Page:Scientific Memoirs, Vol. 1 (1837).djvu/163

Rh experiments made with a substance the three axes of which shall be accurately perpendicular to each other, which is not entirely the case in wood.

It would now remain for us to examine two other series of plates, one taken round the diagonal $$A B$$, and the other round the diagonal $$A C$$; but as it is evident that the arrangements of nodal lines which they would present would differ very little from those of the fourth series, we may dispense with their examination.

Such are, in general, the phænomena which are observed in bodies which, like that we have just examined, possess three axes of elasticity: collected into a few propositions, the results we have obtained are reducible to the following general data.

1st. When one of the axes of elasticity occurs in the plane of the plate, one of the nodal figures always consists of two straight lines, which intersect each other at right angles, and one of which invariably places itself in the exact direction of this axis; the other figure is then formed by two curves which resemble the branches of a hyperbola.

2nd. When the plate contains neither of the axes in its plane, the two nodal figures are constantly hyperbolic curves; straight lines never enter into their composition.

3rd. The numbers of vibrations which accompany each mode of division are, in general, higher as the inclination of the plane to the axis of greatest elasticity becomes less.

4th. The plate which gives the sharpest sound, or which is susceptible of producing the greatest number of vibrations, is that which contains in its plane the axis of greatest elasticity and that of mean elasticity.

5th. The plate which is perpendicular to the axis of greatest elasticity is that from which the gravest sound is obtained, or which is susceptible of producing the least number of vibrations.

6th. When one of the axes is in the plane of the plate, and the elasticity in the direction perpendicular to this axis is equal to that which itself possesses, the two nodal systems are similar; they each consist of two straight lines which intersect each other rectangularly, and they occupy positions 45° from each other. In a body which possesses three unequal axes of elasticity there are only two planes which possess this property.

7th. The transverse axis of the nodal curves always occurs in the direction of the least resistance to flexion; it hence follows, that when in a series of plates this axis places itself in the direction at first occupied by the conjugate axis, it is because the elasticity in this direction has become relatively less than in the other.

8th. In a body which possesses three unequal axes of elasticity, there are four planes in which the elasticity is so distributed that the two