tin' Rciatoiy Motion of B^lcs,- ^^r 



^ ^S?3bc7?">;Vd?S^ Confequently, 



the line of the arc PL being = -^ — zzz ~~ -^ -^ ; 



and this fine being to radius as the flvixion of the arc CL to tlie 

 meafure of the angle of contacl of the polar track on the 7?jovea- 

 ble fpherical furface with a great circle, we find that meafure 



The meafure of the angle of con tad of the track of the 

 momentary pole, in the immoveable fpherical furface, with a 

 great circle, will accordingly be 



^T- ^, =';7 h^^^ JKC-- ~'' ^y"^^''^^^S of which- 



meafure we may defcribe, by points, the track of the momeiir 

 tary pole in the fpherical furface lafl mentioned. 



There are other methods of finding that track ; but I know 

 none that is lefs difficult than this method, or in any refped 

 more fatisfa6lory. 



The radius of the leffer circle, which is the circle of curva- 

 ture of the polar track in our immoveable fpherical furface, 

 will be = 



'V'i^o-iq.of tliemeaf.of theang.ofcont. '^ ff^l^"^ . ■^^-^jT^^jT^^ .n—'&Qy' ' 



When B is=:o, or very fmall in comparifon with D, and 

 D/»" is lefs than C^% the lafl: mentioned radius will be equal, or 



nearly equal, to the invariable quantitv -. ; 



the track of the pole in the immoveable fpherical furface being 

 then exadly, or very nearly, alefler circle. At the fame time, 



the 



