42 MEMOIRS NATIONAL ACADEMY OF SCIENCES. [Voi.xiv. 



with V. Zeipel's tables, those numerical quantities which are in disagreement are inclosed in 

 brackets. There are also certain mathematical developments useful to the reader. These 

 relations are sometimes taken from v. Zeipel and sometimes supplement his text. 



Certain simple functions of the elliptic integrals Tj""", defined by Z 19, eqa. (73), (74), (7.5), 

 are tabulated in Table I (cf. Z 23). 



Tables II-IVw^ (cf. Z 2G-32), giving the partial derivatives of the perturbative function, 

 are computed according to Z 24, eq. (77), by means of Table I and B 184, Tables XVI-XVIII 

 and B (Ger.) 182, Tables XII-XIV. 



The eUmination of Jwpiter's mean anomaly from the argument gives Z 25, eq. (78), in 

 which the coefficients are derived from Table II-IV vy^ by the formulae given in .S 61. These 

 coefficients are tabulated in Tables V-VII w' (cf. Z 33-39). 



