148 FELIX SAVART’S RESEARCHES ON THE 
It is almost useless to observe that the plates taken in the directions 
1, II, III, inclined on the other side of the axis A X the same number 
of degrees as the plates 1, 2, 3, would present exactly the same pheeno- 
mena as these latter. This observation being equally applicable to the 
following series, we shall not mention it again. 
Seconp Sertes—Plates taken round the axis A Z of least elasticity 
and perpendicular to the plane C Y AX; figs. 9 and 10. 
As in the preceding case, one of the nodal systems of the plates of 
this series consists of two lines crossed rectangularly, one of which, @ z, 
corresponds with the axis A Z; whence it follows that the second may 
be considered as the projection of the two other axes on the plane of 
the plate, which, whatever its inclination may be, ought consequently 
to possess a greater elasticity in the direction fg than in the direction 
az: thus the hyperbolic system of this series cannot present the trans- 
formations which we saw in the preceding series, where ed, fig. 8, possesses 
sometimes a less, at other times a greater elasticity than that of ay. 
In the present case, a z remaining constantly the axis of least elasticity, 
the resistance to flexion in the direction fg goes on gradually increasing 
from the plate No. 1 to the plate No. 6 parallel to the plane A X BZ, 
and the branches of the hyperbola straighten themselves in proportion as 
the plates more nearly approach this last position. As to the sounds which 
correspond to each of these nodal systems, it is observed that they ascend 
gradually from No. 1 to No. 6, and that the sound of the hyperbolic 
system is sharper in a part of the séries than that of the system of crossed 
lines, whilst they become graver in the other part. There is therefore a 
certain inclination for which the sounds of the two systems ought to be 
equal; and this evidently would have taken place in the present expe- 
riment for a plate intermediate to No. 4.and No. 5. 
The interval between the gravest and the sharpest sound of each 
series was an augmented fifth. 
Tuirp SerrEes.—FPlates taken round the axis A X of greatest elasticity, 
and perpendicular to the plane A Y D Z; figs. 11 and 12. 
The elastic state of these plates cannot present such remarkable dif- 
ferences as those we have observed in the preceding series; for, being 
all cut round the axis of greatest elasticity, they can only contain in 
their plane that of least or that of mean elasticity, or lastly, those in- 
termediate between these limits, which do not vary greatly from each 
other. Thus it is seen that their modes of division differ very little from 
each other, and that the sounds which correspond to them present 
rather slight differences, although they go on ascending in proportion 
as the plates more nearly approach containing the axis of mean elas- 
ticity in their plane. Here, as in the other series, one of the nodal 
