Word Finder - constants

definition

That which is permanent or invariable.

definition

A quantity that remains at a fixed value throughout a given discussion.

definition

Any property of an experiment, determined numerically, that does not change under given circumstances.

definition

An identifier that is bound to an invariant value; a fixed value given a name to aid in readability of source code.

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.