noun

definition

A slope or incline.

definition

A rate of inclination or declination of a slope.

definition

Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x that is, the amount by which y changes for a certain (often unit) change in x equivalently, the inclination to the X axis of the tangent to the curve of the graph.

definition

The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.

definition

A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ

definition

A gradual change in color. A color gradient; gradation.

adjective

definition

Moving by steps; walking.

example

gradient automata

definition

Rising or descending by regular degrees of inclination.

example

the gradient line of a railroad

definition

Adapted for walking, as the feet of certain birds.

Examples of gradient in a Sentence

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

The gradient below the mountains averages 7.5 ft.

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

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

The steepest gradient is on the western main line.

Single gradient lenses are shaded lighter on the bottom and darker on the top.

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

Rate at which work is done against a gradient.

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

The lens choices were gray, blue gradient, red gradient and brown..

Depending on the location, you may be able to choose from several other colors in addition to gray and brown, plus you can choose a gradient tint if you'd like.

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

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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