180 



accompany the internal processes going on in the system. The sen- 

 sorium is the more sensible to the impressions made by these internal 

 causes, inasmuch as all the avenues to external impressions are closed, 

 and the mind is deprived of the control it exercises, during its waking 

 hours, over the train of its thoughts, by the help of the perceptions 

 derived from the senses, and the employment of words for detaining 

 its ideas, and rendering them objects of steady attention, and subjects 

 of comparison. 



March 14, 1833. 



The Rev. WILLIAM BUCKLAND, D.D., Vice-President, in the 



Chair. 



A paper was read, entitled, " On the Figures obtained by strewing 

 Sand on Vibrating Surfaces, commonly called Acoustic Figures." By 

 Charles Wheatstone, Esq. Communicated bv Michael Faraday, Esq. 

 D.C.L. F.R.S. 



The author, after adverting to the imperfect notice taken by Gali- 

 leo and by Hooke of the phenomena which form the subject of this 

 paper, ascribes to Chladni exclusively the merit of the discovery of 

 the symmetrical figures exhibited by plates of regular form when 

 made to sound. He proposes a notation, by means of two numbers 

 separated by a vertical line, for expressing the figures resulting from 

 the vibrations of square or rectangular plates. He gives a table of 

 the relative sounds expressed both by their musical names and by the 

 number of their vibrations, of all the modes of vibration of a square 

 plate, as ascertained by the experiments of Chladni. He then pro- 

 ceeds to class and analyse the various phenomena observed under 

 these circumstances, and shows that all the figures of these vibrating 

 surfaces are the resultants of very simple modes of oscillation, occur- 

 ring isochronously, and superposed upon one another ; the resultant 

 figure varying with the component modes of the vibration, the num- 

 ber of the superpositions, and the angles at which they are superposed. 

 In the present paper, which forms the first part of his investigation, 

 he confines himself to the figures of square and other rectangular 

 plates. 



The author finds that the principal results of the superposition of 

 two similar modes of vibration are the following : — first, the points 

 where the quiescent lines of each figure intersect each other remain 

 quiescent points in the resultant figure ; secondly, the quiescent lines 

 of one figure are obliterated, when superposed, by the vibratory parts 

 of the other ; thirdly, new quiescent parts, which may be called points 

 of compensation, are formed whenever the vibrations in opposite di- 

 rections neutralize each other $ and, lastly, at other points, the mo- 

 tion is as the sum of the concurring, or the differences of the opposing 

 vibrations at these points. After considering various modes of binary 

 superposition, the author examines the cases of four co-existing su- 

 perpositions. 



When the vibrations of the superposed modes are unequal in inten- 

 sity, there is formed a figure intermediate between the perfect re- 



