Improvements in Science. Ill 



endeavoured to bring the latter to the same state of ad- 

 vancement as the first. In regard to the theory of strings 

 and rods, he has brought forward several new facts. In 

 musical rods, hitherto, the situation of the nodes of vibra- 

 tion, was only known by means of empirical rules laid 

 down by Chladni. These gave a very uncertain result, so 

 that Chladni recommended in acoustic experiments, the 

 tight application of a soft roller of cork or caoutchouc to 

 each rod, in order to produce a pure note. Weber shows,* 

 that Euler has given an equation which exhibits in all cases 

 the situation of the node of vibration, and which, is to be 

 employed for fastening the rods, so that they give pure and 

 powerful notes. By this equation, the situation of the node 

 of vibration is shewn to be for 



The fundamental tone (grundton) 0*2240 from each end. 

 The first falsetto tone . . . 0-13205 from each end and 



in the middle. 



The second falsetto tone . . „„..„, ( from each end. 



When a cord, as commonly happens, is stretched between 

 two fixed points and struck, it takes between these two 

 points a curved position, and consequently, a greater length 

 with necessarily a greater tension. The influence of this 

 greater tension must become greater in proportion to the 

 extent which the cords have for vibrating in ; and, hence, 

 it follows, that the tone of the cord when it is strong, must 

 be higher than when it is weak. This difference is parti- 

 cularly remarkable, when the tension of the cord is not 

 great. In most stringed instruments, however, it is not 

 observable to the ear. Should, says Weber, more instru- 

 ments be constructed in future, after the manner of the 

 mercantile harmonichord, where each tone swells and de- 

 creases by itself; so it will lead to dissonance, when no 

 compensation is allowed for greater tension combined with 

 greater vibration. This compensation, is, therefore, pro- 

 duced by bending the cord over two bridges, in such a 

 manner, that it may pass over the one and under the other. 

 The angle of these bridges is not sharp but round, and 

 should the cord be struck, so that the vibration happens 

 in one of the bridges' vertical planes, so by great vibrations, 



* J»hresbericht, 1834. Popgendorff's Ann. xxviii. 1. 



