the Rotatory Motion of Bodies. 323 



to E as a to the fine of the angle />P«, it follows, that the 



fine of pVu will be =: ■ — ^— ^ ~ / "^ , , and its co{ine = 



— — ■ ^ , / ^ . Therefore, that cofine being to radius as 



( — J the fluxion of the arc PQ to (z) the fluxion of the polar 



o 



track on the Iphericai iurfaee, J2 will be = — == ■ 



-/D?/?- - C/ X V Dn^~ B/ 

 Now,, P/jIvN being a quadrant of a great circle (touching the 

 faid polar track at P), and NAN a diameter of that circle ; if 

 we put w to. denote the diflance of any particle ^^^ of the? 

 parallelopipedon from that diameter, and G to denote the ac- 

 celerative force of any fuch particle when iv is-ia ; the motive 



force F {='- — -J X v/D';?2'«^ - BCa'y^), computed above,will be = ' 

 -^ y^the fum of all the w'-xp-, which fum, by computation, is 

 found =: - X D-;;.V-BC.V • Confequentiy, 



G will be ^^3 X^ ^^, _ DW-.y ^.'.'+.V ■ BC/ - But, by 

 what. I have done in the' Fhilofophical . Tranfa^ions for the 

 year i jyy, — will be =: 1; •= the velocity wherewith the 



momentary pole; changies its place in the fpherical furface ta 

 which it is referred. Therefore, 



V will be = -^ X ^^^,^„,,._ ^^j^^_^c^ ; =!nd - =^ 1 ,, 



2 



the fluxion of the time = — x 



ny d^ + b"- . Wtrrn'--b^nr + cV + d';.'' . BC>' 



^ V-D^VC-ZX ^^D«^-B/x D^wSjVBCA' 



