a few miles west of the citadel of Gaur, as may be gathered from Rennell and Buchanan. Dr Hunter (New Slalisf. Ace. Qchngal, vii. p. 65) says its very site has not been accurately determined. It is pessible that it may h “'0 been cut away by the waters of the Ganges, a branch of which has flowed near; but Buchanan had evidently visited it, and Creighton marks the rampart muddy in his map of Gaur. Janlmtdbdd was a name given by lumayun to Gaur; and other names of royal cities appear on coms, such as Firuuibcid, H usailuibdd, Sluthr-i-nao, &c., which are probably names otlicially attached to new foundations of ortions of the great Gaur group of cities, but which gained no popu ar currency.
In addition to the works quoted in this article, the pa )L’X‘S of Mr E. Thomas and Mr H. Blochmann in the journals of the toyal and Bengal Asiatic Societies have been consulted.
GAUSS, Carl Friedrich (1777–1855), an eminent German mathematician, was born of humble parents at Brunswick, April 23, 1777, and was indebted for a liberal education to the notice which his talents procured him from the reigning duke. His name became widely known by the publication, in his twenty-fifth year (1801), of the Dis- quisitiones Arithmeticee. In 1807 he was appointed director of the Gettingen Observatory, an Office WhiCh he retained to his death: it is said that he never slept away from under the roof of his observatory, except on one occasion, when he accepted an invitation from Humboldt to attend a meeting of natural philosophers at Berlin. In 1809 he published at Hamburg his Theoria .lIotus C'orporum C’or‘les— tium, a work which gave a powerful impulse to the true methods of_astronomical observation 5 and his astronomical workings, observations, calculations of orbits of planets and comets, &c., are very numerous and valuable. He continued his labours in the theory of numbers and other analytical subjects, and communicated a long series of memoirs to the Royal Society of Sciences at Gettingen. His first memoir on the theory of magnetism, I ntensitas vis mrlgnetieee terrestris ad mensuram absolutam revocata, was published in 1833, and he shortly afterwards proceeded, in conjunction with Professor Wilhelm Weber, to invent new apparatus for observing the earth’s magnetism and its changes; the in- struments devised by them were the declination instrument and the bifilar magnetometer. With Weber’s assistance be erected in 1833 at Gettingen a magnetic observatory free from iron (as Humboldt and Arago had previously done on a smaller scale), where he made magnetic observations, and from this same observatory he sent telegraphic signals to the neighbouring town, thus showing the practicability of an electromagnetic telegraph. He further instituted an asso- ciation (Magnetische Verein), composed at first almost en- tirely of Germans, whose continuous observations on fixed term-days extended from Holland to Sicily. The volumes of their publication, Resultate aus der Beobaeht-unyen des Magnetische-n Vereins, extend from 1836 to 1839; and in those for 1838 and 1839 are contained the two important memoirs by Gauss, Allyemeine Theorie der Erclmuynet- ismus, and the Allyemez'ne Lehrsdtze—on the theory of forces attracting according to the inverse square of the distance. The instruments and methods thus due to him are substantially those employed in the magnetic observa- tories throughout the world. He co-operated in the Danish and Hanoverian measurements of an arc and trigonometrical operations (1821-48), and wrote (1843, 1846) the two memoirs Ueber Geyenstc'inde der hijhern Geoddsie. Connected with observations in general we have (1812—26) the memoir Theoria combinationis observationum erroribus minimis obnoxia, with a second part and a supplement. Another memoir of applied mathematics is the Dioptrische Unter- suchzmgen, 1840. Gauss was well versed in general litera- ture and the chief languages of modern Europe, and was a member of nearly all the leading scientific societies in Europe. He died at Giittingen early in the spring of 1855. The centenary of his birth was celebrated (1877) at his native place, Brunswick.
Gauss‘s collected works have been recently published by the ltoynl Society of (lettingen, in 7 vols. 4to, Giitt., 1863—71, edited by J. Schering,—(1) the Disquisitiones Arithmeticte, Theory of Numbers, (3) Analysis, Geometry and .lIethod of Least Squares, (5) .lluthemutical Physics, (6) Astronomy, and (7) the Theoria .lIotus Corporum Callesti-um. They include, besides his various works and memoirs, notices by him of many of these, and of works of other authors in the Gott-iuyen gelehrle .lnseigen, and a con- siderable amount of previously unpublished matter, Nach- lass. Of the memoirs in pure mathematics, comprised for the most part in vols. ii., iii. , and iv. (but to these must be added those on Attractions in vol. v.), it may be safely said there is not one which has not signally contributed to the progress of the branch of mathematics to which it belongs, or which would not require to be carefully analysed in a history of the subject. Running through these volumes in order, we have in the second the memoir, Summatio quarundam serierum singularimn, the memoirs on the theory of biquadratic residues, in which the notion of complex numbers of the form a+bi was first introduced into the theory of numbers; and included in the .Vachlass are some valuable tables. That for the conversion of a fraction into decimals giving the complete period for all the prime numbers up to 997) is a specimen of the extraordinary love which Gauss had for long arithmetical calculations 5 and the amount of work gone through in the construction of the table of the number of the classes of binary quadratic forms must also have been tremendous. In vol. iii. we have memoirs relat- ing to the proof of the theorem that every numerical equa- tion has a real or imaginary root, the memoir on the IlypeI'yeometric Series, that on Interpolation, and the memoir Determinatio Attractiouis—in which a planetary mass is considered as distributed over its orbit according to the time in which each portion of the orbit is described, and the question (having an implied reference to the theory of secular perturbations) is to find the attraction of such a ring. In the solution the value of an elliptic function is found by means of the arithmetico-geometrical mean. The Nachlass contains further researches on this subject, and also re- searches (unfortunately very fragmentary) on the lemniscate- function, &c., showing that Gauss was, even before 1800, in possession of many of the discoveries which have made the names of Abel and Jacobi illustrious. In vol. iv. we have the memoir Allyemeine Auflosuny, on the graphical representation of one surface upon another, and the Dis- qu-isitiones generates circa supeiy’icies cur-ms. And in vol. v. we have a memoir 0n the Attraction of Homogeneous Ell i1)- soicls, and the already mentioned memoir Allyemeiue Lehr— siilze, on the theory of forces attracting according to the inverse square of the distance.
born at Geneva on the 25th of August, 1790. His father Georges Marc Gaussen, a member of the council of two hun- dred, was descended from an old Languedoc family which had been scattered at the time of the religiouspersecutions in France. At the close of his university career, Louis was ordained in 1816 to the ministry of the Swiss Reformed Church at Satigny near Geneva, where he formed intimate relations with J. E. Cellerier, who had preceded him in the pastorate, and also with the members of the dissenting con- gregation at Bourg-de-Four (Eglise du temoignage), which had been formed under the influence of the preaching of the Haldanes in 1817. In 1819 he published in conjunc- tion with Cellérier a French translation of the Second Helvctic Confession, with a preface expounding the views he had reached upon the nature, use, and necessity of con- fessions of faith; and in 1830, for having discarded the
official catechism of his church as being insufficiently