284 OUTLINES OF NATURAL PHILOSOPHY. 



weight per inch remaining the same, the celerity of 

 vibration is inversely as the length. 



The problem of the musical chord was first resolved, 

 and the preceding theorems investigated, by BROOK 

 TAYLOR, in his Meihodus incrementorum, prop. 21. 

 23., Sec. His solution, though very ingenious and 

 extending to most of the cases that occur in nature, 

 was not general, nor complete, when mathemati- 

 cally considered. The first complete solution was 

 given by D'ALEMBERT, in the Berlin Memoirs for 

 1747, and it led him at the -same time to discoveries 

 which form a great era in the history of the Diffe- 

 rential and Integral Calculus. Mem. de Berlin, 

 1747, p. 214., &c. 



381. When the sounds of different musical 

 strings are compared, a certain difference between 

 them is perceived by the ear, which is called dif- 

 ference of tone; and this difference is also expres- 

 sed by saying, that the one sound is graver, and 

 the other more acute ; the variations of tone are 

 found to have a constant or fixed relation to the 

 comparative celerities of vibration. 



As the string performs more vibrations in a given 

 time, the sound it yields becomes more acute ; and 

 as it vibrates more slowly, the sound is graver. 

 This is easily brought to the test of experiment. 

 The strings that vibrate faster, either from the 

 greater tension, or their smaller length and weight, 



invariably 



