14-2 FELIX savart's researches on the 



itself on tliem iu a single position ; and that there is a second position 

 in which two hyperbolic curved lines are obtained which are accompa- 

 nied, according to the different cases, by a sound Avhich differs more or 

 less from that which is produced when the crossed lines occur. Plates 

 are also met with which are incapable of assuming the mode of di- 

 vision formed of two straight lines, and in which only two systems of 

 hyperbolic curves are obtained, sometimes similar, yet giving different 

 sounds. In short, I have yet found no body for which the same nodal 

 figure can place itself in every direction ; which seems to indicate 

 that there are very few solid substances which possess the same pro- 

 perties throughout. But what appears still more extraordinary is, that 

 if in the same body, a mass of metal for instance, plates are cut accord- 

 ing to different directions, some are suscejitible of the mode of division 

 consisting of two lines which cross each other rectangularly, whilst 

 others present only two systems of hyperbolic curves. In both cases, 

 the sounds of the two systems may differ greatly : there may, for example, 

 be an interval between them of more than a fifth. 



To arrive at the discovery of the experimental laws of this kind of 

 phaenomena, it would be necessary therefore to be able to study them, 

 at first in the most simple cases, for example, upon bodies the elastic 

 state of which, previously known, would differ only according to two di- 

 rections. This would obtain in a body which might be composed by 

 placing flat plates formed of two heterogeneous substances upon each 

 other in such a manner that all tlie odd plates might be of one substance, 

 and all the even plates of another, the elasticity in all directions of the 

 plane of each of them being the same. But it has appeared to me dif- 

 ficult to attain this condition, since I have yet found no body the elasti- 

 city of which was the same in all directions. 



The most simple structure after the preceding would be that of a body 

 composed of cylindrical and concentric layers, the nature of which should 

 be alternately different for the layers next each other, as is nearly the 

 case in the branch of a tree free from knots. It is evident that the elasti- 

 city ought to be sensibly the same in every direction of the plane of 

 a plate cut perpendicularly to the axis of the cylinder, and it ought to 

 differ greatly from that which is observed in the direction of the axis. 

 Consequently we shall commence by examining this first case ; after 

 which we shall pass to that in which the elasticity would be different ac- 

 cording to three directions perpendicular to each other, as would take 

 place in a body composed of flat plates alternately of two different sub- 

 stances, and the elastic state of which would not be the same, according 

 to two directions perpendicular to each other. Wood fulfills again 

 these different conditions; for in a tree of very considerable diameter, the 

 ligneous layers may be considered as sensibly plane for a small number 

 of degrees of the circumference ; and if we confine ourselves to plates of 



