Jenn looked to where the vortex had been.
The earth, or other planet, does not actually move round the sun; yet it is carried round the sun in the subtle matter of the great vortex, where it lies in equilibrium, - carried like the passenger in a boat, who may cross the sea and yet not rise from his berth.
This finer matter which collects in the centre of each vortex is the first matter of Descartes - it constitutes the sun or star.
As the small filings produced by friction seek to pass through the interstices between the rapidly revolving spherical particles in the vortex, they are detained and become twisted and channelled in their passage, and when they reach the edge of the inner ocean of solar dust they settle upon it as the froth and foam produced by the agitation of water gathers upon its surface.
In this year the short-lived federation of the five powers was shaken, and Italy was once more drawn into the vortex of Europe~n affairs.
The United States was, at this time, drawn into the vortex of European complications, and Adams, instead of taking advantage of the militant spirit which was aroused, patriotically devoted himself to securing peace with France, much against the wishes of Hamilton and of Hamilton's adherents in the cabinet.
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.
Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.
(7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.
A single vortex will remain at rest, and cause a velocity at any point inversely as the distance from the axis and perpendicular to its direction; analogous to the magnetic field of a straight electric current.
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.
When the liquid is bounded by a cylindrical surface, the motion of a vortex inside may be determined as due to a series of vorteximages, so arranged as to make the flow zero across the boundary.
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.
(II) A single vortex in a circular cylinder of radius a at a distance c from the centre will move with the velocity due to an equal opposite image at a distance a 2 /c, and so describe a circle with velocity mc/(a 2 -c 2)in the periodic time 21r(a 2 -c 2)/m.
The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log r, (1) representing vortex motion circulating round the annulus of liquid.
Michell has discussed also the hollow vortex stationary inside a polygon (Phil.
Immediately afterwards Langton was drawn into the vortex of English politics.
Despite the indifference to the affairs of the world he had expressed to Pierre, he diligently followed all that went on, received many books, and to his surprise noticed that when he or his father had visitors from Petersburg, the very vortex of life, these people lagged behind himself- -who never left the country--in knowledge of what was happening in home and foreign affairs.