16 CELESTIAL MECHANICS: LEUSCHNER 



epoch 1805, and his own elements of Pallas for the same epoch. This 

 computation led to a set of mean Elements (F). With these mean 

 elements for epoch 1810 and similar elements for Jupiter (Laplace) 

 a second computation of general perturbations due to Jupiter was 

 undertaken. This computation led to the following results: 



The mean motion of Pallas oscillates between 18/7 of QJ. motion 

 0".2153, and 1894 revolutions of Pallas = 737 of Jupiter. A new 

 value for Jupiter's mass = 1/1042.86. Then follows (1816-1817) the 

 computation of perturbation tables due to Jupiter, Saturn and Mars. 

 In this latter work, Gauss was assisted by Encke and Nicolai. 



In Astronomisches Jahrbuch 1816, page 234, Bode gives the best 

 set of elements by Gauss up to that time (Elements G). 



About 1824, Encke 7 used Gauss' elements based on early oppositions 

 and computed the perturbations due to Jupiter. He reports that 

 Gauss' elements with Jupiter's perturbations represent the opposition 

 of 1823 as follows: 



1823 Aa AS 



Oct. 9 +13:2 +25^6 



He then gives Elements (H) for the epoch 1826, and with these 

 computes the next ephemeris. 



For the opposition in 1825, Encke 8 reports that the correction to 

 the ephemeris is very large. But if the perturbations are included, 

 the difference between observation and computation is as follows: 



1825 Aa AS 



March 23 +4276 33"2 



He then gives a set of elements for the epoch 1827, and computes 

 an ephemeris for 1827. 



By 1834 Encke 9 reports a deviation of Pallas from computed 

 places amounting to 5'. He states this may be due to use of Laplace's 

 value for Jupiter's mass. It will be necessary to recompute elements 

 covering all observations. 



In A. N. No. 636, Encke publishes osculating Elements I for each 

 year from 1831 to 1838; his fundamental starting elements are for 

 the epoch of 1810, January 0. In B. J. 1838, p. 286, Encke draws atten- 

 tion to an error which he had committed in neglecting the corrections 

 for the secular variation of the obliquity. In the British Nautical 

 Almanac for 1837 Airy points out this error to which Encke refers. 



Galle 10 undertook the reinvestigation of the orbit based on opposi- 

 tions 1816, 1821, 1827, 1830, 1834, 1836, making use of Airy's value for 

 the mass of Jupiter 1/1048.69. The former perturbations were retained 



