SECT. XVII. V1BKATIXG PLATES. 145 



divide the plate into four equal triangles, each pair of which will 

 make their excursions on opposite sides of the plate. The nodal 

 lines and pitch vary not only with the point where the bow is 

 applied, but with the point by which the plate is held, which 

 being at rest necessarily determines the direction of one of the 

 quiescent lines. The forms assumed by the sand in square 

 plates are very numerous, corresponding to all the various modes 

 of vibration. The lines in circular plates are even more remark- 

 able for their symmetry, and upon them the forms assumed by 

 the sand may be classed in three systems. The first is the dia- 

 metrical system, in which the figures consist of diameters dividing 

 the circumference of the plate into equal parts, each of which is 

 in a different state of vibration from those adjacent. Two dia- 

 meters, for example, crossing at right angles, divide the circum- 

 ference 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 centre with the plate ; and the third is 

 the compound system, where the figures assumed by the sand 

 are compounded of the other two, producing very complicated 

 and beautiful forms. Galileo 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. 184). 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 component 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 vibrations 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. 185). 



M. Savart's experiments on the vibrations of flat glass rulers 

 are highly interesting. Let a lamina of glass 27 in< 56 long, 0'59 



