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[ 13 ] 



The quantity of matter in the annulus is 2/, and the diflance 

 of the centre of gyration from the centre of the earth is v'i ; and 

 by the property of that centre, if the whole matter of the an- 

 nulus were colletfted into that point, any force applied to move 

 it about the centre C, would generate the fame angular velocity, 

 in the fame time, as it would do in the ring itfelf. And fince 

 this force T cs adls at the fame diflance \/^ from the centre of 

 the annulus, it is the fame thing as if it were direcflly applied 

 to the body to move it. Now to find the motion generated, 

 fince the fpace defcribed in a given time, is as the force diredlly, 



p c s f* h fc s 

 and the matter moved inverfely, therefore p- .- h: : —— ■ -z^— 



= the fpace defcribed by the centre of gyration in i". And 

 ■ip JI (the circumference of the circle whofe radius is the diflance 

 of the centre of gyration from the centre of the annulusj : 360° : : 



- _^ : ';6o X the angle through which the rinc; is drawn 



in i" hy the adlion of the fun, when at the greateft 'diflance 

 from the nodes. 



But the force of the fun when at any other diflance from 

 the nodes, as at H, will be lefs ; and the mean quantity of the 

 force may thus be iiiveftigated. Draw the great circle ^ H G P, 

 and making radius = i, let the arch C H = 2, fine of C H = jy; 

 then in the fphcerical triangle C H G, Rad [\): S. CU. (y) : : S. 

 angle D C A (s) : S. H G = sy. But it has been already proved, 



that 



