By a careful application of the silk bow-string, X Y Q can be drawn,
which, itself in close proximity to A, passes more nearly through F₁,
F₂, &c. than is possible for any line which passes exactly through A.
X Y Q will be found not only to intersect all the small circles, but
to cut off a considerable arc from each. Measure off X P a distance of
10", and erect the perpendicular P Q; then, if _R_ be the load, and
_F_ the corresponding friction, we must have from similar triangles—
_AY_
_F_ - ———— × 1 lb.
0"·1 _PQ_
————————————————— = ——————.
_R_ _PX_
By measurement it is found that _AY_ = 0"·14, and _PQ_ = 2"·53.
We have, therefore,
_F_ = 1·4 + 0·253 _R_.