# Constants Sentence Examples

- If the variables of the quantic f(x i, x 2) be subjected to the linear transformation x1 = a12Et2, x2 = a21E1+a2252, E1, being new variables replacing x1, x 2 and the coefficients an, all, a 21, a22, termed the coefficients of substitution (or of transformation), being
**constants**, we arrive at a transformed quantic f% 1tn n n-1 n-2 52) = a S +(1)a11 E 2 + (2)a2E1 E 2 +ï¿½ï¿½ï¿½ in the new variables which is of the same order as the original quantic; the new coefficients a, a, a'...a are linear functions 0 1 2 n of the original coefficients, and also linear functions of products, of the coefficients of substitution, of the nth degree. - § 327, who shows that a composite or stratified dielectric composed of layers of materials of different dielectric
**constants**and resistivities would exhibit the property of residual charge. - 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. - Van der Waal's equation (p-I- a/v 2) (v - b) = RT contains two
**constants**a and b determined by each particular substance. - 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. - 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. - 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. - A binary form of order n contains n independent
**constants**, three of which by linear transformation can be given determinate values; the remaining n-3 coefficients, together with the determinant of transformation, give us n -2 parameters, and in consequence one relation must exist between any n - I invariants of the form, and fixing upon n-2 invariants every other invariant is a rational function of its members. - Hermite expresses the quintic in a forme-type in which the
**constants**are invariants and the variables linear covariants. - / f = k1.(S-mia)5+k2(S-m2a)5+k3(6-m3a)5; and we have merely to determine the
**constants**k1, k2, k3. - 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. - The latter gives values of the
**constants**a and b for different samples of iron and steel, some of which are shown in the following table :- K=a+bH For most samples of steel the straight-line law was found to hold approximately up to H=3; in the case of iron and of soft steel the approximation was less close. - Soc., 1903, 71, 30), experimenting with wires of iron, steel and nickel, showed that in weak fields the change of resistance was proportional to a function a12-+b14-{-cl', where a, b and c are
**constants**for each specimen. - 2 The results are too numerous to discuss in detail; some of those to which special attention is directed are the following: In Swedish iron and tungsten-steel the change of elastic
**constants**(Young's modulus and rigidity) is generally positive, but its amount is less than 0.5%; changes of Young's modulus and of rigidity are almost identical. - 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 nickel-steels containing about 50 and 70% of nickel the maximum increase of the
**constants**is as much as 7 or 8%. - 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.' - Other arrangements of the
**constants**n, a, b, a' will give the results of special problems considered by J. - The simplest method of determining it numerically is, therefore, that adopted by Faraday.4 Table Dielectric
**Constants**(K) of Solids (K for Air = I). - Pp. 98-148 (Breslau, 1905); also see Landolt and Bornstein's Tables of Physical
**Constants**(Berlin, 1894) If we have a number of such condensers we can combine them in " parallel " or in " series." - They show that the dielectric constant of a liquid generally undergoes great reduction in value when the liquid is frozen and reduced to a low temperature.1 The dielectric
**constants**of gases have been determined by L. - Fleming and James Dewar on dielectric
**constants**at low temperatures: " On the Dielectric Constant of Liquid Oxygen and Liquid Air," Proc. Roy. - Soc., 1897, 60, p. 360; " Note on the Dielectric Constant of Ice and Alcohol at very low Temperatures," ib., 1897, 61, p. 2; " On the Dielectric
**Constants**of Pure Ice, Glycerine, Nitrobenzol and Ethylene Dibromide at and above the Temperature of Liquid Air," id. - P. 299-this paper describes the cone condenser and methods used; " Further Observations on the Dielectric
**Constants**of Frozen Electrolytes at and above the Temperature of Liquid Air," id. - P. 381; " The Dielectric
**Constants**of Certain Organic Bodies at and below the Temperature of Liquid Air," id. - P. 358; " Ors the Dielectric
**Constants**of Metallic Oxides dissolved or suspended in Ice cooled to the Temperature of Liquid Air," id. - [[Table Iv]].-Dielectric
**Constants**(K) of Gases at '15°' C. and 760 mm. - Writing formulae (3r) and (33) for the energy and entropy with indeterminate
**constants**A and B, instead of taking them between limits, we obtain the following expressions for the thermodynamic functions in the case of the vapour: " =Solog e 0 - R log e p - ncp/D+A". - 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. - If do is the angular displacement of the roller corresponding to displacements, dO of the disk, and ds of the point of application of P, a, and C
**constants**, then d4) = x _ ¢Pds = C.Pds, and therefore 4) = C f 82 Pds; that is, the angular displacement of the roller measures the work done during the displacement from s 1 to s 2 . - Here there are two arbitrary
**constants**, which may be adjusted in various ways. - Ricks, "On the Variation of the
**Constants**of Electricity Supply Meters, with Temperature and Current," Electrician (1897), 39, 573. - National standards of length are not legally now referred to natural standards or to physical
**constants**, but it has been shown by A. - 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. - N being the refractive index, A the wave-length, and A, B, C, &c.,
**constants**depending on the material, which diminish so rapidly that only the first three as here written need be taken into account. - 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 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. - CONSTANTZA (
**Constants**), formerly known as Kustendji or Kustendje, a seaport on the Black Sea, and capital of the department of Constantza, Rumania; 140 m. - If D is the measured deviation of a ray, and Do, Xo, c and a are four
**constants**, the equation A=Ao-{ (D - D °) l /a seems to represejlt the connexion between deviation and wavelength with considerable accuracy for prisms constructed with the ordinary media. - 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. - 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. - N's N (I +µ) (s+o.)2 Here and N are
**constants**, while s as before is an integer number. - Taking the Trunk and Main Branch Series, we find they depend altogether on the four
**constants**: al, b, a', b', while N is a universal constant identical with that deduced from the hydrogen series. - 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. - From the relation between the critical
**constants**Pk Vk/Tk = 37 R or T k /P k = 3 . - 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. - 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. - For a very complete set of tables of dielectric
**constants**of solids, liquids and gases see A.