140 FELIX SAVARt's RESEARCHES ON THE 



§ 1. Statement of the Means of Examination employed in these 

 Researches. 



Circular plates which produce normal vibrations are susceptible of 

 several modes of division ; sometimes they are divided into a greater or 

 fewer number of equal sectors, always even in number, which perform 

 their vibrations in the same time ; at other times they are divided into 

 a greater or fewer nimiber of concentric zones ; and these two series of 

 modes of division again may be combined together, so that the acoustic 

 figures which result are circular lines divided into equal parts by dia- 

 metrical nodal lines. 



If the plate which is caused to sound is perfectly homogeneous, cir- 

 cular, and equal in thickness, it is obvious that in the case when the 

 figure consists of diametrical lines only, tlie system which they form 

 ought to be capable of placing itself in every direction, that is to say, 

 that any point whatever of the circumference of the plate, being taken 

 as the place of excitation, this single condition determines the position 

 of the nodal figure, since the point directly put in motion is always the 

 middle of a vibrating part. In the case of circular lines, under the con- 

 ditions we have just supposed, these lines would be exactly concentric 

 with the circumference of the plate. These results are a natural conse- 

 quence of the symmetry which is supposed to exist either in the form or 

 in the structure of the plate ; but if this symmetry is deranged, it will 

 easily be conceived that an acoustical figure composed of diametrical 

 nodal lines ought no longer to place itself in a direction depending 

 solely on the position of the point of excitation, and that, with regard to 

 a figure consisting of circular lines, these lines ought to be modified, and 

 will become, for example, elliptical or of some other more complicated 

 form. It is thus that the system of two nodal lines which intersect 

 each other rectangularly, can upon an elliptical plate only place itself 

 in a single position, which is on the axes of the ellipse. There is how- 

 ever a second position in which this mode of division can establish it- 

 self ; but then it is modified in its form, and it resembles the two 

 branches of a hyperbola, the transverse axis of which corresponds with 

 the greater axis of the ellipse : in this latter case, the number of vibra- 

 tions is less than in the first, and more so as the axes of the ellipse differ 

 more from each other. A similar phaenomenon is observed when the 

 same mode of division is attempted to be produced on a circular plate 

 of brass, of very equal thickness, and in which several parallel saw-cuts 

 have been made, penetrating only to a small distance from the surface : 

 one of the crossed nodal lines always corresponds to a saw-cut which 

 has been made in the direction of a diameter, and the system of the two 

 hyperbolic lines arranges itself in such a manner that the same saw-cut 

 becomes the conjugate axis of the hyperbola. Thus, in both cases, 



