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XLil. On the Spiral V'lhratmi of a Stick or Rod. Bjy 

 G. F. F. Chladni *. 



T 



, -I- H E vibrations hitherto known of a fiick or rod, that 

 Js to fay, of an elaftic body extended in a certain diredion, 

 are either tranfvcrfal vibration?, where the rod or the parts 

 into which it divides itfelf vibrate fidewards, in fiich a man- 

 ner as to form a great number of curved Hnes; or longitudinal 

 vibratioris, where the rod or each of its parts contracts and 

 extends itfelf according to the direftion of its length, fo that 

 It fometimes rcfts againfl one and fometimes ligainft the 

 other of the vibration nodes. The former kind of vibrations 

 were firft determined by Daniel Bernoulli, and afterwards, in 

 a more complete manner, by Eulcr, in the Tranfaftions of 

 the Imperial Academy of Sciences for 1769: hut the latter 

 were firft made known by mvfelf in a paper on the longi- 

 tudmal vibrations of rods and firings, pub'lidied at Erfurt in 

 lyQ'^j and which may be found alio in the IVanfiiftions of 

 the Elcdoral Academy of Sciences of that city. For fome 

 time I have obferved, that, befides thcfc two diredtions of 

 vibrating motion, there is a third, where the hkI, or each 

 part mto which it divides itfelf, turns alternately to the right 

 and left in a fpiral form, while the vibration nodes or The 

 boundaries of the vibrating parts remain motionU;fs, as in 

 the other kinds of vibration. Such fpiral vibrations may be 

 produced with moft eafe on a fufficicntly long cylindric rod, 

 the furface of which has been mode as fmooth as pofllble, if 

 the rod be held gently between t\^o finoers .it the place where 

 there is a vibration node, and if it be nibbed in a fpiral di- 

 reftion in a vibrating part with a piece "Of woollen rag held 

 between the fingers ot the other hand. When the rod is of 

 wood or metal, the rag muft be previouflv llrewcd over with 

 refill ; but when a glafs rod, or, what is the fame thing, a 

 thermometer or barometer tube is employed, it mufl"^ be 

 inoiftened with water, or be ftrewcd over with very fine fand. 

 The ways in which a rod, wlun it is cither entirely free, or 

 faftened at (Hie end and free at the olher, or tafiened at both 

 ends, can divide itfelf into vibrating parts, and the pofition 

 of the vibration nodes, arc entirely llie fame as in the cafe of 

 longitudinal vibrations. The {liarpncfs and flatnefsof the tone 

 depend alio on the fame laws; and therefore, to avoid all un- 

 ncceflary prolixity, I fliall refer to the above-mentioned eHay 



• From Drr GeJtllJibaftNatwfurfibcnda Firumti %u Berlin NeteScbrifltHk 

 y»l. 11. 1799. ■' 



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