The n-Body Problem in General Relativity

1 IN THE MONOGRAPH SERIES directed by Henri Villat several fasci- cules have been devoted to Relativity. First there are the general presentations ofTh. De Donder (nos. 8 14 43 58) and then those more specifically devoted to Einsteinian gravitation - notably Georges Darmoiss contribution (no. 25) and that of J. Haag (no. 46) on the Schwarzschild problem. The present fascicule takes its place alongside the two latter monographs but it has been conceived and composed in such a way that it may be read and understood by anyone with a knowledge of the principles of Absolute Differential Calculus and of Relativity - either from the original exposi- tions of Einstein Weyl or Eddington or in French from Cartans excel- 2 lent works (for everything having to do with mathematical theories) and 3 from Chazys (for Relativity and Celestial Mechanics) or naturally from Levi-Civitas The Absolute Differential Calculus (first edition London and Glasgow Blackie and Son 1927) where the two original papers written in Italian are brought together: namely Calcolo differenziale assoluto and Fondamenti di meccanica relativistica (Bologna Zanichelli). As for the present fascicule it is hardly necessary to point out that as its title indicates we seek to establish in the simplest possible terms the rela- tivistic aspect of what Newton and those who followed him regarded as the key to ordinary Celestial Mechanics.