LE VERRIER'S THEORY OF THE MOTION OF THE 

 PLANETS JUPITER AND SATURN. 



By Robert T. A. Innes, F.R.A.S. 



This theory and the tables based on it are printed in vols. X., XI. 

 and XII. of the Annales of the Paris Observatory. It is founded 

 directly on Lagrange's variation of constants. The tables furnish 

 the instantaneous values of the six elements instead of the three 

 co-ordinates actually required. For this reason their use is arduous. 

 Besides this the error of the tables, considering their age, is large 

 and irregular. The tables for Saturn are to be replaced by others 

 by Mons. Gaillot, who has revised or completed the theory of 

 Saturn, 



A later and more successful theory for these planets, which will 

 be referred to later on, is due to Dr. Hill. 



At its sitting of 7th December, 1908, the French Academy of 

 Sciences fixed for the Damoiseau prize of £80 in 191 1 the following : 

 " To perfect Le Verrier's Tables of Jupiter." 



Le Verrier's tables of Jupiter are used in the Connaissance des 

 Temps; Hill's in the Nautical Almanac, the American Ephemeris, 

 and the Berliner Jahrhuch. 



The following table shows the reduction which must be applied 

 to the heliocentric ephemeris in the Connaissance des Temps to 

 reduce it to that of the Nautical Almanac, or in other words to 

 reduce Le Verrier's places to Hill's. The last two columns show 

 the corrections to the Nautical Almanac indicated by places derived 

 from photographs taken at the Greenwich Observatory.* 



Hill's tables represent the longitude of Jupiter in 1908-9 within 

 2", whilst Le Verrier's error is about 13". 



The perturbations in Hill's tables have been computed by 

 Hansen's method, which furnishes directly the three co-ordinates 

 required. If the perturbations depending on the second and 

 higher products of the masses are at all important, the formulae of the 

 variation of elements become remarkably involved ; Hansen had 

 drawn attention to this point and to the advantage his methods 

 offer, so long ago as i83if: and when it is a mere matter of getting 

 tables to give a major planet's position during several centuries, 

 Hansen's methods are better than any other, although they have 

 not perhaps every advantage that has been claimed for them. In 

 his latest theories of Uranus and Neptune, Newcomb adopted 



*See Mon. Notices R.A.S., Vol. LXVIII.. p. 585, and Vol. LXIX., p. 676. 

 t Untersuchung uber die Gegenseitigen Storungendes Jupiters und Saturns, 

 JBerlin. pp. XIV.-XV. 



