ELASTICITY OF REGULARLY CRYSTALLIZED BODIES. 147 
will be seen, on causing them to vibrate in the same mode of trans- 
versal motion, that they produce the same sound. It also follows, because 
the elasticity in the direction ay is sometimes smaller and sometimes 
greater than that which exists in the direction of cd, that the first axis 
of the nodal hyperbola ought to change its position to be able to remain 
always eae to that, of the lines ay, ed, which possess the 
ticity, it becomes the pentose axis of the fy perbob whilst in Nos. 4, 
5 and 6, the elasticity being greater. in the direction ed than in that 
of a y, the transverse axis of the hyperbola places itself on the latter 
line. As the ratio of the two elasticities varies only gradually, it is 
obvious that the modifications impressed on the hyperbolic system ought 
in the same manner to be gradual: thus the summits of these curves, 
at first separated in No. 1 by a certain distance (which will depend on 
the nature of the wood), will approach nearer and nearer, for the fol- 
lowing plates, until they coalesce as in No. 3, at a certain degree of 
inclination, which was 45° in the experiment to which I now refer, but 
which might be a different number of degrees for another kind of wood. 
At the point where we have seen that the élasticities are equal in’ the 
direction of the axis, the two Gurves: transform’ themselves: into ‘two 
straight lines which intersect each other rectangularly, after which they 
again separate; but their separation is effected in a’ direction perpen- 
dicular to that of their coalescence. The sounds of the’ hyperbolic’ 
system follow nearly the same’ course as those of the system of crossed 
lines; that is to say, they become higher in proportion as the plates 
more nearly approach being parallel to the axis of greatest elasticity ; 
but it deserves to be remarked, that the plate No. 3, for which'the elas? 
ticity is the same in the two directions ay, ed; is that between'the two 
sounds {of which there is the greatest interval: this’ evidently depends’ 
on the elasticity in the two directions:a y, cd being very different from 
that which exists in the other directions of the plate. 
Lastly, it is to be remarked that, in the four first plates, the sound of 
tlie hyperbolic system is sharper than that of the system of crossed 
lines, and‘that it is the contrary for the plate No. 6, which renders it 
necessary that there should be between No. 4 and No. 6 a plate, the 
sounds of which are equal, which in the present case is exemplified in 
No.5, although its two modes of division differ greatly from each other. 
There is another thing remarkable in this plate; its two modes of di- 
Vision can transform themselves gradually into éach other by changing 
the position of the place of excitation, so that the two points e and ce! 
becoming two nodal centres, are in every chi in the conditions 
indicated by fig. 4. 
__ The interval included between the grayest and the sharpest sounds 
of this series was an augmented sixth. 
L2 
