inate _k l_ is to be drawn. The latter, in like manner, determines
the sixth _m n_, and so of the others, to the last but one _y z_.

"The points _g i k m o q s u w y_ so obtained, starting from the
point _e_, are those where the diameter of the bow is successively
reduced 3/10 of a millimetre (.012 inch). Now, these points have been
determined by the successively decreasing lengths of the ordinates
drawn from the same points, and their respective distances
progressively decrease from the point _e_ to the point B.

"If we subject these data to calculation, we shall find that the
profile of the bow is represented by a logarithmic curve, of which
the ordinates increase in arithmetical progression; while the
abscissae increase in geometrical progression; and lastly, that the
curvature of the profile will be expressed by the equation

y = - 3.11 + 2, 57 log. _x_;

and, in varying _x_ from 175 to 165 tenths of a millimetre, the
corresponding values of _y_ will be those of the radii (or
semi-diameters) of the transverse circular section of the bow at
corresponding points in the axis."

CHAPTER VII.

LUPOT--PECCATTE--SPURIOUS STAMPING--PANORMO--W. J. B. WOOLHOUSE'S
CALCULATIONS.

I have spoken at length of Dodd and Tourte--two names that stand out
in the history of the bow with remarkable prominence--and before
proceeding with the general list of bow makers, great and small, I
propose to speak of Peccatte and Lupot, whose genius was inferior
only to that of Tourte in that they were followers rather than
originators.

Francois Lupot was a brother of Nicolas Lupot the violin maker. He,
however, devoted all his energies to the manufacture of bows, and, in
his best work, is considered by many to nearly equal Tourte. But
unfortunately the standard of excellence in Lupot's bows varies to a
considerable extent, and, while some are truly magnificent others are
very inferior. This is a fact that cannot be too widely made known in
the interests of intending purchasers. The guarantee of genuineness
alone is not sufficient for anyone desiring a bow for use, and,
unless he has the requisite knowledge and experience himself he
should always first submit a bow to a professional man of repute for
his judgment as to its qualities for a player. Many of Lupot's sticks
are stamped "LUPOT," sometimes in two or three places, but it has
been doubted whether he did this himself or not. In general it is
thought that it was done af