338 HISTORY OF ACOUSTICS. 



the solution was published in 1715, in his Methodus 

 Incrementorum. Taylor's solution was indeed im- 

 perfect, for it only pointed out a form and a mode 

 of vibration, with which the string might move 

 consistently with the laws of mechanics; not the 

 mode in which it must move, supposing its form to 

 be any whatever. It showed that the curve might 

 be of the nature of that which is called the com- 

 panion to the cycloid ; and, on the supposition of 

 the curve of the string being of this form, the 

 calculation confirmed the previously established 

 laws by which the tone, or the time of vibration, 

 had been discovered to depend on the length, ten- 

 sion, and bulk of the string. The mathematical 

 incompleteness of Taylor's reasoning must not pre- 

 vent us from looking upon his solution of the pro- 

 blem as the most important step in the progress 

 of this part of the subject: for the difficulty of 

 applying mechanical principles to the question being 

 once overcome, the extension and correction of the 

 application was sure to be undertaken by succeed- 

 ing mathematicians; and, accordingly, this soon 

 happened. We may add, moreover, that the sub- 

 sequent and more general solutions, require to be 

 considered with reference to Taylor's, in order to 

 apprehend distinctly their import; and further, that 

 it was almost evident to a mathematician, even 

 before the general solution had appeared, that the 

 dependence of the time of vibration on the length 

 and tension, would be the same in the general case 



