[ 17 ] 



about a diameter of the equator ; therefore the part of it which - 

 is employed in giving motion to the ring, bears a very fmali 

 proportion to the v/hole force, and it is this fmall part only 

 which is counteraded and rendered inefEcient ; for the fphere 

 itfelf has no centrifugal force, whereby it endeavours to re- 

 volve round a momentary axis. Hence the motive force being 

 given, viz. the force on the ring, the angtilar motion generated 

 will be inverfely as the inertia of the matter moved ; now the 

 inertia of the annulus is = the matter of the annulus x v/F 

 (the diftance of its centre of gyration from the centre of the 

 ring) •, and the inertia of the fphere and ring together is = the 

 matter in them x ^/T ; therefore the angular velocity of the ring 

 muft; be diminifhed in the ratio of the inertia of the ring to 

 the inertia of the ring and fphere together, in order to have 

 the angular velocity which now will be produced in the ring, 

 in confeg^uence of its connedlion with the fphere, by the coun- 

 terading force. That is, if a be the angular velocity of the 

 ring and fphere united, the angular velocity which that part 

 of the force which is counteraded could produce in the ring 



.„ , inertia of the ring i ^, , ,,, 



•will be = ,2 X . -■ Trrr—Tu-^ = a x • The 250'h part 



inertia or the Iphere 250 



therefore of the whole force only is now efficient in moving the 



ring round its diameter ; but this part is = the centrifugal force, 



and therefore it is this part only of the whole folar force which 



is countera(3;ed. , 



Vol. VII. C Hence 



