In course of time the star, with its expansive force diminished, suffers encroachments from the neighbouring vortices, and at length they catch it up. If the ' Princip. part ii.
Such a reduced and impoverished star is a planet; and the several planets of our solar system are the several vortices which from time to time have been swept up by the central sun-vortex.
Such in mere outline is the celebrated theory of vortices, which for about twenty years after its promulgation reigned supreme in science, and for much longer time opposed a tenacious resistance to rival doctrines.
At a time when the Cartesian system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it.
If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.
For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.
99, p. 167), using Froude's turbine to obtain the highly resisting spiral vortices, and arranging passages in the casing for the entry of water at the hub of the wheel and its exit at the circumference.
The air-ways k, k, in the fixed vanes establish communication between the cores of the vortices and the atmosphere.
We might thus examine a structure formed of an aggregation of very thin vortex rings, which would move across the fluid without sensibly disturbing it; on the other hand, if formed of stronger vortices, it may transport the portion of the fluid that is within, or adjacent to, its own structure along with it as if it were a solid mass, and therefore also push aside the surrounding fluid as it passes.
The study of these vortices has led to the discovery of a magnetic field in sun-spots, apparently caused by electric convection in the vortices.
They too were once vortices, swallowed up by some other, which at a later day fell a victim to the sweep of our sun.
Whilst Protestant opponents put him in the list of atheists like Vanini, and the Catholics held him as dangerous as Luther or Calvin, there were zealous adherents who ventured to prove the theory of vortices in harmony with the book of Genesis.
This notion, it is plain, tended rather towards Descartes's theory of vortices than towards Newton's theory of gravitation.