November 3, 1923] 



A'A TURE 



645 



disproved by Prof. .Vndoyer's work, of which the first 

 volume is now published. The author is not only an 

 accomplished mathematician, whose official position 

 places him in direct contact with the work of astronomi- 

 cal computation on the widest scale, but he is also one 

 who has displayed an altogether exceptional faculty 

 in the arid task of calculating mathematical tables. 

 He is therefore in an excellent position to make an 

 instructive contribution to the subject of celestial 

 mechanics, and his work will be received with gratitude. 

 The present volume is largely concerned with the 

 theory of the determination of orbits. This may 

 suggest comparison " with several classical works on 

 that subject. But the treatment it receives here is 

 distinguished by its manner of combining two distinct 

 points of view. The practical nature of the problem is 

 always insisted on, and the needs of the astronomical 

 computer are served by numerical examples drawn 

 from actual practice. At the same time the subject 

 is treated not as a mere precursor, but as an integral 

 part of celestial mechanics. Thus the points of 

 fundamental importance receive a much more critical 

 discussion than has been usual in those treatises which 

 have a more restricted practical outlook. A short 

 digression on the method of least squares is inserted 

 for the determination of a Keplerian orbit based on any 

 number of observations, and a more elaborate section 

 on the theory of interpolation leads up to the calcula- 

 tion of perturbations by numerical quadratures under 

 several forms. 



The volume concludes with two chapters, one 

 developing the series relative to elliptic motion and 

 the other dealing with the expansion of the disturbing 

 J function, as required in the theory of the major planets. 

 The second volume, which will complete the work, 

 will deal with the theory of the moon, the rotations 

 of the earth and of the moon, and the theory of the 

 Galilean satellites of Jupiter. The whole will form a 

 very valuable contribution to a subject of which the 

 interest, being many-sided, will not easily be exhausted. 

 (2) Prof. Andoyer's " Cours d'astronomie," of 

 which the first volume now -appears in a considerably 

 modified form, has reached its third edition. To this 

 sufficient evidence that it has met with a favourable' 

 reception in France, it may be added that it is an 

 excellent example of the class of work to which it 

 belongs. Its subject is what is generally known in 

 P>ngland as spherical astronomy, though geometrical 

 astronomy would be a more appropriate name with 

 proper regard to its matter and its methods. The 

 function of such works is to provide for the student, 

 who already possesses the necessary mathematical 

 equipment, an avenue to an exact knowledge of 

 astronomy, apart from any deep acquaintance with 



NO. 2818, VOL. I 12] 



celestial mechanics. Thus the contents of the present 

 volume may be summarised under its four sections. 

 The first book provides an introduction to spherical 

 trigonometry and spherical co-ordinates in general. 

 The second introduces the usual systems of astronomical 

 co-ordinates and time, and explains the reductions for 

 refraction, parallax, and aberration. Precession, nuta- 

 tion, and time form the main subjects of the third book, 

 which begins with an outfine of the ideas of dynamical 

 astronomy ; a complementary chapter on the deter- 

 mination of an orbit from three observations 

 (Lagrange's method) might be transferred from the 

 end of the volume, if indeed the inclusion of this 

 chapter can be justified at all. The fourth and last 

 book deals very fully with the calculation of eclipse 

 phenomena, and the volume ends with a note on the 

 ecclesiastical calendar. It will be seen that these topics 

 mainly follow familiar lines of choice, and, as would 

 be expected from the author, the treatment is through- 

 out sound and scholarly. 



Rightly or wrongly, we approach this work from the 

 point of view of the general mathematical student 

 rather than of the professional astronomer. The 

 latter, as a specialist, must be prepared to dig deep 

 for his knowledge. The former will find here a selection 

 of fundamental problems treated with fullness and 

 academic elegance. Whether such a work will inspire 

 him with a true and abiding interest in astronomy 

 appears more doubtful. The author is probably 

 addressing himself to a more advanced type of student 

 than we have in mind, and nothing could be more 

 unjust than to express disappointment with a work on 

 the ground that it does not fulfil a purpose which was 

 never intended by the writer. There is, however, 

 room for an introduction to astronomy addressed to 

 the mathematician who has no professional aim in the 

 science, and for the ideal book of this kind we may 

 still have long to wait. 



(3) Dr. Frischauf's work has also reached a third and 

 enlarged edition, but in this case the first edition 

 appeared more than fifty years ago. This vitality it 

 owes to genuine merit, for in a short compass it has 

 provided a succession of German students with a 

 concise and lucid introduction to the problems involved 

 in the determination of orbits. The elementary 

 section on Keplerian motion follows closely the lines 

 of the Theoria Motus, and the practical methods which 

 are then explained are those of Olbers for the parllbolic 

 orbit and of Gauss for the elliptic orbit. The outlook 

 is thus in a sense restricted, though the modifications 

 introduced by Gibbs are explained and some indication 

 is given of the method of calculating perturbations 

 by mechanical quadratures. But the distinguishing 

 feature of the work lies in its historical sections, which. 



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