The Thickness of the Earth's Crust. 423 



4. But the disturbing force producing precession and nutation 

 does exist. It consists of two parts, one constant and the other 

 variable and periodical. The constant part is that which produces 

 the steady precession of the axis (and which I call for convenience 

 the precessional force) ; the other produces the nutation. T will con- 

 sider the precession first. Suppose now, for the sake of argument, 

 that at the present moment, as M. Delaunay imagines, the crust and 

 the fluid are revolving precisely as one mass, all previous differences 

 of motion, even under the action of the disturbing force which pro- 

 duces precession and nutation, having been annihilated by friction 

 and viscidity. I ask, what will be the action of the precessional 

 force from this moment ? It tends to draw the pole of the crust 

 towards the pole of the ecliptic : and this tendency, as mathematical 

 physicists well understand, combined with the rotary motion of the 

 crust, produces this singular result, viz., the pole does not move 

 towards the pole of the ecliptic, but shifts in a direction at right 

 angles to the line joining the poles towards the west ; so that the 

 inclination of the axis to the ecliptic remains constant, but the axis 

 shifts towards the west. The space through which it shifts in an 

 infinitesimal portion of time varies as the length of the time and the 

 force directly, and as the inertia of the mass to be moved inversely. 

 The inertia of the mass depends upon the thickness of the crust only ; 

 for the friction of the fluid against the inner surface of the crust 

 (which might, as I have shown, in the course of years produce a 

 sensible effect) cannot do so during the infinitesimal portion of time 

 I am considering before the precession is actually produced. The 

 precessional force has its full effect in producing the precession of the 

 solid crust, the fluid not having time to diminish that effect before 

 the axis has assumed a new position ; and in this new position of the 

 axis the precessional force is precisely the same in amount as before, 

 to go on causing the precession as before. The precessional force, is 

 in fact, ever alive and active, and shows this in incessantly producing 

 the effect I have described ; and the precession goes on 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 cause [the dis- 

 turbing forces which give rise to precession 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 con- 

 nection 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 protuberant 

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



