INTRODUCTION. 



The results recorded in these pages are the outcome of an effort to supplement the author's 

 lectures on celestial mechanics in the University of California by extensive numerical application 

 in the field of perturbations. 



During the summer of 1901 the Watson trustees of the National Academy of Sciences 

 agreed to engage students and graduates of the University of California in the work of computing 

 the perturbations of the minor planets discovered by Watson on condition that the author 

 would assume the immediate direction of the work and sole responsibility to the trustees for its 

 success. The original scope of the undertaking as fixed by Prof. Simon Newcomb, chairman 

 of the Watson trustees, was to embrace the numerical development of the perturbations, 

 including terms only of the first order with respect to the mass of Jupiter, by Hansen's method; 

 a correction of the elements by means of the differences between the computed and observed 

 positions for all available oppositions; and the construction of tables to facilitate the computa- 

 tion of positions to the nearest minute of arc, from the date of discovery to 1930. 



As the undertaking is now nearing completion, it is deemed advisable to make the tables 

 available to astronomers in advance of the details of the investigations. The present series, 

 containing the tables of twelve planets, is to be followed by several others, which will contain 

 the tables of the remaining planets, and possibly also the detailed investigations. 



Many difficulties of a theoretical as well as a practical nature were encountered during the 

 progress of the work, necessitating departures from the general program for individual planets, 

 particularly for planets of the Hecuba type. 



It is unnecessary to enter here upon a discussion of the progress and organization of the 

 investigation. It is sufficient to say that all computations were done independently by two 

 computers.'frequently by different methods, and that the system of checks used makes it highly 

 probable that the results are free from numerical error. Particular attention was paid to the 

 investigation of the differences between the theoretical and observed positions. The origin 

 of all unusually large residuals has been traced. When they occur they are, in general, accounted 

 for by higher order perturbations of Jupiter, or by perturbations of other major planets, or by 

 the fact that sufficiently accurate initial elements of the disturbed planet were not available 

 for the rigid computation of the coefficients of the perturbations. Corrections to the perturba- 

 tions, due to the differences between the initial and final elements of a planet may be included, 

 if it be deemed necessary, in subsequent series. Much useless labor has been caused by 

 erroneous identifications of the Watson planets on the part of the observers. A comparison 

 of the tables with future observations will be necessary to decide whether all erroneous 

 observations have been eliminated. 



Actual work was commenced in August, 1901, with Dr. Russell Tracy Crawford and 

 Dr. Frank Elmore Ross as computers. They continued in the work for one year, and in that 

 time computed, under the author's direction, the perturbations of ten planets in duplicate, by 

 Hansen's method. Tables of seven of these are included in the present series: (105) Artemis, 

 (128) Nemesis, (133) Cyrene, (139) Juewa, (161) Aihor, (174) Phaedra, and (179) Klytaemnestra. 

 Since then the computations have been carried on almost entirely by university students, except 

 that Dr. Burt L. Newkirk was appointed in September, 1903, a special assistant and was 

 assigned with Miss Adelaide M. Hobe chiefly to take charge of some twelve piece computers 

 in revising perturbations, correcting elements, and constructing tables. Doctor Newkirk 

 and Miss Hobe have also developed the perturbations of (115) Thyra and (93) Minerva. The 

 tables of Minora, however, contained in this series, are based on a previous investigation by 



Dr. W. S. ElCHELBEKGER. 



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