of the Earth's Rotation. 535 



gular) such as to have the same resultant effect, the retarding 

 influence of the moon's attraction would be that of 4'1 x 10 15 

 tons force acting in the plane of the equator and in a line passing 

 the centre at ^ of a foot distance. Or it would be the same as 

 a simple frictional resistance (as of a friction-brake) consisting 

 of 4*1 x 10 15 tons force acting tangentially against the motion 

 of a pivot or axle of about \ inch diameter. To estimate the 

 retardation produced by this, we shall suppose the square of the 

 earth's radius of gyration, instead of being f, as it would be if 

 the mass were homogeneous, to be ^ of the square of the radius . 

 of figure, as it is made to be, by Laplace's probable law of 

 the increasing density inwards, and by the amount of precession 

 calculated on the supposition that the earth is quite rigid. 

 Hence (if we take y=32*2 feet per second generated per 

 second, and the earth's mass as 6*1 x 10 21 tons) the loss of an- 

 gular velocity per second, on the other suppositions we have 

 made, will be 



32-2x4-lxl0 15 x-02 - ' 2 . 

 or 2*94 x 10~ 21 . 



6-1 xl0 21 x |(21 xlO 6 ) 





The loss of angular velocity in a century would be 31 J x 10 8 

 times this, or '93 x 10 -11 , which is a3 much as ^Tv" °f 



2-7T 



RfiACM ' ^ e P resen t angular velocity. Thus in a century the 



earth would be rotating so much slower that, regarded as a 

 time-keeper, it would lose about one second and a quarter in 

 ten million, or four seconds in a year. And the accumulation 

 of effect of uniform retardation at that rate would throw the 

 earth as a time-keeper behind a perfect chronometer (set to 

 agree with it in rate and absolute indication at any time) by 200 

 seconds at the end of a century, 800 seconds at the end of two 

 centuries, and so on. In the present very imperfect state of clock- 

 making (which scarcely produces an astronomical clock two or 

 three times more accurate than a marine chronometer or good 

 pocket-watch), the only chronometer by which we can check the 

 earth is one which goes much worse — the moon. The marvel- 

 lous skill and vast labour devoted to the lunar theory by the great 

 physical astronomers Adams and Delaunay, seem to have settled 

 that the earth has really lost in a century about ten seconds of 

 time on the moon corrected for perturbations. M. Delaunay has 

 suggested that the true cause may be tidal friction, which he 

 has proved to be probably sufficient by some such estimate as 

 the preceding*. But the many disturbing influences to which 



* It seems hopeless, without waiting for some centuries, to arrive at 



2 n2 



