S*cr. XVII. VIBRATION OF PAPER AND VELLUM. 143 



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 pave- 

 ment. 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 repre- 

 sents the motion of the nodes of the moon, is again 

 reflected back to the moon, and may be traced in the 

 nutation of the 1 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 vibrat- 

 ing plates may be exhibited 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 removed slowly in 

 a horizontal direction, the forms on the paper will cor- 

 respond 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 paper will vary by de- 

 grees; and when the vibrating disc is perpendicular to 

 the horizon, the sand on the paper will form into straight 

 lines parallel to the surface oT the disc, by creeping along it 

 instead of dancing up and down. If the disc be made to 

 turn round its vertical diameter while vibrating, the nodal 

 lines on the paper will revolve, and exactly follow the 



