iyi8] Vibrations: Mechanical, Musical, and Electrical 251 



to say, the heavy bob loses but little amplitude, while that of the 

 light bob grows from zero to its maximum. With bobs as 5:1, the 

 heavy bob loses appreciably, while the light one proceeds to its 

 maximum. 



As the coupling increases from zero the ratio of the periods of 

 the superposed vibrations of the coupled pendulums usually in- 

 creases continuously till it equals or exceeds 2:1. AVhen, however, 

 both lengths and masses are unequal, the short length having the 

 heavy bob, a new feature appears. As the coupling gradually 

 increases from zero, the ratio of the periods at first diminishes, 

 reaches a minimum, and then increases. Thus the number of 

 vibrations in a beat cycle at first increases, reaches a maximum, and 

 then decreases. These special effects are shown in Fig. 2. They 

 were theoretically predicted and then experimentally confirmed. 

 The maximum number of vibrations in the beat cycle occurs for the 

 highest coupling shown in the figure, viz. 6*8 per cent. The 

 details as to bobs, lengths and couplings are all indicated on the 

 figure. The able collaboration of Miss H. ^I. Browning in this 

 work was gratefully acknowledged. 



V. — Brass Instruments and the Low " F." 



Leaving the pendulums which have only two vibrations at a time, 

 the case of brass instruments with a number of simultaneous vibra- 

 tions was next considered. It is well known that the vibrations 

 from most musical instruments are what is called compound. They 

 consist of a series of tones of commensurate frequencies sounded 

 together. Thus, if the pitch of the note is said to be 100 per second, 

 there is not only a prime tone of this frequency, but also a second 

 tone of 200 per second, a third of 3o0 per second, and so forth. 

 This law applies to strings, to open parallel pipes, and to a complete 

 cone with its base open. It also applies as a close approximation to 

 the brass instruments in general use. This approximation is trace- 

 able to the departure from the strictly conical form as regards the 

 mouthpiece, the bell, and the special shape of the intermediate 

 portion. 



In these brass instruments the possibility of this compound tone, 

 or multiple resonance, is utilised for the production of distinct notes. 

 Thus, out of the tones possible to the instrument the player may 

 elicit the set 200, 400, 600, 800, etc.; or the set 300, 600, 900, 

 1200, etc. These would be said to have the pitches of their primes,- 

 or lowest components 200 or 300 respectively. Or, to put it musi- 

 cally, they would be the octave or the twelfth of the fundamental 

 (or pedal) possible on the instrument. The pedal of the instrument 

 is not usually employed for musical purposes, but can be sounded if 

 specially wished. Now, there is a tradition among players of brass 



