59 2 The Smithsonian Institution 



methods, Admiral C. H. Davis, then Superintendent of the 

 "American Ephemeris," undertook an English translation, 

 which was finally published by the firm of Little & Brown, 

 publishers, of Boston, in 1857. 



The expense of the publication was shared by the Institu- 

 tion, and a number of copies were subscribed for as exchanges 

 and distributed in exchange for other books among foreign 

 correspondents. Without this aid, the work, so essential to the 

 advance of practical astronomy, could not have been issued. 



TABLES FOR DETERMINING PERTURBATIONS OF PLANETS 



IN determining the mutual action of any two planets in the 

 solar system, there are certain quantities depending upon the 

 ratio of the mean distances of these bodies from the sun, which 

 must first be computed. The number of these quantities, and 

 the labor necessary to compute each one of them, make this 

 first step in the reduction of the mutual action of the two plan- 

 ets to numbers a serious work. The tables 1 published by the 

 Institution and calculated by Professor J. D. Runkle, accom- 

 plish in a very satisfactory way the desired end of shortening 

 the calculations referred to. Their use gives practically the 

 same advantage in the computations to which they are 

 applied that is afforded in arithmetical operations by a table 

 of logarithms. The tables and the supplements contain 

 the quantities which relate to the major planets and to the 

 asteroids also. 



It is proper to add that the general theory, thus reduced 

 to numbers, is due to Leverrier; and that Walker had pre- 

 viously printed (in an appendix to the "American Ephemeris" 

 for 1857) a tabulation of the Leverrier coefficients. 



1 " New Tables for Determining the Values the ratio of the mean distances," 1856, in Vol- 

 of the Coefficients in the Perturbative Func- time IX of the " Smithsonian Contributions 

 tion of Planetary Motion, which depend upon to Knowledge," fifth paper. 



