SCIENCE. 



S57 



SCIENCE: 



A Weekly Record of Scientific 

 Progress. 



JOHN MICHELS, Editor. 



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SATURDAY, NOVEMBER 26, 1881. 



THE SATELLITES OF MARS. 

 The outer satellite of Mars was seen here on Nov. 

 15th, and by an observation of Nov. 20th its position 

 was 



WASHINGTON, M. T. 



h. m. p. s. 

 1881. Nov. 20, 13 15, 71°. 7, 45 ".6. 



This satellite is therefore neai the predicted place. 

 An hour later Phobos seemed to be visible, also near 

 the computed position, but the sky had become a 

 little thick and I could not be certain of seeing this 

 satellite. 



The planet will continue to approach the earth un- 

 til December 21, and the satellites will become bright- 

 er. It is possible, therefore, that they may be observed 

 for nearly two months during the present opposition. 



A. Hall. 



Washington, D. C, Nov. 22, 1881. 



THEORY OF THE MOON'S MOTION* 

 About a year ago the Vice-President of the Physi- 

 cal Section of our chief scientific association remarked, 

 in his farewell address : " there are many subjects in 

 astronomy that need investigation, but in most cases 

 the labor required is very great, and the completion 

 of the work would occupy a long time. * * * 

 The lunar theory has been a vexed question for the 

 last two centuries, and may remain so for a long time 

 to come." If persistent, painstaking, and conscien- 

 tious effort have aught to do with such a matter, we 

 must add to the list of distinguished lunar theorists, in- 

 cluding Plana, Damoiseau, Hansen, and Delaunay, the 

 name of Stockwell. We cannot say that his researches 

 have yet met with that notice to which they are perhaps 

 rightly entitled. Mr. Stockwell has published a num- 



* John N. Stockwell, Ph. D. (Introductory.) 



ber of monographs on many points connected with the 

 lunar theory during the last six or seven years ; and 

 his works show great familiarity with, and expertness 

 in, the involved computations of this sort of astrono- 

 mical research. 



If we may judge from the appearance of the 

 pamphlet before us, Mr. Stockwell has now quite ter- 

 minated his lunar investigations, and intends to com- 

 plete the publication of his finished theory of the 

 moon's motion at some early date. In his Introduc- 

 tion he has sketched the early historic development of 

 the question with that explicitness which we should 

 expect rather to have seen in some thorough elemen- 

 tary text-book ; strangely, he devotes twice as much 

 space to the ante-Newtonian aspect of the problem as 

 to the most remarkable developments of the mathe- 

 matical theory which have occurred since his time. 

 He makes no mention of Damoiseau, who takes high 

 rank not only among pure lunar theorists, but among 

 the constructors of tables of the moon. His tables 

 are well known to have been the first ever constructed 

 from pure theory. 



Though the age of the great lunar investigators is 

 now gone, there are some very surprising results of 

 Mr. Stockwell's " new method of analysis " to which the 

 attention of the few theorists now working at the moon's 

 motion might well be directed. He instances several 

 comparisons of the values of his co-efficients with 

 those obtained by Delaunay in his very refined devel- 

 opment; in one case he obtains, by a rapidly-converg- 

 ing series of four terms, a result identically the same 

 with that of Delaunay's series of seven terms; and re- 

 marks, " the four terms of my development are more 

 accurate than the seven terms of Delaunay's, since the 

 seventh term of the latter series is thirty times greater 

 than the fourth term of the former." There is noth- 

 ing new in the fact that the sum of a very small 

 number of terms should come out equal to a very 

 large series, but if theorists can be brought to 

 acknowledge the essential accuracy of the " new 

 method," Mr. Stockwell must no doubt be credited 

 with effecting an enormous advance in mathematical 

 astronomy. Mr. Stockwell has shown satisfactorily 

 to himself the correctness and value of his method, 

 and the facility of its application — he must now 

 address himself to the equally difficult task of making 

 others see it in the same light. 



It seems a wholesale assertion on the part of Mr. 

 Stockwell that there are " several terms of considera- 

 ble magnitude in the theories of La Place, Plana, 

 Pontc'coulant and Delaunay, which are not functions 

 of the disturbing force •" and we should, at first blush, 

 be inclined to place much confidence in his demon- 

 stration that the general integral assumes the indeter- 

 minate form in special cases which occur in those 

 theories. It is certainly a most important oversight, 

 and leads us to believe that the lunar theorists who 

 followed La Place would have done much better to 

 have built up theories of their own with entire inde- 

 pendence of what anyone else had done. It is a re- 

 markable fact if this discovery has been left for Mr. 

 Stockwell to make. He concludes : " if the compu- 

 tations of the present work are correct, astronomers 

 I have carried their approximations to terms of the fifth. 



