Record. xliii 



This is the admission of a rigorous solution for the general prob- 

 lem of celestial mechanics, of which Anding's statement: "The 

 problem of celestial mechanics is the representation of the motions of 

 the heavenly bodies by means of the Newtonian Law of Gravitation, 

 while at the same time the constants entering that representation, 

 and the system of reference and the time are so determined as to 

 give the best possible representation," is too narrow in that he as- 

 signs the law of attraction, and so fixes the form of the equations of 

 motion. 



The existence postulate of the planetary problem may be written: 

 "It is possible to choose for the Solar system measures of length and 

 time, a set of masses, a system of reference and a law of force, such 

 that the behavior of the system is representated." 



Does such a choice exist? The question may be stated in two 

 essentially different ways: 



A. Does a choice exist such that the resulting equations repre- 

 sent the behavior of the system to within errors less than the prob- 

 able errors of observation in the neighborhood of a given epoch? 



B. Does a choice exist such that the resulting equations rigorously 

 represent the behavior of the system for all time? 



An affirmation of B may be termed the Postulate of Causality, and 

 a denial of B, but an affirmation of A, the Postulate of Contingence. 

 It will be of interest to inquire into the answer to A by examining 

 the degree of approximation attained in the representation of the 

 motions of the solar system. 



Using mean solar time, the masses of theoretical astronomy, the 

 trihedron of the fundamental catalogue, and the Newtonian law of 

 attraction, we find that the outstanding differences for the following 

 are: 



1. Mercury: A secular perturbation in the longitude of the 

 perihelion of 41" a century. 



2. Venus: A secular perturbation in the longitude of the node of 

 10" a century. 



3. Mars: A secular perturbation in the longitude of the peri- 

 helion of 8" a century. 



4. Moon: A difference of about 5" a century between the theo- 

 retical and observed values of the acceleration of the longitude. 



5. Encke's Comet: A shortening of about 2^^ hours in its 3.3 

 year period at each revolution. 



Various attempts at modifying the planetary theory proving un- 

 satisfactory, Seeliger in 1906 so modified the solar system itself 

 as to remove the difference in the motions of Mercury, Venus and 

 Mars. 



So far as Encke's Comet is concerned, it is now recognized that 

 the presence of a resisting medium in the neighborhood of the sun, 

 as first assumed by Encke himself, is not an adequate explanation 

 of the variation in its period and it remains one of the outstanding 

 problems. 



