462 



NA TURE 



[September 6, 1900 



Period in days. 



Observed 



Computed 



Under 390 ... 020 ... 020 



390-420 ... 018 ... o"i9 



420-450 ... 015 ... 0-13 



Over 450 ... O'lo .. 008 



This statement in itself constitutes a proof of my assertion, 

 and renders it unnecessary for me to add anything further on 

 this point. Any one who cares to plot down the values for the 

 periods given by Dr. Chandler must arrive at the conclusion 

 that the comparison of the curve so obtained, with the magnetic 

 and auroral curves, gives indeed a convincing argument in 

 favour of the earth-magnetic hypothesis. 



I have next to consider the changes in the values of the obliquity 

 as observed at Greenwich due to the eleven-years period of solar 

 activity. 



In my paper, A.N. 3619, I have discussed fully the reduction 

 of these values to a uniform and homogeneous system, as well as 

 the elimination from them of the secular variation and the 

 influence of the "great" sun-spot and aurora period. The 

 resulting curve (Fig. i, curve 2) exhibits the utmost conformity 

 with those of the earth-magnetic and latitude phenomena. 



This fact is of the highest significance, inasmuch as it affords 

 added testimony to the accuracy of the data on which my 

 research is founded. The curves communicated show that at 

 times, when the amplitude of latitude-variation reaches maximum 

 values (i^ years after minimum displays of magnetic dis- 

 turbance), the Greenwich obliquity attains small values ; while 

 at times, when the amplitude is at a minimum (i| years after 

 maximum displays of magnetic disturbance), the obliquity appears 

 to be excessively great. This leads at once to the conclusion 

 that whenever the amplitude is great, the minimum latitude for 

 the Greenwich meridian must occur near the time of the winter 

 solstice, and that when the amplitude is small just the reverse 

 •ought to take place. Now Dr. Chandler's statistics in A.J. 277 

 afford ample means of testing this conclusion. In point of fact 

 they show that at times of maximum amplitude the epochs of 

 minimum latitude for the Greenwich meridian have always 

 occurred on some date between the beginning of November and 

 the end of February, while at times of amplitude-minima these 

 epochs, with the exception of the first in 1840, are comprised 

 within the interval from May to August. The mean date in the 

 former case is January 10, and in the latter July 16; and the 

 mean deviation of a single epoch from these two dates is not 



> more than about + 40 days. 



I consider that, in spite of the great uncertainty which 



> naturally attaches to researches of so delicate a character, the 

 ■evidence afforded by these results is to be taken as a proof 

 that the residuals in the obliquity, far from being accidental, 



. are really caused by latitude-variation. Thus, owing to the 

 great extension of the series of Greenwich solar observations, 

 these residuals form an excellent test of my assertion that the 

 motion of the pole depends on 'the intensity of the earth- 

 magnetic forces. 



As regards the corrections to the right-ascensions of the 

 stars derived from Greenv/ich observations of the sun, I need 

 -.only state that after subtracting the secular variation found by 

 Mr. Thackeray {M.N. June 1896), the resulting values give 

 curve 3 of Fig. i, which, in spite of somewhat large accidental 

 discrepancies, is in general agreement with all the others, 

 especially with that of the obliquity. 



Having thus shown that my contention with regard to a con- 

 nection between the eleven-years period of auroral displays 

 and magnetic disturbances and the motion of the earth's pole 

 of rotation appears to be borne out by all the facts which con- 

 stitute the sum of our present knowledge of the peculiar pheno- 

 mena relating to latitude-variation, I next consider the "great" 

 period of aurorae, which, as already stated, is synchronous with 

 the great period of solar activity. 



For this purpose I exhibit in Fig. 2 curves showing the great 

 aurora-period according to Loomis' annual numbers, and the 

 great spot-period in Wolf's relative numbers. 



The interval comprised by this great period is according to 

 Wolf equal to six small cycles, i.e. sixty-six years. Now this 

 lis exactly the period of Dr. Chandler's long inequality of latitude- 

 variation. The smallest amplitudes and greatest periods of 

 liatitude-variation, according to Chandler's formula, fell in 1782 

 and 1848, almost exactly at the times of greatest auroral 

 displays ; whereas the greatest amplitudes and smallest periods 



NO. 1 6 JO, VOL. 62] 



occurred in 1815 and 1881, i.e. just at the times when the 

 display of aurorse reached a minimum. 



But in addition to this there are other facts which point to an 

 influence on the earth's motion exercised by some force varying 

 with the great period of solar activity. In my previous papers 

 I have discussed at some length the evidence afforded by the 

 curves representing the observed residuals of the obliquity, and 

 Prof. Newcomb's corrections to the right-ascension of the sun 

 relative to a fundamental system of fixed stars. I therefore 

 need not here dwell upon their importance as strongly support- 

 ing my hypothesis. 



A reference to curves i, 2 and 3 of Fig. 2 will show how 

 exquisitely parallel are their courses, and how complete is their 

 agreement, not only with the changes in the displays of aurorse 

 and solar activity, but also with Dr. Chandler's long period 

 inequality. It seems utterly inconceivable that a correspondence 

 so consistent can be attributed merely to accident. 



It remains to state briefly one or two very important and 

 interesting deductions made from the results of the last ten 

 years' researches into the phenomena of latitude-variation. 



The frequency of aurorae and magnetic disturbances, as is well 

 known, shows, in addition to the variations associated with 

 changes of solar activity, other fluctuations depending on the 

 season of the year — a fact which has been closely investigated 

 and corroborated by Mr. Ellis. It appears that the magnetic 

 disturbances recorded at Greenwich reveal decided maxima at 

 the equinoxes and minima at the solstices, thus betraying, like 

 the aurorse, a half-yearly period. 



Now the foregoing results point to the conclusion that the 

 distance of the pole of instantaneous rotation from the pole of 

 figure depends on the display of earth-magnetic forces. Hence 

 in the course of a year this distance must become twice com- 

 paratively short and twice comparatively long; i.e. instead of 

 being circular, the path described by the pole of rotation 

 round the pole of figure must be elliptical — the mean pole 

 being situated at the centre of the ellipse. If the period of 

 polar motion were exactly one year, the position of the axes of 

 this ellipse referred to a fixed meridian would remain unaltered. 

 But from Dr. Chandler's investigations we know the period of 

 latitude-variation to be on the average 428 days. Hence the 

 efifect of seasonal change in the earth-magnetic forces must 

 consist in continuously rotating the axes of the polar ellipse in 

 a direction opposite to that of the motion of the pole. These 

 conclusions are well corroborated by the observed facts, and are 

 clearly revealed in the plate appended to Prof. Albrecht's latest 

 " Bericht." The comparatively great eccentricity of the ellipses 

 admits of a tolerably accurate determination of the angles 

 between their major axes and the Greenwich meridian. If the 

 magnitudes of these angles be computed (Table vi. of my 

 paper, A.N. 3649), it will be found that they exhibit quite un- 

 mistakably the progressive change of position of the ellipse 

 with regard to the meridian, the average angular distance between 

 two successive positions of the major axes being about 33°. 



But a closer examination of these figures shows that they indi- 

 cate fluctuations in this average amount which stand in a 

 remarkable connection with the varying display of magnetic 

 disturbances. 



The motion of the ellipse appears to have been largely pro- 

 gressive in 1892, 1894 and 1898 ; while it has been very slight, 

 and at times even retrograde, in 1890, 1893 ^iid 1896. In the 

 first-mentioned years the ellipses are also more irregular and 

 distorted than in the others, indicating a more vehement and 

 spontaneous character of the forces acting on the motion of the 

 pole. Now, according to Mr. Ellis, these years were the only 

 ones in which magnetic disturbances of the character " great" 

 occurred at Greenwich, while in the last-named years his 

 statistics show that there prevailed a decided magnetic calm. 

 While leaving the final confirmation of this interesting fact to 

 future observations, it does not seem too much to say that m 

 the face of existing evidence it is difficult to retain the idea that 

 a coincidence so peculiar can possibly be ascribed to mere 

 accident. 



The results of my researches may be thus shortly sum- 

 marised : — 



i. The changes in the motion of the pole of rotation round 

 the pole of figure are in an intimate connection with the varia- 

 tions of the earth-magnetic forces. 



ii. Inasmuch as the latter phenomena are in a close relation 

 with the state of solar activity, the motion of the pole is also 



