The leading incidents in the narrative of the discovery of Uranus and Neptune present a great dissimilarity—Uranus was discovered by accident, Neptune by design. Telescopic power revealed the former, while theory disclosed the latter. In one case optical appliance afforded the direct means of success, while in the other the unerring precision of mathematical analysis attained it. The telescope played but a secondary part in the discovery of Neptune, for this instrument was employed simply to realize or confirm what theory had proven. Certain irregularities in the motion of Uranus could not be explained but on the assumption of an undetected planet situated outside the known boundaries of the system. Two able geometers applied themselves to study the problem of these irregularities, and to deduce from them the place of the disturbing body. This was effected independently by Messrs. Le Verrier and Adams; and Dr. Galle of Berlin, having received from Le Verrier the leading results of his computations, and the intimation that the longitude of the suspected planet was then 326°, found it with his telescope on the night of September 23, 1846, in longitude 326° 52′. The calculated place by Professor Adams was 329° 19′ for the same date. The name given to the new planet was Neptune. When the elements were computed it was found that they presented rather large differences with those theoretically computed by Le Verrier and Adams. It was also found that the planet had been previously observed by Lalande on May 8 and 10, 1795, but its true character escaped detection. This astronomer had observed a star of the eighth magnitude on May 8; but on May 10, not finding the same star in the exact place noted on the former evening, he rejected the first observation as inaccurate and adopted the second, marking it doubtful. Lalande, like Le Monnier, the unsuspecting discoverer of Uranus, let a valuable discovery slip through his hands. Neptune revolves round the sun in 60,126 days, which is equal to rather more than 164½ of our years. His mean distance from the sun is 2,792,000,000 miles, and his usual diameter 2″.7. He exceeds Uranus in dimensions, his real diameter being 37,000 miles. Our knowledge of this distant orb is extremely limited, owing to his apparently diminutive size and feebleness. No markings have ever been sighted on his miniature disk, and we can expect to learn nothing until one of the large telescopes is employed in the work. No doubt this planet exhibits the same belted appearance as that of Uranus, and there is every probability that he possesses numerous satellites.