A Compendium Of Spherical Astronomy With Its Applications To The Determination And Reduction Of Positions Of The Fixed Stars

PREFACE. THE present volume is the first of a projected series having the double purpose of developing the elements of Practical and Theoretical Astronomy for the special student of the subject, ancl of serving as a handbook of convenient reference for the use of the - cvorlcing astronomer in applying methods and fornlulae. lhe plan of the series has been suggested by the authors experience as a teacher at the Johns Hopkins Uni versity, and as an invest. igator. The first has led him to thc view that the wants of the student are best subserved by a quite elementary and condensed treatment of the subject, without any attempt to go far into details not admitting of immediate practical application. As an investigator he has frequently been impressed with the amount of time consumed id searching for the formulae and data, even of an elementary kind, which should be, in each case, best adapted to the work in hand. The most urgent want which the work is intended to supply is that of improved methods of deriving and reducing the positions. and proper motions of the fixed stars. Nodifications of the older methods are made necessary by the long period, 150 years, through which positions of the ahrs now have to be reduced, and by the extension of a tromctrica1 and statistical researches to a great and constantly increasing number of telescopic stars. Especial attention has therefore been given to devising the most expeditious and rigorous methods of trigonornetric reduction of star positions, and to the construction of tables to facilihte the work. Other features of the work arc A condensed treatment of the theory of errors of observation and of thc method of least squares an attempt to presentthe theory of astronornical refraction in a concise and elementary form witllout dctracting from rigour of treatment a new dovcloplncnt of the theory of precession, now rendered necessary by the long period through which star places have to be reduced the basing of formulae relating to celestial coordinates on the new values of the constants now used in the national ephernerides a concise developlrient of the rigorous theory of proper motions the trigonometric reduction of polar stars to apprent place, and the development of what the author deems the most advantageous methods of correcting and com bining observed positions of stars as found in catalogucs. Although the theory of astronomical instruments is not in cluded within the scope of the present work, it is necessary, in using star catalogues, to understand the inethods of deriving the results therein found from observations. The principles of the ideal transit instrument and meridian circle, omitting all details arising from imperfections of the instrument, nie elegant and simplc, and at the same tiine sufficient for the purpose in question. They are therefore briefly set forth in the chapter on deriving mean positions of stars from meridian observations. A pedagogical feature of the work is the ort to give objective reality to geometric conceptions in every branch of the subject. Ihe deduction of results by purely algebraic processes is therefore always supplemented, when convenient, by geometric construction. Whenever such a construction is represented on the celestial sphere, the latter is, in the absence of any reason to the contrary, shown as seen from the . centre, so that the figure shows thc sky as one actually looks up atit. Exceptions to this are some times necessary when planes and axes of reference have to be studied in connection with their relation to the sphere...