Constants Sentence Examples

Here there are two arbitrary constants, which may be adjusted in various ways.

The difference of potential between two solutions of a substance at different concentrations can be calculated from the equations used to give the diffusion constants.

Hermite expresses the quintic in a forme-type in which the constants are invariants and the variables linear covariants.

Hesse showed independently that the general ternary cubic can be reduced, by linear transformation, to the form x3+y3+z3+ 6mxyz, a form which involves 9 independent constants, as should be the case; it must, however, be remarked that the counting of constants is not a sure guide to the existence of a conjectured canonical form.

Thus the ternary quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester.

When the magnetizing current is twice reversed, so as to complete a cycle, the sum of the two deflections, multiplied by a factor depending upon the sectional area of the specimen and upon the constants of the apparatus, gives the hysteresis for a complete cycle in ergs per cubic centimetre.

He applied his method with good effect, however, in testing a large number of commercial specimens of iron and steel, the magnetic constants of which are given in a table accompanying his paper.

The field due to a coil can be made as nearly uniform as we please throughout a considerable space; its intensity, when the constants of the coil are known, can be calculated with ease and certainty and may be varied at will'through wide ranges, while the apparatus required is of the simplest character and can be readily constructed to suit special purposes.

In nickel the maximum change of the elastic constants is remarkably large, .amounting to about 15% for Young's modulus and 7% for rigidity; with increasing fields the elastic constants first decrease and then increase.

In a 29% nickel-steel, magnetization increases the constants by a small amount.

Rowland,' whose careful experiments led to general recognition of the fact previously ignored by nearly all investigators, that magnetic susceptibility and permeability are by no means constants (at least in the case of the ferromagnetic metals) but functions of the magnetizing force.

The final achievement of Lagrange in this direction was the extension of the method of the variation of arbitrary constants, successfully used by him in the investigation of periodical as well as of secular inequalities, to any system whatever of mutually interacting bodies.'

He also devoted much attention to the pyroelectric phenomena of crystals, which served as the theme of one of the two memoirs he presented for the degree of D.Sc. in 1869, and to the determination of crystallographic constants.

The raw materials are selected with great care to assure chemical purity, but whereas in most glasses the only impurities to be dreaded are those that are either infusible or produce a colouring effect upon the glass, for optical purposes the admixture of other glass-forming bodies than those which are intended to be present must be avoided on account of their effect in modifying the optical constants of the glass.

The simplest method of determining it numerically is, therefore, that adopted by Faraday.4 Table Dielectric Constants (K) of Solids (K for Air = I).

Here is carried out the work of standardizing measuring instruments of various sorts in use by manufacturers, the determination of physical constants and the testing of materials.

If suitable values are chosen for these constants, the formula can be made to represent the dispersion of ordinary transparent media within the visible spectrum very well, but when extended to the infra-red region it often departs considerably from the truth, and it fails altogether in cases of anomalous dispersion.

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.

The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a node within the circle; the particular case when b= 2a is known as the trisectrix.

The constant a has the same value I 2 for crown and flint glass, so that there are only three disposable constants left.

If within the range5100-3700A, the constants are determined once for all, the formula seems capable of giving by interpolation results accurate to o 2 A, but as a rule the range to which the formula is applied will be much less with a corresponding gain in the accuracy of the results.

A homogeneous oscillation is one which for all time is described by a circular function such as sin(nt+ a), t being the time and n and a constants.

The first of the forms which contains three disposable constants did good service in the hands of their authors, but breaks down in important cases when odd powers of s have to be introduced in addition to the even powers.

The second form contains two or three constants according as N is taken to have the same value for all elements or not.

It then possesses four adjustable constants, and more can therefore be expected from it.

As he takes N to be strictly the same for all elements the equation has only three disposable constants A, a and b.

This form has the advantage that the constants of the equation when applied to the spectra of the alkali metals show marked regularities.

If we compare Balmer's formula with the general equation of Ritz, we find that the two can be made to agree if the ordinary hydrogen spectrum is that of the side branch series and the constants a', b, c and d are all put equal to zero.'

If s represents the series of integer numbers the distribution of frequency may be represented by C+Bs2, where C and B are constants.

If we wish to be more general, while still adhering to Deslandres' law as a correct representation of the frequencies when s is small, we may write n - A (s+ 1 1) 2 - - a Po+Pi(s + c) -F +pr(s+ c)r' where s as before represents the integer numbers and the other quantities involved are constants.

A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.

But, on the other hand, no one pretends to have found the rigorous expression for the law, and the appropriate approximation may take quite different forms when constants which are large in one case are small in the other.

Omitting correction terms depending on the temperature and on the inductive effect of the earth's magnetism on the moment of the deflecting magnet, if 0 is the angle which the axis of the deflected magnet makes with the meridian when the centre of the deflecting magnet is at a distance r, then zM sin B=I+P+y2 &c., in which P and Q are constants depending on the dimensions and magnetic states of the two magnets.

The value of the constants P and Q can be obtained by making deflexion experiments at three distances.

Attempts have been made to co-ordinate this ionizing power of solvents with their dielectric constants, or with their chemical properties.

The physical constants associated with the name will scarcely be changed, since the proportion of the "companions" is so small.

Main as chief assistant at the Royal Observatory, Greenwich, and at once undertook the fundamental task of improving astronomical constants.

Every time, therefore, that a speculum is repolished, the future quality of the instrument is at stake; its focal length will probably be altered, and thus the value of the constants of the micrometer also have to be redetermined.

It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine.

That of Biot is far more complicated and troublesome, but admits greater accuracy of adaptation, as it contains five constants (or six, if 0 is measured from an arbitrary zero).

The omission of the additive arbitrary constants of integration in (8) is equivalent to a special choice of the origin 0 of co-ordinates; viz.

To obtain the complete solution of (II) we must of course superpose the free vibration (6) with its arbitrary constants in order to obtain a complete representation of the most general motion consequent on arbitrary initial conditions.

The resulting Z+R equations are not as a rule easy of application, owing to the fact that the moments and products of inertia A, B, C, F, G, H are not constants but vary in conse- 0 quence of the changing orientation of the body with respect to the co-ordinate axes.

On assuming the directorship of the Nautical Almanac he became very strongly impressed with the diversity existing in the values of the elements and constants of astronomy adopted by different astronomers, and the injurious effect which it exercised on the precision and symmetry of much astronomical work.

A valuable summary of a considerable part of this work, containing an account of the methods adopted, the materials employed, and the resulting values of the various quantities involved, was published in 1895, as a supplement to the American Ephemeris for 1897, entitled The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy.

At the international conference, which met at Paris in 1896 for the purpose of elaborating a common system of constants and fundamental stars to be employed in the various national ephemerides, Newcomb took a leading part, and at its suggestion undertook the task of determining a definite value of the constant of precession, and of 1 Lionville, t.

At the time when Maxwell developed his theory the dielectric constants of only a few transparent insulators were known and these were for the most part measured with steady or unidirectional electromotive force.

Experimental methods were devised for the further exact measurements of the electromagnetic velocity and numerous determinations of the dielectric constants of various solids, liquids and gases, and comparisons of these with the corresponding optical refractive indices were conducted.

He investigated the optical constants of the eye, measured by his invention, the ophthalmometer, the radii of curvature of the crystalline lens for near and far vision, explained the mechanism of accommodation by which the eye can focus within certain limits, discussed the phenomena of colour vision, and gave a luminous account of the movements of the eyeballs so as to secure single vision with two eyes.

If, in the first place, monochromatic aberrations be neglected - in other words, the Gaussian theory be accepted - then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction.

If all three constants of reproduction be achromatized, then the Gaussian image for all distances of objects is the same for the two colours, and the system is said to be in " stable achromatism."

If r be the number of quotients in the recurring cycle, we can by writing down the relations connectin g the successive p's and q's obtain a linear relation connecting p nr +m, t'(n-1)r +m, +m in which the coefficients are all constants.

The work falls into two parts, which treat of the asymptotes and singularities of algebraical curves respectively; and extensive use is made of the method of counting constants which plays so large a part in modern geometrical researches.

The points in question have since been called (it is believed first by Dr George Salmon) the circular points at infinity, or they may be called the circular points; these are also frequently spoken of as the points I, J; and we have thus the circle characterized as a conic which passes through the two circular points at infinity; the number of conditions thus imposed upon the conic is = 2, and there remain three arbitrary constants, which is the right number for the circle.

The expression 2 is that of the number of the disposable constants in a curve of the order m with nodes and cusps (in fact that there shall be a node is I condition, a cusp 2 conditions) and the equation (9) thus expresses that the curve and its reciprocal contain each of them the same number of disposable constants.

The determination of the constants in Gauss's theory of terrestrial magnetism occupied him at intervals for over forty years.

In the language of algebra putting m l, m2, m 3, &c. for the masses of the bodies, r1.2 r1.3 r2.3, &c. for their mutual distances apart; vi, v 2, v 3, &c., for the velocities with which they are moving at any moment; these quantities will continually satisfy the equation orbit, appear as arbitrary constants, introduced by the process of integration.

In a case like the present one, where there are two differential equations of the second order, there will be four such constants.

The result of the integration is that the co-ordinates x and y and their derivatives as to the time, which express the position, direction of motion and speed of the planet at any moment, are found as functions of the four constants and of the time.

Putting a, b, c, d, for the constants, the general form of the solution will be x = fl (a,b,c,d,t) y = f2(a,b,c,d,t) From these may be derived by differentiation as to t the velocities dt =f '1(a,b,c,d,t) = x'  ?

The arbitrary constants, a, b, c and d, are the elements of the orbit, or any quantities from which these elements can be obtained.

This fact is fully expressed by the equations (4) where we have constants on one side of the equation equal to functions of the variables on the other.

Not less comprehensive has been the work carried out by Professor Newcomb of raising to a higher grade of perfection, and reducing to a uniform standard, all the theories and constants of the solar system.

The determination of the curves of constant retardation depends upon expressing the retardation in terms of the optical constants of the crystal, the angle of incidence and the azimuth of the plane of incidence.

The optical constants (refractive index and co-efficient of extinction) of the metal may then be obtained from observations of the principal incidence and the elliptic polarization then produced.

One method consists in finding directly the elliptic constants of the vibration by means of a quarterwave plate and an analyser; but the more usual plan is to measure the relative retardation of two rectangular components of the stream by a Babinet's compensator.

This is the equation to a parabola, and is equivalent to the empirical formula of Avenarius, with this difference, that in Tait's formula the constants have all a simple and direct interpretation in relation to the theory.

It simplifies the theory, and gives a possible relation between the constants, but it does not appear to remove the complication above referred to, which seems to be inseparable from any conduction theory.

They were constants in a world where humans and their inventions passed through the world, less significant than an exhaled breath.

The class that defines the constants that are used to identify generic SQL types, called JDBC types.

I am using the modification of the Eshelby approach to model for the elastic constants of porous coatings.

Just as physical constants provide " boundary conditions " for the physical universe, mathematical constants somehow characterize the structure of mathematics.

These are TAB format, byte-length specifiers and Hollerith constants.

Curiously, however, the basic properties of these materials (band gap, elastic constants, piezoelectric constants) are not well known.

These differences arise because one or more stability constants has a bad value or indeed should not be present or should not be included.

Quarks Most uses of the resource manager involve defining names, classes, and representation types as string constants.

In biological systems the reference values are often encoded genetically, in the binding constants of proteins for their allosteric effectors.

It is not, generally, possible to use hexadecimal or decimal constants in this fashion.

Consider the language obtained from 1 K = by adding a denumerably infinite stock of new individual constants c 0, c 1, .

The wavelength associated with the vector resultant of these three orthogonal propagation constants is just the free space wavelength lambda.

A public constructor for this class has been purposely omitted and applications should use one of the constants from this class.

The time constants and relative weightings yielded temporal window functions that heavily emphasize information occurring within the very temporal center of the window.

I am analyzing synchrotron X-ray diffraction patterns and to work out the diffractometer constants I refined a silicon pattern.

For the few cases where data are available - data, however, belonging to engines representing standard practice in their construction and in the design of cylinders and steam ports and passages - the law connecting p and v is approximately linear and of the form p=c - bv (28) where b and c are constants.

Kauffmann (Ber., 1906, 39, p. 1 959) attempted an evaluation of the effects of auxochromic groups by means of the magnetic optical constants.

In that case the main branch is found to represent the new series if a' and b 1 are also put equal to zero, so that n l r I I N = 4 - y2' where r takes successively the values 1.5, 2.5, 3.5 A knowledge of the constants now determines the trunk series, which should be n I I N - (I,5)2 The least refrangible of the lines of this series should have a wavelength 4687.88, and a strong line of this wave-length has indeed been found in the spectra of stars which are made up of bright lines, as also in the spectra of some nebulae.

Poisson's application to them in 1809 of Lagrange's theory of the variation of constants; Philippe de Pontecoulant successfully used in 1829, for the prediction of the impending return of Halley's comet, a system of " mechanical quadratures " published by Lagrange in the Berlin Memoirs for 1778; and in his Theorie analytique du systeme du monde (1846) he modified and refined general theories of the lunar and planetary revolutions.

The analysis is extended to a consideration of rate constants for chemical reactions between solutes in solution.

The range column shows the range of specifiable values in the system constants.

Static variables can be used to emulate constants, values that do n't change.

I am analyzing synchrotron x-ray diffraction patterns and to work out the diffractometer constants I refined a silicon pattern.

Only the constants of the excited triplet state may be varied.

Your underhanded attempt to be glib and smarmy does n't undermine or change those historical constants.

While Bob and Jillian have been the constants on the show, there have been other trainers involved as well.

There are notable differences, but some constants.

Silbermann, whose chief theoretical achievement was the recognition that the heat of neutralization of acids and bases was additively composed of two constants, one determined by the acid and the other by the base.

It is well known that singly, doubly and trebly linked carbon atoms affect the physical properties of substances, such as the refractive index, specific volume, and the heat of combustion; and by determining these constants for many substances, fairly definite values can be assigned to these groupings.

But, at the same time, the constants in the above relation are not identical with those in the corresponding relation empirically deduced from observations on fatty hydrocarbons; and we are therefore led to conclude that a benzene union is considerably more stable than an ethylene union.

Eliminating a and b between these relations, we derive P k V k /Tk= 8R, a relation which should hold between the critical constants of any substance.

By actual observations it has been shown that ether, alcohol, many esters of the normal alcohols and fatty acids, benzene, and its halogen substitution products, have critical constants agreeing with this originally empirical law, due to Sydney Young and Thomas; acetic acid behaves abnormally, pointing to associated molecules at the critical point.

If we express the pressure, volume and temperature as fractions of the critical constants, then, calling these fractions the " reduced " pressure, volume and temperature, and denoting them by 7r, 0 and 0 respectively, the characteristic equation becomes (7+3/0 2)(30-i) =80; which has the same form for all substances.

Obviously, therefore, liquids are comparable when the pressures, volumes and temperatures are equal fractions of the critical constants.

From the relation between the critical constants Pk Vk/Tk = 37 R or T k /P k = 3 .

An important connexion between heats of combustion and constitution is found in the investigation of the effect of single, double and triple carbon linkages on the thermochemical constants.

It contains four independent constants; two of these may be calculated from the heats of combustion of saturated hydrocarbons, and the other two from the combustion of hydrocarbons containing double and triple linkages.

In the article Crystallography the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to 'a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.

In such crystals each component plays its own part in determining the physical properties; in other words, any physical constant of a mixed crystal can be calculated as additively composed of the constants of the two components.

Let s be the area of a single turn of the standard coil, n the number of its turns, and r the resistance of the circuit of which the coil forms part; and let S, N and R be the corresponding constants for a coil which is to be used in an experiment.

In nickel-steels containing about 50 and 70% of nickel the maximum increase of the constants is as much as 7 or 8%.

The hypothesis that the state was steady, so that interchanges arising from convection and collisions of the molecules produced no aggregate result, enabled him to interpret the new constants involved in this law of distribution, in terms of the temperature and its spacial differential coefficients, and thence to express the components of the kinetic stress at each point in the medium in terms of these quantities.

Further Physical Properties of Sea-water.---The laws of physical chemistry relating to complex dilute solutions apply to seawater, and hence there is a definite relation between the osmotic pressure, freezing-point, vapour tension and boiling-point by which when one of these constants is given the others can be calculated.

Van der Waal's equation (p-I- a/v 2) (v - b) = RT contains two constants a and b determined by each particular substance.