264 Rev. E. Hill — On Changes in the Earth's Axis. 



given in an appendix. The main results may be obtained by general 

 reasoning without symbols. But in every case a considerable knovp- 

 ledge of Rigid Dynamics is required ; so the non-mathematical reader 

 must, I fear, take the statements on trust. Mr. Darwin considers the 

 case of the earth undergoing a very slow and small deformation; 

 slow, so that thousands of years are required for the change, and 

 small, so that the change when made shall not have greatly altered 

 the shape. This will shift the axis of figure away from that original 

 position in which it coincided with the axis of rotation. But move- 

 ments will thus be set up in the Earth such that coincidence will be 

 periodically regained. And the separation between the Poles will 

 be at all times so exceedingly small that for all practical purposes 

 they are coincident. In fact, the distance between the Poles cannot 

 ever exceed about one-third the distance oVer which the pole of figure 

 would be shifted by these deformations in a period of 300 days. lilow 

 this, with such elevations as we at present know, of a few feet in a 

 century or the like, would be a quantity almost microscopic. Thus 

 Professor Twisden's tide-waves cannot arise, since the change required 

 to produce them cannot come into existence. 



Having thus settled that the two axes keep together in the body, 

 the next question to be considered is their position in space. Is it 

 altered or not ? Do the coincidence-restoring movements bring back 

 the axis of figure to the position in space from which it started, or 

 does the rotation-pole follow the figure-pole in its wanderings ? Is 

 the Earth not tilted or tilted ? Is not or is the obliquity changed ? 

 The calculations show that it is not to any perceiDtible degree. For 

 instance, the process of production of an ice-cap reaching down to 

 lat. 45° would not alter the obliquity by '0005 of one second. Hence 

 the deformation will produce a change equivalent to the second case : 

 the orange impaled on the needle differently. It will bring other 

 parts of the Earth into the Arctic regions, while the axis of rotation 

 retains a practically unchanged position in space. The alteration in 

 climate would be of the second kind, one whose evidence might be 

 expected to include some traces of the former ice-cap. 



Having thus worked out the effects of Deformation, Mr. Darwin 

 calculates how much deformation can be produced by any conceivable 

 elevation of land. He investigates very skilfully the shapes and 

 positions of regions of upheaval and subsidence which would be most 

 effective for change. He takes the case of an ocean bed 15000 feet 

 deep elevated into a continent 1100 feet high (which is a little above 

 the average), and obtains the new positions of the axis of figure 

 corresponding to various assumed areas of such elevation and like 

 depression of the surface. The possible alteration of position is not 

 great. A continent equal to Africa elevated, and an equal area de- 

 pressed in the most effective shapes and positions, would produce a 

 change in the position of the Pole of less than two degrees. More- 

 over, this is obtained on the supposition that the elevation and de- 

 pression are obtained by the actual removal of matter from the surface 

 of the one area, and its deposition on the other. If we adopt the 

 easier supposition that elevation is produced by the expansion of sub- 



