jAlfUAEY 12, 1900.] 



SCIENCE. 



47 



1840. This is still the fundamental me- 

 moir ou the subject of which it treats, and 

 must be regarded as one of the most per- 

 fect models of mathematical exposition. 

 In respect to clearness and elegance, 

 indeed, the works of Gauss are unsur- 

 passed. " In his hands," as Todhunter 

 has said,* " Latin and German rival 

 French itself for clearness and pi'ecision." 

 " Alles gestaltet sich neu unter seinen 

 Handen," was the tribute f of Bessel ; and 

 the lapse of two generations has served 

 only to increase admiration for the genius 

 and industry which made Gauss one of the 

 most conspicuous figures in the science of 

 the nineteenth century. 



The importance of the theory of the po- 

 tential function when considered in its his- 

 torical aspects is found to consist not so 

 much in die rich harvest of results it has 

 afforded in the field of gravitation, as in its 

 direct bearing on the developments of other 

 branches of mathematical physics. For 

 the points of view and the analytical 

 methods of the ISTewtonian function have 

 been adapted and extended with brilliant 

 success to the interpretation of almost all 

 kinds of mechanical phenomena. Thus it 

 has come about that we have now to deal 

 with many kinds of potential, as logarithmic 

 potential, velocity potential, displacement 

 potential, electric potential, magnetic po- 

 tential, thermodynamic potential, etc., 

 each of which bears a more or less close 

 mathematical analogy to the Newtonian 

 function. 



In the closing paragraph of his Exposi- 

 tion du Systeme du Monde, Laplace refers 

 to the immense progress made in astronomy 

 since the geocentric theory was displaced 

 by the heliocentric theory of the solar sys- 

 tem. This progress is specially remarkable 

 when we consider that it depended on the 



* History of the Theories of Attraction and Figure 

 of the Earth, Vol. II., p. 235. 

 t In a letter to Olbers, 1818. 



discovery, so humiliating to man, of the 

 relatively insignificant dimensions and in- 

 conspicuous role of our planet. But we 

 agree with Laplace that "Les resultats 

 sublimes auxquels cette decouverte I'a con- 

 duit sont bien propres a le consoler du rang 

 qu'elle assigne a la Terre, en lui montrant 

 sa propre grandeur dans I'extreme petitesse 

 de la base qui lui a servi pour mesurer les 

 cieux." All astronomy is based on a 

 knowledge of the size, the shape and the 

 mechanical properties of the earth ; and it is 

 not sui'prising, therefore, that a large share 

 of the mathematical investigations of the 

 century should have been directed to the 

 science of geodesy. Founded in the middle 

 of the last centurj' by Clairaut* and his 

 contemporaries ; recast by Laplace and 

 Legendref (1752-1833) in the early part 

 of this century ; systematized and extended 

 to a remarkable degree by the German 

 geedesists, led especially by the incompar- 

 able Bessel ;% this science has now come to 

 occupy the leading position in point of per- 

 fection of methods and precision of results. 

 So great, in fact, has been the growth of 

 this science during the century that recent 

 writers have found it desirable to subdivide 

 the subject into two parts called mathe- 

 matical geodesy and physical geodesy re- 

 spectively, though both parts are nothing if 

 not mathematical. § 



In a former address I have considered 

 somewhat in detail certain of the more 



* Clairaut's work, ThiJorie de la Figure de la Terre, 

 Paris, 1743, was the pioneer work in physical geodesy. 



t The name of Legendre is famous in geodesy by 

 reason of his beautiful theorem which makes the so- 

 lution of a geodetic triangle almost as easy as the so- 

 lution of a plane triangle. 



J Bessel 's contributions to astronomy and geodesy 

 are collected in Abhandlungen von F. W. Bessel, 

 herausgegeben von Rudolf Eugelmann, in drei 

 Biinden, Leipzig, Wilhelm Engelmann, 1875. 



§ See, for example. Die Mathematischen und 

 Physikaliachen Theorieen der Hoheren Geodasie von 

 Dr. F. R. Helmert, Leipzig, B. G. Teubner, Teil I., 

 1880 ;TeilII., 1884. 



