all numbers that give the same remainder when they are divided by the same number. In his "General Disquisitions on Curved Surfaces" he established the famous theorem that in whatever way a flexible and inextensible surface may be deformed, the sum of the principal curvatures at each point will always be the same. The calculations of the elements of the asteroids Pallas, Ceres, Juno, and Vesta, were made by Gauss, and attracted all the more attention because they furnished the first occasions on which all the elements of a planet had to be determined in a short time and by a small number of observations. The methods were not yet even fixed, because no one had taken up the subject. The process adopted by Gauss was simple and confessedly worthy of the attention of astronomers. Gauss has been called the godfather of the planet Vesta, from his having selected the name for it. In two papers on the comets of 1811, he gave a new and much more simple method than had been practiced before to determine the elements of a comet with the smallest number of observations. While actively engaged in the measurement of the degree in Hanover, Gauss devised the instrument known as the heliotrope, which has since come into general use in all geodesic observations.
Gauss engaged also in researches on magnetism, concerning which he published a paper in 1833 on the intensity of terrestrial magnetism. He and Prof. Wilhelm Weber invented new magnetic apparatus, including the declination instrument and the bifilar magnetometer. They erected at Göttingen an observatory, free from iron, where he made magnetic observations, and—anticipating the electro-magnetic telegraph—sent telegraphic signals to a neighboring town.
His collected works, edited by E. J. Schering, have been recently published by the Royal Society of Göttingen in seven volumes. With them are included notices by him of many of the memoirs, and of works of other authors in the "Göttingen gelehrte Anzeigen," and a considerable amount of previously unpublished matter. Gauss was a member of all the important learned societies.
One of Gauss's last acts was, a little while before his death, to have engraved at the foot of his portrait, as giving the best summary of his views and labors, the lines from Shakespeare's "King Lear":
"Thou, Nature, art my goddess; to thy laws
My services are bound."
