ON POSSIBLE DISPLACEMENTS OF THE EARTH S AXIS OF FIGURE. 35 



3. On possible Displacements of the Earth's Axis of Figure pro- 

 duced by Elevations and Depressions of her Surface. By the 

 Kev. J. F. Twisden, M.A., Professor of Mathematics in the 

 Staff College. Communicated by John Evans, Esq., F.R.S., 

 Y.P.G.S. (Read February 21st, 1877.) 



1. In the Anniversary Address delivered to the Geological Society 

 on the 18th Eebruaryl876, by its President, J. Evans, Esq., the follow- 

 ing passage occurs (p. 62): — "Taking our globe with the distribution 

 of land and water as at present existing, I should like to inquire 

 of mathematicians what would be the theoretical result of such a 

 slight modification, geologically speaking, as the following : — Assume 

 an elevation to the extent, on an average, of 4000 feet over the 

 northern part of Africa, the centre of the elevation being, say, in 20° 

 north latitude. Assume that this elevation forms only a portion of a 

 belt around the whole globe, inclined to the equator at an angle of 20°, 

 and having its most northerly point in the longitude of Greenwich, 

 and cutting the equator at 90° of east and west longitude. Assume 

 that along this belt the sea-bottom and what little land besides Africa 

 it would traverse were raised 4000 feet above its present level over a 

 tract 20° in width. Assume further that the elevation of this belt was 

 accompanied by corresponding depression on either side of it, so as to 

 leave the total volume of the mineral portion of the earth unaffected. 

 Would not such a modification of form bring the axis of figure about 

 15° or 20° south of the present, and on the meridian of Greenwich — 

 that is to say, midway between Greenland and Spitzbergen? and 

 would not, eventually, the axis of rotation correspond in position with 

 the axis of figure ? " 



2. The question whether there has been in past ages a consider- 

 able change in the geographical position of the earth's axis of revo- 

 lution, is said to be one that presents points of great interest to 

 geologists. Whether this be so or not, the above extract has the 

 merit of putting the question into a distinct form, in which it admits 

 of a precise answer. The investigation of which an outline is given 

 in the following pages was undertaken with a view to answering 

 the question as put in the above extract ; it also throws some light 

 on the question of the amount of elevation and depression needed to 

 effect a considerable change in the position of the earth's axis of maxi- 

 mum moment of inertia, or axis of figure. It may be observed that the 

 forces by which the elevations and depressions are effected do not 

 come under discussion. 



3. The method of representing the motion of a rigid body about its 

 centre of gravity by means of the momental ellipsoid and the invariable 

 plane is well known. Eor the purpose of the present question it will 

 be enough to mention a simpler construction, which will represent 

 the motion with sufficient accuracy. It is known that at present the 



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