August 24, 19 16] 



NATURE 



531 



earth's surface by observations of the stars, we are in 

 crtect measuring the angular distance between the 

 axis of rotation of the earth and the vertical line, or 

 line through the zenith, at the point of observation. 

 If, now, this axis of rotation moves, the observed lati- 

 tude of the place will change, and if we prolong the 

 observations over a suthcient time, we ought to find 

 that this observed latitude fluctuates backwards and 

 forwards about a mean value with the same periodicity 

 as that in which the earth's pole of rotation moves 

 round the pole of figure. 



Every observer who is engaged in making observa- 

 tions to determine the precise positions of the stars, 



\ a class of observation which up to a few years ago 

 occupied a very large fraction of the time and energies 

 of astronomers, is actually continually determining 

 and redetermining the latitude of his instrument. 

 There is thus an enormous mass of latitude observa- 

 tions available for examination, and it should prove 

 a not too difficult task to analyse these with the object 

 of detecting a periodic variation. Two causes, how- 

 ever, militated against success in this inquiry : first, 

 the very small magnitude of this variation ; and, 

 secondly, the fact that the earth is by no means rigid, 

 and hence that the true period of the precessional 

 rotation differs very substantially from the Eulerian 

 period of 305 days. 



' All the earlier attempts to find evidence of this varia- 



tion were, in fact, hampered by this preconceived 



, notion of the ten-month period ; the observations were 

 carefully scrutinised with the view^ of detecting it, a 

 process, as we now see, foredoomed to failure. It 

 would be a useless task to recount here the various 



{ attempts that were made. Two of these, however, 

 I should not like to pass over without notice, those 

 of C. A. F. Peters, at Pulkowa, and Clerk Maxwell 

 in this country. 



Peters in his great and classic memoir on the parallax 

 of the fixed stars devoted one section to a discussion 

 on the variability of the latitude in a ten-month period. 

 He found that the actual variation derived from the 

 observations was of so minute a magnitude that it 

 was well within the limits of unavoidable sources of 

 error, and he therefore concluded that if there was 

 any separation of the two poles it was too small to 

 be detected by observation. 



Clerk Maxwell examined the Greenwich observa- 

 tions of Polaris in 185 1-4, and thought he found 

 some small indications of maxima at about ten-month 



j intervals, but he considered the results as very doubt- 



• ful, and that more observations would be required 

 to establish the existence of so small a fluctuation. 



Substantially the same result was derived by other 

 inquirers. Astronomers were therefore satisfied, up 

 to the year 1884, that the earth's axis of figure was 

 so nearly coincident with its axis of rotation that the 

 difference between the two was inappreciable to the 

 most refined observations. All methods of observa- 

 tion and all principles of the reduction of observations, 

 both of astronomers and of geodesists, were tacitly 

 based upon the idea of absolute coincidence between 

 the two axes. 



In 1884 the subject was independently reopened by 

 two men — Chandler in America, and Kiistner at Bonn 

 — and entirely fresh light was thrown upon it. Their 

 work was simultaneous and quite independent. I will 

 take Chandler's first. 



In 1884-5 ^^ took a thirteen-month series of observa- 

 tions at Harvard with an instrument of his own 

 devising, to which I will revert later. These observa- 

 tions showed a progressive change in the derived lati- 

 tude, which appeared to him of a greater magnitude 

 than could be accounted for bv any instrumental 

 errors. He, however, hesitated to ascribe it to a real 



NO. 2443, VOL. 97] 



change in the latitude without further confirmatory 

 observations, which he could not then make. He 

 therefore put these observations aside, and was, six 

 years later, drawn to re-examine them by the publica- 

 tion of some of Kiistner's results, which were also 

 only explicable on the hypothesis of an actual varia- 

 tion in the latitude of the place of obser\'ation. It 

 was, however, quite obvious to Chandler that his 

 series of observations contained no warrant for an 

 Eulerian period of ten months, and he therelore, to 

 quote his own words, "deliberately put aside all teach- 

 ings of theory, because it seemed to me high time 

 that the facts should be examined by a purely induc- 

 tive process; that the nugatory results of all attempts 

 to detect the existence of the 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 un- 

 fettered by any preconceived notions whatever." This 

 bold rejection of theory and appeal to observation 

 alone was rewarded with immediate success, and 

 Chandler was able to show that his observations of 

 1884-5 contained unmistakable evidence of the rotation 

 of the one pole about the other in a p>eriod of, not 

 305 days, but 428 days. Wherein, then, lay the de- 

 ficiency of Euler's investigation? As already hinted, 

 this arose from the assumption of rigidity, and it was 

 shown first by Newcomb, and afterwards, more com- 

 pletely, by Hough, that the 428-day period was fully 

 in accord with a degree of elastic yielding of the 

 earth quite consonant with probabilitv. Hough 

 showed that if the earth were as rigid as steel the 

 period would become 440 days; that the actual period 

 is somewhat shorter than this means that the earth 

 as a whole is decidedly more rigid than steel, a result 

 which accords perfectly with other known phenomena 

 which depend upon the earth's elasticity, such as the 

 rate of propagation of earthquake waves. 



Immediately following on this initial success 

 Chandler undertook a prolonged and most laborious 

 examination of old observations and reached results 

 which have not completely borne the test of subse- 

 quent review. He was confident that the whole move- 

 ment of the pole might be explained as the super- 

 position of two rotations, one circular, with a 428-day 

 period, and one elliptical, with a period of a year. 

 He thought, further, that there was evidence that the 

 longer period had varied in past times, and that in 

 1770 it was less than a year. This last result was 

 traversed by Newxomb, who showed its extreme im- 

 probability. While fully bearing in mind the lessons 

 of past experience as to the unwisdom of relying too 

 closely upon pure theory, we cannot resist the con- 

 clusion that to accept any large change in the 428-dav 

 period within recent years would be to set aside the 

 whole dynamical justification for accepting this period 

 as a reality, it being quite impossible to admit that 

 the elastic constants of the earth can be subject to 

 any appreciable alteration within such time as a 

 century or so. 



As regards an annual period, we should now prefer 

 to say that, while there are doubtless seasonal trans- 

 fers of material upon the earth, such as the accumu- 

 lation and melting of Arctic ice, which may produce 

 a movement of the pole with an approach to a vearlv 

 periodicity, the part of the movement due to a true 

 annual period is very small, and is quite masked bv 

 large; irregular disturbances. We shall be on safe 

 ground if we say that the observed polar motion is 

 compounded of a precessional rotation in a period of 

 something very near 428 days at an average distance 

 of 20 ft. from the mean pole, with an irregular move- 

 ment superimposed on it ; this irregular movement 

 having sometimes the effect of mcdifv^ng the nte of 



