144 FELIX SAVART’S RESEARCHES ON THE 
being capable of transforming itself into the rectangular system, when 
the position of the point put directly in motion is made to vary. 
Examining with care the nodal lines in fig. 2, it is found equally that 
its two nodal systems can thus change themselves one into the other; 
and the same phenomenon is reproduced in the plate No. 4, in which 
the values of the extreme elasticities differ still more, and in which the 
points a and 6 recede from each other at the same time as the curves 
become more straightened. In the plate No. 5, parallel to the axis A Y, 
these curves are no longer susceptible of assuming any other position 
than that indicated in the figure. Thus, in No. 1, the centres a and b 
coalesce into one, and there is only a single figure consisting of two 
crossed lines, the system of which can assume any position; these centres 
afterwards gradually receding, the modes of division can change them- 
selves from one into the other, and at last, when the branches of the 
curve are nearly straight lines, the two figures become perfectly fixed. 
The existence of these nodal points or centres is, without doubt, a 
very remarkable phenomenon, and which it will be important to study 
with great care. In order to give an accurate idea of it, I have in fig. 4 
indicated by a dotted line the successive modifications which the two 
hyperbolic lines assume when the plate is fixed at one of the points a 
or 6, and the place of excitation moves gradually from e to e! e’’, passing 
over a quarter of the circumference of the plate. When the motion is 
excited in the vicinity of e", the curves are by the union of their sum- 
mits transformed into two straight lines which intersect each other 
rectangularly ; and it is obvious that if it had been excited near e’, 
the two branches of the curve would re-appear, but with this peculiarity, 
that their transverse axis would take the position assumed by the conju- 
gate, when the motion was produced on the other side of e’’. 
As to the numbers of the vibrations which correspond to each mode 
of division, for the different degrees of inclination of the plates, it will 
be seen by examining fig. 3, that, at first equal in No. 1, they go on 
continually increasing and receding from each other up to No. 5, which 
contains the axis of the cylinder; and it is indeed evident, that the elas- 
ticity in the direction perpendicular to the axis remaining the same for 
all the plates, whilst that which is perpendicular to this direction goes 
on continually increasing, this ought to be, in general, the progress of 
the phenomenon. 
These experiments were made with plates of oak 8:4 cent. (3°3071 
inches) in diameter, and 3™7 (1456 inch) in thickness: they were 
repeated with plates of beech-wood, and analogous results were ob- 
tained; only the ratio between the two elasticities not being the same, 
the interval between the two sounds of each plate was found to be 
greater. 
The most general consequence that can be deduced from the pre- 
