316 



SCIENCE 



[N. S. Vol. XXXVI. No. 923 



terested in the computational field of astron- 

 omy. 



A second edition, rewritten and enlarged 

 under the editorship of Professor Buchholz, 

 appeared in 1899 ; and the third edition, edited 

 again hy Professor Buchholz, has grown by 

 the addition of one hundred and fifty pages to 

 such large proportions that the volume is both 

 bulky and heavy. An eleven-hundred-page 

 book can not be handled conveniently, and a 

 continued use of the book will put its binding 

 to a severe test. The press-work is all that 

 could be desired and the diagrams are excel- 

 lent. 



The computational field of astronomy — per- 

 haps we might say the book-keeping, or 

 auditing department — has for some peculiar 

 reason appropriated the title of " theoretical 

 astronomy." It is not peculiarly theoretical; 

 rather it is the link which binds together the 

 worker in celestial mechanics and the observ- 

 ing astronomer. To the observing astronomer 

 it brings the results of theory; and as the ob- 

 serving astronomers are the " practical " as- 

 tronomers, and are the more numerous, per- 

 haps this misnomer can be charged to them. 

 At any rate, a science so old and so exact as 

 astronomy should be a little more careful with 

 its titles. The " practical " astronomers are 

 no more practical than other astronomers, and 

 the computing astronomer has no monopoly 

 of the theoretical aspect of the subject. And 

 so we warn the uninitiated not to anticipate 

 in this book an account of that delightful 

 body of theory which constitutes the science 

 of astronomy. It is, on the contrary, an ex- 

 haustive treatise by an auditor explaining in 

 detail the best methods of making up the as- 

 tronomical accounts. 



The subject matter of the volume is divided 

 into nine parts and subdivided into one hun- 

 dred and thirty-three " Vorlesungen." The 

 topics treated are : I., Calculation of the Posi- 

 tion of a Celestial Object from its Orbital 

 Elements; II., Calculation of an Orbit from 

 Given Observations; III., Determination of 

 the Parabolic Orbits of Comets ; IV., Determi- 

 nation of Elliptic Orbits; V., Determination 

 of Elliptic Orbits from Four Observations, 



Only Three of Which are Complete; VI., On 

 Mechanical Quadrature and the Methods of 

 Special Perturbations; VII., Calculation of 

 an Orbit from Many Observations According 

 to the Methods of Least Squares; VIII., Cal- 

 culation of Double Star Orbits; IX., On the 

 Determination of the Orbits of Meteors; 

 Supplement I., Tables; Supplement II., 

 Leuchner's Method of Computing Orbits. 



The principal additions which have been 

 made since the second edition are contained 

 in Part IV., in the tables, and in Supplement 

 II., all of which relate to Leuschner's method 

 of computing orbits. Of the three essentially 

 distinct methods of computing orbits, viz., 

 the methods of Gauss, Laplace and Gibbs, the 

 one of Gauss, with various modifications, has 

 been the one generally employed. The method 

 of Laplace contained computational difficul- 

 ties which have precluded its use. 



Recognizing the theoretical advantages of 

 Laplace's method, and also its computational 

 disadvantages, Professor A. O. Leusehner, of 

 the University of California, has given a 

 great deal of study to its improvement. As a 

 result of his work he has evolved a method 

 which he has designated " The Short Method " 

 (an unfortunate title for various reasons). 

 Leuschner's method, with the aid of the tables 

 he has constructed for it, is decidedly prac- 

 tical, and we are glad to see an adequate ac- 

 count of it given in this new edition of 

 Ivlinkerfues's " Theoretische Astronomic." 



We look in vain, however, for a valuable 

 improvement to Gauss's method given in 1901 

 by Professor F. E. Moulton, of the University 

 of Chicago.' After the heliocentric distances 

 have been determined there are difficulties, 

 both theoretical and practical, according to 

 Gauss, in the determination of the elements 

 a, e, 10. Not only is the method of Professor 

 Moulton theoretically more direct than that 

 of Gauss but it is computationally much more 

 simple; moreover, it makes no assumption as 

 to the species of the conic. 



In the way of a minor error we notice that 

 the formula for parabolic orbits, 



' Astronomical Journal, No. 510. 



