At barometric pressures such as exist between 18 and 36 kilometres above the ground the mobility of the ions varies inversely as the pressure, whilst the coefficient of recombination a varies approximately as the pressure.
The conductivity, which varies as the product of n into the mobility, will thus vary inversely as the pressure, and so at 36 kilometres will be one hundred times as large as close to the ground.
Proteaceae), an Australian genus of trees with very thick, woody, inversely pear-shaped fruits which split into two parts when ripe.
The imports of potatoes into the United Kingdom vary, to some extent inversely; thus, the low production in 1897 was accompanied by an increase of imports from 3,921,205 cwt.
Viscosity increases with density, but oils of the same density often vary greatly; the coefficient of expansion, on the other hand, varies inversely with the density, but bears no simple relation to the change of fluidity of the oil under the influence of heat, this being most marked in oils of paraffin base.
By geometrical consideration it can be shown that the angle subtended by p, as seen from F, must be inversely as the square of its distance r.
An explanation of the failure of the usual dilution law in these cases may be given if we remember that, while the electric forces between bodies like undissociated molecules, each associated with equal and opposite charges, will vary inversely as the fourth power of the distance, the forces between dissociated ions, each carrying one charge only, will be inversely proportional to the square of the distance.
Coulomb, who by using very long and thin magnets, so arranged that the action of their distant poles was negligible, succeeded in establishing the law, which has since been confirmed by more accurate methods, that the force of attraction or repulsion exerted between two magnetic poles varies inversely as the square of the distance between them.
(5) The uniformity of the field is not in this case disturbed by the influence of ends, but its strength at any point varies inversely as the distance from the axis of the ring.
(22) It will be seen that, whereas the couple varies inversely as the cube of the distance, the force varies inversely as the fourth power.
A thin sheet of magnetic matter magnetized normally to its surface in such a manner that the magnetization at any place is inversely proportional to the thickness h of the sheet at that place is called a magnetic shell; the constant product hI is the strength of the shell and is generally denoted by 4, or 4.
He found that the susceptibility for unit of mass,.K, was independent of both pressure and magnetizing force, but varied inversely as the absolute temperature,.
Putting t°= - 182 in the equation given above for Curie's results, we get K X Io 6 = - 1.66, a value sufficiently near that obtained by Fleming and Dewar to suggest the probability that the diamagnetic susceptibility varies inversely as the temperature between-182° and the melting-point.
Curie has shown, for many paramagnetic bodies, that the specific susceptibility K is inversely proportional to the absolute temperature 0.
Hence may be deduced an explanation of the fact that, while the susceptibility of all known diamagnetics (except bismuth and antimony) is independent of the temperature, that of paramagnetics varies inversely as the absolute temperature, in accordance with the law of Curie.
Coulomb, 2 however, by using long and thin steel rods, symmetrically magnetized, and so arranged that disturbing influences became negligibly small, was enabled to deduce from his experiments with reasonable certainty the law that the force of attraction or repulsion between two poles varies inversely as the square of the distance between them.
Being thus inversely proportional to R.
In his experiments upon this subject Fraunhofer employed plates of glass dusted over with lycopodium, or studded with small metallic disks of uniform size; and he found that the diameters of the rings were proportional to the length of the waves and inversely as the diameter of the disks.
In different gratings the lengths of the spectra and their distances from the axis were inversely proportional to the grating interval, while with a given grating the distances of the various spectra from the axis were as i, 2, 3, &c. To Fraunhofer we owe the first accurate measurements of wave-lengths, and the method of separating the overlapping spectra by a prism dispersing in the perpendicular direction.
We have ultimately G =o, H = (7rV)- 1, so that 1 2 = I / 12V 2, or the illumination is inversely as the square of the distance from the shadow of the edge.
Thus, arguing inversely, we may learn something of the respective natures of these influences and of the way in which the nervous system is affected secondarily.
Taking advantage of these results, Henri Pitot (1695-1771) afterwards showed that the retardations arising from friction are inversely as the diameters of the pipes in which the fluid moves.
He supposed that the surface of the fluid, contained in a vessel which is emptying itself by an orifice, remains always horizontal; and, if the fluid mass is conceived to be divided into an infinite number of horizontal strata of the same bulk, that these strata remain contiguous to each other, and that all their points descend vertically, with velocities inversely proportional to their breadth, or to the horizontal sections of the reservoir.
- If two liquids of different density are resting in vessels in communication, the height of the free surface of such liquid above the surface of separation is inversely as the density.
In the more general case of the convective equilibrium of a spherical atmosphere surrounding the earth, of radius a, (1-1?-=(n+ I) Po --a 2 dr, (12) gravity varying inversely as the square of the distance r from the centre; so that, k = po/po, denoting the height of the homogeneous atmosphere at the surface, 0 is given by (n+I)k(I -9/6 0) =a(I -a/r), (13) or if c denotes the distance where 0=o, 0 _a (14) 0 r c -a' When the compressibility of water is taken into account in a deep ocean, an experimental law must be employed, such as p - po=k(P - Po), or P/po=I+(p-p0)/A, A=kpo, (15) so that A is the pressure due to a head k of the liquid at density under atmospheric pressure po; and it is the gauge pressure required on this law to double the density.
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.
Projected perpendicularly against a plane boundary, the motion is determined by an equal opposite vortex ring, the optical image; the vortex ring spreads out and moves more slowly as it approaches the wall; at the same time the molecular rotation, inversely as the cross-section of the vortex, is seen to increase.
In primitive religions inclusive of almost every serious offence even in fields now regarded as merely social or political, its scope is gradually lessened to a single part of one section of ecclesiastical criminology, following inversely the development of the idea of holiness from the concrete to the abstract, from fetishism to mysticism.
Gravis, heavy), in physical science, that mutual action between masses of matter by virtue of which every such mass tends toward every other with a force varying directly as the product of the masses and inversely as the square of their distances apart.
Hooke, contemporaries of Newton, saw that Kepler's third law implied a force tending toward the sun which, acting on the several planets, varied inversely as the square of the distance.
For constant charges and distances the mechanical force is inversely as the dielectric constant.
The fact that there is no electric force in the interior of such a closed electrified shell is one of the most certainly ascertained facts in the science of electrostatics, and it enables us to demonstrate at once that particles of electricity attract and repel each other with a force which is inversely as the square of their distance.
The electric density on the sphere being uniform, the quantities of electricity on these areas are proportional to the areas, and if the electric force varies inversely as the square of the distance, the forces exerted by these two surface charges at the point in question are proportional to the solid angle of the little cone.
Over an ellipsoid, so that its density is everywhere proportional to the thickness of a shell formed by describing round ' The solution of the problem of determining the distribution en an ellipsoid of a fluid the particles of which repel each other with a force inversely as the nth power of the distance was first given by George Green (see Ferrer's edition of Green's Collected Papers, p. 119, 1871).
Hence the electric force E in the interspace 1dRccor the potential V at any point in the interspace is given by varies inversely E = as - the distance distance =A/R from or V the - axis.
Hence the characteristic quality of a tube of electric force is that its section is everywhere inversely as the electric force at that point.
It is not difficult to show that E = - (d 2 -r 2)q/rAP 3 - - (25), in other words, the force at P is inversely as the cube of the distance from A.
If he had ventured to assume the difference of the specific heats constant, it would have followed that F'(t) must vary inversely as T.
EF is the change of volume corresponding to a change of pressure BE when no heat is allowed to escape and the path is the adiabatic BF, EC is the change of volume for the same change of pressure BE when the path is the isothermal BC. These changes of volume are directly as the compressibilities, or inversely as the elasticities.
By experiments at different temperatures between o° and 00° C., they found that the cooling effect per atmosphere of pressure varied inversely as the square of the absolute temperature for air and CO 2.
The simplest assumption which suffices to express the small deviations of gases and vapours from the ideal state at moderate pressures is that the coefficient a in the expression for the capillary pressure varies inversely as some power of the absolute temperature.
(17) in which c is a small quantity (expressing the defect from the ideal volume V =Re/p due to co-aggregation of the molecules) which varies inversely as the nth power of 0, but is independent of p to a first approximation at moderate pressures.
It is not necessary to suppose that c varies inversely as the nth power of the temperature, and that b is constant, as assumed in deducing the expressions for cp, E, and F.
As far as the order to which he carried the approximations - which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart--the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions.
Hydro- statical principles can be applied to density determinations in four typical ways: (I) depending upon the fact that the heights of liquid columns supported by the same pressure vary inversely as the densities of the liquids; (2) depending upon the fact that a body which sinks in a liquid loses a weight equal to the weight of liquid which it displaces; (3) depending on the fact that a body remains suspended, neither floating nor sinking, in a liquid of exactly the same density; (4) depending on the fact that a floating body is immersed to such an extent that the weight of the fluid displaced equals the weight of the body.
The heights of the columns above the surface of junction of the liquids are inversely proportional to the densities of the liquids.
The heights to which the liquids rise, measured in each case by the distance between the surfaces in the reservoirs and in the tubes, are inversely proportional to the densities.
This work included the "Logometria," the trigonometrical theorem known as "Cotes' Theorem on the Circle" (see TRIGONOMETRY), his theorem on harmonic means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as "Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance.
13" or 14" when the magnifying power is loo, and varying inversely as the power.
To maintain e µe constant, compensation for variation of µ is made by inversely varying 0.