30 Astronomy 



The libraries of the British Museum, the India Office, and the Bodleian are 

 particularly rich in Persian manuscripts of Ulugh Beg. The present work em- 

 braces the results of Mr. Knobel's investigation of 23 or 24 Persian and Arabic 

 manuscripts, including three manuscripts partly collated by Dr. Peters in Paris. 

 The object has been to make the work as exhaustive as possible, but it is regretted 

 that the war has prevented a complete collation of the manuscripts possessed 

 by the Bibliotheque Nationale at Paris. 



No. 161. MOULTON, F. R., in collaboration with DANIEL BUCHANAN, THOMAS BUCK, 

 FRANK L. GRIFFIN, WILLIAM R. LONGLEY, and WILLIAM D. MAC- 

 MILLAN. Periodic Orbits. Quarto. In press. 



A large part, though not all, of the periodic orbits treated in this book belong 

 to the problem of three bodies. The first chapter contains certain theorems on 

 implicit functions, the solutions of analytic differential equations, and a new treat- 

 ment of linear homogeneous and non-homogeneous differential equations having 

 periodic coefficients. The second contains a treatment of elliptic motion by the 

 methods which have more general application. This is the simplest astronomical 

 problem in periodic orbits. Certain additional methods are illustrated in the third 

 chapter on the spherical pendulum, with new developments of certain elliptic func- 

 tions. The fourth chapter treats of periodic motion about an oblate spheroid with 

 applications to the motion of Jupiter's fifth satellite. The fifth chapter is devoted 

 to a complete discussion of oscillating satellites in both two and three dimensions, 

 in the case in which two of the bodies are finite and moving in circles, while the 

 third is infinitesimal, and in which the centers of libration are collinear with the 

 finite masses. Chapter VI is a treatment of the same problem by another method 

 having important advantages in certain cases. Chapter VII is a discussion of the 

 problem when the finite bodies move in elliptical orbits. Chapter VIII is a gen- 

 eralization of Lagrange's collinear solutions of the problem of three bodies to the 

 general case of n bodies. Chapter IX is that of Chapter V for the equilateral 

 triangular points of libration. Chapter X treats of the motion in the case in which 

 two masses are equal, the third infinitesimal or finite, and the three always occupy- 

 ing the vertices of an equilateral triangle. Chapter XI treats of satellites and in- 

 ferior planets with application to the lunar theory. Chapter XII treats of superior 

 planets. The problem of Chapter XIII is similar to that of Chapter XI, except that 

 there are four or more bodies. Chapter XIV treats of the orbits of many small 

 masses revolving around one large one. In all cases the existence of the periodic 

 solutions is proved, methods of practically constructing them are given, and 

 numerical illustrations are often added. 



No. 247. BARNARD, E. E. An Atlas of the Milky Way. Quarto, 40 plates. In presi. 



