Bod:es aff'ecJed fy Frisian, 185 



being fubflltuted for v in the lail: article of Cafe II. gives 



i,^,s--ax^ta ^^^ ^j^^ fpace defcribed before the motion become? 



ahxai" ^ 



uniform. 



3. If V has a iefs proportion to a than r a has to r j, it is 

 manifefl, that the rotatory motion will be deftroyed before tiie 

 frogrp[jive\ in which cafe a rotatory motion will be generated 

 in a contrary direction until the two motions become equal, 

 when the fridion will inftantly ceafe, and the body will then 



move on uniformly. Now r a \ r s \\ v '. - — - the progreflive 



velocity deftroyed when the rotatory velocity ceafes, hence 



a = ■ = progreiiive velocity when it begins its 



rotatory motion in a contrary direction ; fubflitute therefore 

 this quantity for a m the expreffion for z in Cafe L and we have 



n^ -]- 2f'i X • a X a X ra — V X r s 



iii~ X ar 



i — r; — for the fpace defcribed after the rota- 



tory motion ceafes before the motion of the body becomes 

 uniform. Now to determine the fpace defcribed before the 

 rotatory motion was all deftroyed, we have (as the fpace from 

 the end of a uniformly retarded motion Varies as the fquare of 



a axra — vxrs aXra — vX rs 



the velocity) a : —p : : -^ : — r^gr— -. — the fpace that 



could have been defcribed from the time that the rotatory 

 velocity was deftroyed, until the progrellive motion would 



Have been deflroyed had the fri6lon continued to acfl ; hence 



._ ^4 



« ax ra — v xrs lav X raX rs — v^ xri^ ■, r i r • i i i 



re- HFU — 2 — — v z = the Ipace deicribed when 



21' '^r X ra 2.\ x ra ^ 



the rotatory motion was all deftroyed, hence 



.1 



rj*+ 2' J X ra X a X a- — : x 2av Xra Xrs — %?" x ri 



z^ ^^^L- + i:^ ■■ -^'whoie fpace da- 



ai xar X2\: 2.b x ra ^ 



fcribed by the body before its motion becomes uniform. 



Vol. LXXV. " B b d ->.- 



