D 
D-VV - BCaV x «W* Z - Dot 4 
the fine of the arc PL being 
the Rotatory Motion of Bodies » 
-• Confequently, 
■ Ca z X V>^a>n z n z y 
• C a~ m z + Cu z n 
a 
- 2 ^D nf 
r v 2 x^D« -_V 
Da' 
: 2 2, 
//; •» • 
Dnfi ~iZu z m L -f- Ca 2 ;C . ^ 2 
and this fine being to radius as- the fluxion of the arc CJL to the 
meafure of the angle of contact of the polar, track on the movea- 
ble fpherical furface with a great circle, we And that meafure 
D«i:-Ca*xDV 2 - 1 
•a . 
m~n~y 
D^-CV x D z otV* 
X 7 Dot 2 — C y 2 X *«X D/2 2 --r- Bp x D~ot z « 2 — BCa 2 ^ D z rn z n z — B C a 2 > 2 ] ^ 
The meafure of the angle of contact of the track of the 
momentary pole, in the immoveable fpherical furface,. with a. 
great circle, will accordingly be 
eT~ 
D 
m 
Cot 2 X D W* -b z ft z -f f V + V 
^ DL/ V - BCaV 
meafure we may defcribe,.. by points, the track of the momen- 
tary pole in the fpherical lurface laid mentioned; 
There are other methods of finding that track ; but I know 
none that is lefs difficult than this method, or in any refpedt 
more fatis factory. 
The radius of the lefler circle, which is the circle of curva- 
ture of the polar track, in our immoveable fpherical furface,. 
will be =: 
===“*■ : ‘ by means of which: 
O’Z 
pD 2 OTV-fiCaV 
*/ 
b z + sf • »*W + <rt ■ " ~~ BC V 
z + iq.of the meat, of the ang. of cont. 
When B is - o, or very {mall, in comparifon with D, and 
V)m z is lefs than CT, the laid mentioned radius will be equal, or 
nearly equal, to the invariable Quantity — :=^.r, 
1 1 4nT1 2 . + 4*4W 
the track of the pole in the immoveable fpherical furface being 
then exactly,, or very nearly, a lefler circle. At the fame time,, 
the 
