TRANSACTIONS 01'" THE SECTIONS. 11 



they must produce, on tlie period and axis of the earth's rotation, eHeets compai-able 

 with those produced bv chanffes 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 ktitudo and west longitude with equal depression in the other two quarters, 

 amounting at greatest to ten centimetres, and graduating regularly from the points 

 of maximum elevation to the points of maximum depression in themiddles of the 

 four quarters, would shift the earth's axis of maximum moment of inertia through 

 ] " 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 

 ])lace suddeulv, the earth's instantaneous axis would experience a sudden shifting of 

 but -r^g" (which we nnxy neglect), and then, relatively to the earth, would com- 

 mence travelling, in a period of 30(3 days, round the fresh axis of maximum moment 

 of inertia. The sea would be set into vibration, one ocean up and aiiother down 

 through a few centimetres, like water in a bath set aswing. The period of these 

 Adbratlons would be from 12 to 2-4 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 11 centimetres from lowest 

 to highest woidd be to be observed, with gradually dimiuishiug amount from 

 century to centurv, as through the dissipation of energy produced by this tide 

 tlie instantaneous" axis of the earth is gradually brought into coincidence with 

 the fresh axis of maximum moment of inertia. " If we multiply these figures by 

 3600, we find what would be the result of a similar sudden upheaval and sub- 

 .sidence 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 consequent 400-metres tide producing a succession of deluges 

 every 306 days for many years, may have taken place ; but it seems more pro- 

 bable 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 oceau- 

 l)eds from'the general level of their supposed molten origin, took place gradually 

 through the thermodynainic melting of solids and the squeezing out of liquid 

 lava from the interior, to which I have ah'eady referred. A slow distortion of 

 the earth as a whole would never produce any great angular separation between 

 the instantaneous 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 Austi-ali.a, 

 and considering further the ellipticity of the equatorial section of the sea-level esti- 

 mated by Capt. Clarke at about ^V" of the mean ellipticity of meridional sections 

 of the sea-level, we need no brush from the comet's tail (a Avholly cliimerical 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 10, 20, 30, 40, or more degrees without at any time any perceptible sudden 

 disturbance of either laud or water. 



Lastlv, as to variations in the earth's rotational period. You all no doubt know 

 how, in" 1853, Adams discovered a correction to be needed in the theoretical calcu- 

 lation with which Laplace followed up his brilliant discovery of the dynamical 

 explanation of an apjiarent 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 apparent acceleration, and how Delaimay in 1866 verified Adams's 

 result and suggested that the explanation may be a retardation of the earth's rota- 

 tion bv tidal friction. The conclusion is that, since the 10th of March, 721 n.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 j;;];j^j;;oo(j 



2* 



