Fluxion

“ A quantity thus increasing by uniform fluxion, is what we now call an independent variable.
Newton continues: "Now those quantities which I consider as gradually and indefinitely increasing, I shall hereafter call fluents, or flowing quantities, and shall represent them by the final letters of the alphabet, v, x, y, and z;...and the velocities by which every fluent is increased by its generating motion (which I may call fluxions, or simply velocities, or celerities) , I shall represent by the same letters pointed, thus, , , , . ”

“ The Velocities or Fluxions are said to primò and ultimò, as the Augments nascent and evanescent. Take therefore the Ratio of the evanescent Quantities, it is the same with that of the Fluxions. It will therefore answer all Intents as well. Why then are Fluxions introduced? Is it not to shun or rather to palliate the Use of Quantities infinitely small? But we have no Notion whereby to conceive and measure various Degrees of Velocity, beside Space and Time, or when the Times are given, beside Space alone. We have even no Notion of Velocity prescinded from Time and Space. ”

“ XXXII. But you will say that, in the use and application of Fluxions, Men do not overstrain their Faculties to a precise Conception of the abovementioned Velocities, Increments, Infinitesimals, or any other such like Ideas of a Nature so nice, subtile, and evanescent. ”

“ The flux and reflux, when seen were quite regular. Every flood began gently, its velocity increasing by degrees, until at length it rushed in with great impetuosity, till it had attained its full hight. Having remained for a little time stationary, it then retired, ebbing gently at first, but afterward sinking away with great swiftness. At every flux the whole body of water seemed to be violently thrown against the bank; but neither during the time of the flux, nor that of the reflux, did there appear even the least wrinkle of a wave on the other parts of the moat. ”

“ The incessant tendency of material forces is toward final equilibrium; and if the quantity of this tendency be finite, a time of repose must come at last. If one portion of the universe be hotter than another, a flux instantly sets in to equalise the temperatures; while winds blow and rivers roll in search of a stable equilibrium. ”

“ But these functions will vary with the position of the point considered with reference to the adjacent molecules. Now the expression for the kinetic energy of the irregular part of the flux,
indicates that the we may regard the infinitesimal element the energy (due to this part of the flux) Let us consider the energy due to the irregular flux which will belong to the above defined element which is not infinitely small, but which has the advantage of being one of physically similar elements which make up the whole medium. ”

“ In some cases the flux is simply proportional to the force and in the same direction, but in other cases we can only affirm that the direction and magnitude of the flux are functions of the direction and magnitude of the force.
The case in which the components of the flux are linear functions of those of the force is discussed in the chapter on the Equations of Conduction, Art. 296. There are in general nine coefficients which determine the relation between the force and the flux. In certain cases we have reason to believe that six of these coefficients form three pairs of equal quantities. ”

“ The Septuagint translators render the flux by ῥύσις (flowing, flux) , the person affected by the flux γονοῤῥυής (having a flux from the genitals) , while they say of ordinary pollution, ὡς ἐὰν ἐξέλθῃ ἐξ αὐτοῦ κοίτη σπέρματος (“if any man’s seed of copulation go out of him”) . Astruc and others wished to refer the flux from the genitals to Lepra (Leprosy) , but in that case the Leprosy must needs have been previously noticeable in the person affected by the flux, and the flux therefore been really a symptom. ”

“ Glycerine is a good tempering substance, and to this may be added a small amount of sulphate of potash.
Fluxing.—The word flux means to fuse or to melt, or to put into a liquid state. The office of a flux is to facilitate the fusion of metals. But fluxes do two things. They not only aid the conversion of the metal into a fluid state, but also serve as a means for facilitating the unity of several metals which make up the alloy, and aid in uniting the parts of metals to be joined in the welding of parts
p. ”

“ The flux of electricity per unit of new surface formed, which will maintain a surface in a constant condition while it is extended, is represented by in numerical value, and its direction, when is negative, is from the mercury into the acid. ”

“ Remember that the flux is a cleaning agent and if the surface is clean, no additional flux is necessary, but if the contrary is true, that is, if the surface is full of oxide and the filler refuses to flow easily, flux is necessary and should be added. ”

“ In this respect the fulguration is extremely like another accident which is known under the name of fulgurites or fulminated tubes, splendid specimens of which may be seen at the museum. As the two cuts in Fig. 2 show, there are irregular tubes, the substance of which, a kind of natural glass, is the product of the solution of siliceous sands that have been struck by lightning. The tube is smooth within, but rugose on the outside, on account of the agglutination of imperfectly melted particles of sand. Fulgurites are generally ramified at their lower end. ”

“ All religions, even the most conservative and traditional, are in constant flux, they either advance or decay.
The above sentence is thus punctuated in the Enclycopedia Britannica and the New Standard Dictionary. We know of no 129meaning of the comma that indicates the real sense relation between “in constant flux” and what follows. Nor is this relation that shown by the colon; for a thing,—for instance, the ocean,—may be in constant flux, and yet not either advance or decay.
The meaning of the language requires “and” after “flux,” preferably with a semicolon before it. ”

“ And some of them, by constantly lying in the blood and mucus, that had flowed from those afflicted with the flux, and which, as before observed, is generally so violent as to prevent their being kept clean, have their flesh much sooner rubbed off, than those who have only to contend with the mere friction of the ship. ”

“ If we consider a constant direction of displacement while the period varies, and will only vary so far as the type of the motion varies, i.e., so far as the manner in which the flux distributes itself among the ponderable molecules and intermolecular spaces, and the extent to which the molecules take part in the motion are changed. ”

“ If in two-dimensional motion the successive increments of flux be represented by increments of a quantity it can be shown that the lines and the lines may be interchanged, the lines of equal flux becoming equipotentials, and vice versâ. ”

“ The occasion was a famous one for solving this important problem: Where does the fluid reside?—in the operators or in the piece of furniture. The solution was as prompt as it was decisive. Scarcely had our hands, in chains, been placed upon this second table than it began to revolve with the most unexpected and the most comic rapidity! Evidently, the fluid was in us, and we were free to apply it in succession to different tables.
We lost no time. In the mood in which we then were, [Pg 242] movement without contact must succeed better than ever. ”

“ Our circulation is a hydraulic problem; our stomach is a mill—a brewing vat—a tanner’s yard—a crucible, or a retort. You yourself, in all the resplendent glory of your braided frock, and your decoration of the Guelph, are nothing but an aggregate of mechanical and chemical inventions, as often going wrong as right ”

“ Whether the first state of electrised clouds is positive or negative, if I could find the cause of that, I should be at no loss about the other, for either is easily deduced from the other, as one state is easily produced by the other. A strongly positive cloud may drive out of a neighbouring cloud much of its natural quantity of the electric fluid, and, passing by it, leave it in a negative state. ”

“ Now, though the laws of nature forbid that water can by any power in itself lift itself up to the height of the reservoir originally holding it, here seems a contradiction. For a time, friction and the resistance of the air appears to be done away with. ”

“ So do flux and reflux—the rhythm of change—alternate and persist in everything under the sky. ”

“ If, however, is any constant dyadic, the variations of will necessarily be homologous with and we may write without other limitation than that is constant,
A second differentiation gives 184. It follows that if we have a differential equation of the form the integral equation will be of the form representing the value of for For this gives and the proper value of for 185. Def.—A flux which is a linear function of the position-vector is called a homogeneous-strain-flux from the nature of the strain which it produces. Such a flux may evidently be represented by a dyadic. ”

“ For, in the next place, our experiments seem to teach that the supposed aversation of Nature to a vacuum is but accidental, or in consequence, partly of the weight and fluidity, or, at least, fluxility of the bodies here below; and partly, and perhaps principally, of the air, whose restless endeavour to expand itself every way makes it either rush in itself or compel the interposed bodies into all spaces where it finds no greater resistance than it can surmount. ”

“ So soon therefore as the Fœtus is excluded, and expos'd to the immediate contact of the ambient Atmosphere, the Vessels and all the Cavities of the Body must necessarily be so compress'd, that the Fluids can't have room for motion, and consequently the Fœtus could have no Life, if Nature had not contriv'd by the motion of the Thorax to remove and admit that pressure alternately, and thereby to impress a motion on the Fluids, which is the Spring of Life. ”

“ The movement of air in flues and other outlets is governed by general laws, like those governing the general movements of fluids, but allowances require to be made for friction in the channels of entrance and outlet.
The theoretical velocity, when friction is not taken into account, may be calculated by a formula based on what is known as the law of Montgolfier, or the law of spouting fluids. ”

“ On the other hand, the flux of heat in any direction at any point of a solid body may be defined as the quantity of heat which crosses a small area drawn perpendicular to that direction divided by that area and by the time. ”

“ Although the third order of lever is particularly inefficient when the fulcrum is rigid and immobile, it possesses singular advantages when these conditions are reversed, i.e. when the fulcrum, as happens with the air, is elastic and yielding. ”

“ Here, indeed, we see illustrated in a way more than usually easy to follow, the eventual balancing of outer actions by inner reactions. The relation between the demand for liquid and the formation of channels that supply liquid, as well as that between the incidence of strains and the deposit of substance which resists strains, are among the clearest special examples of the general truth that the moving equilibrium of an organism, if not overthrown by an incident force, must eventually be adjusted to it. ”

“ First then we see that the revolutions of heavenly bodies are accomplished in calculated times; as also the flux and reflux of the sea. The motion of heavy bodies to the earth, and of light bodies toward the heavens, is accomplished in definite periods, varying with the bodies moved and the medium through which they move. ”

“ Well, just at the last moment there came a sudden flush of current, dredging through the tangles like a wave. I lost one hold, was flung sprawling on my side, and, instinctively grasping for a fresh support, my fingers closed on something hard and cold. ”

“ The conception of a single fluid of this kind, which when accumulated in excess in bodies tends constantly to escape, and seek a restoration of equilibrium by communicating itself to any others where there may be a deficiency, is that which occurs most naturally to the mind, and was accordingly maintained by Franklin, to whom the science of electricity is under great obligations for those decisive experiments which informed us respecting the true nature of lightning. ”

“ As actio in distans is rejected, all the phenomena of motion are traced back to pressure and impulse. The distinction between fluid and solid bodies is based on the greater or less mobility of their parts. ”

“ The fluid, which is propagated hence through one class of nerves, returns in an altered state through another, and the nature of that fluid is spiritual, though not immaterial, any more than, as I before remarked, light or electricity are so. ”

“ The following are empirical laws still waiting to be resolved into the simpler laws from which they are derived: the local laws of the flux and reflux of the tides in different places; the succession of certain kinds of weather to certain appearances of sky; the apparent exceptions to the almost universal truth that bodies expand by increase of temperature; the law that breeds, both animal and vegetable, are improved by crossing; that gases have a strong tendency to permeate animal membranes ”