Word Finder - coefficient

definition

A constant by which an algebraic term is multiplied.

definition

A number, value or item that serves as a measure of some property or characteristic.

definition

Cooperating

We may, by a well-known theorem, write the result as a coefficient of z w in the expansion of 1 - z n+1.

The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..

This coefficient is sometimes called the " angular coefficient," and may be regarded as a measure of the deviations from Boyle's law, 'which may be most simply expressed at moderate pressures by formulating the variation of the angular coefficient with temperature.

It is almost colourless and has a small coefficient of expansion; its hygroscopic properties, its viscous character, and its action on the skin, however, militate against its use.

This, with a knowledge of the temperature of the screw or scale and its coefficient of expansion, would enable the change of screw-value to be determined at any instant.

Less accurate formulae are =p W/(W - W 2), the factor involving the density of the air, and the coefficient of the expansion of the solid being disregarded, and 0 =W/(W - W 1), in which the density of water is taken as unity.

Its advantages rest on its high density and mobility; its main disadvantages are its liability to decomposition, the originally colourless liquid becoming dark owing to the separation of iodine, and its high coefficient of expansion.

Struve also points out that by attaching a fine scale to the focusing slide of the eye-piece, and knowing the coefficient of expansion of the metal tube, the means would be provided for determining the absolute change of the focal length of the object-glass at any time by the simple process of focusing on a double star.

Buchanan found a mean of 20 experiments made by piezometers sunk in great depths on board the " Challenger " give a coefficient of compressibility K=491 X 107; but six of these experiments made at depths of from 2740 to 3125 fathoms gave K=480Xio 7.

On this account it is very difficult to know when all the gas is driven out of a sample of sea-water, and a much larger proportion is present than the partial pressure of the gas in the atmosphere and its coefficient of absorption would indicate.

The maintenance of the conditions of steadiness implied in equation (I) depends upon the constancy of F, and therefore of the coefficient of friction µ between the rubbing surfaces.

The ratio p is given by e"` e, where e= 2.718; µ is the coefficient of friction and 0 the angle, measured in radians,, subtended by the arc of contact between the rope and the wheel.

This apparatus was used to find the temperature coefficient of the frequency of forks, the value obtained - .00011 being the same as that found by Koenig.

The thermal coefficient of expansion of steel and concrete is nearly the same, otherwise changes of temperature would cause shearing stress at the junction of the two materials.

Then the deviation y= DE of the neutral axis of the bent beam at any point D from the axis OX is given by the relation d 2 y Ml dx 2 = EI' where M is the bending moment and I the amount of inertia of the beam at D, and E is the coefficient of elasticity.

When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great.

The definition of the coefficients is that if (I-2h cos cp+h 2)-i be expanded in ascending powers of h, and if the general term be denoted by P„h', then P is of the Legendrian coefficient of the nth order.

For the first time we have a correct and convenient expression for Laplace's nth coefficient."

It is further assumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by then R= Td 2 p, and is called the coefficient of tenuity.

Lastly, to allow for the superior centering of the shot obtainable with the breech-loading system, Bashforth introduces a factor a, called the coefficient of steadiness.

Collecting all the coefficients, into one, we put (I) R = nd 2 p = nd 2 f (v), where and n is called the coefficient of reduction.

We put and call C the ballistic coefficient (driving power) of the shot, so that (6) At = COT, where (7) AT = Av/gp, and AT is the time in seconds for the velocity to drop Av of the standard shot for which C = I, and for which the ballistic table is calculated.

The constant may be any arbitrary number, as in using the table the difference only is required of two tabular values for an initial velocity V and final velocity v; and thus (to) T(V) - T(v) = Ev Ov/gp or fvdv/gp; and for a shot whose ballistic coefficient is C (II) t=C[T(V) - T(v)].

Denoting by S(v) the sum of all the values of AS up to any assigned velocity v, (is) S(v) =E(OS)+ a constant, by which S(v) is calculated from AS, and then between two assigned velocities V and v, V AT, = vAv or rvvdv vgp gp' and if s feet is the advance of a shot whose ballistic coefficient is C, (17) s=C[S(V) - S(v)].

Given the ballistic coefficient C, the initial velocity V, and a range of R yds.

In the Weston standard cell cadmium and cadmium sulphate are substituted for zinc and zinc sulphate; it has the advantage of a much smaller coefficient of temperature variation than the Clark cell.

The equations finally arrived at are DX2(A2_ 2) (x2_ A2m)2+g2A2 ' DgA3 (A A l m) 2 +g 2 A2 ' where is the wave-length in free ether of light whose refractive index is n, and A m the wave-length of light of the same period as the electron, is a coefficient of absorption, and D and g are constants.

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.

Let A and C be two fixed disks, and B a disk which can be brought at will within a very short distance of either A or C. Let us suppose all the plates to be equal, and let the capacities of A and C in presence of B be each equal to p, and the coefficient of induction between A and B, or C and B, be q.

The rate of diminution of amplitude expressed by the coefficient a in the index of the exponential is here greater than the coefficient b expressing the retardation of phase by a small term depending on the emissivity h.

He investigated the expansibility of gases by heat, determining the coefficient for air as 0.003665, and showed that, contrary to previous opinion, no two gases had precisely the same rate of expansion.

The coefficient of heating of a calorimeter when it is below the temperature of its surroundings is seldom, if ever, the same as the coefficient of cooling at the higher temperature, since the convection currents, which do most of the heating or cooling, are rarely symmetrical in the two cases, and moreover, the duration of the two stages is seldom the same.

The Resistance R Could Be Deduced From A Knowledge Of The Temperature Of The Calorimeter And The Coefficient Of The Wire.

Nickel is used for the manufacture of domestic utensils, for crucibles, coinage, plating, and for the preparation of various alloys, such as German silver, nickel steels such as invar (nickel, 35.7%; steel, 64.3%), which has a negligible coefficient of thermal expansion, and constantan (nickel, 45%; copper, 55%), which has a negligible thermal coefficient of its electrical resistance.

Further, by suitably choosing the positions of the deflectors and the coefficient of torsion of the fibre, it is possible to make the temperature coefficient vanish.

The factor (P+P) cos 0h sin 0 is called the vIrtual coefficient of the two screws which define the types of the wrench and twist, respectively.

We assume that in limiting equilibrium we have F tsR, everywhere, where u is the coefficient of friction.

Since an, = a,r, the coefficient of Q, in the expression for qr is identical with that of Q,- in the expression for q,.

The total pressure exerted between the rubbing surfaces is the resultant of the normal pressure and of the friction, and its obliquity, or inclination to the common perpendicular of the surfaces, is the angle of repose formerly mentioned in 14, whose tangent is the coefficient of friction.

The more recent experiments of Lasche (Zeitsch, Verein Deutsche Ingen., 1902, 46, 1881) show that the product of the coefficient of friction, the load on the bearing, and the temperature is approximately constant.

To express this symbolically, let dii represent the area of a portion of a pair of rubbing surfaces at a distance r from the axis of their relative rotation; p the intensity of the normal pressure at du per unit of area; and f the coefficient of friction.

Let Ti be the tension of the free part of the band at that side towards which it tends to draw the pulley, or from which the pulley tends to draw it; 1, the tension of the free part at the other side; T the tension of the band at any intermediate point of its arc of contact with the pulley; 0 the ratio of the length of that arc to the radius of the pulley; do the ratio of an indefinitely small element of that arc to the radius; F=TiT2 the total friction between the band and the pulley; dF the elementary portion of that friction due to the elementary arc do; f the coefficient of friction between the materials of the band and pulley.

The diameter of the orifice was 3 millims., from which that of the jet is deduced by the introduction of the coefficient 8.

Its specific heat is 0.05701 (Regnault) or 0.0559 (Bunsen); its coefficient of linear expansion is 0.0000-1921.

It is better then to define the coefficient of absorption as a quantity k such that kln of the light is absorbed in i/nth part of a centimetre, where n may be taken to be a very large number.

There is another coefficient of absorption (K) which occurs in Helmholtz's theory of dispersion (see Dispersion).

It is closely related to the coefficient k which we have just defined, the equation connecting the two being k= 4lrK/X,X being the wavelength of the incident light.

The small amount of red transmitted is at first quite overpowered by the green, but having a smaller coefficient of absorption, it becomes finally predominant.

Neglecting quantities of the second order, the pressure on the pulley is TdO, and the friction is MTd9 where p, is the coefficient of friction between the belt and the pulley.

For a single pulley of diameter D, turning on a fixed pin of diameter d, the relation of the effort E to the load W, where f is the coefficient of friction, is expressed by E/W = (D-pfd)/(D - fd) _ 1 +2fd/D approximately.