"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 millimètre (.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 abscissæ 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 millimètre, 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.
François 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 afterwards by dealers. This is certainly the case with the few Tourtes that are stamped with their maker's name, for it is an ascertained fact that the Tourtes never stamped their work. There are only two instances on record of Tourte marking a stick, and in each case it consisted of a minute label glued into the slot bearing the following inscription: "Cet archet a été fait par Tourte en 1824, âge de soixante-dix-sept ans." (This bow was made by Tourte in 1824, aged 77 years).
An important addition, said to have been instituted by Lupot, was the metal plate which lines the groove in the nut and prevents the wearing away of the nut by friction with the stick.