- Mr . Wildbore on 
ties of the points A, B, and C, in directions perpendicular 
to ZA, ZB, and ZC, being computed in like manner are 
zXcof ZC+;Xcof. ZB g Xcof. ZC + *Xcof. ZA a|1 ,^ ZA + yXcof.ZS 
TZA ’ i- zlj ’ . f - ZC 
c ^_ + ^y c’z -f a a- al)( j - A* .x'll t ail d if each of 
or 
✓ly + iV’ v'cV + flV' ‘Sa** + b , f 
the fquares of thefe be added to each correfpondent fquare 
of the three former, the rebuking lums will be zr +/, 
z z +x z , and x 1 + y\ which are the fquares of the abfolute 
velocities of the poles A, B, and C, along their own pro- 
per tracks in abfolute fpace, the operation thus proving 
itfelf. Hence we gain a clear idea of the motion of the body, 
during the time that the oCtant ABC takes in palling under Z, 
beginning at fome point V in C3 (or in AB as the cafe may 
happen) and ending at lome point W m CA , that is, the 
point Z enters the oftant when V touches Z, and quits it 
at W, the motion of the body or fpherical furface that revolves 
with it under Z, being in the fenfe from W towards V ; that 
is, W approaching the fixed point Z whilft V recedes from it. 
And fince both the directions and velocities of the poles A, B, 
and C, in abfolute fpace are given above, their tracks alfo may 
be determined by means of quadratures, as wall be Ihewn here- 
after. Again, the track VZW, on the moving fpherical fur- 
face, which always paffes under, or, fome point of which, 
always touches Z as the body revolves ; and the velocity with 
which it paffes under it in every pofition may hence be deter- 
mined. Thus, from the equation above found for the value of 
'S, - rnr-F-TK j 
55, is eafily obtained cof. CZ 2 = m l c\ z = 
c z X a 2 — b- 
a z xb 2 -c 2 
x cof. AZ 2 — 
1 <1 Jl , > 
m c a X a 
-xST + wVCS the equation of the curve VZW 
u — c 
upon the moving fpherical furface, which will alfo be found to 
KA 
