SECT, xvii.] VIBRATION OF PAPER AND VELLUM. 165 



one is twice or three times longer than the other, be placed 

 side by side, and if the shorter be sounded, its vibrations will 

 be communicated by the air to the other, which will be thrown 

 into such a state of vibration that it will be spontaneously 

 divided into segments equal in length to the shorter string. 

 When a tuning-fork receives a blow and is made to rest upon 

 a piano-forte during its vibration, every string which, either 

 by its natural length or by its spontaneous subdivisions, is 

 capable of executing corresponding vibrations, responds in a 

 sympathetic note. Some one or other of the notes of an 

 organ are generally in unison with one of the panes or with 

 the whole sash of a window, which consequently resounds 

 when those notes are sounded. A peal of thunder has fre- 

 quently the same effect. The sound of very large organ-pipes 

 is generally inaudible till the air be set in motion by the un- 

 dulations of some of the superior accords, and then its sound 

 becomes extremely energetic. Recurring vibrations occasion- 

 ally influence each other's periods. For example, two adja- 

 cent organ-pipes nearly in unison may force themselves into 

 concord ; and two clocks, whose rates differed considerably 

 when separate, have been known to beat together when fixed 

 to the same wall, and one clock has forced the pendulum of 

 another into motion, when merely standing on the same stone 

 pavement. These forced oscillations, which correspond in 

 their periods with those of the exciting cause, are to be traced 

 in every department of physical science. Several instances of 

 them have already occurred in this work. Such are the tides, 

 which follow the sun and moon in all their motions and pe- 

 riods. The nutation of the earth's axis also, which corre- 

 sponds with the period, and represents the motion of the 

 nodes of the moon, is again reflected back to the moon, and 

 may be traced in the nutation of the lunar orbit. And, 

 lastly, the acceleration of the moon's mean motion repre- 

 sents the action of the planets on the earth reflected by the 

 sun to the moon. 



In consequence of the facility with which the air commu- 



