If the force K H be directed obliquely to the axis, it will be
equivalent to two forces (76.), one K L perpendicular to the axis,
and the other K M parallel to it. The effect of each of these may
be investigated as in the preceding cases.
In all these observations the body has been supposed to be submitted
to the action of one force only. If several forces act upon it, the
direction of each of them crossing the axis either perpendicularly
or obliquely, or taking the direction of the axis or any parallel
direction, their effects may be similarly investigated. In the same
manner we may determine the effects of any number of forces whose
combined results are mechanically equivalent to forces which either
intersect the axis or are parallel to it.
(184.) If any force be applied whose direction lies in a plane oblique
to the axis, it can always be resolved into two elements (76.), one of
which is parallel to the axis, and the other in a plane perpendicular
to it. The effect of the former has been already determined, and
therefore we shall at present confine our attention to the latter.
Suppose the axis to be perpendicular to the paper, and to pass through
the point G, _fig. 71._ and let A B C be a section of
the body. It will be convenient to consider the section vertical and
the axis horizontal, omitting, however, any notice of the effect of the
weight of the body.
Let a weight W be suspended by a cord Q W from any point Q. This
weight will evidently have a tendency to turn the body round in the
direction A B C. Let another cord be attached to any other
point P, and, being carried over a wheel R, let a dish S be attached to
it, and let fine sand be poured into this dish until the tendency of
S to turn the body round the axis in the direction of C B A
balances the opposite tendency of W. Let the weights of W and S be
then exactly ascertained, and also let the distances G I and
G H of the cords from the axis be exactly measured. It will be
found that, if the number of ounces in the weight S be multiplied by
the number of inches in G H, and also the number of ounces in W
by the number of inches in G I, equal products will be obtained.
This experiment may be varied by varying the position of the wheel R,
and thereby changing the direction of the string P R, in which
cases it will be always found necessary to vary the weight of S in
such a manner, that when the number of ounces in it is multiplied by
the number of inches in the distance of the string from the axis, the
product obtained shall be equal to that of the weight W by the distance
G I. We have here used ounces and inches as the measures of weight
and distance; but it is obvious that any other measures would be
equally applicable.
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