ts diameter is 0^m, 008-6/10 (.34 inch).

"From this cylindrical or prismatic portion the diameter of the bow
decreases up to the head, where it is reduced to 0^m, 005-3/10 (.21
inches). This gives a difference of 0^m, 003-3/10 of a millimetre
(.13 inch) between the diameters of the extremities; from whence it
follows that the stick comprises ten points where its diameter is
necessarily reduced by 3/10 of a millimetre (.012 inch) reckoning
from the cylindrical portion.

"After proving by a great number of Tourte's bows that these ten
points are not only found always at decreasing distances on the same
stick, but also that the distances are perceptibly the same, and that
the situations of the points are identical on different bows compared
together, M. Vuillaume sought to ascertain whether the positions of
the ten points could not be obtained by a geometrical construction,
by which they might be found with certainty; and by which,
consequently, bows might be made whose good condition should be
always settled _a priori_. This he attained in the following manner.
At the extremity of a right line A B, equal to 0^m, 700 (27.56
inches), that is to say the length of the bow, raise a perpendicular
A C, equal to the length of the cylindrical portion, namely 0^m, 110
(4.33 inches).

"At the extremity B of the same line, raise another perpendicular B
D, of the length 0^m, 022 (.866 inches) and unite the upper
extremities of these two perpendiculars, or ordinates by a right line
C D, so that the two lines A B and C D, may lie at a certain
inclination to each other.

"Take the length 0^m, 110 (4.33 inches) of the ordinate A C with the
compasses, and set it off on the line A B, from A to _e_: from the
point thus obtained, draw another ordinate (parallel to A C and
perpendicular to A B), until it meets the line C D.

"Between these two ordinates A C and _e f_--the latter of which is
necessarily less than the former--lies the cylindrical portion of the
bow, whose diameter, as before stated, is 0^m, 008-6/10 (.34 inch).

"Then take the length of the ordinate last obtained, _e f_, and set
it off, as before, on the line A B, from _f_ to _g_, and at the point
_g_ draw a third ordinate _g h_, the length of which must also be set
off on the line A B, to determine thereon a new point _i_, from which
to draw the fourth ordinate, _i j_: the length of which, likewise,
when set off on the line A B, determines the point where the fifth
ord