142 FELIX SAVART’S RESEARCHES ON THE 
itself on them in 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 which 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 susceptible 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 
phenomena, 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 the 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 
totwo directions perpendicular to each other. Wood fulfills again 
these different conditions; for ina 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 
