SCIENTIFIC NEWS. -- OJ] 



case of the second, abstracting the spring: hut the converse 

 does not hold. 



The essential difference between the questions of the Stretche.l 

 movement, considered i a each of* these points of view, in P archn, ent. 

 the case of a simple line, leads us immediately to conceive, 

 that we must find differences of the same kind, and in par- 

 ticular a great increase of difficulties, when we introduce 

 two dimensions into the calculation. The acoustic pheno- 

 mena exhibited by parchment stretched, as on a drum-head, 

 are referable to those of the chord ; the phenomena of me- 

 tallic phu.es, to those of the spring. 



Euler, in his paper de Motu oibratorlo Tympanornm, has Drums, 

 considered the parchment as composed of threads crossing 

 each otb,er at right angles. A geometrician of the Institute 

 has published in one of its volumes some researches on this 

 subject, contemplating it in the same point of view. The 

 differential equation of the motion, which is partial and of 

 the 2d order, cannot be summed up, at least in finite terms. 



In his paper de Sono Campanarum Euler attempts to re- Bells, 

 duce the vibrations of hard surfaces formed by revolution 

 to those of circular elastic rings, of winch he considers them 

 as an assemblage, situate in planes perpendicular to the axis 

 of revolution, and supposing the effect of the vibration to 

 be a variation of the lengths of their diameters. He here 

 arrives at an equation with partial differences of the 4th or- 

 der, not summable in finite terms. 



This is all that geometricians have been able to effect with Hypotheses 



regard to the problems of sonorous bodies considered in the m> } tobead - 



° ' ... nutted, 



case of two dimensions ; and even introducing simplifica- 

 tions, which, it cannot be denied, alter the natural state of 

 things, so that the results of analysis cannot be applicable. 

 These hypothetical simplifications are particularly inad- 

 missible in respect to vibrating surfaces of metal, or a sub- 

 stance naturally elastic. In the most simple case, that of" a 

 plane, it is obvious, that Euler's hypothesis of the vibration Euletfsnot 

 of surfaces of revolution is not applicable. We have not a PP" caW *' 

 even the differential equations of the motion for vibrations 

 of this kind, considering their phenomena as nature pre- 

 sents them ; and to find these equations would be an inter- 

 esting subject of meditation to geometricians, which would 



contribute 



