148 RECURKIXG VIBRATIONS. 



motion by the undulations of some of the superior accords, and 

 then the sound becomes extremely energetic. Kecurring vibra- 

 tions occasionally influence each other's periods. For example, 

 two adjacent organ-pipes nearly in unison may force themselves 

 itito 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 periods. The nutation 

 of the earth's axis also, which corresponds with the period, and 

 represents the motion of the nodes of the moon, is again re- 

 flected 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 represents the action of the planets on the earth 

 reflected by the sun to the moon. 



In consequence of the facility with which the air communicates 

 undulations, all the phenomena of vibrating plates may be ex- 

 hibited by sand strewed on paper or parchment, stretched over 

 a harmonica glass or large bell-shaped tumbler. In order to 

 give due tension to the paper or vellum, it must be wetted, 

 stretched over the glass, gummed round the edges, allowed to 

 dry, and varnished over, to prevent changes in its tension from 

 the humidity of the atmosphere. If a circular disc of glass be 

 held concentrically over this apparatus, with its plane parallel to 

 the surface of the paper, and set in vibration by drawing a bow 

 across its edge, so as to make sand on its surface take any of 

 Chladni's figures, the sand on the paper will assume the very 

 same form, in consequence of the vibrations of the disc being 

 communicated to the paper by the air. "When the disc is re- 

 moved slowly in a horizontal direction, the forms on the paper 

 will correspond with those on the disc, till the distance is too 

 great for the air to convey the vibrations. If the disc while 

 vibrating be gradually more and more inclined to the horizon, 

 the figures on the pajvr will vary by degrees ; and, when the 

 vibrating disc is perpendicular to the horizon, the sand on the 

 paper will form into straight lines parallel to the surface of the 



