Sept. 14, 1876] 



NATURE 



431 



years 1842 and 1872, and containing the following statement of 

 his conchisions : — 



" The investigation of the ten month period of latitude from 

 the Washington prime vertical observations from 1862 to 1867 

 is completed, indicating a co-efficient too small to be measured 

 with certainty. The declinations with this instrument are sub- 

 ject to an annual period which made it necessary to discuss those 

 of each month separately. As the series extended through a full 

 five years, each month thus fell on five nearly equidistant points 

 of the period. If x and y represent the co-ordinates of the axis 

 of instantaneous rotation on June 30, 1864, then the observations 

 of the separate months gave the following values of .^ zxiA.y : — 



y weight. 



weight. 



Accepting these results as real they would indicate a radius of 

 rotation of the instantaneous axis amounting, at the earth's sur- 

 face, to 5 feet and a longitude of the point in which this axis 

 intersects the earth's surface near the north pole such that on 

 July II, 1864, it was 180° from Washington, or 103° east of 

 Greenwich. The excess of the co-efficient over its probable 

 error is so slight that this result cannot be accepted as any- 

 thing more than a consequence of the unavoidable errors of 

 observation. " 



From the discordant character of these results we must not, 

 however, infer that the deviations indicated by Peters, Maxwell, 

 and Newcomb are unreal. On the contrary any that fall within 

 the limits of probable error of the observations ought properly 

 to be regarded as real. There is in fact a vera causa in the tem- 

 porary changes of sea-level due to meteorological causes, chiefly 

 winds, and to meltings of ice in the polar regions and return 

 evaporations, which seems amply sufficient to account for irre- 

 gular deviations of from ^" to -^■^' of the earth's instantaneous 

 axis from the axis of maximum inertia, or, as I ought rather to 

 say, of the axis of maximum inertia from the instantaneous axis. 



As for geological upheavals and subsidences, if on a very large 

 scale of area, they must produce, on the period and axis of the 

 earth's rotation, effects comparable with those produced by 

 changes of sea- level equal to them in vertical amount. For 

 simplicity, calculating as if the earth were of equal density 

 throughout, I find that an upheaval of all the earth's surface in 

 north latitude and east longitude, and south latitude and west 

 longitude, with equal depressions in the other two quarters, 

 amounting at greatest to 10 centimetres, and graduating regu- 

 larly from the points of maximum elevation to the points 

 of maximum depression in the middles of the four quarters, 

 would shift the earth's axis of maximum moment of inertia 

 through i" on the north side towards the meridian of 90° 

 W. longitude, and on the south side towards the meridian 

 of 90° E. longitude. If such a change were to take place 

 suddenly, the earth's instantaneous axis would experience a 

 sudden shifting of but ^^' (which we may neglect) and then, 

 relatively to the earih, would commence travelling, in a period 

 of 306 days, round the fresh axis of maximum moment of inertia. 

 The sea would be set into vibration, one ocean up and another 

 down through a few centimetres, like water in a bath set aswing. 

 The period of these vibrations would be from twelve to twenty- 

 four hours, or at most a day or two ; their subsidence would 

 probably be so rapid that after at most a few months they would 

 become insensible. Then a regular 306 days' period tide of 

 1 1 centimetres from lowest to highest would be to be observed, 

 with gradually diminishing amount from century to century, as 

 through the dissipation of energy produced by this tide, the 

 instantaneous axis of the earth is gradually brought into coinci- 

 dence with the fresh axis of maximum moment of inertia. If 

 we multiply these figures by 3,600, we find what would be the 

 result of a similar sudden upheaval and subsidence of the 

 earth to the extent of 360 metres above and below previous 



levels. It is not impossible that in the very early ages 

 of geological history such an action as this, and the con- 

 sequent 400 metres tide producing a succession of deluges every 

 306 days for many years may have taken place ; but it seems 

 more probable that even in the most ancient times of geological 

 history the great world wide changes, such as the upheavals of the 

 continents and subsidences of the ocean beds from the general 

 level of their supposed molten origin, took place gradually 

 through the thermo-dynamic melting of solids and the squeezing 

 out of liquid lava from the interior to which I have already 

 referred. A slow distortion of the earth as a whole would 

 never produce any great angular separation between the instan- 

 taneous axis and axis of maximum moment of inertia for the time 

 being. Considering, then, the great facts of the Himalayas and 

 Andes, and Africa and the depths of the Atlantic, and America 

 and the depths of the Pacific, and Australia, and considering far- 

 ther the eliipticity of the equatorial section of the sea-level esti- 

 mated by Capt. Clarke at about yV of the mean eliipticity of meri- 

 dional sections of the sea-level, we need no brush from the comet's 

 tail, a wholly chimerical cause which can never have been put 

 forward seriously except in ignorance of elementary dynamical 

 principles, to account for a change in the earth's axis ; we need 

 no violent convulsion producing a sudden distortion on a great 

 scale with change of the axis of maximum moment of inertia 

 followed by gigantic deluges ; and we may not merely admit, 

 but assert as highly probable, that the axis of maximum inertia 

 and axis of rotation, always very near one another, may have 

 been in ancient times very far from their present geographical 

 position, and may have gradually shifted through ten, twenty, 

 thirty, forty, or more degrees without, at any time, any percep- 

 tible sudden disturbance of either land or water. 



Lastly, as to variations in the earth's rotational period : — 

 You all, no doubt, know how in 1853 Adams discovered a cor- 

 rection to be needed in the theoretical calculation with which 

 Laplace followed up his brilliant discovery of the dynamical 

 explanation of an apparent acceleration of the moon's mean 

 motion, shown by records of ancient eclipses ; and how he found 

 that when his correction was applied, the dynamical theory of the 

 moon's motion accounted for only about half of the observed appa- 

 rent acceleration ; and how Delaunay in 1866 verified Adams's 

 result, and suggested that the explanation may be a retardation of 

 the earth's rotation by tidal friction. The conclusion is that since 

 March 19, 721 B.C., a day on which an eclipse of the moon was seen 

 in Babylon, commencing "when one hour after her rising was fully 

 passed," the earth has lost rather more than aoooooo of her rota- 

 tional velocity, or as a timekeeper, is going slower by ii^ seconds 

 per annum now than then. According to this rate of retardation, 

 if uniform, the earth at the end of a century would, as a time- 

 keeper, be found 22 seconds behind a perfect clock, rated and set 

 to agree with her at the beginning of the century. Newcomb's sub- 

 sequent investigations in the lunar theory have on the whole tended 

 to confirm this result, but they have also brought to light some re- 

 markable apparent irregularities in the moon's motion, which, if 

 real, refuse to be accounted for by the gravitational theory without 

 the influence of some unseen body or bodies passing near enough 

 to the moon to influence her mean motion. This hypothesis 

 Newcomb considers not so probable as that the apparent irregu- 

 larities of the moon are not real and are to be accounted for by 

 irregtilarities in the earth's rotational velocity. If this is the true 

 explanation it seems that the earth was going slow from 1850 to 

 1862, so much as to have got behind by 7 seconds in these 12 years, 

 and then to have begun going faster again so as to gain 8 seconds 

 1862 to 1872. So great an irregularity as this would require some- 

 what greater changes of sea-level, but not many times greater, 

 than the British Association Committee's reductions of tidal 

 observations for several places in different parts of the world, 

 allow us to admit to have possibly taken place. The assumption 

 of a fluid interior, which Newcomb suggests, and the flow of a 

 large mass of the fluid "from equatorial regions to a position 

 nearer the axis," is not, from what I have said to you, admissible 

 as a probable explanation of the remarkable acceleration of rota- 

 tional velocity which seems to have taken place about 1862 ; but 

 happily it is not necessary. A settlement of 14 centimetres in 

 the equatorial regions with corresponding rise of 28 centimetres 

 at the poles, which is so slight as to be absolutely undiscoverable 

 in astronomical observatories, and which would involve no change 

 of sea-level absolutely disproved by reductions of tidal observa- 

 tions hitherto made would suffice. Such settlements must occur 

 from time to time ; and a settlement of the amount suggested 

 might result from the diminution of centrifugal force due to 150 

 or 200 centuries' tidal retardation of the earth's rotational speed. 



