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SCIENCE. 



[N. S. Vol. III. No. 62. 



science of astro-meclianics is started by 

 Newton, that of thermal conductivity re- 

 ceives its first treatment, at the liands of 

 Fourier, more than a century later. In ad- 

 dition to these two causes, ever since the 

 discovery of the telescope the application of 

 optical means to the discovery of whatever 

 might be found in the heavens has always 

 had a fascination for mankind. And, as 

 the ability to coordinate and correlate the 

 facts observed much enhances the enjoy- 

 ment of scientific occupation, it has resulted 

 that many who began as observers ended 

 as mathematical astronomers. Thus our 

 science has had relatively a large number 

 of cultivators. 



A thoroughly satisfactory history of our 

 subject is yet to be written. We have 

 only either slight sketches of the whole, 

 or elaborate treatments of special divisions 

 of the science, and none of them coming 

 down to recent times. Among the former 

 may be mentioned Gautier's Essai historique 

 sur le problhne des trots corps, which appeared 

 in 1817. Also Laplace's historical chapters 

 in the last volume of the Mecanique Celeste. 

 Todhunter's History of the theories of at- 

 traction and the figure of the earth is an 

 example of the latter class. Such books as 

 Todhunter's — of which Delambre has given 

 an earlier example in his Histoire de I'Astron- 

 omie — can hardly be regarded as history ; 

 they resemble rather extensive tables of 

 contents of the literature examined, accom- 

 panied by short comments. However, in 

 many cases, they are more useful to the 

 student than formal histories would be, as, 

 when judiciously compiled, they may, as 

 epitomes in our libraries, take the place of 

 a large mass of scientific literature. The 

 History of Physical Astronomy, by Robert 

 Grant, is a book that comes down to 1850, 

 and professedly covers the whole of our 

 subject. But only one- third of this book is 

 devoted to astro-mechanics, the rest dealing 

 with what is reallv observational and de- 



scriptive astronomy. Moreover, the author 

 indulges so much in diffuse veins of writing, 

 that but a small fraction of the 200 pages 

 is really given to purely historic statement. 

 As far as the lunar theory is concerned, 

 the third volume of M. Tisserand's Traite 

 de Mecanique Celeste constitutes a fair history. 

 But it must be borne in mind that the 

 author's plan is to notice only the disquisi- 

 tions having a first-class importance; hence 

 his history is incomplete in this respect. 



In America we are not well situated for 

 investigations of this character, on account 

 of the meagerness of our libraries. Of no 

 inconsiderable number of memoirs and even 

 books, having at least some importance in 

 our subject, there exist no copies in the 

 United States. Hence, should an American 

 be inclined to undertake the task of writing 

 the history of our subject, he must at least 

 perform some of the work abroad. 



In the present discourse it is proposed to 

 touch very lightly the more important steps 

 made since the middle of the century, the 

 time at our disposal not admitting fuUer 

 treatment. 



And first we will take up Delaunay's 

 method, proposed for employment in the 

 lunar theory, but quite readily extended to 

 all classes of problems in dynamics. The 

 first sketch of this method, given of course 

 by the author himself, appeared in the 

 Comptes Rendus of the Paris Academy of 

 Sciences, in 1846. It professes to be merely 

 an extract from a memoir offered for publi- 

 cation in the collections of the Academy, 

 which must, however, have been afterwards 

 withdrawn to make place for the two vol- 

 umes of the Theorie du Mouvement de la I/une. 

 When this extract is compared with the 

 earlier chapters of the latter work, it is per- 

 ceived that Delaunay has, to some extent, 

 modified and improved his method in the 

 interim between 1846 and 1860. In this 

 long period nothing appeared from the 

 author on this subject. He must have been 



