140 VIBRATION OF PLATES. SECT. XVII. 



those adjacent. Two diameters, for example, crossing 

 at right angles, divide the circumference into four equal 

 parts ; three diameters divide it into six equal parts ; 

 four divide it into eight, and so on. In a metallic plate, 

 these divisions may amount to thirty-six or forty. The 

 next is the concentric system, where the sand arranges 

 itself in circles, having the same center with the plate ; 

 and the third is the compound system, where the figures 

 assumed by the sand are compounded of the other two, 

 producing veiy complicated and beautiful forms. Ga- 

 lileo seems to have been the first to notice the points of 

 rest and motion in the sounding-board of a musical 

 instrument ; but to Chladni is due the whole discovery 

 of the symmetrical forms of the nodal lines in vibrating 

 plates (N. 179). Professor Wheatstone has shown in 

 a paper read before the Royal Society, in 1833, that all 

 Chladni' s figures, and indeed all the nodal figures of 

 vibrating surfaces, result from very simple modes of 

 vibration, oscillating isochronously, and superposed upon 

 each other ; the resulting figure varying with the com- 

 ponent modes of vibration, the number of the super- 

 positions, and the angles at which they are superposed. 

 For example, if a square plate be vibrating so as to make 

 the sand arrange itself in straight lines parallel to one 

 side of the plate, and if, in addition to this, such vibra- 

 tions be excited as would have caused the sand to form 

 in lines perpendicular to the first had the plate been 

 at rest, the combined vibrations will make the sand form 

 in lines from corner to corner (N. 180). 



M. Savait's experiments on the vibrations of flat glass 

 rulers are highly interesting. Let a lamina of glass 

 27 in -56 long, 0-59 of an inch broad, 0-06 of an inch in 

 thickness, be held by the edges in the middle, with its 

 flat surface horizontal. If this surface be strewed with 

 sand, and set in longitudinal vibration by rubbing its 

 under surface with a wet cloth, the sand on the upper 

 surface will arrange itself in lines parallel to the ends of 

 the lamina, always in one or other of two systems 

 (N. 181). Although the same one of the two systems 

 will always be produced by the same plate of glass, yet 

 among different plates of the preceding dimensions, even 

 though cut from the same sheet side by side* one will 



