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inversely

inversely Sentence Examples

  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • being thus inversely proportional to R.

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  • 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,.

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  • 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,.

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  • - 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.

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  • Coulomb proved that this mechanical force varies inversely as the square of the distance between the centres of the spheres.

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  • - 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.

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  • 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.

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  • Proteaceae), an Australian genus of trees with very thick, woody, inversely pear-shaped fruits which split into two parts when ripe.

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  • 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.

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  • 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.

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  • (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.

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  • (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.

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  • The same would be the case if the magnetization of the filament varied inversely as the area of its cross-section a in different parts.

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  • 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.

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  • 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.

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  • Curie has shown, for many paramagnetic bodies, that the specific susceptibility K is inversely proportional to the absolute temperature 0.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Hence the characteristic quality of a tube of electric force is that its section is everywhere inversely as the electric force at that point.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • (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.

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  • 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.

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  • 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.

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  • 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.

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  • The heights of the columns above the surface of junction of the liquids are inversely proportional to the densities of the liquids.

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  • 13" or 14" when the magnifying power is loo, and varying inversely as the power.

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  • To maintain e µe constant, compensation for variation of µ is made by inversely varying 0.

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  • (14) In this equation we have the combined laws of Boyle and Charles: When the temperature of a gas is kept constant the pressure varies inversely as the volume, and when the volume is kept constant the pressure varies as the temperature.

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  • The law that, caeteris paribus, n varies inversely as the thickness may be tested by forming a string of four lengths of the single thread used before, and consequently of double the thickness of the latter, when, for the same length and tension, the compound thread will exhibit double the number of ventral segments presented by the single thread.

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  • to be resisted varies inversely as the depth of the girder.

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  • Among the critics of the views put forward in this book was a Jesuit, Franciscus Linus (1595-1675), and it was while answering his objections that Boyle enunciated the law that the volume of a gas varies inversely as the pressure, which among English-speaking peoples is usually called after his name, though on the continent of Europe it is attributed to E.

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  • Assuming, however, that the agreement is close enough for practical requirement, the conbustion of the cordite may be considered complete at this stage P, and in the subsequent expansion it is assumed that the gas obeys an adiabatic law in which the pressure varies inversely as some mtn power of the volume.

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  • The county is to be found in every state of the Union, but its importance varies inversely with the position held in the system of local government by that smaller and older organism, the town.

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  • In the latter case, the densities of the fluids will be inversely proportional to the volumes thus displaced.

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  • Also W = (V +IA)w i; or w1=W/(V+/A), w p =W/(V+plA), and wn =W/(Vd-nIA), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.

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  • The true order of discovery, however, was as follows: (a) Sir Christo p her Wren made many experiments before the Royal Society, which were afterwards repeated in a corrected form by Sir Isaac Newton in the Principia, experimentally proving that bodies of ascertained comparative weights, when suspended and impelled against one another, forced one another back by impressing on one another opposite changes of velocity inversely as their weights and therefore masses; that is, by impressing on one another equal and opposite changes of momentum.

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  • It shows that the bodies impress on one another opposite changes of velocity inversely as their weights or masses; and that in doing so they always begin by reducing one another to a joint mass with a common velocity, whatever they may do afterwards in consequence of their elasticities.

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  • If the bodies though of the same substance are of different sizes, the magnitudes of the additions of velocity are found to be inversely proportional to the volumes of the bodies.

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  • The Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.

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  • It is golden yellow, somewhat inversely conical in shape and about 2 in.

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  • The leaf in its contour is somewhat obovate, or inversely egg-shaped, and its base is oblique.

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  • In the steady state, the product kdO/dx must be constant, or the gradient must vary inversely as the conductivity, if the latter is a function of 0 or x.

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  • The corresponding gradient is of the order of z° C. in ioo ft., but varies inversely with the conductivity of the strata at different depths.

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  • The areas of successive surfaces vary as their radii, hence the rate of transmission Q/AT varies inversely as the radius r, and is Q/2lrrlT, if 1 is the length of the cylinder, and Q the total heat, calculated from the condensation of steam observed in a time T.

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  • By the use of a revolving mirror similar to that used by Sir Charles Wheatstone for measuring the rapidity of electric currents, he was enabled in 1850 to demonstrate the greater velocity of light in air than in water, and to establish that the velocity of light in different media is inversely as the refractive indices of the media.

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  • Having reached so far as to perceive that the central force of the solar system must decrease inversely as the square of the distance, and applied vainly to Wren and Hooke for further elucidation, he made in August 1684 that journey to Cambridge for the purpose of consulting Newton, which resulted in the publication of the Principia.

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  • Also the diameter of the pencil or parallel rays emerging from the eye-lens to the diameter of the object-lens inversely as, the magnifying power of the telescope.

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  • A parallax of 0.01" denotes a distance a hundred times as great, and so on, the distance and parallax being inversely proportional.

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  • Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.

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  • Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

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  • It is interesting to remark that the simple result found in equation (25) (according to which the effect of the deviation of the vapour from the ideal state is represented by the addition of the term (c-b)/V to the expression for log p) is independent of the assumption that c varies inversely as the n th power of 9, and is true generally provided that c-b is a function of the temperature only and is independent of the pressure.

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  • viz, the pitch of any screw varies inversely as the square of that diameter of the conic which is parallel to its axis.

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  • The moment of inertia about any radius of the quadric (39) therefore varies inversely as the square of the length of this radius.

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  • We may notice also the case of an attractive force varying inversely as the FIG.

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  • Thus the unit of velocity is that of a point describing the unit of length in the unit of time; it may be denoted by LTi, this symbol indicating that the magnitude of the unit in question varies directly as the unit of length and inversely as the unit of time.

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  • Ihe number which expresses a physical quantity of any particular kind will of course vary inversely as the magnitude of the corresponding unit.

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  • Again, the time of falling from a distance a into a given centre of force varying inversely as the square of the distance will depend only on a and on the constant u of equation (15).

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  • that is to say, their velocities are opposite as to inwardness and outwardness and inversely proportional to their areas.

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  • And from this, and from the property of a rigid body, already stated in 29, it follows, that the components along a is ne of connection of all the points traversed by that line, whether -in the driver or in the follower, are equal; and consequently, that the velocities of any pair of points traversed by a line of connection are to each other inversely as the cosines, or directly as the secants, of the angles made by the paths of those points with the line of connection.

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  • That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.

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  • of 39 it appears that the angular velocities of a pair of wheels whose axes meet in a point are to each other inversely as the sines of the angles which the axes of the wheels make with the line of contact.

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  • Through any point 0 in this common perpendicular draw 0A1 parallel to B~C~ and OAi parallel to B2C,; make those lines pro B1 C2 portional to the angular velocities D ~ about the axes to which they are P respectively paiallel; complete the ~ B2 parallelogram OA1 EA2, and draw the diagonal OE; divide BiBf in D into C, two parts, inversely proportional to the angular velocities about the axes which they respectively adjoin; A2 through D parallel to OE draw DT.

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  • Hence, in any pair of circular wheels which work together, the numbers of teeth in a complete circumference are directly as the radii and inversely as the angular velocities.

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  • The angular velocities of the screws are inversely as their numbers of threads.

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  • The angular velocities of a pair of connected circular pulleys or drums are inversely as the effective radii.

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  • Eng., 1883) showed that when oil is supplied to a journal by means of an oil bath the coefficient of friction varies nearly inversely as the load on the bearing, thus making the product of the load on the bearing and the coefficient of friction a constant.

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  • 129) be the axis of a pivot, and let RPC be a portion of a curve such that at any point P the secant of the obliquity to the normal of the curve of a line parallel to the axis is inversely proportional to the ordinate PY, to which the velocity of P is proportional.

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  • It increases with the sectional area of the rope, and is inversely proportional to the radius of the curve into which it is bent.

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  • In balancing the mechanism of a steam engine it is often sufficiently accurate to consider the motion of the pistons as simple harmonic, and the effect on the framework of the acceleration of the connecting rod may be approximately allowed for by distributing the weight of the rod between the crank pin and the piston inversely as the centre of gravity of the rod divides the distance between the centre of the cross head pin and the centre of the crank pin.

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  • Herbert Spencer, again, before the decline in question set in, put forward the hypothesis that "the ability to maintain individual life and the ability to multiply vary inversely"; in other words, the strain upon the nervous system involved in the struggle for life under the conditions of modern civilization, by reacting on the reproductive powers, tends towards comparative sterility.

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  • Thus, all other considerations being set aside, mortality tends to vary inversely with the proportion of the population at the healthy period 5 to 25.

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  • The second of these essays (De La nature de l'air) contains the statement of the law that the volume of a gas varies inversely as the pressure, which, though very generally called by the name of Mariotte, had been discovered in 1660 by Robert Boyle.

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  • Cavendish measured the capacity of disks and condensers of various forms, and proved that the capacity of a Leyden pane is proportional to the surface of the tinfoil and inversely as the thickness of the glass.

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  • Starting from the fact that if an electrified globe, placed within two hemispheres which fit over it without touching, is brought in contact with these hemispheres, it gives up the whole of its charge to them - in other words, that the charge on an electrified body is wholly on the surface - he was able to deduce by most ingenious reasoning the law that electric force varies inversely as the square of the distance.

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  • Coulomb has made his name for ever famous by his invention and application of his torsion balance to the experimental verification of the fundamental law of electric attraction, in which, however, he was anticipated by Cavendish, namely, that the force of attraction between two small electrified spherical bodies varies as the product of their charges and inversely as the square of the distance of their centres.

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  • He ascertained the distribution of electricity among several spheres (whether equal or unequal) placed in contact in a straight line; and he measured the distribution of 2 In 1878 Clerk Maxwell repeated Cavendish's experiments with improved apparatus and the employment of a Kelvin quadrant electrometer as a means of detecting the absence of charge on the inner conductor after it had been connected to the outer case, and was thus able to show that if the law of electric attraction varies inversely as the nth power of the distance, then the exponent n must have a value of 2 t Isua.

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  • These investigations led him to the announcement of the fundamental law of action between elements of current, or currents in infinitely short lengths of linear conductors, upon one another at a distance; summed up in compact expression this law states that the action is proportional to the product of the current strengths of the two elements, and the lengths of the two elements, and inversely proportional to the square of the distance between the two elements, and also directly proportional to a function of the angles which the line joining the elements makes with the directions of the two elements respectively.

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  • Ohm introduced the clear idea of current strength as an effect produced by electromotive force acting as a cause in a circuit having resistance as its quality, and showed that the current was directly proportional to the electromotive force and inversely as the resistance.

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  • If we imagine the current in the conductor to be instantaneously reversed in direction, the magnetic force surrounding it would not be instantly reversed everywhere in direction, but the reversal would be propagated outwards through space with a certain velocity which Maxwell showed was inversely as the square root of the product of the magnetic permeability and the dielectric constant or specific inductive capacity of the medium.

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  • Coulomb experimentally proved that the law of attraction and repulsion of simple electrified bodies was that the force between them varied inversely as the square of the distance and thus gave mathematical definiteness to the two-fluid hypothesis.

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  • It was then assumed that each of the two constituents of the neutral fluid had an atomic structure and that the so-called particles of one of the electric fluids, say positive, repelled similar particles with a force varying inversely as a square of the distance and attracted those of the opposite fluid according to the same law.

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  • For a single lens of very small thickness and given power, the aberration depends upon the ratio of the radii r: r', and is a minimum (but never zero) for a certain value of this ratio; it varies inversely with the refractive index (the power of the lens remaining constant).

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  • From this he showed that the rise of the liquid in tubes of the same substance is inversely proportional to their radii.

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  • The actual force between the particles arises in part from their mutual gravitation, which is inversely as the square of the distance.

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  • Hence the mean height to which the fluid rises is inversely as the radius of the tube.

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  • The force, therefore, with which the two plates are drawn together consists first of a positive part, or in other words an attraction, varying inversely as the square of the distance, and second, of a negative part of repulsion independent of the distance.

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  • The pitch of the note, though not absolutely definite, cannot differ much from that which corresponds to the division of the jet into wave-lengths of maximum instability; and, in fact, Savart found that the frequency was directly as the square root of the head, inversely as the diameter of the orifice, and independent of the nature of the fluid - laws which follow immediately from Plateau's theory.

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  • The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?

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  • In 1869 van Tieghem laid stress on anatomical evidence as a key to the morphology of the cone-scales; he drew attention to the fact that the collateral vascular bundles of the seminiferous scale are inversely orientated as compared with those of the carpellary scale; in the latter the xylem of each bundle is next the upper surface, while in the seminiferous scale the phloem occupies that position.

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  • Eichler, one of the chief supporters of the simpler view, does not recognize in the inverse orientation of the vascular bundles an argument in support of the axillary-bud theory, but points out that the seminiferous scale, being an outgrowth from the surface of the carpellary scale, would, like outgrowths from an ordinary leaf, naturally have its bundles inversely orientated.

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  • The theory refers to radiation homogeneous at all points within a single closed boundary maintained at uniform temperature; in the actual case we have a double boundary, one the sun's surface, and the other infinitely remote, or say, non-existent, and at zero temperature; and it is assumed that the density of radiation in the free space varies inversely as the squares of the distance from the sun.

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  • The rate of increase of velocity towards any isolated aperture through which water passes into the side of a well sunk in a deep bed of sand is, in the neighbourhood of that aperture, inversely proportional to the square of the distance therefrom.

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  • A body can move round the sun in an elliptic orbit having the sun in its focus, and describing equal areas in equal times, only under the influence of a force directed towards the sun, and varying inversely as the square of the distance from it.

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  • The periodic time varying inversely as n, this equation expresses Kepler's third law.

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  • When bodies revolve at different distances around a centre, their velocities must be such that the centrifugal force of each shall be balanced by the attraction of the central mass, and therefore vary inversely as the square of the v(m i v -+m 2 vz+

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  • It is of interest to note that, very approximately, this deforming force varies inversely as the cube of the distance of the attracting body.

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  • We have also in any case the relations (41) (42) (43) of the current, C, for any given pair of metals, was found to vary directly as the difference of temperature, t-t', between the hot and cold junctions, and inversely as the resistance, R, of the circuit.

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  • Edin., 1867-68), Tait was led to the conclusion that " the thermal and electric conductivities of metals varied inversely as the absolute temperature, and that the specific heat of electricity was directly proportional to the same."

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  • Mag., July 1898), that the value of s varies inversely as the absolute temperature.

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  • DBbereiner he substituted a glass tube closed by a plug of plaster of Paris, and with this simple appliance he developed the law now known by his name "that the diffusion rate of gases is inversely as the square root of their density."

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  • Stokes, and which were published in the Proceedings of the Royal Society for 1855, that he discussed the mathematical theory of signalling through submarine cables, and enunciated the conclusion that in long cables the retardation due to capacity must render the speed of signalling inversely proportional to the square of the cable's length.

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  • However, the number of close lexical neighbors is strongly, inversely correlated with root size.

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  • On the near side, the seawall makes an elbow crooked inversely, and its end too has a lighthouse.

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  • Increasing levels of leisure activity were inversely associated with D-dimer, von Willebrand factor, nephelometric fibrinogen, and viscosity.

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  • linearity of the transfer function is inversely proportional to the sensitivity.

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  • magnetic flux was inversely proportional to twice the charge on an electron.

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  • However, the number of close lexical neighbors is strongly, inversely correlated with root size.

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  • The constant power throughout the entire speed range produces a torque curve inversely proportional to the speed.

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  • The loading time is inversely proportional to the part load.

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  • The degree of distance seemed to be inversely proportionate to age and time spent in the group.

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  • During the avalanches, particles of different sizes often segregate out into inversely graded layers with the large grains on top of the fines.

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  • The time to conception was inversely related to the number of motile sperm seen.

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  • In passing from one part of the spectrum to another, A is the only quantity which varies, and we have the important law: - When light is scattered by particles which are very small compared with any of the wave-lengths, the ratio of the amplitudes of the vibrations of the scattered and incident lights varies inversely as the square of the wave-length, and the ratio of intensities as the inverse fourth power.

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  • 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.

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  • The degree of dependence of any people upon environ ment varies inversely as the degree of culture or civilization, which for this purpose may perhaps be defined as the power of an individual to exercise control over the individual and over the environment for the benefit of the community.

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  • Proteaceae), an Australian genus of trees with very thick, woody, inversely pear-shaped fruits which split into two parts when ripe.

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  • 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.

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  • 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.

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  • 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.

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  • We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

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  • 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.

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  • 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.

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  • (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.

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  • (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.

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  • The same would be the case if the magnetization of the filament varied inversely as the area of its cross-section a in different parts.

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  • 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.

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  • 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.

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  • Curie has shown, for many paramagnetic bodies, that the specific susceptibility K is inversely proportional to the absolute temperature 0.

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  • 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.

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  • 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.

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  • The linear dimension of the diffraction pattern is inversely as that of the aperture, and the brightness at corresponding points is as the square of the area of aperture.

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  • being thus inversely proportional to R.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • Coulomb proved that this mechanical force varies inversely as the square of the distance between the centres of the spheres.

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  • For constant charges and distances the mechanical force is inversely as the dielectric constant.

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  • 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.

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  • 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.

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  • 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).

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  • 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.

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  • Hence the characteristic quality of a tube of electric force is that its section is everywhere inversely as the electric force at that point.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • (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.

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  • 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.

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  • 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.

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  • 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.

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  • The heights of the columns above the surface of junction of the liquids are inversely proportional to the densities of the liquids.

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  • 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.

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  • 13" or 14" when the magnifying power is loo, and varying inversely as the power.

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  • To maintain e µe constant, compensation for variation of µ is made by inversely varying 0.

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  • (14) In this equation we have the combined laws of Boyle and Charles: When the temperature of a gas is kept constant the pressure varies inversely as the volume, and when the volume is kept constant the pressure varies as the temperature.

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  • The law that, caeteris paribus, n varies inversely as the thickness may be tested by forming a string of four lengths of the single thread used before, and consequently of double the thickness of the latter, when, for the same length and tension, the compound thread will exhibit double the number of ventral segments presented by the single thread.

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  • If the two materials are disposed symmetrically, the amount of load carried by each would be in direct proportion to the coefficient of elasticity and inversely as the moment of inertia of the cross section.

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  • to be resisted varies inversely as the depth of the girder.

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  • Among the critics of the views put forward in this book was a Jesuit, Franciscus Linus (1595-1675), and it was while answering his objections that Boyle enunciated the law that the volume of a gas varies inversely as the pressure, which among English-speaking peoples is usually called after his name, though on the continent of Europe it is attributed to E.

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  • Assuming, however, that the agreement is close enough for practical requirement, the conbustion of the cordite may be considered complete at this stage P, and in the subsequent expansion it is assumed that the gas obeys an adiabatic law in which the pressure varies inversely as some mtn power of the volume.

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  • The county is to be found in every state of the Union, but its importance varies inversely with the position held in the system of local government by that smaller and older organism, the town.

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  • In the latter case, the densities of the fluids will be inversely proportional to the volumes thus displaced.

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  • Also W = (V +IA)w i; or w1=W/(V+/A), w p =W/(V+plA), and wn =W/(Vd-nIA), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.

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  • In this case we have w p = W/(N -{- p)lA; or the density of the liquid varies inversely as N+p, that is, as the whole number of scale-divisions between the bottom of the tube and the plane of flotation.

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  • The true order of discovery, however, was as follows: (a) Sir Christo p her Wren made many experiments before the Royal Society, which were afterwards repeated in a corrected form by Sir Isaac Newton in the Principia, experimentally proving that bodies of ascertained comparative weights, when suspended and impelled against one another, forced one another back by impressing on one another opposite changes of velocity inversely as their weights and therefore masses; that is, by impressing on one another equal and opposite changes of momentum.

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  • It shows that the bodies impress on one another opposite changes of velocity inversely as their weights or masses; and that in doing so they always begin by reducing one another to a joint mass with a common velocity, whatever they may do afterwards in consequence of their elasticities.

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  • If the bodies though of the same substance are of different sizes, the magnitudes of the additions of velocity are found to be inversely proportional to the volumes of the bodies.

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  • The Galileo-Newton theory of motion is that, relative to a suitably chosen base, and with suitable assignments of mass, all accelerations of particles are made up of mutual (so-called) actions between pairs of particles, whereby the two particles forming a pair have accelerations in opposite directions in the line joining them, of magnitudes inversely proportional to their masses.

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  • It is golden yellow, somewhat inversely conical in shape and about 2 in.

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  • The leaf in its contour is somewhat obovate, or inversely egg-shaped, and its base is oblique.

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  • In the steady state, the product kdO/dx must be constant, or the gradient must vary inversely as the conductivity, if the latter is a function of 0 or x.

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  • The corresponding gradient is of the order of z° C. in ioo ft., but varies inversely with the conductivity of the strata at different depths.

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  • The areas of successive surfaces vary as their radii, hence the rate of transmission Q/AT varies inversely as the radius r, and is Q/2lrrlT, if 1 is the length of the cylinder, and Q the total heat, calculated from the condensation of steam observed in a time T.

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  • Its chief ideas are - (1) That, owing partly to the want of ability in historians, and partly to the complexity of social phenomena, extremely little had as yet been done towards discovering the principles which govern the character and destiny of nations, or, in other words, towards establishing a science of history; (2) That, while the theological dogma of predestination is a barren hypothesis beyond the province of knowledge, and the metaphysical dogma of free will rests on an erroneous belief in the infallibility of consciousness, it is proved by science, and especially by statistics, that human actions are governed by laws as fixed and regular as those which rule in the physical world; (3) That climate, soil, food, and the aspects of nature are the primary causes of intellectual progress, - the first three indirectly, through determining the accumulation and distribution of wealth, and the last by directly influencing the accumulation and distribution of thought, the imagination being stimulated and the understanding subdued when the phenomena of the external world are sublime and terrible, the understanding being emboldened and the imagination curbed when they are small and feeble; (4) That the great division between European and non-European civilization turns on the fact that in Europe man is stronger than nature, and that elsewhere nature is stronger than man, the consequence of which is that in Europe alone has man subdued nature to his service; (5) That the advance of European civilization is characterized by a continually diminishing influence of physical laws, and a continually increasing influence of mental laws; (6) That the mental laws which regulate the progress of society cannot be discovered by the metaphysical method, that is, by the introspective study of the individual mind, but only by such a comprehensive survey of facts as will enable us to eliminate disturbances, that is, by the method of averages; (7) That human progress has been due, not to moral agencies, which are stationary, and which balance one another in such a manner that their influence is unfelt over any long period, but to intellectual activity, which has been constantly varying and advancing: - "The actions of individuals are greatly affected by their moral feelings and passions; but these being antagonistic to the passions and feelings of other individuals, are balanced by them, so that their effect is, in the great average of human affairs, nowhere to be seen, and the total actions of mankind, considered as a whole, are left to be regulated by the total knowledge of which mankind is possessed"; (8) That individual efforts are insignificant in the great mass of human affairs, and that great men, although they exist, and must "at present" be looked upon as disturbing forces, are merely the creatures of the age to which they belong; (9) That religion, literature and government are, at the best, the products and not the causes of civilization; (10) That the progress of civilization varies directly as "scepticism," the disposition to doubt and to investigate, and inversely as "credulity" or "the protective spirit," a disposition to maintain, without examination, established beliefs and practices.

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  • By the use of a revolving mirror similar to that used by Sir Charles Wheatstone for measuring the rapidity of electric currents, he was enabled in 1850 to demonstrate the greater velocity of light in air than in water, and to establish that the velocity of light in different media is inversely as the refractive indices of the media.

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  • Having reached so far as to perceive that the central force of the solar system must decrease inversely as the square of the distance, and applied vainly to Wren and Hooke for further elucidation, he made in August 1684 that journey to Cambridge for the purpose of consulting Newton, which resulted in the publication of the Principia.

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  • Also the diameter of the pencil or parallel rays emerging from the eye-lens to the diameter of the object-lens inversely as, the magnifying power of the telescope.

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  • A parallax of 0.01" denotes a distance a hundred times as great, and so on, the distance and parallax being inversely proportional.

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  • Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.

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  • Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).

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  • It is interesting to remark that the simple result found in equation (25) (according to which the effect of the deviation of the vapour from the ideal state is represented by the addition of the term (c-b)/V to the expression for log p) is independent of the assumption that c varies inversely as the n th power of 9, and is true generally provided that c-b is a function of the temperature only and is independent of the pressure.

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  • viz, the pitch of any screw varies inversely as the square of that diameter of the conic which is parallel to its axis.

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  • The moment of inertia about any radius of the quadric (39) therefore varies inversely as the square of the length of this radius.

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  • We may notice also the case of an attractive force varying inversely as the FIG.

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  • Thus the unit of velocity is that of a point describing the unit of length in the unit of time; it may be denoted by LTi, this symbol indicating that the magnitude of the unit in question varies directly as the unit of length and inversely as the unit of time.

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  • Ihe number which expresses a physical quantity of any particular kind will of course vary inversely as the magnitude of the corresponding unit.

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  • Again, the time of falling from a distance a into a given centre of force varying inversely as the square of the distance will depend only on a and on the constant u of equation (15).

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  • that is to say, their velocities are opposite as to inwardness and outwardness and inversely proportional to their areas.

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  • And from this, and from the property of a rigid body, already stated in 29, it follows, that the components along a is ne of connection of all the points traversed by that line, whether -in the driver or in the follower, are equal; and consequently, that the velocities of any pair of points traversed by a line of connection are to each other inversely as the cosines, or directly as the secants, of the angles made by the paths of those points with the line of connection.

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  • That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.

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  • of 39 it appears that the angular velocities of a pair of wheels whose axes meet in a point are to each other inversely as the sines of the angles which the axes of the wheels make with the line of contact.

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  • Through any point 0 in this common perpendicular draw 0A1 parallel to B~C~ and OAi parallel to B2C,; make those lines pro B1 C2 portional to the angular velocities D ~ about the axes to which they are P respectively paiallel; complete the ~ B2 parallelogram OA1 EA2, and draw the diagonal OE; divide BiBf in D into C, two parts, inversely proportional to the angular velocities about the axes which they respectively adjoin; A2 through D parallel to OE draw DT.

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  • Hence, in any pair of circular wheels which work together, the numbers of teeth in a complete circumference are directly as the radii and inversely as the angular velocities.

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  • The angular velocities of the screws are inversely as their numbers of threads.

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  • The angular velocities of a pair of connected circular pulleys or drums are inversely as the effective radii.

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  • Eng., 1883) showed that when oil is supplied to a journal by means of an oil bath the coefficient of friction varies nearly inversely as the load on the bearing, thus making the product of the load on the bearing and the coefficient of friction a constant.

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  • 129) be the axis of a pivot, and let RPC be a portion of a curve such that at any point P the secant of the obliquity to the normal of the curve of a line parallel to the axis is inversely proportional to the ordinate PY, to which the velocity of P is proportional.

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  • It increases with the sectional area of the rope, and is inversely proportional to the radius of the curve into which it is bent.

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  • In balancing the mechanism of a steam engine it is often sufficiently accurate to consider the motion of the pistons as simple harmonic, and the effect on the framework of the acceleration of the connecting rod may be approximately allowed for by distributing the weight of the rod between the crank pin and the piston inversely as the centre of gravity of the rod divides the distance between the centre of the cross head pin and the centre of the crank pin.

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  • But there are cases in which the motions of both bodies are appreciable, and must be taken into accountsuch as the projection of projectiles, where the velocity of the recoil or backward motion of the gun bears an appreciable proportion to the forward motion of the projectile; and such as the propulsion of vessels, where the velocity of the water thrown backward by the paddle, screw or other propeller bears a very considerable proportion to the velocity of the water moved forwards and sideways by the ship. In cases of this kind the energy exerted by the effort is distributed between the two bodies between which the effort is exerted in shares proportional to the velocities of the two bodies during the action of the effort; and those velocities are to each other directly as the portions of the effort unbalanced by resistance on the respective bodies, and inversely as the weights of the bodies.

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  • Herbert Spencer, again, before the decline in question set in, put forward the hypothesis that "the ability to maintain individual life and the ability to multiply vary inversely"; in other words, the strain upon the nervous system involved in the struggle for life under the conditions of modern civilization, by reacting on the reproductive powers, tends towards comparative sterility.

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  • Thus, all other considerations being set aside, mortality tends to vary inversely with the proportion of the population at the healthy period 5 to 25.

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  • The second of these essays (De La nature de l'air) contains the statement of the law that the volume of a gas varies inversely as the pressure, which, though very generally called by the name of Mariotte, had been discovered in 1660 by Robert Boyle.

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  • Cavendish measured the capacity of disks and condensers of various forms, and proved that the capacity of a Leyden pane is proportional to the surface of the tinfoil and inversely as the thickness of the glass.

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  • Starting from the fact that if an electrified globe, placed within two hemispheres which fit over it without touching, is brought in contact with these hemispheres, it gives up the whole of its charge to them - in other words, that the charge on an electrified body is wholly on the surface - he was able to deduce by most ingenious reasoning the law that electric force varies inversely as the square of the distance.

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  • Coulomb has made his name for ever famous by his invention and application of his torsion balance to the experimental verification of the fundamental law of electric attraction, in which, however, he was anticipated by Cavendish, namely, that the force of attraction between two small electrified spherical bodies varies as the product of their charges and inversely as the square of the distance of their centres.

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  • He ascertained the distribution of electricity among several spheres (whether equal or unequal) placed in contact in a straight line; and he measured the distribution of 2 In 1878 Clerk Maxwell repeated Cavendish's experiments with improved apparatus and the employment of a Kelvin quadrant electrometer as a means of detecting the absence of charge on the inner conductor after it had been connected to the outer case, and was thus able to show that if the law of electric attraction varies inversely as the nth power of the distance, then the exponent n must have a value of 2 t Isua.

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  • These investigations led him to the announcement of the fundamental law of action between elements of current, or currents in infinitely short lengths of linear conductors, upon one another at a distance; summed up in compact expression this law states that the action is proportional to the product of the current strengths of the two elements, and the lengths of the two elements, and inversely proportional to the square of the distance between the two elements, and also directly proportional to a function of the angles which the line joining the elements makes with the directions of the two elements respectively.

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  • Ohm introduced the clear idea of current strength as an effect produced by electromotive force acting as a cause in a circuit having resistance as its quality, and showed that the current was directly proportional to the electromotive force and inversely as the resistance.

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  • If we imagine the current in the conductor to be instantaneously reversed in direction, the magnetic force surrounding it would not be instantly reversed everywhere in direction, but the reversal would be propagated outwards through space with a certain velocity which Maxwell showed was inversely as the square root of the product of the magnetic permeability and the dielectric constant or specific inductive capacity of the medium.

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  • Coulomb experimentally proved that the law of attraction and repulsion of simple electrified bodies was that the force between them varied inversely as the square of the distance and thus gave mathematical definiteness to the two-fluid hypothesis.

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  • It was then assumed that each of the two constituents of the neutral fluid had an atomic structure and that the so-called particles of one of the electric fluids, say positive, repelled similar particles with a force varying inversely as a square of the distance and attracted those of the opposite fluid according to the same law.

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  • For a single lens of very small thickness and given power, the aberration depends upon the ratio of the radii r: r', and is a minimum (but never zero) for a certain value of this ratio; it varies inversely with the refractive index (the power of the lens remaining constant).

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  • From this he showed that the rise of the liquid in tubes of the same substance is inversely proportional to their radii.

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  • The actual force between the particles arises in part from their mutual gravitation, which is inversely as the square of the distance.

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  • Hence the mean height to which the fluid rises is inversely as the radius of the tube.

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  • The force, therefore, with which the two plates are drawn together consists first of a positive part, or in other words an attraction, varying inversely as the square of the distance, and second, of a negative part of repulsion independent of the distance.

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  • The pitch of the note, though not absolutely definite, cannot differ much from that which corresponds to the division of the jet into wave-lengths of maximum instability; and, in fact, Savart found that the frequency was directly as the square root of the head, inversely as the diameter of the orifice, and independent of the nature of the fluid - laws which follow immediately from Plateau's theory.

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  • The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?

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  • In 1869 van Tieghem laid stress on anatomical evidence as a key to the morphology of the cone-scales; he drew attention to the fact that the collateral vascular bundles of the seminiferous scale are inversely orientated as compared with those of the carpellary scale; in the latter the xylem of each bundle is next the upper surface, while in the seminiferous scale the phloem occupies that position.

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  • Eichler, one of the chief supporters of the simpler view, does not recognize in the inverse orientation of the vascular bundles an argument in support of the axillary-bud theory, but points out that the seminiferous scale, being an outgrowth from the surface of the carpellary scale, would, like outgrowths from an ordinary leaf, naturally have its bundles inversely orientated.

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  • The theory refers to radiation homogeneous at all points within a single closed boundary maintained at uniform temperature; in the actual case we have a double boundary, one the sun's surface, and the other infinitely remote, or say, non-existent, and at zero temperature; and it is assumed that the density of radiation in the free space varies inversely as the squares of the distance from the sun.

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  • The rate of increase of velocity towards any isolated aperture through which water passes into the side of a well sunk in a deep bed of sand is, in the neighbourhood of that aperture, inversely proportional to the square of the distance therefrom.

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  • A body can move round the sun in an elliptic orbit having the sun in its focus, and describing equal areas in equal times, only under the influence of a force directed towards the sun, and varying inversely as the square of the distance from it.

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  • The periodic time varying inversely as n, this equation expresses Kepler's third law.

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  • When bodies revolve at different distances around a centre, their velocities must be such that the centrifugal force of each shall be balanced by the attraction of the central mass, and therefore vary inversely as the square of the v(m i v -+m 2 vz+

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  • It is of interest to note that, very approximately, this deforming force varies inversely as the cube of the distance of the attracting body.

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  • The curve has important mechanical relations, in particular it is the orbit of a particle moving under the influence of a central force which varies inversely as the square of the distance of the particle; this is the gravitational law of force, and the curve consequently represents the orbits of the planets if only an individual planet and the sun be considered; the other planets, however, disturb this orbit (see Mechanics).

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  • We have also in any case the relations (41) (42) (43) of the current, C, for any given pair of metals, was found to vary directly as the difference of temperature, t-t', between the hot and cold junctions, and inversely as the resistance, R, of the circuit.

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  • Edin., 1867-68), Tait was led to the conclusion that " the thermal and electric conductivities of metals varied inversely as the absolute temperature, and that the specific heat of electricity was directly proportional to the same."

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  • Mag., July 1898), that the value of s varies inversely as the absolute temperature.

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  • DBbereiner he substituted a glass tube closed by a plug of plaster of Paris, and with this simple appliance he developed the law now known by his name "that the diffusion rate of gases is inversely as the square root of their density."

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  • Stokes, and which were published in the Proceedings of the Royal Society for 1855, that he discussed the mathematical theory of signalling through submarine cables, and enunciated the conclusion that in long cables the retardation due to capacity must render the speed of signalling inversely proportional to the square of the cable's length.

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  • During the avalanches, particles of different sizes often segregate out into inversely graded layers with the large grains on top of the fines.

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  • There are also indications that among the disabled income is inversely related to severity of disablement.

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  • Inversely, if the confidence is low, people tend to save more money than spend.

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  • Inversely, you should know that despite the bad reputation video games sometimes get, there are some benefits also.

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  • The intensity of light delivered is inversely related to the distance between the light source and the skin surface.

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  • 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.

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  • We therefore have the fundamental theorem that the angular velocity of the body around the centre of attraction varies inversely as the square of its distance, and is therefore at every point proportional to the gravitation of the sun.

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  • 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.

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  • 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.

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  • For constant charges and distances the mechanical force is inversely as the dielectric constant.

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  • In this case we have w p = W/(N -{- p)lA; or the density of the liquid varies inversely as N+p, that is, as the whole number of scale-divisions between the bottom of the tube and the plane of flotation.

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