204 



NATURE 



[October 14, 1920 



work, but also undertook the expense of printing: 

 the tables, which accordingly were ready for dis- 

 tribution in 1857. As his earliest researches on 

 the subject were published in 1829, it may be 

 taken that the work filled the main part of 

 Hansen's life for a period of about thirty years. 



No excuse is needed for recalling these circum- 

 stances at the moment, sixty years later, when 

 Hansen's tables are on the point of being finally 

 superseded. They are not faultless, it is true, and 

 for many years past certain corrections introduced 

 by Newcomb have been adopted in the national 

 ephemerides. But, on the whole, they have 

 served the practical needs of two generations ad- 

 mirably. In Hansen's theory, on which the tables 

 are based, the number of periodic terms had 

 grown to about three hundred. Those which 

 depend on the solar action were for the most part 

 well determined, but those which arise from 

 planetary action were neither complete nor ac- 

 curate. It is but fair to remember, however, that 

 in previous tables the latter class of terms had 

 been ignored altogether. Considered purely as 

 tables in the technical sense, Hansen's possess 

 acknowledged merits. As a practical computer 

 himself, he had the advantage of great experience 

 and exceptional natural gifts. It is said that in 

 a matter of four-figure logarithms he rarely had 

 need to refer to the tables. 



But during the later stages of his researches 

 Hansen was not the only worker on the large 

 scale in the field of lunar theory. Some ten years 

 earlier Delaunay had begun the construction of 

 a theory in purely algebraic form by an original 

 method of integration, and by 1867 that part 

 which depends on the direct action of the sun had 

 been completed and published. His intention had 

 been to add those complementary parts which still 

 remained necessary and to proceed to the reduc- 

 tion of the whole to a numerical and tabular form. 

 This was not to be. Historical events supervened 

 and delayed the progress of the work. Then in 

 1872 he lost his life by drowning, and his life's 

 work, which had always been pursued without 

 assistance, came to an untimely end. Yet his 

 projects were destined to be accomplished by 

 other hands. The planetary inequalities were 

 calculated by Radau in an admirable memoir, and 

 under his direction the reduction of Delaunay's 

 theory to tabular form was completed before the 

 death of Radau in 191 1. From 1915 the lunar 

 ephemeris in the " Connaissance des Temps " is 

 based on these tables. Prof. Brown remarks justly 

 that the value of the purely algebraic development 

 is not seen at its best in the numerical form, owing 

 to the slow convergence of certain classes of co- 

 efficients. He also criticises the form of the tables 

 NO. 2659, VOL. io6a 



but this is a matter which will chiefly concern 1 

 the French computer, and need not affect our ' 

 appreciation of an independent lunar ephemeris. 

 The value of Delaunay's method is not confined 

 to his own application of it to the lunar theory. 

 But even this can be no ordinary work, which, 

 executed within a few years of Hansen's, assumes 

 a new vitality after lying dormant for half a 

 century. 



The new tables of Prof. Brown will be used for 

 the first time in the Almanacs of 1923, and a coo- 

 fident hope may be expressed that they will con- 

 tinue in use for a very long time to come. They 

 are the final outcome of thirty years' work, and, 

 long as this time is, Prof. Brown is to be con- 

 gratulated equally on the rapidity and on the 

 thoroughness of his labours. For the number of 

 terms now included falls little short of 1500, and, 

 so far as can be now seen, the expression of the 

 effects of purely gravitational action cannot pro- 

 fitably be pushed further. hW. this work, which 

 is completely new from the beginning, was not 

 contemplated as an integral plan from the start, 

 but grew by successive stages, as Prof. Brown 

 tells us, out of a suggestion by Sir G. H. Darwin 

 to make a study of Hill's papers. The preparation 

 of the theory, which was published in the Memoirs 

 of the Royal Astronomical Society, was finished 

 in 1908, and the liberality of Yale University in 

 undertaking the whole cost of the tables made it 

 possible to proceed with plans for the final stage 

 without delay and without anxiety. Thus the 

 author has been spared some of the cares which 

 fell to the lot of Hansen. None the less, the 

 British Admiralty has once again played a small 

 part in the matter, though in a different way. 

 With proofs and MS. continually crossing the 

 Atlantic during the war, it is recorded that only 

 one set of returning proofs was lost. 



It is unnecessary to recall the details of the 

 author's theory. Hill, to whom its foundations 

 are very largely due, was, like Hansen, a prac- 

 tised computer. Though his researches in this 

 field have incidentally enriched celestial mechanics, 

 and even mathematics in general, with new and 

 fertile conceptions, his motive was essentially a 

 practical one. It was to find a path which would 

 lead to the highest possible accuracy in the final 

 results with the greatest economy of labour. The 

 soundness of his ideas can be properly tested and 

 appreciated at no stage short of the fulfilment 

 which Prof. Brown has given to them in this great 

 work. There can be no doubt not only that 

 Prof. Brown has accomplished a worthy and most 

 valuable task, but that he has also with equal 

 judgment employed in the course of it the best 

 available methods. ♦ 



