1878.] 



Estimate of Geological Time. 



181 



great as if the whole change took place by a single convulsion. Bnt 

 where the impulses take place at hazard there will he a certain average 

 effect on the radius of the " wabble," which, as far as I can see, Pro- 

 fessor Haughton makes no attempt to determine. It seems, therefore, 

 an unjustifiable assumption that sufficient time must elapse between 

 the successive impulses to reduce the radius of the " wabble " to 5 feet, 

 for if the impulses took place more frequently they might tend to 

 some extent to counteract one another. If this assumption is unjusti- 

 fiable, then Professor Haughton's estimate of time falls with it. 



In my paper on the " Influence of Geological Changes on the 

 Earth's Axis of Rotation," 1 * I have considered the effects of a slow 

 continuous distortion of the earth. The results there attained would, 

 of course, have been identical, had I considered the effects of a series 

 of infinitely small and infinitely frequent earthquakes. I presume 

 Professor Haughton will agree with me in thinking this supposition 

 more consonant with geological science than the larger earthquakes 

 which he postulates. 



I will now show, from the results of my paper, that without calling 

 in any effects ivhatever of tidal friction, Asia and Europe might have 

 been gradually upheaved in 19,200 years, without leaving any 

 " wabble " sufficiently large to be detected astronomically, and, more- 

 over, that at no time during the elevation could the " wabble " have 

 been detected had astronomers been in existence to make observations ; 

 and further, that under certain not improbable suppositions, this 

 estimate of time may be largely reduced. Let a be the angular 

 velocity of the principal axis relatively to the solid earth, arising from 

 the continuous elevation of the continent; n the earth's angular 

 velocity of rotation ; C, A the greatest and least principal moments of 



inertia of the earth ; and /u = — — — n. 



-A. 



Then, in section 2 of my paper, I show that the extremity of the 

 instantaneous axis describes a circle at the earth's surface in 306 days, 

 and that this circle passes through the extremity of the principal 

 axis, and touches the meridian along which the principal axis is 

 travelling with velocity a in consequence of the postulated geolo- 

 gical change. Strictly speaking, the curve described by the instan- 

 taneous axis, is a trochoid, because the circle travels in the earth along 

 with the principal axis ; but the motion of the circle is so slow com- 

 pared with that of the instantaneous axis along its arc, that it is more 

 convenient to say that the instantaneous axis describes a circle which 

 slowly changes its position. It must be noticed that this circle is 

 unlike the " wabble " considered by Dr. Haughton, inasmuch as the 

 extremity of the principal axis lies on its arc instead of being at its 



* " Phil. Trans.," vol. clxvii, pfr. I, p. 271. 



