Contribution to the Relativistic Problem of n Bodies (I)

It is well known that the relativistic problem of n bodies cannot be stated in a precise manner without assuming a certain number of more or less arbitrary hypotheses in order to obtain the abstraction of material points. Two attempts have been made recently to arrive at the schematic case of n points. The first one is due to Prof. T. Levi Civita and is based upon the method of approximations used in 1916 by Droste and de Sitter but with rather too much haste as is shown by Levi Civita. The second one is due to Prof. A. Einstein and is based upon a new method of successive approximations. It leads to results different from those arrived at by Levi Civita, in particular with regard to the secular acceleration of the centre of masses.