68 POPULAR LECTURES AND ADDRESSES. 



instead of being r, as it would be if the mass were 

 homogeneous, to be J 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 

 c <r=32'2 feet per second generated per second, and 

 the earth's mass =5-3 x io 21 tons) the loss of 

 angular velocity per second, on the other supposi- 

 tions we have made, will be 



32*2 x 3-3 x io 15 x -02 



-7^5 , or 27 x icr 21 . 



5-3 x IO 21 xj (21 x IO C ) 2 



The loss of angular velocity in a century would 

 be 31^ X io 8 times this, or 8'5 x io~ 12 , which is 



I'l6 27T 



as much as 7 of , the present angular vel- 



10' 06400 



ocity. Thus in a century the earth would be 

 rotating so much slower that, regarded as a time- 

 keeper, it would lose about n6 seconds in ten 

 million, or 3-6 seconds in a year. And the accu- 

 mulation 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 180 seconds 

 at the end of a century, 720 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 



