VIBRATION OF STRINGS. 337 



mechanical causes and laws would explain. But 

 this problem, as might be expected, was not at- 

 tacked till mechanical principles, and the modes of 

 applying them, had become tolerably familiar. 



As the vibrations of a string are produced by 

 its tension, it appeared to be necessary, in the first 

 place, to determine the law of the tension which 

 is called into action by the motion of the string ; 

 for it is manifest that, when the string is drawn 

 aside from the straight line into which it is 

 stretched, there arises an additional tension, which 

 aids in drawing it back to the straight line as soon 

 as it is let go. Hooke (On Spring^ 1678) deter- 

 mined the law of this additional tension, which he 

 expressed in his noted formula, " Ut terisio sic vis," 

 the force is as the tension ; or rather, to express 

 his meaning more clearly, the force of tension is 

 as the extension, or, in a string, as the increase 

 of length. But, in reality, this principle, which is 

 important in many acoustical problems, is, in the 

 one now before us, unimportant ; the force which 

 urges the string towards the straight line, depends, 

 with such small extensions as we have now to con- 

 sider, not on the extension, but on the curvature ; 

 and the power of treating the mathematical difficulty 

 of curvature, and its mechanical consequences, was 

 what was requisite for the solution of this problem. 



The problem, in its proper aspect, was first at- 

 tacked and mastered by Brook Taylor, an English 

 mathematician of the school of Newton, by whom 

 VOL. ii. Z 



