Now, by the use of trigonometry, we have the length of the line _A
f_ (radius of the arc _a_) and all the angles given, to find the length
of _f B_, or _A B_, or both _f B_ and _A B_. By adopting this policy we
can verify the measurements taken from our drawings. Suppose we find by
the graphic method that the distance between the points _A B_ is 5.78",
and by trigonometrical computation find the distance to be 5.7762". We
know from this that there is .0038" to be accounted for somewhere; but
for all practical purposes either measurement should be satisfactory,
because our drawing is about thirty-eight times the actual size of the
escape wheel of an eighteen-size movement.
HOW THE BASIS FOR CLOSE MEASUREMENTS IS OBTAINED.
Let us further suppose the diameter of our actual escape wheel to be
.26", and we were constructing a watch after the lines of our drawing.
By "lines," in this case, we mean in the same general form and ratio of
parts; as, for illustration, if the distance from the intersection of
the arc _a_ with the line _b_ to the point _B_ was one-fifteenth of the
diameter of the escape wheel, this ratio would hold good in the actual
watch, that is, it would be the one-fifteenth part of .
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