382 Mr. Hennessy on the Connexion between the Rotation of 



whether we examine the action of one or both as affecting the 

 earth's rotation, we can therefore examine the change in C^ 

 either when it is diminished or increased : it will be found 

 most convenient to examine its change in the former case. 

 Of the two principal causes which operate in diminishhig Cj 

 or degrading the level of the land, a knowledge of the inten- 

 sity of one will suffice for our purposes. We shall therefore 

 proceed to find an equation expressing merely the diminution 

 of Ci from the transportation of solid matter from the high 

 levels of the parallelopipeds to their lower levels. This course 

 is adopted from the conviction, that however little is our pre- 

 sent knowledge of the degradation of land, an accurate esti- 

 mate of its annual amount can be obtained with more certainty 

 than a knowledge of the subsidences of portions of the earth's 

 crust produced by causes comparatively hidden. 



Let //j, ^25 ^3> &c. be the heights of any places above the 

 level of the internal surface of the shell, from which are trans- 

 ported in the same time the masses p^, jSg* J^a* &c., then by the 

 theory of moments, the result will be in effect the same as if 

 the entire mass p^ -\- P^ H-i's + ••••> oi" P were carried from 

 the distance 



U _ ^l?I + /^2P2 + ^3P3 + '--- (15 X 



Similarly, if fj, Zg, /g, &c. represent the heights of any places 

 above the same level to which any masses (7,, §'2, g-g, &c. are 

 transported, the resulting mechanical action will be in effect 

 the same as if the whole mass g'j + §'2 + §'3 + ••••> oi* P were 

 removed to the distance from the internal surface of the shell 

 expressed by the formula 



TT _hi\ + iiii + h % + "" /^R^ 



^^-- Q vio-; 



After the removal of P from Uj to Ug, let Cj become Cg, then 

 C2 will evidently be expressed by the formula 



C2 = C,-|(Ui-U2); (17.) 



where jw. = Sj (H + D) s + 82 D 5', the mass of the zone of the 

 shell. By means of the equation (14.), we can calculate the 

 thickness of the shell when P is at Uj ; and its thickness when 

 P is at U2, can be obtained by (17.). We can then find G, 

 which being used in the equations (13.), will serve to point 

 out any particular values of A and B. The same process 

 being performed for every zone, the value of J in (10.) will be 

 obtained, and by the final substitution in (2.) of Ij + J for I, 

 and Ii + J' for I' (J' being the value of J when Cj changes to 



