182 



Mr. G. H. Darwin on Geological Time, [Mar. 14, 



centre. It is also shown in the same section that the diameter of the 



circle is equal to — . 



fi 



I will now suppose that the geological changes begin suddenly from 

 rest, and proceed at such a rate that the variations in the position of 

 the principal axis are imperceptible to astronomical observation. I 

 will suppose, therefore, that the extremity of the instantaneous axis 

 is never more than 5 feet distant from the extremity of the principal 

 axis. Now, 5 feet at the earth's surface, subtends very nearly '05" at 



the earth's centre, and, therefore, to find a on this supposition, — 



must be put equal to *05". 



ytt is an angular velocity of 360° in 306 days, and if we wish to 

 express a in seconds of arc per annum, jx must be expressed in those 

 units, and *05" must be expressed in circular measure. Thus 



a =lx -05x — x 360x60 x 60 x 865 ' 25 

 2 648000 306 



18-263 3 , 



= — 7r =_ very nearly. 



306 16 J J 



Therefore, a is an angular velocity of 1° (or 69 miles) in 19,200 years. 



But, according to Professor Haughton, 69 miles is the displacement 

 of the earth's principal axis, due to the elevation of Europe and Asia ; 

 hence, at this rate of elevation, Europe and Asia would have been 

 heaved up in 19,200 years. 



Now, if the elevation be supposed to stop suddenly, then the in- 

 stantaneous axis cannot, at the time of the stoppage, be more than 

 5 feet distant from the axis of figure, and it may even be coincident 

 with it. Therefore the stoppage cannot set up a " wabble " of more 

 than 10 feet in diameter, and it may set up none at all. But even this 

 maximum " wabble ; ' of 10 feet, would, according to Professor Haugh- 

 ton, be imperceptible, and a fortiori the circle of 5 feet in diameter, 

 described in the course of the elevation, would be imperceptible. 



On any of the following suppositions, the elevation might be much 

 more rapid, without increasing the residual " wabble " : — 



(1.) The stoppage of the elevation to take place at a time when the 

 instantaneous axis is separated from the principal axis by a small 

 angle. 



(2.) The elevation partly counterbalanced by simultaneous eleva- 

 tions in other parts of the world, so that the upheaval of Europe and 

 Asia would not displace the pole of figure by so much as 69 miles. 



(3.) The elevation partly or altogether produced by the in- 

 tumescence of the strata immediately underlying those continents. 

 (See Part YI of my paper above referred to.) 



(4.) The elevation not uniform but more rapid in the earlier 



