No. 3.] 



MINOR PLANETS— LEUSCHNER, GLANCY, LEVY. 



137 



^{(1 -e cos £) W-[{l-e cos e) U'j} 



Table XXX\TII. — All the l)racketed quantities probably contain only the accumulation 

 of the discrepancies in Tables XXIX6, XXXVI, and XXXVII. This is a very important 

 table, and it is from differences in (P (t?) that the perturbations may be expected to differ most. 



PERTtJRBATIONS OF THE RADIUS VECTOR. 



1« 



If TFand ^ E are tabidated and the computation is performed in duplicate, it is not necessary 



to make the long developments and the auxiliary tables in Z §(3, 99-114. For this reason the 

 formulae in §6 have not been checked and the list of errata does not cover this section. 

 The essential formulae are giA'en in Z 99. By Z 7, eq. (3G), 



,= _lTf-is+iw^+ 



• ■^=m+^p (o,+o, + o,+ 



) + 



In order to parallel the form of ndz, we write 



where (di+d^+d^) is given by Z 93, eq. (150) 



Hence the computation proceeds as follows: the perturbation is computed by eq. (36), 

 the argmnent is replaced by t?, and a corrective term which is the product of (di + d^ + d^) 

 and the derivative of the function with respect to i? is added. The perturbation v is then 

 expressed as a function of i?. It is tabulated in Table XLIII. 



Table XLIII. — If there are no errors of calculation in the construction of the table, all the 

 discrepancies are due to the accimaulation of other discrepancies previously discussed. 



The perturbation v =f{6) includes 



where the tabulated numbers signify the degrees of the terms included and where only IF, and E, 

 are inclusive of third degree. 



