Principles of progreffive and rotatory Motion. 565 
AyEZ. Let lcm, perpendicular to ab, be the axis about 
which the plane begins to revolve, and />, q be two equal 
particles of the plane fimilarly fituated in refpeil to ab, 
alfo qb, pa perpendicular to lcm. Now the centrifugal 
force of p.j or its force in the direition ap ispxap , and 
that of q in the direction bq is q x bq ; to determine now 
how thefe forces will ailed! the motion of the plane, we 
may obferve in the fir ft place, that the force p x ap, ail- 
ing at a in the plane, muft tend to give it a motion 
about an axis perpendicular to the plane ; but as an equal 
force q x qb ails at q to give it a motion in a contrary di- 
reition, it is evident that the two forces will dellroy each 
other, fo far as they tend to generate any motion in the 
plane about an axis perpendicular to it ; and hence it is 
manifeft, that if the parts of the plane a ys, azb, be 
fimilar, and fimilarly fituated in refpeil to ab, the plane, 
after the commencement of the motion, will have no 
tendency to revolve about an axis perpendicular to it, 
Alfo, as the centrifugal force of each particle ails in a 
direilion parallel to ab, it can give the plane no ten- 
dency to revolve about that line as an axis, and confe- 
quently the plane of rotation will be preferved as in ipfo 
motus initio. Conceiving therefore the plane on each 
lide the line ab to be fimilar, and fimilarly fituated, 
fuppofe another plane to be fixed upon this, whofe parts 
4 E 2 on 
