$to Air. Wildbore on 
1 • 
too. If £ — o, then e z =x* +f + z\ the motion being then 
round what M. Euler and M. d’Alembert call the initial 
axis, or that about which the body at reft would be firft ur^ed 
to move by any external forces adting upon it ; and which they 
have determined with fo much labour; though here it follows, 
as a necefi'ary confequence, that the force with which the bodv is 
turned round this initial axis is= or a force ~ 
\ r t t 
the fum of the forces round the axes vvhofe poles are A, B, 
and C. 
\q 
Moreover, by the general laws of all motion, — — — , — - , and 
. . 
m * • • 
I I 2 j i I 
/ - — are the velocities with which the pole of the mo- 
mentary axis fhifts its place in directions perpendicular to 
BO, along BO and along its own track on the lurface refpec- 
dlively. And it is by taking the fluxions of thefe, and 
dividing each fluxion bv that of the time, that the acce- 
lerating forces are had, which are due to fuch alteration of 
place of the momentary pole ; and thefe muft by no means be 
confounded with the forces before found— —and -X/Go — <?/3 
g t g* 
in thofe diredtions, thefe laft pertaining to the tendency of the 
lurface itfelf to motion at O, and the others to the fhifting 
of the pole of the axis upon the furface, which are different 
motions, as will more clearly appear from what follows. 
The preceding general properties of motion obtain in all 
bodies revolving round a center at reft, be their motion ever fo 
irregular; the three great circles bounding an odtant of the 
fpherical furface revolving with the body are alfo taken ad libi - 
turn, being any fuch circles whatever upon the furface ; and . 
hence the following very important confequence is drawn, viz* 
* ¥ 
