310 SCIENTIFIC NEWS. 



ral waves, sepavated by nodes, or points of rest; and he de- 

 termined the absolute number of vibrations that constitute 

 each note, deduced in the first place from delicate and cu- 

 rious experiments, which he compared afterward with the 

 algebraic formulae derived from the theory of the centres of 

 oscillation; as appears in the Memoirs of the Academy for 

 3713. 



Taylor. Taylor, in his Methodus Incrementorutn, published in 



1717*, treated the problem more profoundly, on the hypo- 

 thesis, that the forces acting on the material points of the 

 system are proportional to their distances from a right line 

 drawn from one fixed point to the other, so that these points 

 all arrive at the right line at the same time. Twenty or 



Bernoulli. thirty years after Daniel Bernoulli farther developed the 

 theory of Taylor; but for the general and strict solution of 

 the problem we are indebted to d'Alembert and Euler. 

 These great geometricians first employed the differential 

 equation of the motion of the sonorous chord, which is with 



D'Alembert & partial differences, and of the 6econd order. This equation 

 er * was first found and summed np by d'Alembert, but Euler 



was more sensible of its generality. 



Fonorous An equation of the same order is applicable to the osciU 



tubes, lations of air in tubes; and does not change, when from the 



case of the simple line we proceed to cases of two or three 

 dimensions. 



strings ^ n tne P r °bhirns of which we* are speaking the order of 



the differential equation of the motion is connected with the 

 manner, in which we consider the effects of elasticity in the 

 body moved. It has been here applied to a chord stretched 

 between two points. If the chord be let loose at one of 

 these points, being perfectly flexible, it is incapable of pro-? 

 ducing any acoustic phenomenon. 



and springs. It is otherwise if the chord be a spring properly so called. 



In this case, confining it if you please to a single fixed 

 point, the spring set to vibrate will produce a perceptible 

 seund, if its oscillations exceed '24 per second: but the dif- 

 ferential equation of this movement will be of the 4th or- 

 der. The first problem may be considered as a particular 



* Taylor's paper on the motion of tense strings was published in the 

 Phil. Trans, for 1713. 



case 



