1877.] The Rev. S. Haughton on Physical Geology. 539 



These equations may be transformed, after some reductions, into the 

 following : — 



^£l2 — T sin 9m r7;/ _ — flu 2 . ) 



-Fsin 2udu-^du i 

 ? 2 



\ (10) 



Adu = (C - A)rdt—T cos 2m du, 

 Cdr =0. 



The second and third of these equations are the same as the second 

 and third of (7), and the first may be integrated as follows : — 

 The sum of (_dir), taken through an entire circumference, is 

 2(^r)=2- du. 



Hence, if we assume the value of p to remain constant during a single 

 wabble, and then to change by a small quantity, remaining constant for 

 the next wabble, and so on; if 



PqJ Pv Pi ?n 



be the successive values of p, we have, since the periodic term 



destroys itself, 



C 2 * . 

 1 sin 2ti 



J 



du 



7T F d U 



A 

 7T F du 



and. in general, 

 or. writing 



&C. &( 



&c. &c. ; 



7T F du 



A 



7T F du 



A 



Po 



Pi 



&c. &c., 



Pn_ -ny 



— — O 4 



> (11) 



Po 



The equatorial component of rotation, p, therefore diminishes in geo- 

 metrical progression, and finally disappears altogether, leaving the earth's 

 rotation round the axis of figure OC equal to r. 



If we know the value of y (depending on the friction), we are now 

 prepared to calculate from (11) how long it would take to reduce p t 

 to p n - 



