Current density

“ If one forms the integral over the system completed in this way, one finds the value zero; for the same reason, at a stationary electric current, by which the integral of the current density vanishes over the entire current-area. ”

“ The standard maximum flux density which is adopted in electro-technical work is 2500, hence in the construction of the cores of alternating-current electromagnets and transformers iron has to be employed having a known hysteretic constant at the standard flux density. ”

“ Parallel to each of these directions there moves a stream or torrent of corpuscles. Now, in order to give it no more than the necessary size, the transverse section of this current has the same contour as [159] the orthogonal projection of the visible universe upon the plane of this section.
Sixth. The different parts of a single current are sensibly of equal density, either where contemporary portions of sensible magnitude or successive portions occupying sensible times in traversing a given surface are compared. The densities of different currents are also equal. ”

“ The stability of any phase with respect to continuous changes depends upon the same conditions with respect to the second and higher differential coefficients of the density of energy regarded as a function of the density of entropy and the densities of the several components, which would make the density of energy a minimum, if the necessary conditions with respect to the first differential coefficients were fulfilled. ”

“ What is meant by a limit to density except in so far as it is combined with heat, is that whatever density may be given to matter by compression when it is in a heated state, a greater density will be found in it when it is deprived of that heat; that whatever may be the density of any part of the interior of the earth in its present state, that density will be increased when the earth becomes cooled down to the temperature derived from the heat of the sun, or to absolute zero of temperature, if such there be, on account of shrinking in cooling ”

“ The quantity within brackets rapidly approaches unity as increases, so that at a distance from the boundary equal to times the breadth of the strip , the actual density is greater than the normal density by about of the normal density. ”

“ They are illustrations of the general fact that when the density varies rapidly with the temperature, determinations of density for the same temperature and pressure by different observers, or different determinations by the same observer, exhibit discordances which are entirely of a different order of magnitude from those which occur with substances of normal or constant densities, or which occur with the same substance at temperatures at which the density approaches a constant value. ”

“ But the elasticity is the same thing as the power of resisting compression, which in the case of air we know to be about 15 pounds to the square inch; so that the ether, if equally dense, would balance a pressure of 15 million million pounds to the square inch—that is, it would require a pressure of about 750 millions of tons to the square inch to condense ether to the density of air. On the other hand, its density, if any, must be so infinitesimally small that the earth moving through it in its orbit with a velocity of 1,100 miles a minute suffers no perceptible retardation. ”

“ If we suppose the thickness of the shell to diminish indefinitely while its density increases, we ultimately arrive at the conception of a surface-density varying as the perpendicular from the centre on the tangent plane, and since the resultant attraction of this superficial distribution on any point within the ellipsoid is zero, electricity, if so distributed on the surface, will be in equilibrium.
Hence, the surface-density at any point of an ellipsoid undisturbed by external influence varies as the distance of the tangent plane from the centre.
Distribution of Electricity on a Disk. ”

“ If, then, we suppose one body to have twice the diameter of the other, but to be of the same density, it follows that at corresponding points of the interior, the hydrostatic pressure will be twice as great in the larger body. The density being the same, it follows that the temperature must be twice as high in order that equilibrium may be maintained. It follows that the stars of the greatest mass will be at the highest temperature, unless their volume is so great that their density is less than that of the smaller stars. ”

“ Pure water at any definite temperature, for instance that of snow melting under inappreciable pressure, furnishes an invariable standard of density, and by comparing equal bulks of various substances with a like bulk of ice-cold water, as regards the velocity produced in a unit of time by the same force, we should ascertain the densities of those substances as expressed in that of water. Practically the force of gravity is used to measure density; for a beautiful experiment with the pendulum, performed by Newton and repeated by Gauss, shows that all kinds of matter gravitate equally. ”

“ The doctrine that the interior nucleus of the Earth is fluid, whether accepted or rejected, does not materially affect this argument. It appears, that in some cases, at least, the melting of substances is prevented, by their being subjected to extreme pressure; but the density, the element from which we reason, is measured by methods quite independent of such questions. ”

“ If is the density on either surface of the bowl at a given point when the bowl is at potential zero, and is influenced by the rest of the sphere electrified to density , then, when the bowl is maintained at potential , we must increase the density on the outside of the bowl by , the density on the supposed enveloping sphere. ”

“ Hence the attraction on a body at the bottom of the mine would be, on the whole, less than the attraction on a body on the top in the. ratio of one to two.
If, however, the earth be not of uniform density, but its density increase towards the centre, then though the attracting mass which acts on a body at the bottom of a mine be smaller, yet the diminution in the force of gravity so occasioned may be more than compensated by the comparative nearness of the attracted body to the denser parts of the earth. ”

“ By progressive cooling, still other elements would be removed from the gaseous mass, which would form the atmosphere of the non-gaseous nucleus. We may suppose an arrangement of the condensed matters at the centre according to their respective specific gravities, and thus the fact that the density of the earth as a whole is about twice the mean density of the matters which form its solid surface may be explained. ”

“ If this were so, and comets composed of the elementary gases, some of them would have very respectable masses, as the nuclei are frequently not more than 5,000 miles in diameter, and consequently it becomes important to examine the principle. From all experiments the density of an elastic fluid is directly as the compressing force; and if a cylinder reached to the top of our atmosphere, compressed by the gravitation of the earth, considered equal at each end of the cylinder, it would represent the actual compressing force to which it owes its density. ”

“ Now, from the Harton Colliery experiments, in 1854, in which the earth's weight was estimated by comparing the vibrations of a pendulum at the mouth of the mine with those of a similar pendulum at a depth of about 1,260 feet, it appeared that the earth's density is rather more than 61⁄2 times that of water, corresponding to an increase in our estimate of the earth's mass by nearly 1,100 millions of millions of millions of tons, or by more than a sixth of the entire mass resulting from the most trustworthy former measurements. ”

“ Again, if the gravity of the particles of the fluid be the same at all distances, and the distances be in Arithmetical progression, the densities will be in a Geometrical progression, as Dr. Halley has found. If the gravity be as the distance, and the squares of the distances be in Arithmetical progression, the densities will be in Geometrical progression. And so in infinitum. These things will be so, when the density of the fluid condensed by compression is as the force of compression, or, which is the same thing, when the space possessed by the fluid is reciprocally as this force. ”

“ Our conception of matter, if it is to be composed of electrons, is necessarily rather like the conception of a solar system, or rather of a milky way; where there are innumerable dots here and there, with great interspaces between. So that the average density of the whole of the dots or material particles taken together,—that is to say, their aggregate mass compared with the space they occupy,—is excessively small. ”

“ If the gas to be weighed is then let into the globe, its weight can be determined from the increase in the weight of the globe. It is necessary, however, that the temperature and pressure of the air about the balance should remain constant for both weighings, as the weight of the globe in air will (according to the laws of hydrostatics) vary with its density. The volume of the air displaced, and its weight, must therefore be determined by observing the temperature, density, and moisture of the atmosphere during the time of experiment. ”

“ Now, when our system was initially at rest, yet the surfaces and were not hindered to emanate, then the energy density is initially present in , and it is the question, what is happening with the energy quantity when the system is suddenly brought to velocity . The previous consideration indicates that the energy amount has to be completely absorbed by the surfaces and ; no part of it may be transformed into mechanical work. ”

“ The standard substances employed to determine relative densities are: water for liquids and solids, and hydrogen or atmospheric air for gases; oxygen (as 16) is sometimes used in this last case. Other standards of reference may be used in special connexions; for example, the Earth is the usual unit for expressing the relative density of the other members of the solar system. Reference should be made to the article Gravitation for an account of the methods employed to determine the “mean density of the earth.” ”

“ A point to be observed is that the actual or total mass of any gas thus liberated at the planet's surface has no bearing on the ultimate height of the atmosphere which it would constitute. When the expansive motion is completed, the density properties of the atmosphere would of course depend on the initial mass of gas liberated, but for any given value of gravity it is the energy properties of the gas per unit mass, or what might be termed its specific energy properties, which really determine the height of its atmosphere. ”

“ On Earth this cannot be done reliably, since gravity causes smaller grains to settle toward the bottom of the green compact, producing parts of irregular density, composition, and strength (proportional to final density) .
On Earth, large presses, sometimes also operating at high temperatures, are required to squeeze the parts to 99% or more of final density from original densities of 70-90%. Major changes in physical dimensions may occur. ”

“ If R converges to a point (x, y, z, t) , then the quotient of this mass, and the volume of R approaches a limit μ (x, y, z, t) , which is known as the mass-density at the space-time point (x, y, z, t) .
The principle of conservation of mass says—that for an infinitely thin space-time filament, the product μdJ, where μ = mass-density at the point (x, y, z, t) of the filament (i.e., the principal line of the filament) , dJ = contents of the cross-section normal to the t axis, and passing through (x, y, z, t) , is constant along the whole filament. ”

“ The circumstance that the experiments at the two highest pressures (301 and 279mm) give results exceeding the calculated values considerably more than any other experiments at adjacent temperatures may seem to indicate that the densities increase with the pressures more rapidly than the formula allows; but the differences are not too large to be ascribed to errors of observation, and the experiment at the lowest pressure (84mm) also shows a large excess of observed density. ”

“ As the pressure in the outer portions will be relatively small, the density of the gases will likewise be diminished there. The energetic expansion and, more still, the great heat radiation will lower the temperature at a rapid rate. We have thus to deal with a central body whose inner portion will possess a high density, and which will resemble the mass of the sun, while the outer portion will be attenuated and nebular. ”

“ In order to show that there is nothing extravagant in the supposition of the density of the ether being directly as the square roots of the distances from the axis, we will take a fluid whose law of density is known, and calculate the effect of the centrifugal force, considered as a compressing power. ”

“ It is because we have reason to assert that any [86] ordinary mass of matter consists, like the cosmos, of separated particles, with great intervening distances in proportion to their size, that we are able to maintain that the aggregate density of ordinary stuff, such as water or lead, is very small compared with the continuous medium in which they exist, and of which all particles are supposed to be really composed. So that lead is to the ether, as regards density, very much as the "vacuum" above spoken of is to lead. ”

“ The surface-density when positive is of the same order of magnitude as the thickness of the non-homogeneous film, but is not necessarily small compared with other surface-densities because the volume-densities of the same substance in the adjacent masses are small. Now the potential of a substance which forms a very small part of a homogeneous mass certainly increases, and probably very rapidly, as the proportion of that component is increased. ”