186 ANNUAL REPORT SMITHSONIAN INSTITUTION, 193 3 



work have not been published, but the results are summed up in a 

 small octavo publication entitled " Astronomical Constants." 



As stated above, the immediate object of mo^t of the work of the 

 past in this subject has been the deduction of the positions of the 

 known bodies of the solar system at any time in the past or future, 

 from the laws of motion and gravitation. The deduced positions 

 are compared with those observed in the telescope. The desire to 

 achieve the highest accuracy possible has to many been a sufficient 

 objective. Ultimately, it leads to a knowledge of the extent to 

 which the assumed laws will account for the observed phenomena. 

 The study of the differences between the observed and calculated 

 positions has sometimes given unexpected information concerning 

 the operations of the laws ; at other times it has furnished informa- 

 tion concerning effects other than those produced by the direct action 

 of gravitation. In fact, every considerable increase in accuracy, 

 either of the theory or of the observations, has been followed by 

 discoveries that have stimulated further investigation and the desire 

 for still greater accuracy. 



Newcomb's summary shows that most of the definite differences 

 between theory and observation could be accounted for by small 

 changes in the constants that had been used to calculate the theories. 

 It followed that, in general, the Newtonian laws of motion and 

 gravitation were sufficient to account for the observed phenomena. 

 Only one outstanding deviation was found — one that had previously 

 been indicated by Leverrier, namely, an unexplained motion of the 

 perihelion of Mercury. As is now well known, this has received an 

 explanation through the theory of relativity, and, within the prob- 

 able error of the determination of the motion of Mercury from 

 observation, it is satisfactory. As mentioned above, this is the only 

 difference in the motions of the solar system between the results 

 of the Newtonian and relativity laws that is large enough to be 

 detected at present, and this condition will probably continue for 

 many years to come. 



Nearly another half century has passed since Newcomb's results 

 came into general use; and in the interval observations have been 

 accumulating — chiefly at Greenwich and Washington, where they 

 form part of a continuous program. In that time, only minor 

 differences which could not properly be ascribed to errors of ob- 

 servation, have appeared. Some of these could undoubtedly be 

 diminished by a new discussion of the masses and other elements 

 of the orbits; others are possibly due to slight defects in the calcu- 

 lated theories — defects that it is difficult to avoid altogether with 

 long and involved calculations. Some idea of the small magnitude 

 of these differences can be gained from the statement that the mean 

 annual deviations of any of the great planets from their calculated 



