"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 ordinate _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.