achromatic, Neptune was found to be attended by a satellite. This discovery was the first notable performance of the celebrated two-foot reflector[224] erected by Mr. Lassell at his suggestively named residence of Starfield, near Liverpool. William Lassell was a brewer by profession, but by inclination an astronomer. Born at Bolton in Lancashire, June 18, 1799, he closed a life of eminent usefulness to science, October 5, 1818, thus spanning with his well-spent years four-fifths of the momentous period which we have undertaken to traverse. At the age of twenty-one, being without the means to purchase, he undertook to construct telescopes, and naturally turned his attention to the reflecting sort, as favouring amateur efforts by the comparative simplicity of its structure. His native ingenuity was remarkable, and was developed by the hourly exigencies of his successive enterprises. Their uniform success encouraged him to enlarge his aims, and in 1844 he visited Birr Castle for the purpose of inspecting the machine used in polishing the giant speculum of Parsonstown. In the construction of his new instrument, however, he eventually discarded the model there obtained, and worked on a method of his own, assisted by the supreme mechanical skill of James Nasmyth. The result was a Newtonian of exquisite definition, with an aperture of two, and a focal length of twenty feet, provided by a novel artifice with the equatoreal mounting, previously regarded as available only for refractors.