the Earth and the Geological Changes of its Surface. 383 



Cg), we can ascertain tlie actual change in sidereal time pro- 

 duced by the removal of masses on the surface of the earth 

 from high to low levels. It is evident, that when calculating 

 the value of J' by means of Cg, the masses of the zones of the 

 shell must not be changed from what they were when ob- 

 tained from Cj. 



To show that the general equations which have been ob- 

 tained in the preceding part of this memoir can be applied to 

 the determination of geological questions, the following nume- 

 rical application of them has been made. This problem would 

 be solved if it could be shown that an appreciable change in 

 the length of the day would be produced by an amount of de- 

 gradation of the earth's surface, such as would be within the 

 limits of what geological considerations render probable for 

 the interval of time between the periods when the data may 

 have been obtained for determining the change in time. 



Let T represent any appreciable change in the length of 



the day. Then in the equation i' = t j, t' will become t ± r^'r 

 the upper sign being taken when I'> I, the lower when I'-<I, 

 and the former notation being used. Hence T=t il —-r) in 

 the case now under consideration. But 



I' = I, + l',-l3, I = I,+ I,-l3, 



Ij representing the moment of inertia of the internal heteroge- 

 neous spheroid, I'g — 13 the moment of inertia of the external 

 shell with the mean thickness €5, and I2— 13 the moment of 

 inertia of the shell with the thickness C,. The value of t 

 will therefore be represented by the formula jr > ,<; 



If C„ Cg, and D the mean depth of the sea, be supposed 

 the same at every latitude, and if we substitute the values of 

 Ij, I2, I'g and I3, found upon these suppositions in the above 

 equations, we shall have, when we solve it with respect to Cg, 



C2=D-/3 + ^J-|%~D + Ci)(/3-D + C/-^[k(«-D) 



03-D)4 + ^((«-D + CO(^-D + CO'^-(«-D)(/3-D)4)]|. ' 



P V 

 But C2=C.-^= — , 



V representing Uj — Ugj or the mean vertical space through 

 which the mass P is transported. Eliminating Cg between 

 the last two equations, and we shall obtain 



