12 Archdeacon Pratt on the Method of determining the 



We may conclude perhaps that the same effect would be pro- 

 duced, though in a much longer time, if the interior were not a 

 solid sphere, but a fluid mass. 



The above reasoning shows that if the disturbing force produ- 

 cing precession and nutation did not exist, and the interior of 

 the earth were fluid (whatever the thickness of the crust), it may- 

 be fairly assumed that the motion of rotation of the crust would 

 now, the earth having existed so many ages, be exactly what it 

 would have been had the earth been one solid mass, all difference 

 of motion having been long ago annihilated by the internal fric- 

 tion and viscidity. 



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 will call for con- 

 venience the precessional force) ; the other produces the nutation. 

 I will consider 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 produces 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, pro- 

 duces 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 incli- 

 nation 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 infi- 

 nitesimal 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 preces- 

 sional 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 produ- 

 cing the effect I have described; and the precession goes on 



