CELESTIAL MECHANICS: LEUSCHNER 47 



bench's Elements H. 9 (1898, August 18.5, 34 observations, August 

 26.5, 16 observations, and September 9.5, 26 observations, heliocentric 

 arc about 8.) The set J 11 is based upon nine normal places, although 

 Dr. Chandler's value of the mean motion was taken (Elements G) 

 and the other elements determined by varying the ratio of the ex- 

 treme geocentric distances. The normal places are well represented. 



Elements K, Russell, 12 are the same as J 11 except for changes in 

 M, (o, and </> based upon observations in 1899.0 at the Chamberlin 

 and Lick Observatories. The representation August 17, 1898, to May 

 20, 1899, is satisfactory except for the normal place of November 11.5 

 for which Aa s .28, AS 3". 



Elements L are merely the preceding ones brought up to the epoch 

 1900.0 and mean equinox of 1900.0. In his article 13 Russell develops 

 the general perturbations of the major axis of Eros by the action of 

 Mars. He does this by Le Verrier's method of interpolation. Rus- 

 sell finds eight terms of the general perturbations of the mean longi- 

 tude larger than 1".50. The largest is 35" with a period of about 

 1000 years. The greatest displacement due to the first 7 terms will 

 be +38" in 1927 and 53" in 1959 in mean longitude, and "will 

 eventually lead to a valuable determination of the mass of Mars." 

 Russell then gives tables of the perturbative function, perturbations 

 of log a and perturbations of the mean longitude. 



Elements M 14 were developed by Robbins from Elements G by 

 applying special perturbations of Venus, Earth, Mars, Jupiter, and 

 Saturn by the method of the variation of constants. (Nautical 

 Almanac 1837, appendix.) 



Elements N 15 are due to H. Osten, who has computed eight normal 

 places based upon Elements P, with special perturbations of Venus, 

 Earth, Mars, Jupiter, and Saturn according to Encke's method. 



Millosevich has produced numerous sets of elements. Elements O 16 

 were computed from observations made during the interval August 14 

 to September 21, 1898. An observation by Millosevich October 8. 

 gives Aa l s .93, AS +7".5. 



Elements P 17 were computed from a normal place of date August 

 14.5 and Millosevich's observations on September 21 and October 24, 

 1898. Millosevich states that Berberich's ephemeris requires a correc- 

 tion of +131 8 in a and +5'.5 in 8 on December 23, 1898. 



Elements Q 18 are from photographic observations at Greenwich by 

 the variation of the distances. Later 19 he stated that there is an 

 error of about 2 s in his ephemeris after five months. 



Elements R 19 are based upon four normal places and are Elements 

 P improved by the method of variation of the distances. They rep- 

 resent 17 normal places from 1000 observations in 1898-1899 perfectly. 



