TABLES OF MINOR PLANETS DISCOVERED BY JAMES C. WATSON. 



By Armin O. Leuschner, Anna Kstelle Glancy, and Sophia II. Levy. 



INTRODUCTION. 



Those planets whose mean daily motions are approximately 600" are classed with the 

 planet Hecuba, or, in the group for which 



n' 



n 



^i(l-w) 



where n' and n are the mean daily motions of Jupiter and the planet, respectively, and w is a 

 small quantity. 



Among the minor planets discovered by James C. Watson there are several of this type. 

 In the course of the general program of deteVmining the perturbations of the Watson asteroids, 

 there arose the necessity of computing special tables for the Hecuba group in preparation for 

 the application of Bohlin's method to individual planets. 



General tables for the group h were in the process of construction, under the direction of 

 Professor Leuschner,' according to the method of Bohlin,' when tables for this group were 

 published by H. v. Zeipel.' The computers. Dr. Sidney D. Townley and Miss Adelaide M. Hobe, 

 made a comparison of their tables with those of v. Zeipel and found certain discrepancies 

 Because of this fact the completion of the tables for the Hecuba group was deferred. These 

 discrepancies have been explained, as a result of a careful investigation, and the tables have 

 been completed by Miss A. Estelle Glancy and Miss Sophia H. Levy, under the direction of 

 Professor Leuschner. 



In the completion of the tables, v. Zeipel's method and order of procedure have gener- 

 aJly been followed. There are numerous discrepancies between our tables and v. Zeipel's. As 

 far as possible, with the aid of the original manuscript, kindly forwarded by the author, we have 

 traced the source of these disagreements. In some of the more comphcated functions it was 

 not possible to do so, and these discrepancies remain unexplained. Our own results, however, 

 are substantiated by the employment of independent developments. Further, where we found 

 terms omitted which were of the same order as those which were included, we frequentlj' 

 extended the tables. In this connection, it is pertinent to remark that it is very difficult to set 

 up a consistent criterion for the omission of terms. With the exception of a few scattered 

 neghgible terms, our tables are published in full. They contain terms which may ordinarily be 

 omitted, yet their numerical magnitudes depend upon the elements of the particular planet 

 imder consideration, and their use is left to the comjiuter's judgment. Many of them are 

 incomplete, i. e., the tabulated coefficients do not necessarily include all the terms of a given 

 degree in the eccentricities or mutual inclination or of the small quantity w, which depends 

 upon the difference between the planet's and twice Jupiter's mean motion. In other words, the 

 coefficients may not contain all the terms of a given degree having the factors 



IV, TjP, fj'l, f 



which are defined on page 12. But, assuming certain numerical limits for the fundamental 

 auxiliary functions, the coefficients are of this magnitude. The value of the additional terms 

 will be shown best in an application of our tables to the same planet for which v. Zeipel computed 

 the perturbations. 



Unless stated otherwise, the references to Bohlin refer to the French edition and are 

 designated by B. References to v. Zeipel are designated by Z. 



' Memoirs of the National Academy of Sciences, Vol. X, Seventh Memoir, p. 200. 



' Forraeln uud Tafein zur gruppenweisen Berechnung der allgemeinen Storungen benachbarter Planetcn (I'psala, ISPC). 



Sur le Dfiveioppement des I'erturhations Plan^taires (Stoclcholm, 1002). 

 • Angenaherte Jupiterstorungen f ilr die Ueculia-Gnippe (St. Pfitersbourg, 1902). 



9 



