789] 
GAUSS. 
545 
observatories 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 lieber Gegenstände der hohem Geodäsie. Connected with 
observations in general we have (1812—26) the memoir Theoria combinationis observ 
ationum erroribus minimis obnoxia, with a second part and a supplement. Another 
memoir of applied mathematics is the Dioptrische Untersuchungen, 1840. Gauss was 
well versed in general literature and the chief languages of modern Europe, and was 
a member of nearly all the leading scientific societies in Europe. He died at Göttingen 
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 Royal Society of 
Göttingen, in 7 vols. 4to, Gött., 1863—71, edited by E. J. Schering,—(1) the Dis 
quisitiones Arithmetics, (2) Theory of Numbers, (3) Analysis, (4) Geometry and Method 
of Least Squares, (5) Mathematical Physics, (6) Astronomy, and (7) the Theoria Motus 
Corporum Coelestium. They include, besides his various works and memoirs, notices by 
him of many of these, and of works of other authors in the Göttingische gelehrte 
Anzeigen, and a considerable amount of previously unpublished matter, Nachlass. Of 
the memoirs in pure mathematics, comprised for the most part in vols. II., in., 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 singidarium, the memoirs on 
the theory of biquadratic residues, in which the notion of complex numbers of the 
form a + Ы was first introduced into the theory of numbers; and included in the 
Nachlass 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; 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. ill. we have 
memoirs relating to the proof of the theorem that every numerical equation has a 
real or imaginary root, the memoirs on the Hyper geometric Series, that on Interpolation, 
and the memoir Determinatio Attractionis—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 researches (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 Allgemeine Auflösung..., on the 
graphical representation of one surface upon another, and the Disquisitiones generales 
circa superficies curvas. And in vol. v. we have a memoir On the Attraction of 
Homogeneous Ellipsoids, and the already mentioned memoir Allgemeine Lehrsätze..., on 
the theory of forces attracting according to the inverse square of the distance. 
С. XI. 
69