KARL FRIEDRICH GAUSS 241 



already possessed at that time his 'method of least squares,' 

 discovered in his eighteenth year, which allowed the in^ 

 fluence of the inevitable errors of observation to be made as 

 small as possible in working out results. This was the 

 beginning of a series of discoveries of the planetoids which 

 lie between Mars and Jupiter; up to to-day about a thousand 

 of them have been found. The method of calculation, 

 according to which all of them are followed in their courses, 

 was first published by Gauss in the year 1809, in his Theoria 

 motus corporum coelestium (Theory of the Motion of the 

 Heavenly Bodies), in which he actually goes beyond La- 

 place's Mecanique celeste, which at that time had already 

 partly appeared. 



As regards our investigation and knowledge of nature, 

 however, all this amounted to nothing more than skill in 

 calculation according to Newton's inverse square law; none 

 the less, in absence of this skill it would never have been so 

 certain that this law holds without exception, and to the ut- 

 most limit of observation, throughout the whole solar 

 system. It is just by this experimental verification of new 

 conclusions, capable of exact tests, that all natural laws are 

 continually put to the best possible proof concerning their 

 agreement with reality. In this connection we should also 

 mention the calculation - in 1846, and so within Gauss' 

 lifetime - of the orbit of the most distant planet Neptune 

 from the slight observed disturbances of Uranus, a par- 

 ticular shining example of the justified triumph of know- 

 ledge, gained on the basis of the methods of Laplace and 

 Gauss, a hundred and sixty years after Newton had shown 

 the way with his Principia. 



In another direction Gauss is to be regarded as completing 

 the work of Laplace, again on the basis of Newton's ideas, in 

 his Foundation of the Theory of the Form of Liquid in a State 

 of Equilibrium (1830) where he endeavours to attain the 

 greatest strictness in mathematical calculation, without 



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