150 FELIX SAVART’S RESEARCHES ON THE 
plane; also, the plate No. 4, fig. 10, which passes through one of the 
diagonals X Y or A C, and which is perpendicular to the plane C Y A X, 
contains also A E in its plane; and lastly, the plate No. 3 of fig. 12, 
parallel to the plane ADE X, is cireumstanced in the same manner. 
Thus, if 7 sé, fig. 15, is a plane perpendicular to the diagonal A E, and 
if the lines 1, 3, 5 indicate the directions of the three plates we have 
just spoken of, in order to become acquainted with the progress of the 
transformations which connect the modes of division of these plates 
together, it will be sufficient to take round A E, the projection of which 
is in c, a few other plates such as 2, 4,6. The Nos. 1, 2, 3 of fig. 16 
represent this series thus completed, and the dotted line ae indicates 
in all the direction of the diagonal of the cube. 
The nodal system represented by the unbroken lines consists, for 
No. 1, of two crossed nodal lines, one of which, ay, places itself upon 
the axis A Y, and the other in a perpendicular direction; it transforms 
itself in No. 2 into hyperbolic curves, which by the approximation: of 
their summits again become straight lines in No. 3, which contains the 
axis A Y of greatest elasticity: these curves afterwards recede again, 
No. 4, and in the same direction as No. 2; they then change a third 
time into straight lines in No. 5, which contains the axis A Z of least 
elasticity ; and lastly, they reassume the appearance of two hnyperiadtic 
branches in No. 6, 
The transformations of the dotted system are much less complicated, 
since it appears as two straight lines crossed rectangularly in No.1, 
and afterwards only changes into two hyperbolic branches, which con- 
tinue to become straighter until a certain limit, which appears to be at 
No. 3, and the summits of which afterwards approach each other, 
Nos. 5 and 6, in order to-coalesce again in No, 1. 
As to the general course observed by the sounds of the two nodal. sy- 
stems, it is very simple, and it was easy to determine it previously. Thus, 
the plate No. 5, containing in its plane the axis A Z of least elasticity, the 
two gravest sounds of the entire series is heard; these sounds afterwards 
gradually rise until No. 3, which contains the axis A X of greatest 
elasticity ; after which they redescend by degrees in Nos. 2 and 1, (the 
latter contains the axis A Y of intermediate elasticity in its plane,) and 
they return at last to their point of departure in the plates Nos. 6 and 5, 
The transformations of the nodal lines of this series, by establishing 
a link between the three series of plates cut round the axes, makes us 
conceive the possibility of arriving at the determination of nodal sur- 
faces, which we might suppose to exist within bodies having'three rect- 
angular axes of elasticity, and the knowledge of which might enable 
us to determine, @ priori, the modes of division of a circular plate in- 
clined in any manner with respect to these axes. But it is obvious, that 
to attempt such an investigation it would be necessary to base it on 
