50 ASTRONOMY 



The last name which will be mentioned in this field, 

 and perhaps the greatest, is that of Henri POINCARE 

 (1854-1912). His remarkable work " Methodes nouvelles 

 de la Mecanique celeste," furnished a great wealth of new 

 ideas, which were developed with the very highest 

 mathematical skill. Periodic orbits of various types, 

 asymptotically periodic orbits, and integral invariants, 

 were the fundamental conceptions which were examined 

 with all of the resources of modern mathematics and 

 with all of the rigor which modern mathematics demands. 

 It is a modest statement to say that with POINCARE 

 begins a new epoch in celestial mechanics. In addition 

 to his contributions to the theory of the motions of the 

 celestial bodies should be mentioned his contributions to 

 the theory of their figures. It was CLAIRAUT who first 

 showed that an oblate spheroid is a figure of equilibrium 

 of a slowly rotating fluid mass. POINCARE showed that 

 besides the ellipsoidal figures already known there 

 exists an infinity of other forms corresponding to higher 

 rates of rotation. His theorems relating to stable and 

 unstable figures of equilibrium are of great importance. 

 These investigations find their application not merely in 

 the figures of such planets as Jupiter and Saturn but also 

 in the question of the origin of binary and multiple stars. 



With such a wealth of noble tradition in the field of 

 Celestial Mechanics, it is quite safe to assume that the 

 Universities of France, and especially of Paris, will 

 always be a source of inspiration to students who may 

 be interested in this field. 



Geodesy. The monumental works of the French in 

 the pa.st are being paralleled by contemporary contribu- 

 tions. This is well illustrated in the geodetic work in 

 the recent achievement of the expedition under BOUR- 

 GEOIS, which has remeasured with the highest precision 



