September 7, iJ>93] 



NA TURE 



453 



was suggested by the problems of the solar system, we find the 

 names of the leading mathematicians of the last century, 

 d'Alembert, Segner, and Euler, not to mention others. It was 

 the latter who, in 1765, in a work entitled "Theory of the 

 Motion of Solid and Rigid Bodies," gave the equations the 

 final form which Laplace declares seem to him the most simple 

 which can possibly be obtained. (M. C.V. p. 284.) 



The elegant form of these equations was due to the employ- 

 ment of the principle discovered by Segner, viz. that at every 

 point of a body there are at least three principal axes of inertia 

 at right angles to each other, which possess somj very import- 

 ant properties. One of these properties is this — that if the body 

 be set revolving about one of these axes which passes through 

 its centre of inertia, and is understood by outside forces, it will 

 continue to revolve about this axis for ever. If, however, it be 

 started in its revolution about some other axis, the condition of 

 things will be different. 



In the first approximation to the solution of Euler's equations 

 when applied to the earth, we meet with two constants of inte- 

 gration, whose values depend upon the position of the axis of 

 revolution with respect to the principal axis of inertia (from 

 which it can never differ greatly) at the instant which we take 

 as the starting point of our integration. We further find that 

 the presence of these quantities in our equations shows a revo- 

 lution of the instantaneous axis of rotation about the principal 

 axis of inertia. This rotation is in the same direction as the 

 diurnal motion, the angular velocity y being expressed by the 

 formula 



C-A 



Where u is the velocity of diurnal rotation, C and A are the 

 principal moments of inertia of the earth, the first with respect 

 to the polar axis, the second with respect to an equatorial axis, 

 the figure being regarded as that of an ellipsoid of revolution. 

 The ratio 



C-A 

 A 



is found from the value of the constant of nutation, the degree 

 of accuracy being such that the theoretical period of this rota- 

 tion is known probably within one or two days. The value 

 given by Oppolzer is 304 '8 mean solar days. We shall 

 assume it to be 305 days. 



The angular distance between the two axes, evidently very 

 small in case of the earth, can only be determined by ob- 

 servation, and will manifest its existence by fluctuations in the 

 latitude having a period of 305 days. The first attempt to 

 find by observation whether or not this movement was appre- 

 ciable was by Bessel. This method was not well adapted to the 

 purpose, and the result was negative or inconclusive. 



The first quantitative determination which seemed worthy of 

 confidence was made by Dr. C. A. F. Peters, of Pulkowa 

 I " Recherches sur la Parallax des Etoiles Fixes," p. 146), in 

 1842. From a careful series of meridian circle observations 

 carried on for thirteen months he found for the angle between 

 the two axes 'o?!" ± 017. Nyren followed with a careful dis- 

 cussion of the value given by the observations of Peters, 

 Cylden, and himself with the same instrument. The results 

 were •loi", 'las", and -058". Downing found from the 

 ;i;enwich observations from 1868-77 "075" {Monthly Notices, 

 .A.S. March, 1892), while Newcomb found the somewhat 

 mailer value "04" from the Washington prime vertical work. 



These results are in reasonably good accord, and at first sight 

 -eem to show conclusively a real separation of the two axes, 

 'Ut as pointed out by Hall ("American Journal of Science," 

 March, 1885, p 223), the form of the expressions for deter- 

 mining the quantity is such that an apparently real value will 

 nl«ays be obtained. If we assume a uniform rotation of one 

 '>li^ about the other our equations will contain two unknown 

 lantities, x and y, where x = f cos | . >» = p sin {, therefore 

 liatever values we may find for x and_y . p will always have a 

 ,il and positive value. This may, therefore, be nothing more 

 an a function of the errors of observation. The true test 

 was therefore to be sought in the agreement of the values of { 

 when reduced to a co3imon epoch. These were found to be 

 quite discordant, so much so as to throw doubt upon the 

 I reality of the results. The truth, as we now understand 

 ' it, being that Euler's theory, perfect as it is, does not apply 

 without m jdification to the present problem — the earth not 



being strictly a rigid body. Doubts as to the absolute rigidity 

 of the earth had been expressed by more than one investi- 

 gator, and the matter was discussed in 1876 by Lord Kelvin 

 (British Association Reports, 1876, Sections, p. 11), and in 

 1879 by Pri.f. George Darwin [Pliil. Trans, 1S79), in relation 

 to the problems of precession, nutation and tidal action — the 

 conclusion being that the rigidity of the earth is probably be- 

 tween that of steel and glass. The bearing of this upon the 

 present investigation was first pointed out by Newcomb 

 {Monthly Notices) 7\oyal Astronomical Soc.,Vi3.rch,lS<j2),v\i. that 

 in consequence of the elastic yielding of the earth as a whole the 

 peri,od ol this rotation would be lengthened. 



Before considering this matter in detail, however, the exigen- 

 cies of historical continuity require us to glance at some remark- 

 able results of observation. 



In the spring of 1884 Dr. F. Kii tner, of Berlin, began a 

 series of observations, the results of which were destined to 

 awaken a widespread interest in this subject, or, perhaps more 

 properly, to crystallise the interest which already existed. His 

 original purpose was sufficiently modest. The great meridian 

 circle of the observatory requiring some repairs, he proposed 

 to employ the interval while it was out of service in making a 

 limited series of observations with another instrument, the 

 universal transit, according to the Horrebow-Talcott method 

 for the investigation of the constant of aberration. His purpose 

 was not so much that of deriving a new and definitive value of 

 this constant, which should be entitled to rank with the excel- 

 lent results previously obtained, as to test practically the appli- 

 cability of the method to this purpose, and to acquire the 

 experience which at a future time might lead to a favourable 

 result in a more complete series. Possibly it would be over- 

 straining a time-worn simile toe iuipare the modest investigator 

 with Saul, son ol Kish, who, going forth to seek his father's 

 asses, found a kingdom ; but certain it is that his results were 

 vastly more important and far-reaching than anything which he 

 could have anticipated in his original programme. His obser- 

 vations, not numerous, but of the first order of excellence, 

 led to a value of the constant of aberration which appeared 

 to be wholly inadmissible. Many an investigator would 

 have been discouraged with this apparent failure, and 

 the world would have known nothing of it. Not so with 

 Kiiitner. Instead of abandoning the experiment as a 

 failure he set himself resolutely to work to discover the 

 cause of the anomaly. After examining the various causes 

 which might be supposed to have contributed to such a result, 

 personal, instrumental, and refractional, he announced without 

 hesitation that it was due to a change in the latitude itself, viz., 

 that from August to November, 1884, the latitude of Berlin 

 had been from 0.2" to o.3".greater than from March to May in 

 1S84 and 1885. This conclusion was materially strengthened 

 by the examination of a considerable amount of collateral evi- 

 dence, particularly Nyrrn's elaborate series of observations at 

 Pulkowa from 1879 to 1882, employed by the latter in discuss- 

 ing the constant of aberration. This somewhat bold hypothesis 

 naturally provoked much discussion, and many were sceptical 

 as to its truth ; but instead of resorting to polemics, and 

 quoting the authority of Aristotle and the sacred Scriptures on 

 the one side or on the other, means were promptly found for 

 testing it. These comprised both a re-examination of old obser- 

 vations and new ones, undertaken for this express purpose. 

 Among the latter were special series of latitude determinations 

 extending over an entire year or more at Berlin, Potsdam, 

 Prague, and Bethlehem, all by Talcott's method. All of these 

 agreed most satisfactorily in showing the reality of the fluctua- 

 tion during the years 1888, 1889 and 1890. But the final test 

 which should determine whether the changes observed were due 

 to movements of the earth's axis required observations to be 

 carried on simultaneously at points diflering widely in longi- 

 tude. A latitude campaign instituted for this purpose was 

 therefore entered upon in the summer of 1891, under the aus- 

 pices of the International Geodetic Association, operations 

 being carried on at Berlin, Prague, Strassburg, Rockside, San 

 Francisco, and Waikiki. 



Some of the results have been in possession of the public for 

 several months, and they show in the most conclusive manner 

 that we are dealing with a movement of the earth's axis. 



A series of latitude observations was also carried on at Paris 

 from December, 1890, to August, 1891 ; part of the time two 

 different observers were employed using different instruments, 

 their results agreeing almost exactly. {ComJ>tcs /ienJiis, 18^2, 



NO. 1245, VOL. 48] 



