| | | | | | | The total of | | | | | | four thick | | | | | | strings is | 62-3/4 | 27 13-1/4 | 16 12 | 11 1-1/4 | | | | | | | | The total of | | | | | | four small | | | | | | strings is | 52-1/2 | 23 5 | 13 10 | 9 11 | +----------------+------------+------------+------------+------------+ B A C is the average angle formed by a string passing over the bridge of a Violin, and the tension acts equally in the direction A B, A C. [Illustration of angles of the strings.] Take A C=A B. From the point B draw B D parallel to A C. And from the point C draw C D parallel to A B, cutting B D at D. Join A D. Then, if a force acting on the point A, in the direction of A B, be represented in magnitude by the line A B, an equal force acting in the direction A C will be represented by the line A C, and the diagonal A D will represent the direction and magnitude of the force acting on the point A, to keep it at rest. N.B.--The bridge of a Violin does not divide the angle B A C quite equally, but so nearly that A D may be taken as the position of the bridge. Also, the plane passing through the string of a Violin, on both sides of the bridge, is not quite perpendicular to the belly. To introduce this variation into the calculation would render that less simple, and it will be sufficient to state that about the 150th part must be deducted from the downward pressures given in the above table from the first and fourth strings, and about the 300th part for the second and third strings. The total to be deducted for the four strings will not exceed three ounces. On the line A B or A C set off a scale of equal parts, beginning at A, and on A D a similar scale beginning at A. Mark off on the scale A B as many divisions as there are lbs. in the tension of a string, for example 18, and from that point draw a line parallel to B D, cutting A D at the point 8 in that scale. Then, if the tension of a string be 18 lb., the downward pressure on the bridge will be 8 lb.; and therefore for the above angle the downward pressure of any string on the bridge will be 8/18=4/9 of the tension of that string. The whole of the downward pressure of the first string falls upon the Treble Foot of the Bridge. The downward pressure of the second string is about 2/3 the Treble Foot of the Bridge, and 1/3 on the Bass Foot. The downward pressure of the third string is about 1/3 on the Treble Foot, and 2/3 on the Bass Foot. The whole of the downward pressure of the fourth string falls upon the Bass Foot of the Bridge. SECTION IV The Italian School