We have herein a better principle of classification; considering cubic curves, in the first instance, according to singularities, the curves are non-singular, nodal (viz.
It is found that the direction of the moon's equator remains nearly invariable with respect to the plane of the orbit, and therefore revolves with that plane in a nodal period of 18.6 years.
By similar methods, a circular plate may be made to exhibit nodal lines dividing the surface by diametral lines into four or a greater, but always even, number of sectors, an odd number being incompatible with the general law of stationary waves that the parts of a body adjoining a nodal line on either side must always vibrate oppositely to each other.
If the plate be small, it is sufficient, in order to bring out the simpler sand-figures, to hold the plate firmly between two fingers of the same hand placed at any point where at least two nodal lines meet, for instance the centre in (1) and (2), and to draw a violin bow downwards across the edge near the middle of a ventral segment.
During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure.
The common casts of Calamites are of this nature, representing the form of the hollow medulla, and bearing on their surface the print of the nodal constrictions and of the ridges and furrows on the inner surface of the wood.
In the third-order complex the centre locus becomes a finite closed quartic surface, with three (one always real) intersecting nodal axes, every plane section of which is a trinodal quartic. The chief defect of the geometrical properties of these bi-quaternions is that the ordinary algebraic scalar finds no place among them, and in consequence Q:1 is meaningless.
The flame there is much H K' L affected by the nodal pressure changes, while the other two vibrate only slightly.
Let, now, the plate be made in the usual manner to vibrate so as to exhibit two nodal lines coinciding with two rectangular diameters.
But with larger plates, which alone will furnish the more complicated figures, a clamp-screw must be used for fixing the plate, and, at the same time, one or more other nodal points ought to be touched with the fingers while the bow is being applied.