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gradient

Electrostatic fields come from a voltage gradient and can exist when charge carriers are stationary.

Our internal electrical system works by using cells that have built up electrical gradient or energy that can be given off to other cells by direct transfer.

- Annual Variation Potential Gradient.

Above the level plain of absolutely smooth surface, devoid of houses or vegetation, the equipotential surfaces under normal conditions would be strictly horizontal, and if we could determine the potential at one metre above the ground we should have a definite measure of the potential gradient at the earth's surface.

The potential gradient near the ground varies with the season of the year and the hour of the day, and is largely dependent on the weather conditions.

The large difference between the means obtained at Potsdam and Kremsmtinster, as compared to the comparative similarity between the results for Kew and Karasjok, suggests that the mean value of the potential gradient may be much more dependent on local conditions than on difference of latitude.

At any single station potential gradient has a wide range of values.

The two last curves in the diagram contrast the diurnal variation at Kew in potential gradient and in barometric pressure for the year as a whole.

The first line gives the mean value of the potential gradient, the second the mean excess of the largest over the smallest hourly value on individual days.

It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2.0 in May to 3.6 in November.

In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season.

The potential gradient is in all cases lower in summer than winter, and thus the reduction in c 1 in summer would appear even larger than in Table V.

He found the gradient nearly uniform for heights up to 30 to 40 metres above the ground.

The potential difference between the two is recorded, and the potential gradient is thus found.

Some of the earliest balloon observations made the gradient increase with the height, but such a result is now regarded as abnormal.

From observations during twelve balloon ascents, Linke concludes that below the 1500-metre level there are numerous sources of disturbance, the gradient at any given height varying much from day to day and hour to hour; but at greater heights there is much more uniformity.

At most stations a negative potential gradient is exceptional, unless during rain or thunder.

In some localities, however, negative potential gradient is by no means uncommon, at least at some seasons, in the absence of rain.

Lenard, Elster and Geitel, and others have found the potential gradient negative near waterfalls, the influence sometimes extending to a considerable distance.

The Different Elements Potential Gradient, Dissipation, Ionization And Radioactivityare Clearly Not Independent Of One Another.

will give a general idea of the relations of potential gradient to dissipation and ionization.

Table Potential, Dissipation, Ioniz If we regard the potential gradient near the ground as representing a negative charge on the earth, then if the source of supply of that charge is unaffected the gradient will rise and become high when the operations by which discharge is promoted slacken their activity.

A diminution in the number of positive ions would thus naturally be accompanied by a rise in potential gradient.

No distinct relationship has yet been established between potential gradient and radioactivity.

North of this line, near which the temperature is a little over 80° F., the gradient trends somewhat to the east of north, and the temperature is slightly higher on the western than on the eastern side until, in 4 5° N.

Beyond this parallel the gradient is directed towards the north-west, and temperatures are much higher on the European than on the American side.

This distribution is most marked at about 300 fathoms, and disappears at soo fathoms, beyond which depth the lines tend to become parallel and to run east and west, the gradient slowly diminishing.

Taking their origin from a series of lacustrine basins scattered over the plateaus and differing slightly in elevation, the Russian rivers describe immense curves before reaching the sea, and flow with a very gentle gradient, while numerous large tributaries collect their waters from over vast areas.

Dvina flows with a very slight gradient through a broad valley, and reaches the White Sea at Archangel.

an hour up a gradient of 1 in 450.

The gradient or grade of a line is the rate at which it rises or falls, above or below the horizontal, and is expressed by stating either the horizontal distance in which the change of level amounts to r ft., or the amount of change that would occur in some selected distance, such as roo ft., r000 ft.

In America a gradient of r in roo is often known as a r% grade, one of 2 in roo as a 2% grade, and so on; thus a 0-25% grade corresponds to what in England would be known as a gradient of r in 400.

The ruling gradient of a section of railway is the steepest incline in that section, and is so called because it governs or rules the maximum load that can be placed behind an engine working over that portion of line.

Sometimes, however, a sharp incline occurring on an otherwise easy line is not reckoned as the ruling gradient, trains heavier than could be drawn up it by a single engine being helped by an assistant or " bank " engine; sometimes also " momentum " or " velocity " grades, steeper than the ruling gradient, are permitted for short distances in cases where a train can approach at full speed and thus surmount them by the aid of its momentum.

Brunel laid out the Great Western for a long distance out of London with a ruling gradient of i in 1320.

The maximum gradient possible depends on climatic conditions, a dry climate being the most favourable.

In practice the gradient should not exceed i in 221, and even that is too steep, since theoretical conditions cannot always be realized; a wet rail will reduce the adhesion, and the gradients must be such that some paying load can be hauled in all weathers.

It was not till more than half a century later that an American, Sylvester Marsh, employed the rack system for the purpose of enabling trains to surmount steep slopes on the Mount Washington railway, where the maximum gradient was nearly 1 in 22.

The Locher rack, employed on the Mount Pilatus railway, where the steepest gradient is nearly I in 2, is double, with vertical teeth on each side, while in the Strub rack, used on the Jungfrau line, the teeth are cut in the head of a rail of the ordinary Vignoles type.

The lines through them should be, if possible, straight and on the level; the British Board of Trade forbids them being placed on a gradient steeper than i in 260, unless it is unavoidable.

The pull recorded on the diagram includes the resistances due to acceleration and to the gradient on which the train is moving.

Rate at which work is done against a gradient.

Thus a gradient of I in 200 is the same as a half per cent.

Hence if a train is travelling up the gradient at a speed of V ft.

If W I is the weight of the train in pounds, the rate of working against the gradient expressed in horse-power units is H.P.=W,V/550 G.

per hour up a gradient of I in 300, the extra horse-power required will be H.P. _280X2240X58.6 =22 300 X 550 3.

(24) G g This expression may be used to find r„ when the total draw-bar pull is observed as well as the speed, the changes of speed and the gradient.

These considerations also indicate what a difficult matter it is to find the exact rate of working against the resistances, because of the difficulty of securing conditions which eliminate the effect both of the gradient and of acceleration.

First, it must be able to exert a tractive force sufficient to start the train under the worst conditions possible on the railway over which it is to operate - for instance, when the train is stopped by signal on a rising gradient where the track is curved and fitted with a guard-rail.

Secondly, it must be able to maintain the train at a given speed against the total resistances of the level or up a gradient of given inclination.

Sometimes, as on the Central London railway, the acceleration of gravity is also utilized; the different stations stand, as it were, on the top of a hill, so that outgoing trains are aided at the start by having a slope to run down, while incoming ones are checked by the rising gradient they encounter.

gauge, with a ruling gradient of I in 40, a maximum speed of 15 m.

9.5 in.); maximum gradient, I in 50; length of sleepers, 1.70 m.

At a distance from the central core the radiating ridges become less abrupt and descend with a gentle gradient, finally passing somewhat abruptly, at a height of some 7000 ft., into the level plateau.

The bridle road up the mountain leaves Glen Nevis at Achintee; it has a gradient nowhere exceeding 1 in 5, and the ascent is commonly effected in two to three hours.

Hence the absolute velocities of the two ions can be determined, and we can calculate the actual speed with which a certain ion moves through a given liquid under the action of a given potential gradient or electromotive force.

There must, then, be a relation between the rate of change of the concentration and the osmotic pressure gradient, and thus we may consider the osmotic pressure gradient as a force driving the solute through a viscous medium.

On the margins of the plateau there are several gaps or indentations, which can best be likened to gigantic trenches, like railway cuttings, as with an insensible gradient they climb to a higher level.

Their power is proportioned to requirements of load and maximum gradient; the speed is rarely more than 6 or 8 m.

In driving mine passages thatj are to be used for drainage, care is taken to maintain sufficient gradient.

In a sheet-glass tank there is therefore a gradient of temperature and a continuous passage of material from the hotter end of the furnace where the raw materials are introduced to the cooler end where the glass, free from bubbles and raw material, is withdrawn by the gatherers.

Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.

If w vanishes throughout the fluid at any instant, equation (I I) shows that it will always be zero, and the fluid motion is then called irrotational; and a function 4) exists, called the velocity function, such that udx+vdy-{-wdz =-d, (13) and then the velocity in any direction is the space-decrease or downward gradient of cp.

The terms of 0 may be determined one at a time, and this problem is purely kinematical; thus to determine 4)1, the component U alone is taken to exist, and then 1, m, n, denoting the direction cosines of the normal of the surface drawn into the exterior liquid, the function 01 must be determined to satisfy the conditions v 2 0 1 = o, throughout the liquid; (ii.) ' = -1, the gradient of 0 down the normal at the surface of the moving solid; 1 =0, over a fixed boundary, or at infinity; similarly for 02 and 03.

The most elevated summits occur in the north, but even these are of very gentle gradient.

Reynolds, in his investigation, introducing no new form of law of distribution of velocities, uses a linear quantity, proportional to the mean free path of the gaseous molecules, which he takes to represent (somewhat roughly) the average distance from which molecules directly affect, by their convection, the state of the medium; the gas not being uniform on account of the gradient of temperature, the change going on at each point is calculated from the elements contributed by the parts at this particular distance in all directions.

has been observed by Matthews: - It is noticeable that there is a marked vertical temperature gradient only at the end of summer when a warm surface layer is formed, though in August 1904 that was only 8 fathoms thick.

A gradient like this, only 1 in 1,350,000, could give rise only to an extremely feeble surface current polewards and an extremely feeble deep current towards the equator.

In the South Wales system of working, cross headings are driven from the main roads obliquely across the rise to get a sufficiently easy gradient for horse roads, and from these the stalls are opened out with a narrow entrance, in order to leave support on either side of the road, but afterwards widening to as great a breadth as the seam will allow, leaving pillars of a minimum thickness.

A road maybe used as a self-acting or gravitating incline when the gradient is r in 30 or steeper, in which case the train is lowered by a rope passing over a pulley or brake drum at the upper end, the return empty train being attached to the opposite end of the rope and hauled up by the descending load.

Where the load has to be hauled up a rising gradient, underground engines, driven by steam or compressed air or electric motors, are used.

Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (ï¿½2u',ï¿½2vi,ï¿½2w') is the gradient of a continuous function.

In the simplest case, that of uniform translation, these components of the gradient will each be constant throughout the region; at a distant place in free aether where there is no motion, they must thus be equal to -u,-v,-w, as they refer to axes moving with the matter.

The effects of the continent are already visible in the mean annual temperatures, in which the poleward temperature gradient is about twice as strong as it is on the neighboring oceans; this being a natural effect of the immobility of the land surface, in contrast to the circulatory movement of the ocean currents, which thus lessen the temperature differences due to latitude: on the continent such differences are developed in full force.

At Canyon City it passes out of the Rockies through the Grand Canyon of the Arkansas; then turning eastward, and soon a turbid, shallow stream, depositing its mountain detritus, it flows with steadily lessening gradient and velocity in a broad, meandering bed across the prairies and lowlands of eastern Colorado, Kansas, Oklahoma and Arkansas, shifting its direction sharply to the south-east in central Kansas.

The gradient below the mountains averages 7.5 ft.

Thus a fall in the gradient at any point in the course of a stream; any snag, projection or dam, impeding the current; the reduced velocity caused by the overflowing of streams in flood and the dissipation of their energy where they enter a lake or the sea, are all contributing causes to alluviation, or the deposition of streamborne sediment.

Since some ions are more mobile than others, a separation will ensue when water is placed in contact with a solution, the faster moving ion penetrating quicker into the water under the driving force of the osmotic pressure gradient.

Now the velocities u and v of the opposite ions under unit potential gradient, and therefore U and V under unit force, are known from electrical data.

Although it is seldom explicitly stated as an experimental law, it should really be regarded in this light, and may be briefly worded as follows: "The rate of transmission of heat by conduction is proportional to the temperature gradient."

The " gradient of temperature " is the fall of temperature in degrees per unit length along the lines of flow.

The thermal conductivity of the substance is the constant ratio of the rate of transmission to the temperature gradient.

The rate of transmission of heat is Q/AT, and the temperature gradient, supposed uniform, is (B' - B') /x, so that the law of conduction leads at once to the equation Q/AT = k (e' - 0"(/x = kdO/dx.

If the gradient is not uniform, its value may be denoted by dB/dx.

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.

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.

The measurement of the temperature gradient in the plate generally presents the greatest difficulties.

The outward gradient is dO/dr, and is negative if the central hole is heated.

It is the most convenient method, in the case of good conductors, on account of the great facilities which it permits for the measurement of the temperature gradient at different points; but it has the disadvantage that the results depend almost entirely on a knowledge of the external heat loss or emissivity, or, in comparative experiments, on the assumption that it is the same in different cases.

C. Mitchell, under Tait's direction, repeated the experiments with the same bar nickel-plated, correcting the thermometers for stem-exposure, and also varying the conditions by cooling one end, so as to obtain a steeper gradient.

The gradient near the entrance to the calorimeter was deduced from observations with five thermometers at suitable intervals along the bar.

The heat transmitted through the plane x is equal per unit area of surface to the product of k by the mean temperature gradient (de /dx) and the interval of time, T - T'.

The mean temperature gradient is found by plotting the curves for each day from the daily observations.

The heat per second gained by conduction by an element dx of the bar, of conductivity k and cross section q, at a point where the gradient is dB/dx, may be written gk(d 2 6/dx 2)dx.

The chief difficulty, as usual, was the determination of the gradient, which depended on a difference of potential of the order of 20 microvolts between two junctions inserted in small holes 2 cms. apart in a bar 1 .

It was also tacitly assumed that the thermo-electric power of the couples for the gradient was the same as that of the couples for the mean temperature, although the temperatures were different.

Owing to the difficulty of measuring the gradient, the order of divergence of individual observations averaged 2 or 3%, but occasionally reached 5 or io %.

The magnitude of the stress per unit area parallel to the direction of flow is evidently proportional to the velocity gradient, or the rate of change of velocity per cm.

Similarly if A is hotter than B, or if there is a gradient of temperature between adjacent layers, the diffusion of molecules from A to B tends to equalize the temperatures, or to conduct heat through the gas at a rate proportional to the temperature gradient, and depending also on the rate of interchange of molecules in the same way as the viscosity effect.

Of the four main lines which centre on Genoa - (1) to Novi, which is the junction for Alessandria, where lines diverge to Turin and France via the Mont Cenis, and toNovaraandSwitzerland and France via the Simplon, and for Milan; (2) to Acqui and Piedmont; (3) to Savona, Ventimiglia and the French Riviera, along the coast; (4) to Spezia and Pisa - the first line has to take no less than 78% of the traffic. It has indeed two alternative double lines for the passage over the Apennines, but one of them has a maximum gradient of 1: 18 and a tunnel over 2 m.