454 



NA TURE 



[September 7, 1893 



p. 895.) Science acknowledges no national allegiance, 

 but it is interesting to note that this series fails to show any 

 trace of the periodic change ; considering the smallness of the 

 quantity in question and the limited scope of the series this failure 

 proves nothing /TO or con. ^'et Admiral Mauchez expressed the 

 opinion that the fluctuations which the Germans had been attribut- 

 ing to changes of latitude were due to some other cause (C^ot/Zm 

 Rendtis, 1892, p. 862.) It is also noteworthy that the value 

 of the latitude found at this time is o'8" smaller than given by 

 the elaborate investigation of M. Galliot in 1879, in which he 

 employed 1077 observations by ten different observers. {Comptes 

 Rendus, vol. Ixxxvii. p. 684.) In this discussion an annual 

 period, having a semi-amplitude of o'2o" manifested itself 

 somewhat obscurely ; but M. Galliot placed on record his 

 opinion that this had its origin in some cause other than a 

 change in the latitude. 



We have seen how it came about that the reality of periodic 

 fluctuations in the earth's axis was placed beyond dispute. As 

 to the true nature and law of these fluctuations we should pro- 

 bably now be groping in darkness but for the services which Dr. 

 S. C. Chandler has rendered in the way of solving the mystery. 

 Before Dr. Chandler attacked the problem no one appears to 

 have called in question the applicability of Euler's theory to 

 the ca^e of the earth. The impression was indeed quite general 

 that the changes were for the most part of a fortuitous character, 

 produced by precipitation of rain and snow, by ocean currents 

 and aerial currents acting unequally in different hemispheres, 

 and therefore in so far as they might manifest a periodicity, this 

 would be annual in ils character. As early as 1876 Lord 

 Kelvin expressed the opinion .that the causes were some- 

 times sufficient to produce change of half a second in the course 

 of a year. (British Association Reports, 1876, Sections p. 11.) 

 It seemed therefore beyond question that any periodic change 

 must conform to the 305 day period of Euler, or to an 

 annual period, or a combination of the two. The latter 

 hypothesis was worked out very completely by Messrs. R. 

 Radeau {Comptes Rendus, vol. iii. p. 568) and F. R. Helmert 

 (Astronomische Nachtichten, vol. cxxvi. p. 217). 



Matters were in this condition when in 1891 Chandler 

 attacked the problem. The main features of this investigation 

 are given in a series of seven remarkable papers published in 

 the Astronomical Journal, written from time to time while the 

 work was still in progress, and when, as a matter of course, the 

 final result could not be known. Like Kepler, the author car- 

 ries us with him along the successive stage of the investigation, 

 we share with him his triumphs and disappointments, and rejoice 

 with him when well-merited success crowns his efforts. As to 

 his methods and purpose, these are given in his own words. 

 " I deliberately put aside all teachings of theory, because it 

 seemed to me high time that the facts should be examined by a 

 purely inductive process that the nugatory results of all attempts 

 to detect the existence of Eulerian period probably arose from a 

 defect of the theory itself; and that the entangled condition of 

 the whole subject required that it should be examined afresh by 

 processes unfettered by any preconceived notions whatever. . . . 

 The problem which I therefore proposed to myself was to see 

 whether it would not be possible to lay the numerous ghosts in 

 the shape of various discordant residual phenomena pertaining 

 to determinations of aberration, parallaxes, latitudes, and the 

 like, which had heretofore flitted elusively about the astronomy 

 of precision during the century ; or to reduce them to some 

 tangible form by some simple consistent hypothesis. ... It was 

 thought if this could be done, a study of the nature of the 

 forces as thus indicated by which the earth's rotation is 

 influenced might lead to a physical explanation of them." 



From May 29, 1884, to June 25, 1885, almost exactly thetime 

 covered by the observations of Kii^tner, at Berlin, Chandler was 

 observing at Cambridge with the Almucantar. The resulting 

 values of the latitude shared a progressive change, for which there 

 seemed no txplanation unless the change were that of the lati- 

 tude itself. At that time this seemed too radical an hypothesis, 

 so the results were printed as they appeared, leaving the expla- 

 nation to ihe future. The close agreement of Kiistner's results, 

 the verification by the subsequent work at Berlin, Pulkowa, 

 Potsdam, and Prague seemed to warrant the expenditure of the 

 labour involved in a thorough investigation of the entire ."subject. 

 He began with Kiistner's work at Berlin, the vertical circle ob- 

 servations of Gylden and Nyren at Pulkowa, and the precise 

 vertical observations of a Lyrae at Washington 1862-66. These 

 agreed in showing a period of 427 days. The examination of 



observations of circumpolar stars at Melbourne, and of Polaris 

 at Leyden, partially confirmed the result. 



Next came the observations of Bradley at Kew, Wanslead, 

 and Greenwich. Here a very puzzling j/henomenon appeared, 

 the period being only about one year, with an amplitude of 

 nearly an entire second. In discussing the observations of 

 Brindley at Dublin, made during the early part of the present 

 century, an opportunity occurred to wrestle, and that success- 

 fully, with one of the ghosts before referred to, viz., the singu- 

 lar results which Brindley had ob'.ained for the parallaxes of a 

 number of stars, and which led to an interesting discussion 

 between Pond and h-mself. 



Thus series after series was analysed with re-ults in the main 

 encouraging, frequently puzzling, and sometimes disappointing. 

 The law, if such existed, did not appear on the surface. The 

 secret could only be discovered by an elaborate analysis of the 

 material. Accoidingly, forty-five different series, extending 

 from 1837 to 1891, compri-ing more than 33,000 observations, 

 were examined, from which an empirical law w as deduced as 

 follows. 



The velocity of rotation of the pole was a maximum abont 

 1774, the period being about 348 days. Since then the velocity 

 has diminished at an accelerated rate, the period in 1890 being 



443 ''ays- . 



During the last half century the semi-amplitude has remaioM 

 sensibly constant at 0"22". 



Only three of the forty-five series examined, and these among 

 the least precise, intrinsically gave results contradictor; of l]ie 

 general law. The next step in the process was to analyse the 

 observations in a different manner, to discover whether the 

 deviations from the provisional law were real, also in what 

 manner the variations of the period were brought about. For 

 this purpose the results were tabulated chronologically at 

 twenty-day intervals, all reduced to the meridian of Greenwich. 

 As a result the real nature of the phenomenon was most dis- 

 tinctly revealed, and was as follows. 



The observed value of the latitude is the resultant cune 

 arising from two periodic fluctuations superposed upon eidl 

 other. The first of these, and in general the more con-iderable, 

 has a period of about 427 days, and a semi-amplitude of abiMt 

 o'i2". The secoi.d has an annual period with a range variaUe 

 between '04" and "20" during the Last half-century, Th'i man- 

 mum and minimum of this annual cbmp' nent of the variation 

 occur at the meridian of Greenwich about ten days before the 

 vernal and autumnal equimxes respectively, and it becomes 

 zero just before the so's'ices. 



As the resultant of these two motions, the variations of the 

 latitude is subject to systematic alterations in a cycle of seven 

 years' duration, resulting from the commensurability of ihe two 

 term'. According as they conspire or interfere, the total range 

 varies between two-thirds of a second at a maximum to but a 

 few hundredths of a second at a minimum. 



Accompanying the paper is a diagram showing the relation 

 between this theory and the observations of the fifty-four years 

 on which it is based. The agreement, at times almost perfect, 

 at other times shows deviations, apparently systematic, which 

 are perhaps due to imperfect knowledge of the constants, or to 

 erratic deviations of meteorological origin. 



Dr. Chandler finds the general outcome full of promise for 

 the astronomy of precision, showing that observations are free 

 from defects of a systematic character to a much greater extent 

 than has heretofore been supposed. 



As the results of which we have been speaking were an- 

 nounced from time to time they did not pass unchallenged. 

 The reality of the 427 day period was very promptly called in \ 

 question on account of its supposed conflict with dynamic laws. ^ 



Prof. Newcomb, who at first ranked as a sceptic, soon found 1 

 a very plausible explanation by assuming that the earth is not 

 a rigid body as required by Euler's theory. The question j 

 whether the earth as a whole should be regarded as a rigid ■, 

 body has long been more or less an open one. Certainly the ; 

 waters of the ocean introduce an element of mobility, but the 

 investigations of Lord. Kelvin and Prof. Darwin of the bodily ; 

 tides in a viscous spheroid when applied to the earth, gave ; 

 very little, if any, evidence of yielding in case of the latter to : 

 external foi'ces. 



Laplace had discussed with negative results the effect upon • 

 the earth's motion of the mobility of the ocean. (M.C., tome | 

 V. p. 76.) Euler's equations had been modified by l.iouville 1 

 for the case of a body which is slowly changing its form from , 



NO 1245, VOT. 48] 



