the EaiHh and the Geological Changes afit&Sutface^ 377- 



-.*:>!■:,• iji jjyiJi I, i; i< I ■ §■ JiiJij- f 9 Ji'iv/. HDL' id. miiilj^i:ji(l ml » 



iaiti B ai t*i9q*jTuqpijil no'" "~ ^' rfS'juTTo k Jifaj^yxo Ifi'jitvJoii 

 ''fffelib^ .abixo'ioq b od Jauai Ji i£(lj edJBuiuni ib^Ji !o ^\Ai<i 

 vliio jijii f'^Jiaqo'iq JfiriJ daaaj-otl/JOH ^-joij arriiolilj J«ilJ iJvroii>< 

 niiw Jiit^mab airit qo 9^g=<4.jri9g^xo«io»2noiJi»Ti«lfrrt»5 (8>ir 



It IS thus apparent that when the moment of inertia of the 

 earth changes by a known quantity, the change in s^der^,al . 

 time can be calculated. ^ . ^ _ ^ . 



This fact furnishes a method for ascertaining whether,* 

 during certain defined intervals of time, an equilibrium has 

 been maintained between the forces which tend to elevate or 

 to depress the external crust of the earth. If any unknown 

 residual 'phccnomena exist on either side, their existence will 

 be made known by finding the difference between the total 

 mechanical actions exerted by the known elevatory and de* 

 grading forces. 



The earth may be considered as a spheroid surrounded by 

 a thin shell, whose external surface is covered with protube- 

 rances and depressions. A change in the moment of inertia 

 of this shell produces a change in the moment of inertia of 

 the whole earth, which is compounded of that moment, and 

 of the moment of inertia of the internal spheroid. In finding 

 both of those moments of inertia, the following general method,! 

 is employed. I- 



It is well known that if a solid of revolution be supposed to 

 consist of an infinite number of plates perpendicular to the 

 axis, and each plate of an infinite number of concentric rings, 

 tlie moment of inertiaiofitan^jisou&rivm in igoaeralt be ex- 

 pressed by J-} w(iH dfjirnBy) ol bsaocjoiq jthI <-j i\ 

 niiJi dJi £io e^<i:6i.' r^ /*^rt'<J'iis'j''l-l70^ i:»yq<i'ji AivH tiiuij^ 



k'djjfiO yilj lit. 



TT being the ratio of the diameter bf:ai ibircle to its circumfe- 

 rence, r the radius of one of the rmgs, p its density, x the 

 abscissa, and y the ordinate of the generating curve. The 

 distance of the extremities of the zone from the origin of the 

 co-ordinates, are expressed respectively by I and /'. When 

 the body is heterogeneous, it will be found more convenient 

 to transform the rectangular into polar co-ordinates. Let R 

 represent the radius vector of a point in the ring, 9 the angle 

 comprised between the plane of R, y and the plane of x^ y, 

 and ^ the angle comprised between R and the plane of y, z. 

 As R is the same for all points in the ring, the plane of R, y 

 and the plane of x, y coincide, and 6 = 0. If the origin of 

 the co-ordinates be at the extremity of the axis of x^ and if the 

 distance from the point where the radius vector of the ring 



