r 20 Mr. Wildeore on 
let M = themafs or folidity, and 2 d 9 2 c 9 and 2 b y be the three 
dimenfions or length, breadth, and thicknefs of fuch parallelo- 
pipedon ; then it is known that the momentum of inertia 
round the axis on which the dimenfion 2 d is taken will be=r 
|Mx c 2 -f^ 2 , this being no more than the produfl of a particle 
of the body into the fquare of its diftance from luch axis, 
when integrated through the whole body, as is now too well 
known to need the repetition here. Let I (tig. 6 .) be the 
centre of gravity or of inertia (they being both one) of fuch 
parallelopipedon, IB the permanent axis on which the dimen- 
iion 2 c is taken, Cl that on which 2 b is taken, and a perpen- 
dicular to the plane BIC (of the paper) at I that on which 2 d 
is taken; then on the centre I defcribing the quadrant BSC, 
whofe radius BI or Cl may be fuppofed unity; if the body 
once revolve about this laft named axis with an angular velo- 
cityrz zz meafured along the great circle BSC, and no external 
force or impulfe a ft upon it, it is agreed and well known, that 
the centrifugal motive force round fuch axis will beziMsf x 
— — and always being equal in contrary direftions round the 
3 
axis can have no power to alter the place thereof ; but fuch 
motion and motive force continuing always the fame, the axis 
muft be at reft, and the velocity round it uniform for ever. But, 
if the body whilft fo revolving receive (as by hypothefis) an 
impulfe in a dir eft ion parallel to this axis, that is, perpendicu- 
lar to the plane of the circle BCI, and an equal and contrary 
one to keep the centre I ftill at reft, the faid impulfe being 
perpendicular to the motion cannot inftantly alter the angular 
velocity but will give the axis itfelf a motion in a plane 
perpendicular to BCI, and confequently about fome axis SI in 
the plane BCI, round which axis SI the centrifugal motive 
forces 
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