Thickness of the Earth's Crust. 13 



steadily, the amount of it depending upon the mass of the crust 

 thus moved, which the fluid has not time to retard or lessen. 

 M. Delaunay says that " the additional motion due to the above- 

 mentioned causes [the disturbing forces which give rise to pre- 

 cession and nutation] is of such slowness, that the fluid mass 

 which constitutes the interior of the globe must follow along 

 with the crust which confines it, exactly as if the whole formed 

 one solid mass throughout." In reply to this, I say that it is 

 not the slowness of the motion, but the want of solid connexion 

 between the crust and the fluid in contact with it which affects 

 the problem. The motion, whatever its amount, is incessantly 

 being generated by the disturbing force ; and, owing to this want 

 of solid connexion, the friction of the fluid has not time during 

 the successive moments during which the precession is generated, 

 to stop or even sensibly to check it. 



It will thus be seen that at every instant the precessional force 

 proceeding from the action of the sun and moon on the protube- 

 rant part of the earth's mass will, if the earth be a solid mass, 

 have to move the whole mass ; and if the earth have a solid crust 

 only with a fluid interior, the force will have to move only the 

 crust, against the evanescent resistance of the fluid within du- 

 ring so short a space of time as it takes to produce precession. 

 The resulting precessional motion will be different in the two 

 cases ; and therefore the actual amount of the precession which 

 the earth's axis has (and which is a matter of observation) is a 

 good test of the solidity or fluidity of the interior. This is Mr. 

 Hopkins's method. 



The force producing nutation is much smaller, even at its 

 maximum, than the precessional force. Its effect, however, is 

 precisely the same in this respect — that it depends upon the 

 mass of the solid crust, and in no respect upon the friction of 

 the fluid within it, which has not time to influence the nutation 

 before the nutation is actually produced. 



5. I do not here undertake to go into Mr. Hopkins's numerical 

 calculations ; I simply vindicate his method. I do not here con- 

 sider what modification the elasticity of the solid material of the 

 earth may have upon his numerical results. I conceive that it 

 would have no effect, if the disturbing force were constant and 

 there were no nutation. JFor, under the dragging influence (if 

 1 may so call it) of the constant precessional force, the solid 

 material would be under a steady strain, and would communicate 

 the effect of the force, continuously acting, from particle to par- 

 ticle of the solid part as if it were really rigid ; and the resulting 

 precessional motion would be greater or less as the mass of the 

 solid part may be smaller or larger — that is, the solid crust 

 thinner or thicker. But as the disturbing force is not constant, 



