Mr. WlLDBOHE on 
conic fections, is infufficient for determining the motion of 
the body with refpeft to abfolute fpace, becaule at prefenr 
nothing is found but the relations of inertia and velocities. 
In order to determine a point which can be considered as at 
reft in abfolute fpace, and the nature of the body’s motion 
with refpect to it; let Z (fig. 8.) be fuch a point, abfolutely 
at reft itfelf, but fo as to be always touched by the moving 
fpherical furface which revolves with the body. Or, it is the 
lame thing to confider it as a given point upon a concave 
fpherical furface at reft, furroundmg and every where touching 
that fuppofed above to revolve with the body. Through this 
point Z fuppofe quadrantal arcs A/, Bw, and Cn , to be drawn 
from the poles of the three permanent axes, and confequently 
perpendicular to the three fides of the octant ABC, fuppofing 
alfo Z to be at the inftant over fome point of this oftant, and 
that a is greater than b, and b than c, when the velocity of 
the oftant along its three fides muft neceffarily be in the fenfe 
from A towards B, from B towards C, and from C towards 
A ; then (by fpherics) asf. ZA : i :* f. Zw = cof. ZB : f. ZAC 
— coft ZAB :: f Z^ = cof. ZC : f. ZAB = coft ZAC ; alfo, as 
f. BZ : i : : ft Z n = cof. ZC : ft ZBA = cof. ZBC :: ft Z/ = cof. 
ZA : ft ZBC = cof. ZBA ; and as ft CZ : i :: ft Z l — coft ZA : 
ft ZCB = coft ZCA :: ft Zw = coft BZ : ft ZCA = cof. ZCB. 
Now, the velocity % in AB reduced in to the dire&ion of the great 
circle ZA is = z x coftZAB = and the velocity y in the 
X « J~. j / jl 
circle C A reduced into the direction of the great circleZA^jy x coft 
ZAC — , but in a contrary fenfe to the former; con- 
fequently the velocity of the point A along the great circle AZ 
in abfolute fpace, that is, the velocity with which A approaches 
the 
