190 



Mr. Gr. H. Darwin on 



[Dec. 19, 



Now, a couple round in the direction of the arrow, when com- 

 bined with the earth's rotation, would, according to the principle of 

 the gyroscope, canse the pole N to rise above the plane of the paper, 

 that is to say, the obliquity of the ecliptic would diniinish. The same 

 thing would happen, but to a less extent, if the obliquity had been less 

 than 90° ; it would not, however, be nearly so easy to show this from 

 D-eneral considerations. 



o 



Since the forces which act on the earth always pass through N and S, 

 therefore there can be no moment about the axis NS, and the rotation 

 about that axis remains unaffected. This can hardly be said to amount 

 to strict proof that the diurnal rotation is unaffected by the fortnightly 

 tide, because it has not been rigorously shown that the two particles at 

 N and S are a complete equivalent to the varying ellipticity of figure. 



Lastly, the reaction on the moon must obviously be in the opposite 

 direction to that of the curved arrow at ; therefore there is a force 

 retarding her linear motion, the effect of which is a diminution of her 

 distance and of her periodic time. 



The fortnightly tidal effect must be far more efficient for very great 

 viscosities than for small ones, for, unless the viscosity is very great, 

 the substance of the spheroid has time to behave sensibly like a perfect 

 fluid, and the tide hardly lags at all. 



Prop. III. An annular satellite not parallel to the planet's equator 

 attracts the lagging tides raised by it, so as to diminish the inclination 

 of the planet's equator to the plane of the ring, and to diminish the 

 planet's rotation. The effects of the joint action of sun and moon 

 may be explained from this. 



Suppose the figure to represent the planet as seen from vertically 

 over the South Pole S ; let LL' be the nodes of the ring, and LRL' 

 the projection of half the ring on to the planetary sphere. 



If the planet were perfectly fluid the attraction of the ring would 



