1878.] Rev. S. Haughton on Physical Geology. 



449 



occur when the axis of rotation is passing through B, the wabble will 

 immediately cease, for the axes of rotation and of figure will coincide.* 



If t = 304' 75 days, the wabble will be doubled if the next shock 

 occurs at an interval denoted by n% and will be destroyed if the 

 interval is (n + ^)t. 



If the shocks occur at irregular intervals, at the moment of shock 

 the axis of rotation may be anywhere on the circle APBQ, and 

 the mean effect will be found when the axis is at P or Q, which 

 would be a more probable assumption than that made by me, when I 

 placed the axis always at A. Let us now calculate the mean effect 

 when shocks occurring at unknown intervals take place when the 

 axis of rotation is at P or Q. 



Let r denote the radius AO, then we have — 



Radius of 1st wabble = r. 



„ of 2nd „ = r ^2. 



„ of 3rd „ = r \/3. 



„ of nth wabble = r V n. 



If r = 5 feet (the least observable wabble), n, the number of equal 

 shocks required to displace the axis of figure through 69 miles, will be 



69 x 5280 — no a 

 n= = 72,864, 



and 



</n=270. 



This number should be substituted for A' in equation 12 (Note iii, p. 

 543), when we obtain, for the number of years required by tidal fric- 

 tion to destroy the final wabble, 



320,380 years. 



This, as might be expected, is half the time required to destroy the 

 final wabble, when all the shocks were additive at a maximum and 

 occurred when the axis of rotation was passing through A. 



Mr. Darwin has discussed at length the case of the axis of figure 

 moving uniformly, and finds that the axis of rotation will move on a 

 cycloid. I here give an easy geometrical proof of this theorem : — 



Let AOB be a portion of the path uniformly described by the axis 



# If AB be 69 miles, Europasia might hare been manufactured in 152^ days, by 

 two equal sLocts. 



