194 



NA TUBE 



[June 27, 1907 



In the first line of p. 2j " position " is obviously a 

 misprint for " composition," and there are a con- 

 siderable number of such slips throughout the work. 



A fairly full " contents list " is given, but the book 

 would have been more useful if a comprehensive index 

 had been provided. T. A. H. 



THE WORKS OF C. F. GAUSS. 

 Carl Fricdrich Gauss Werke. Siehenter Band. 

 Herausgegeben von der Kon. Gesellschaft der 

 Wissenschaften zu Gottingen. Pp. 650. (Leipzig : 

 B. G. Teubner, 1906.) Price 30 marks. 



THIS volume contains a reprint of Gauss's prin- 

 cipal astronomical work, the " Theoria Motus 

 Corporum Ccelestium," and his unpublished re- 

 searches on planetary perturbations and on the lunar 

 theory. In 1871 the late Prof. Schering brought out 

 a "volume vii." without the cooperation of the 

 Gottingen Academy of Science, containing the 

 " Theoria Motus " and some notes from Gauss's 

 papers ; but for the sake of uniformity the academy 

 considered it desirable to include the " Theoria " in the 

 present volume, which has been edited by Prof. Bren- 

 del, of Gottingen. 



A careful revision of the original edition of 1809 

 brought a few corrections to light, and a re-com- 

 putation of the examples with modern tables of 

 logarithms revealed a number of errors of one or two 

 units of the seventh decimal (caused probably by the 

 absence of decimals in the proportional parts of the 

 old tables) which sometimes gave rise to greater 

 errors in the course of the computation. A list of 

 these corrections is given. Some notes found in 

 Gauss's own copy of the book are added in footnotes. 

 Next follow various notes on elliptic and parabolic 

 motion, partly already published, partly extracted from 

 letters and note-books. Of these the most important 

 is a table for computing the true anomaly in a para- 

 bolic orbit; it was to have formed part of a supple- 

 ment to the " Theoria Motus," dealing with the orbits 

 of comets, which never was written. 



The discovery of the first of the minor planets, 

 Ceres, had obliged Gauss to work out a general 

 method of computing an elliptic orbit. The next step 

 was to determine the perturbations of the motion of 

 Ceres and Pallas, which, particularly in the case of the 

 latter, necessitated new methods owing to the great 

 eccentricity and inclination; and on this work Gauss 

 spent a great deal of time in the years 1802 to 1817. 

 In 1805 he worked out a new method of computing 

 the general perturbations by the variation of the ele- 

 ments, but he never published anything on the sub- 

 ject. The method is essentially the same as that 

 proposed bv Hansen in 1S43 in his paper on absolute 

 perturbations in orbits of any eccentricity and inclin- 

 ation. 



The present volume first gives letters and com- 

 putations on Ceres, after which follow 200 pages 

 devoted to Pallas. Special perturbations by Jupiter 

 for the years 1803-1811 were computed in 1810 and 

 181 1, first for intervals of fifty days, after which the 

 ■work was repeated with periods of 500 days, the 

 NO. 1965, VOL. 76] 



elements for each period being taken from the first 

 computation. The memoir on the theory of general 

 perturbations was written in French, about the 

 year 1815, apparently in answer to a prize question 

 of the Paris Academy, but never finished. In 181 1 

 Gauss began the immense labour of computing the 

 action of Jupiter on Pallas, and finally, with the aid 

 of Encke and Westphal, completed the work by the 

 preparation of tables. The perturbations by Saturn 

 were computed by N'icolai, and this work is preserved 

 at the Heidelberg Obsen-atory; it has naturally nv' 

 been included in the present volume, but hopes av 

 held out that it may be published elsewhere. Finally 

 the last part of the whole work, the action of Mar- 

 was taken in hand, but owing to the press of othi r 

 work it was never completed. It is much to be re- 

 gretted that this fine piece of work, involving an 

 enormous amount of computation, has been unknown 

 until now, and that not even so interesting a result 

 as the increase of the assumed mass of Jupiter wn~ 

 published. Already in 1814 Gauss found from th 

 first nine oppositions of Pallas that Laplace's value 

 I : 1067.09, should be increased to i : 1042-86, a result 

 which differs but little from the most recent deter- 

 minations. If known to Encke, this correction of the 

 mass would have prevented the errors of 5' in the 

 computed geocentric places in 1834, caused by the 

 near approach to Jupiter in 1832 {.4str. Nachr., No. 

 332). Needless to say, the remarkable commensur- 

 ability of the mean motions of Jupiter and Pallas was 

 noticed by Gauss at an early date. 



It appears from letters written to Hansen and Bessel 

 in 1843 that Gauss bitterly regretted having laid this 

 great work aside. Thanks to the skilful editorship 

 of Prof. Brendel, whose task of arranging and inter- 

 preting a vast mass of papers must have been a very 

 difficult one, the work is now accessible in a clear 

 aiid convenient form, and it is to be hoped that some 

 competent hand will complete it. 



Lastly, the volume contains the beginning of a 

 lunar theory, dating from the second half of iSoi. 

 but soon abandoned, probably because vol. iii. of 

 Laplace's " Mt^canique Celeste " came out in the fol- 

 lowing year, and seemed to make work on the motion 

 of the moon unnecessary at that moment. The form 

 in which the perturbations are given is similar to 

 that of Plana (1832). 



Vols. viii. and ix. of the collected works of Gaui 

 have already appeared, .\ tenth and concludin 

 volume is announced, which is to include a general 

 index. J. L. E. D 



NATURE AND FLORAL DESIGN 

 Flowers and Plants for Designers and Schools. By 

 Henry Irving and E. F. Strange. Pp. 95. 

 (London : Hodder and Stoughton, 1907.) Prtce 

 10.S. 6d. net. 



IF designers could be produced by the study of 

 books upon plant form there ought to be a 

 large and flourishing crop of them, since so many 

 elaborate works have appeared on this subject 

 addressed to the supposed needs of such artists. 



4 



II 



