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Rev. S. Haughton on Physical Geology. [June 20, 



of figure ; and let x be the position of the axis of figure at any moment, 

 and y the corresponding position of the axis of rotation, then by the 

 conditions of the problem, fig. 2, 



Ax varies as the time, 

 The angle, Axy=yzx varies as the time. 

 But the angle yzx is proportional to the arc xy : therefore 



Ax varies as arc yx, 



but they are supposed to start together from zero, at the point A. 

 Therefore Ax = arc xy, and the locus of y is the common cycloid, 

 whose generating circle is xyz with diameter equal to the axis of the 

 cycloid PO. 



If the axis of figure therefore travels uniformly, the axis of rotation 

 will describe a cycloid, and the two axes will coincide every 152^- days, 

 at the cusps, and the maximum radius of wabble will be OP, the 

 diameter of the generating circle. 



Mr. Darwin, finally, discusses the following problem : * 

 " 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." 



Mr. Darwin deduces from this that a displacement in the axis of 

 figure, amounting to 69 miles, might be produced in 19,200 years, 

 without ever producing an observable wabble, 

 t My calculation of this problem is as follows : — 



Since OP is 5 feet, the base of the cycloid, AB will be hv, and as 

 this length is described by the axis of figure in half a wabble, we have, 

 if x be the number of years required to describe 69 miles, 



5tt : 69x5280:: 80475 :x. 



2x365-25 



From this I find — 



69x5280x304-75 QRt7K - 



x— =yo/5v years. 



2 x 365-25 x 5tt 3 



This result is half that obtained by Mr. Darwin. 



My object in publishing the latter part of my paper, was to show 

 that if geologists shall ever be in a position to give us exact informa- 

 tion as to the mode of formation of a continent, under certain circum- 

 stances, conclusions of value as to geological time might be deduced 

 from observations made on the wabble of the axis of rotation; but it 

 is clear that, in the present state of our knowledge, such conclusions 

 must be regarded as hypothetical. 



* Ante, p. 182. 



