CELESTIAL MECHANICS: LEUSCHNER 17 



except for the change due to Jupiter's mass. The resulting Elements 

 J represent the heliocentric longitude and latitude as follows : 



1816 1821 1827 1830 1834 1836 



AL 19" +34" +4" 14" +5" 13" 



AB 1 +4 +6 10 +1 +4 



Galle states these differences may be accounted for if the perturba- 

 tions of Saturn and Mars were taken into account. 



In A. N. No. 636 osculating Elements K are published for each 

 year from 1839 to 1850. These were computed by Galle. The start- 

 ing elements are those for epoch 1810, January 0. In computing the 

 special perturbations, Encke and Galle used mass of Jupiter 1/1053.924. 



From 1851 to 1870 Galle 11 continues the special perturbations by 

 Jupiter and later with the elements of Giinther also those by Saturn. 

 These were used in computing the ephemerides published in the 

 Astronomiches Jahrbuch from 1862 to 1870. (See Elements L.) 



Beginning with the year 1871 and continuing to 1919, the Jahrbuch 

 published and used Farley's 12 osculating elements for computing the 

 ephemeris. (See Elements M and N). Farley's computation includes 

 the perturbations by Venus, Earth, Mars, Jupiter and Saturn. His 

 computations are also the basis for the ephemerides published in the 

 British Nautical Almanac. With Farley's elements we have the fol- 

 lowing comparisons: 



Corrections to Ephemerides. 



1883 1892 1895 1906 1908 1914 



Aa -1 B 4 -1?2 -1?0 -2?5 -5?4 -2 s ! 



A5 -J-2'7 +07 +0'8 +8'2 -14-0 +4'3 



In Annales de 1'Observatoire de Paris, Vol. I, Le Verrier pub- 

 lishes the results of his investigation on "Developpement de la 

 fonction perturbatrice relative a Faction de Jupiter sur Pallas. Calcul 

 du terme dont depend une inegalite a longue periode du mouvement 

 de cette derniere planete." Le Verrier states that the aphelion of 

 Pallas is 54 from the intersection of the orbit with Jupiter. Conse- 

 niiently when Pallas is at aphelion the distance from Jupiter is in- 

 creased on account of the great inclination of the orbit. This large 

 inclination diminishes the effect due to the large eccentricity. Le 

 Verrier gives the series for the reciprocal of the distance in a more 

 convergent form and develops the equation in longitude depending 

 on the argument 18 QJ. 7 Pallas. The maximum of the term is 895". 

 In his report before the Paris Academy, 13 Cauchy compares his theory 



