the Rotatory Motion of Bodies. 323 
to E as a to the fine of the angle pYit, it follows, that the: 
fine of pYu will be = — V f X % ~, and its cofine = 
r g*? D~m z n z — B C a 2 7 
~ -" By h Therefore, that cofine being to radius as 
(—) the fluxion of the arc PQ to (2) the fluxion of the polar 
g 
Vd^V-bc^V 
track on the fpherical furface, z will be = - , T __ 
.Now, PyLN 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 difiance of any plrticle (p ) of the 
parallelopipedon from that diameter, and G to denote the ac- 
celerative force of any fucb particle- when w is = a the motive 
Me 2 
force F (— — s X s/Y> z nrt 2 ?f — BCN 2 y 2 ), computed above, will be = 
3 
G 
-a- x the fum of all the w 2 xp; which fum, by computation, is 
founds — x 
3 
M f + /r . I>V,V - b z m z + c 2 a 2 + ft? . BC* 
D Z /»V-BC«V 
D a w V — BCaVj^ 
2 
t ■ ■ 
G will he — - X 
Confequently, 
f+b z . D m n — b z m z + c z a z + d z n . BC/ 
But, by 
what I have done in the Philofophical Rranf actions for the 
year 1 777> f be ~ v ~ the velocity wherewith the 
momentary pole changes it's place in the fpherical furface to 
which it is referred. Therefore, 
v will be = i X 
D z m z n z — BCAyP 
; and - =■ T, 
d z + b z . D z m 2 n z - b z m z + c z a 2 + ft? . BC/ „ 
the fluxion of the time = — ■ x + <ra 2 + a 2 ,? . BC/ 
* / Vn?-C /X V D« 2 ~By 2 X DTV-BCtfV 
