454 THE PRINCIPLES OF SCIENCE. [CHAP. 



occur in all cases of rhythmical motion. If a musical note 

 is sounded in a room containing a piano, the string corre- 

 sponding to it will be thrown into vibration, because every 

 successive stroke of the air-waves upon the string finds 

 it in like position as regards the vibration, and thus adds 

 to its energy of motion. But the other strings being incap- 

 able of vibrating with the same rapidity are struck at 

 various points of their vibrations, and one stroke will 

 soon be opposed by one contrary in effect. All pheno- 

 mena of resonance arise from this coincidence in time of 

 undulation. The air in a pipe closed at one end, and about 

 12 inches in length, is capable of vibrating 512 times in 

 a second. If, then, the note C is sounded in front of the 

 open end of the pipe, every successive vibration of the air 

 is treasured up as it were in the motion of the air. In 

 a pipe of different length the pulses of air would strike 

 each other, and the mechanical energy being transmuted 

 into heat would become no longer perceptible as sound. 



Accumulated vibrations sometimes become so intense 

 as to lead to unexpected results. A glass vessel if touched 

 with a violin bow at a suitable point may be fractured with 

 the violence of vibration. A suspension bridge may be 

 broken down if a company of soldiers walk across it in 

 steps the intervals of which agree with the vibrations of 

 the bridge itself. But if they break the step or march 

 in either quicker or slower pace, they may have no per- 

 ceptible effect upon the bridge. In fact if the impulses 

 communicated to any vibrating body are synchronous with 

 its vibrations, the energy of those vibrations will be un- 

 limited, and may fracture any body. 



Let us now consider what will happen if the strokes be 

 not exactly at the same intervals as the vibrations of the 

 body, but, say, a little slower. Then a succession of strokes 

 will meet the body in nearly but not quite the same position, 

 and their efforts will be accumulated. Afterwards the 

 strokes will begin to fall when the body is in the opposite 

 phase. Imagine that one pendulum moving from one ex- 

 treme point to another in a second, should be struck by 

 another pendulum which makes 61 beats in a minute; 

 then, if the pendulums commence together, they will at 

 the end of 30^ beats .be moving in opposite directions. 

 Hence whatever energy was communicated in the first 



