592 



rate discussion of the various problems which present themselves in 

 the determination of the movements of planets and comets from ob- 

 servations made on them under any circumstances, was not published 

 before 1809. Gauss was not usually very prompt in making public 

 his researches, but retained them in his own hands until, by repeated 

 correction and examination, they had assumed a form which satisfied 

 his own judgment of what was equally due to the requirements of 

 science and his own honour ; and the work of which we are now 

 speaking exhibits, in a very remarkable degree, the effects of this 

 severe system of revision, in the skilful adaptation and reduction of 

 methods and formulae, and in the careful estimate of the circum- 

 stances under which they may be most advantageously employed. 

 We find in it no evasion of difficulties, and no resort to methods of 

 approximation only, when the means of accurate determination are 

 at hand. His aim was in every instance to obtain results of the 

 same order of correctness with the observations upon which they were 

 founded ; and with a view of securing the full benefit of observations 

 which furnish, as is usual in astronomy, data more numerous than 

 the unknown elements which they are required to determine, he has 

 given in the work which we are now considering the first completely 

 developed theory of the method of least squares, more especially as 

 applicable to astronomy, and of the means of estimating the degree 

 or measure of precision which its application affords ; and though he 

 was anticipated in the publication of this method by Legendre, there 

 is every reason to believe that it was with him an original discovery ; 

 for he is said to have been in possession of it as early as 1795. No 

 other work in later times has contributed so much as this to the 

 complete and scientific discussion of astronomical observations ; and 

 its influence is traceable in the form which those discussions have 

 assumed in the writings of Bessel, Hansen, Struve, Encke, and other 

 eminent astronomers, which have done so much honour to Germany. 

 It would be impossible in the brief space allowed for this notice to 

 pass in review Gauss's various essays on subjects of pure and applied 

 mathematics some of them of great importance which were gene- 

 rally communicated to the Royal Society of Gottingen, though most 

 of them were separately published : amongst them we find two de- 

 monstrations of the resolvability of equations with rational terms 

 into simple or quadratic factors ; others on magic squares ; on qua- 



