VIBRATION OF STRINGS. 335 



voured also, about the same time, to determine the 

 number of vibrations of a standard note, or, as he 

 called it, fixed sound. He employed two methods, 

 both ingenious and both indirect. The first was 

 the method of beats. Two organ-pipes, which form 

 a discord, are often heard to produce a kind of howl., 

 or wavy noise, the sound swelling and declining at 

 small intervals of time. This was readily and 

 rightly ascribed to the coincidences of the pulsa- 

 tions of sound of the two notes after certain cycles. 

 Thus, if the number of vibrations of the notes were 

 as fifteen to sixteen, every fifteenth vibration of 

 the one would coincide with every sixteenth vibra- 

 tion of the other, while all the intermediate vibra- 

 tions of the two tones would, in various degrees, 

 disagree with each other; and thus every such cycle, 

 of fifteen and sixteen vibrations, might be heard as 

 a separate beat of sound. Now, Sauveur wished 

 to take a case in which these beats were so slow 

 as to be counted 5 , and in which the ratio of the 

 vibrations of the notes was known from a know- 

 ledge of their musical relations. Thus if the two 

 notes form an interval of a semitone, their ratio will 

 be that above supposed, fifteen to sixteen; and if 

 the beats be found to be six in a second, we know 

 that, in that time, the graver note makes ninety 

 and the acuter ninety-six vibrations. In this man- 

 ner Sauveur found that an open organ-pipe, five 

 feet long, gave one hundred vibrations in a second. 

 4 Ac. Sc. Hist. 1700, p. 131. 



