ro8 
Mr. Wildbore on 
into the direction perpendicular to HO at O is— dz x f. ROE=* 
, alfo the acceleration bx at O perpendicular to AO reduced 
g 
into the direction perpendicular to BO = bx x f. DOS = 
, hence the whole acceleration along DE at O, which ma- 
b AO 
y@x 
g 
nifeftly arifes from thefe three, is — — — —gy, and the acce- 
g g 
lerative force — which, properly reduced, becomes — 
g t 
~ as before. And the force which is compounded of the two 
gt - j 
forces e x ^ and - % is = % V “fiS - 4- y ' = ^ + y + <5* 
gt g i g t 1 
adting perpendicular to the track of O upon the moving fpheri- 
cal furface; and - — f S ' x + is the accelerating force adling 
along the midcircle, or that which is 90 diftant from O, to 
alter the velocity about the natural or momentary axis whofe 
pole is O. Hence, anfwerable to the three accelerating forces 
P * rv> 
and - , round the axes whofe poles or ends A, B, and C, 
i t i. 
are always the fame invariable points upon the moving fpherical 
furface, there arife three other accelerating forces, namely, 
e x , and fe-t ; the two former adting at the 
gt 7 gt t 5 
pole of the momentary axis, and the latter is that whereby the 
velocity about the momentary axis is altered. 
scholium 1 . 
From the preceding inveftigation of the forces e x and 
gt 
* it follows, that they are not at all affedted in expreffion by 
the 
