Books › An Encyclopedia of the Violin, 1925 › scan 146
Scan 146
An Encyclopedia of the Violin, 1925
20 lines. Read by computer on 28 September 2026. Printed page 120. See the scan on archive.org.
1line, AC, is drawn, representing the length of the cylindrical portion, that is, 0 m, 110 (4 3/10"). At the extremity, B, of the same line, another perpendicular one is drawn, BD, whose length is 0 m, 022 (17/20"); and a straight line, CD, is used to unite the upper extremities of these two perpendicular lines or uprights in such wise that between them the two lines AB and CD form an angle.
3"Setting down the length, 0 m, 110 (4 3/10") of the upright AC, by means of the compasses, this length is carried back upon AB, and at its extremity another upright, EF, is ruled until the line CD is met, the new upright EF, consequently, being shorter than the upright AC. It is between these two uprights AC and CF, that the cylindrical portion of the violin bow is located, its diameter being, as has already been established, 0 m, 008 6/10 (1/3")."
5"Now, having established the length of the upright EF, it is brought back to the line AB, starting from the point F, and a point G results, on which a third upright, GH, is ruled, whose length is also established in order to bring it back from point G on the AB line, and to fix a new point, I, on which the fourth upright, IJ, is ruled, whose length similarly brought back to line AB, establishes the point at which the fifth upright, KL, is ruled. This, under the same conditions, established the sixth MN, and the procedure is continued in this manner until the upright before the last is reached.
7"The points G, I, K, M, O, Q, R, S, V, W and Y, thus obtained after starting from point E, are those at which the diameter of the bow is successively reduced 3/10 of a millimeter (about 2/27")."
9"Now these points have been determined by the successively decreasing lengths of the uprights ruled on the said points, and their respective distances from one another are decreased progressively, from point E to point B.
11"If these results are submitted to mathematical consideration, it will be found that the profile of the bow is represented by a logarithmic whose uprights increase in arithmetical progression; while the long lines increase in geometric progression, so that in the end the curvature of the bow profile may be expressed in the following equation:
13gr—3, 11 2, 5 log. X
15and by varying the X from 175 to 765 tenths of a millimeter, the values corresponding will be those of the rays.
17"Thus the exact theoretic schema of the violin bow may be formulated. By an analogous process of line drawing, it is easy to establish the proportions of the viola bow and of the violoncello bow."
19Another important point, which calls for elucidation is that of the bow with fixed nut, and we give the following explanation of the invention in Vuillaume's own words:
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