PHYSICS-NINETEENTH CENT. SOUND. 537 



Among those who applied mathematical analysis to the transverse 

 vibration of cords was Dr. BROOK TAYLOR (16851731). A little 

 later the same problem was treated by the Bernouillis, Euler, Riccati, 

 Lagrange, and others. From these investigations the following laws 

 of vibrating cords ultimately emerged, and were confirmed by experi- 

 ment : 



(i). When different tensions are applied to the same length of string, 

 the frequency of vibrations is directly as the square root of the tension. 



(2). When different lengths of the same string at the same tension are 

 taken, the frequency of vibrations .is inversely as the length. 



"(3)- When the tension and the length of string are unchanged, but the 

 weight of the string is altered, then the frequency of the vibrations is 

 inversely as the square root of the weight of the string. 



If we must look to Pythagoras as the ancient founder of acoustical 

 science, we may justly regard E. F. F. CHLADNI (1756 1827) as the 

 aufhor of the modern aspects of the science. Chladni's father was 

 Professor of Law at Wittenberg in Saxony, and destined his son to 

 a legal career. The son's education was so strictly conducted that 

 the period of youth was for him one of bitterness. The continual 

 restraint imposed upon him developed by a natural reaction a stronger 

 inclination towards occupation of his own choice. In deference to 

 his father's wishes, however, Chladni studied at Wurtemberg and at 

 Leipzig, and was admitted to the degree of Doctor in Law and in 

 Philosophy. But on his father's death he abandoned the legal pro- 

 fession, and devoted himself entirely to the study of nature, which 

 had always been his most pleasing, although hitherto but secondary, 

 occupation. He had, at the age of nineteen, begun to learn the 

 elements of the musical art, and he soon observed that the physical 

 theory of sound was in a very backward state. He was seized with 

 the desire of doing something to fill up this void in science. In 1785 

 he made a number of experiments, in the course of which he observes 

 that plates of glass or metal gave different sounds, according to the 

 manner in which they were held or struck. An account of some 

 experiments on bells suggested to him the use of the violin-bow to 

 throw his plates into vibration ; and as the means of revealing the 

 nature of the vibrations, he was induced, by reading of Lichtenberg's 

 figures (in which powdered sulphur, etc., is strewn on an electrified 

 plate), to try the plan of sprinkling his plates with a light powder. 

 Chladni accordingly scattered a little fine sand over a circular plate, 

 and when the plate was thrown into vibrations, he saw the sand arrange 

 itself into well-defined radiating trains, showing the position of nodal 

 lines (Fig. 253). This was a new phenomenon, and after some re- 

 flection on its cause, Chladni multiplied and varied the experiments, 

 and discovered methods of producing an amazing variety of the sand 



