THE SCIENTIFIC SPIRIT IN GERMANY. 



183 



cated to Von Zach in the course of the year 1801, and 

 enabled him and Olbers to rediscover the first of the 

 small planets, Ceres, which Piazzi had observed on the 

 1st of January 1801 at Palermo, and afterwards lost as 

 it approached the region of the sun's light. Through 

 this Gauss placed himself on a level with the great 

 French astronomers Laplace, Lalande, and others. The 

 new professor of mathematics and director of the obser- 

 vatory of Gottingen was admitted into the august com- 

 pany of the Paris academicians, who then ruled, and since 

 the death of Euler had almost monopolised, the mathe- 

 matical studies of the world. Although Gauss thus 

 introduced the higher and abstract branches of exact 

 science into the programme of a German university, 

 and established a link between Paris and Germany 

 in mathematics, as Humboldt had done shortly before 

 in the natural sciences, fully a quarter of a century 

 was to elapse before the spirit of exact research, and is. 



Scientific 



of the higher mathematics, really began to leaven the the^nl 

 German universities. It then at length entered the field slcond 



as a third and equally important agent by the side of the century. e 



This was achieved to perfection, 

 a proof of the usefulness of the 

 method being the fact that Gauss 

 succeeded in finishing in one hour 

 a calculation which had taken Euler 

 three days, and had resulted in his 

 blindness. The second problem 

 arises from the fact that the num- 

 ber of observations is always in 

 excess of the number mathemati- 

 cally necessary, and that, owing to 

 the unavoidable inaccuracies, dif- 

 ferent sets of observations give 

 slightly different orbits. How are 

 these to be used so as to give the 



most correct average result ? This 

 involves a question in probabilities. 

 As early as 1795 Gauss was in pos- 

 session of the so-called method of 

 least squares, which occurred to him 

 so naturally that he suspected that 

 Tobias Mayer must have already 

 known about it. It also occurred 

 independently to Legendre, who 

 was the first to publish it, in 1806, 

 in his ' Nouvelles methodes pour la 

 determination des orbites des co- 

 rnetes. ' See Sartorius, ' Gauss zum 

 Gediichtniss,' p. 41 sqq. 



