Word Finder - linear

definition

Having the form of a line; straight or roughly straight; following a direct course.

definition

Of or relating to lines.

definition

Made, or designed to be used, in a step-by-step, sequential manner.

example

a linear medium

definition

(of leaves) Long and narrow, with nearly parallel sides.

definition

Of or relating to a class of polynomial of the form y = ax + b .

definition

A type of length measurement involving only one spatial dimension (as opposed to area or volume).

example

a linear meter

Given certain linear and angular measurements, the area must be so and so.

This variation, however, is not always linear.

The linear width of the band (e) is the increment of which alters p by 27r, so that e =27r /tr.

The partial differential coefficient of T with respect to a component of velocity, linear or angular, will be the component of momentum, linear or angular, which corresponds.

This applies also to quaternions, but not to extensive quantities, nor is it true for linear algebras in general.

One of the most important questions in investigating a linear algebra is to decide the necessary relations between a and b in order that this product may be zero.

If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.

In a somewhat similar way a dark linear interruption in a bright ground may be visible, although its actual width is much inferior to the half wave-length.

A linear error in the spacing, and a general curvature of the lines, are eliminated in the ordinary use of a grating.

The vapour tension may approximate to a linear function of the composition, and the curve will then be practically a straight line.

If we assume that s is a linear function of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =o

Other favourite types' of equation for approximate work are (I) p=RO/v±f(v), which makes p a linear function of 0 at constant volume, as in van der Waal's equation; (2) v=RO/p+f(p), which makes v a linear function of 0 at constant pressure.

There are two main design proposals for the future linear collider.

The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and denoting by the resultant axial linear momentum of the circulation.

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.

The word is also used as a unit of linear measurement of the magnifying power of a lens or microscope.

In this instrument a considerable linear relative movement of the divided lens corresponds with a comparatively small separation of the double image, so that simple verniers reading to 6 1 0 in.

Apart from speculation, the first definite evidence for the molecular structure of matter occurs when it is found that certain physical phenomena change their whole nature as soon as we deal with matter of which the linear dimensions are less than a certain amount.

It follows that the average distance apart of the molecules in the gaseous state is roughly ten times as great as in the solid or liquid state, and hence that in the gaseous state the molecules are at distances apart which are large compared with their linear dimensions.

The genus is represented in Europe, north Asia, North America and Australia, and is characterized by oblong or linear stem-leaves, flowers in.

The failure seems (§ 2) to be due to difficulty in realizing the numerical expression of an area or a solid in terms of a specified unit, while the same difficulty does not arise in the case of linear measure or liquid measure, where the number of units can be ascertained by direct counting.

The ideas of moment and of centroid are extended to geometrical figures, whether solid, superficial or linear.

The simplest case is that in which u is constant or is a linear function of x, i.e.

Generally, if the area of a trapezette for which u is an algebraical function of x of degree 2n is given correctly by an expression which is a linear function of values of u representing ordinates placed symmetrically about the mid-ordinate of the trapezette (with or without this mid-ordinate), the same expression will give the area of a trapezette for which u is an algebraical function of x of degree 2n + 1.

The velocity of propagation of a torsional disturbance along a wire of circular section may be found by the transfer of momentum method, remembering that we must now replace linear momentum by angular momentum.

The unit of linear measure is the wall, which is subdivided into wah or sauk, a wah or kup, and into 9 1 6 wah or niew.

Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

It has in fact been found, with the very great precision of which optical experiment is capable, that all terrestrial optical phenomenareflexion, refraction, polarization linear and circular, diffraction - are entirely unaffected by the direction of the earth's motion, while the same result has recently been extended to electrostatic forces; and this is our main experimental clue.

Another powerful reason for taking the aether to be stationary is afforded by the character of the equations of electrodynamics; they are all of linear type, and superposition of effects is possible.

Now the kinetics of a medium in which the parts can have finite relative motions will lead to equations which are not linear - as, for example, those of hydrodynamics - and the phenomena will be far more complexly involved.

The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.

In these the furcal branches are linear or rudimentary, the shell is without rostral sinus, and, besides distinguishing characters of the second 2ntennae, they have always a branchial plate well developed on the first maxillae, which is inconstant in the other tribe.

For engineering and manufacturing purposes the more important linear gauges are, however, now used, adjusted to some fundamental unit of measure as the inch; although in certain trades, as for wires and flat metals, gauges continue to be used of arbitrary scales and of merely numerical sizes, having no reference to a legal unit of measure; and such are rarely accurate.

Both as regards structure and habits, the leopard may be reckoned as one of the more typical representatives of the genus Felis, belonging to that section in which the hyoid bone is loosely connected with the skull, owing to imperfect ossification of its anterior arch, and the pupil of the eye when contracted under the influence of light is circular, not linear as in the smaller cats.

The twigs are densely clothed with flat spreading linear leaves of a fine glossy green above and glaucous beneath; in the old trees they become shorter and more rigid and partly lose their distichous habit.

This frame or tube is so constructed of iron and brass (one-third iron and two-thirds brass) that its temperature coefficient of linear expansion is the same as that of the platinumsilver alloy.

As the frame has the same linear expansion as the wire, external changes of the temperature will not affect their relative length, but if the fine wire is heated by the passage of an electric current, its expansion will move the indicating needle over the scale, the motion being multiplied by the gear.

The linear ridges of this mIddle section are often called the Alleghany Mountains.

They agree with primitive nephridia in being of ectodermic origin, in consisting of perforated cells in linear series, and in having no communication with the coelom.

The rice plant is an annual grass with long linear glabrous leaves, each provided with a long sharply pointed ligule.

The slit of the collimator confines the light to a nearly linear source, the beam diverging from each point of the source being subsequently made parallel by means of a lens.

In order to record line spectra it is by no means necessary that the receiving instrument (bolometer or radiometer) should be linear in shape, for the separation of adjacent lines may be obtained if the linear receiver be replaced by a narrow slit in a screen placed at the focus of the condensing lens.

If the linear velocity of the cups in feet a second is V 1, and the linear velocity of the jet is V2, then the velocity of the jet relative to the cup is V2 - V1 feet a second, and if the whole energy of the water is to be given up to the cups, the water must leave the cup with zero absolute velocity.

This will become zero if V 1 is 2V 2, that is, if the linear velocity of the cupcentres is one-half that of the jet of water impinging upon them.

The form of the leaf shows a very great variety ranging from the narrow linear form with parallel sides, as in grasses or the needle-like leaves of pines and firs to more or less rounded or orbicular - descriptions of these will be found in works on descriptive botany - FIG.

The first leaves produced by the young plant are linear,the second are sagittate and hastate, the third are rounded-cordate and the next are orbicular.

The flow of heat may still be linear if the horizontal layers of the soil are of uniform composition, but the quantity flowing through each layer is no longer the same.

This gives an average value of the conductivity over the range, but it is better to observe the temperatures at three distances, and to assume k to be a linear function of the temperature, in which case the solution of the equation is still very simple, namely, 0+Ze6 2 =a log r+b, (3) where e is the temperature-coefficient of the conductivity.

The chief uncertainty of this method is the area from which the heat is collected, which probably exceeds that of the central column, owing to the disturbance of the linear flow by the projecting bulb of the calorimeter.

As in the case of steady-flow methods, by far the simplest example to consider is that of the linear flow of heat in an infinite solid, which is most nearly realized in nature in the propagation of temperature waves in the surface of the soil.