A View of Sir Isaac Newton's PhilosophyPemberton, Henry
Science
A View of Sir Isaac Newton's Philosophy
Pemberton, Henry
Newton, Isaac, 1642-1727. Principia
34. IF the lever should consist of two arms making an angle at the
point C (as in fig. 26.) yet if the forces are applied perpendicularly
to each arm, the same proportion will hold between the forces applied,
and the distances of the center, whereon the lever rests, from the
points to which they are applied. That is, the weight at E will be to
the force in F in the same proportion, as C F bears to C E.
35. BUT whenever the forces applied to the lever act obliquely to the
arm, to which they are applied (as in fig. 27.) then the strength of
the forces is to be estimated by lines let fall from the center of
the lever to the directions, wherein the forces act. To balance the
levers in fig. 27, the weight or other force at F will bear the same
proportion to the weight at E, as the distance C E bears to C G the
perpendicular let fall from the point C upon the line, which denotes
the direction wherein the force applied to F acts: for here, if the
lever be put into motion, the power applied to F will begin to move in
the direction of the line F G; and therefore its first motion will be
the same, as the motion of the point G.
36. WHEN two weights hang upon a lever, and the point, by which the
lever is supported, is placed in the middle between the two weights,
that the arms of the lever are both of equal length; then this lever is
particularly called a balance; and equal weights equiponderate as in
common scales. When the point of support is not equally distant from
both weights, it constitutes that instrument for weighing, which is
called a steelyard. Though both in common scales, and the steelyard,
the point, on which the beam is hung, is not usually placed just in the
same straight line with the points, that hold the weights, but rather
a little above (as in fig. 28.) where the lines drawn from the point
C, whereon the beam is suspended, to the points E and F, on which the
weights are hung, do not make absolutely one continued line. If the
three points E, C, and F were in one straight line, those weights,
which equiponderated, when the beam hung horizontally, would also
equiponderate in any other situation.
[Illustration]
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