# How to use *Coefficient* in a sentence

We may, by a well-known theorem, write the result as a

**coefficient**of z w in the expansion of 1 - z n+1.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.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..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.AdvertisementIt 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.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.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.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.AdvertisementThe 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.AdvertisementWhen 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.AdvertisementCollecting 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.AdvertisementIn 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.AdvertisementHe 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.AdvertisementThe 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.AdvertisementTo 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.AdvertisementThere 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.AdvertisementThe resistance of the rope to bending causes an additional resistance, which experiment shows can be expressed in the form Wd 2 /cD where c is a

**coefficient**.Considering the equations ax +by +cz =d, a'x +b'y +c' z =d', a"x+b"y+cnz=d" and proceeding to solve them by the so-called method of cross multiplication, we multiply the equations by factors selected in such a manner that upon adding the results the whole

**coefficient**of y becomes = o, and the whole**coefficient**of z becomes = o; the factors in question are b'c" - b"c', b"c - be", bc' - b'c (values which, as at once seen, have the desired property); we thus obtain an equation which contains on the left-hand side only a multiple of x, and on the right-hand side a constant term; the**coefficient**of x has the value a(b'c" - b"c') +a'(b"c - bc") +a'(bc' - b'c), and this function, represented in the form a, b,c, a' b'c', a" b" c" is said to be a determinant; or, the number of elements being 32, it is called a determinant of the third order.By what precedes it appears that there exists a function of the n 2 elements, linear as regards the terms of each column (or say, for shortness, linear as to each column), and such that only the sign is altered when any two columns are interchanged; these properties completely determine the function, except as to a common factor which may multiply all the terms. If, to get rid of this arbitrary common factor, we assume that the product of the elements in the dexter diagonal has the

**coefficient**+ 1, we have a complete definition of the determinant, and it is interesting to show how from these properties, assumed for the definition of the determinant, it at once appears that the determinant is a function serving for the solution of a system of linear equations.Any determinant I a,' b, I formed out of the elements of the original determinant, by selecting the lines and columns at pleasure, is termed a minor of the original determinant; and when the number of lines and columns, or order of the determinant, is n - I, then such determinant is called a first minor; the number of the first minors is = n 2, the first minors, in fact, corresponding to the several elements of the determinant - that is, the

**coefficient**therein of any term whatever is the corresponding first minor.With the latest accepted diminution of the eccentricity, the

**coefficient**is 5.91".According to Plucker, the

**coefficient**of cubical dilatation at moderately low temperatures is 0.0001585.The Peltier

**coefficient**may also be expressed in volts or microvolts, and may be regarded as the measure of an E.M.F.If the quantity of heat absorbed and converted into electrical energy, when unit quantity of electricity (one ampere-second) flows from cold to hot through a difference of temperature, dt, be represented by sdt, the

**coefficient**s is called the specific heat of electricity in the metal, or simply the**coefficient**of the Thomson effect.Like the Peltier

**coefficient**, it may be measured in joules or calories per ampere-second per degree, or more conveniently and simply in microvolts per degree.In this case, however, in order to account for the phenomenon of the Peltier effect at the junctions, it is necessary to suppose that there is a real convection of heat by an electric current, and that the

**coefficient**P or pT is the difference of the quantities of heat carried by unit quantity of electricity in the two metals.Assuming the correctness of these, friction is generally measured in terms simply of the total pressure between the surfaces, by multiplying it by a "

**coefficient**of friction" depending on the material of the surfaces and their state as to smoothness and lubrication.Both at very high and very low pressures the

**coefficient**of friction is affected by the intensity of pressure, and, just as with velocity, it can only be regarded as independent of the intensity and proportional simply to the total load within more or less definite limits.These experiments distinctly point to the conclusion, although without absolutely proving it, that in such cases the

**coefficient**of kinetic friction gradually increases as the velocity becomes extremely small, and passes without discontinuity into that of static friction.The relation then between the work expended and the actual cooling work performed denotes the efficiency of the process, and this is expressed by Qt/(Q2-Q1); but as in a perfect refrigerating machine it is understood that the whole of the heat Q i is taken in at the absolute temperature T 11 and the whole of the heat Q2, is rejected at the absolute temperature T2, the heat quantities are proportional to the temperatures, and the expression T,/(T 2 -T,) gives the ideal

**coefficient**of performance for any stated temperature range, whatever working substance is used.The ideal

**coefficient**of performance is about 1, but the actual**coefficient**will be about 8 i after allowing for the losses incidental to working.He dealt with the

**coefficient**of performance as a common basis of comparison for all machines, and showed that the compression vapour machine more nearly reached the theoretic maximum than any other (Bayerisches Industrie and Gewerbeblatt, 1870 and 1871).Therefore,

**coefficient**alpha will be equal to zero.Also plotted is a curve for the minimum buckling stress

**coefficient**.The correlation

**coefficient**between adjacent pairs of axes can be viewed by clicking an axis with the right mouse button.The last stage can be used to estimate a stress diffusion

**coefficient**.The regression

**coefficient**for a straight line through origin is.Alternatively, the absorption

**coefficient**maps can be calculated based on an adequate model of the sample.We therefore suggest that the linear attenuation

**coefficient**be treated as a separate unit.The quantity t is known as the Kendall rank correlation

**coefficient**tau.To calculate the intracluster correlation

**coefficient**, and thereby refine the estimation of the sample size needed for the trial.The degree of relationship between three or more sample populations may be quantified using the multiple correlation

**coefficient**.One factor that had a high correlation

**coefficient**was the rate of unemployment.A robust measure of numerical model parameter sensitivity was employed, namely the rank order correlation

**coefficient**.Correlation

**Coefficient**The r-squared correlation**coefficient**The r-squared correlation**coefficient**should also remain high.Two voxel-based similarity measures, the linear correlation

**coefficient**and the entropy correlation**coefficient**, are used.The ratio K o = s ' he ratio K o = s ' h / s ' z is known as the

**coefficient**of earth pressure at rest.For wings, 92% of the data for the pitching moment

**coefficient**increment are predicted to within ± 0.02.The effect of wing area extension on the profile drag

**coefficient**increments may be neglected provided that the area extension is small.The recent analysis now included in the Data Items shows that the lift

**coefficient**increment at maximum lift**coefficient**has a Reynolds number dependence.The bars represent the best fit

**coefficient**of the suitably scaled wavelet to the data over the interval around the bar.For very accurate work it is desirable that the base-plate, the slide and the scale should be of nickel steel, having the same thermal

**coefficient**of expansion as glass.The

**coefficient**of this rise is equivalent to half a vibration (o.5) per degree Fahr.If the two circuits are in tune so that the numerical product of capacity and inductance of each circuit is the same or C L, = C L +CL and if k is the

**coefficient**of coupling then the natural frequency of each circuit is n = I /2w / (CL), and when coupled two oscillations are set up in the secondary circuit having frequencies n and n2 such that n = n0/ (i - k) and n = nh,/ (I +k).By division we obtain n 3 = 2.121/K i, or n=(2.121/K i) i, the

**coefficient**of association being thus determined.If we regard the thermal effect at each junction as a measure of the potential-difference there, as the total thermal effect in the cell undoubtedly is of the sum of its potentialdifferences, in cases where the temperature

**coefficient**is negligible, the heat evolved on solution of a metal should give the electrical potential-difference at its surface.Auxiliary Theorem.-The

**coefficient**of l l i xl2x13...Moreau (C. R., 1900, 130, pp. 122, 412, 562) that if K is the

**coefficient**of the Hall effect (I) and K' the analogous**coefficient**of the Nernst effect (i.) (which is constant for small values of H), then K' = Ka/p, v being the**coefficient**of the Thomson effect for the metal and p its specific resistance.If the two materials are disposed symmetrically, the amount of load carried by each would be in direct proportion to the

**coefficient**of elasticity and inversely as the moment of inertia of the cross section.The resistance of the air is reduced considerably in modern projectiles by giving them a greater length and a sharper point, and by the omission of projecting studs, a factor called the

**coefficient**of shape, being introduced to allow for this change.The

**coefficient**of correlation is 0.5699, which indicates that the standard deviation of an array is equal to that of the leaves in general multiplied by 1 / I - (0.5699) 1; and performing this multiplication, we find 1.426 as the standard deviation of an array.The number of coefficients is 2(m+ r) (m+2); but there is no loss of generality if the equation be divided by one

**coefficient**so as to reduce the**coefficient**of the corresponding term to unity, hence the number of coefficients may be reckoned as 1(m-1-- 1) (m+2) - r, that is, Zm(m+3); and a curve of the order in may be made to satisfy this number of conditions; for example, to pass through Zrn(m+3) points.Every extra moment that is calculated allows another recursion

**coefficient**to be found.The rate of movement of this boundary gives the sedimentation

**coefficient**s.Explain what is meant by the Peltier

**coefficient**and thermoelectric power.Arrhenius has pointed out that the

**coefficient**of affinity of an acid is proportional to its electrolytic ionization.The generating function is I - z2' 52 For 0 =3, (alai +a2a2+a3a3) 10; the condition is clearly a1a2a3 = A3 = 0, and since every seminvariant, of proper degree 3, is associated, as

**coefficient**, with a product containing A3, all such are perpetuants.The

**coefficient**K/(i +171-K) is positive for ferromagnetic and paramagnetic substances, which will therefore tend to move from weaker to stronger parts of the field; for all known diamagnetic substances it is negative, and these will tend to move from stronger to weaker parts.Reference to a geometrical interpretation seems at first sight to throw light on the meaning of a differential

**coefficient**; but closer analysis reveals new difficulties, due to the geometrical interpretation itself.The number by which an algebraical expression is to be multiplied is called its

**coefficient**.Thus in 3a the

**coefficient**of a is 3.But in 3.4a the

**coefficient**of 4a is 3, while the**coefficient**of a is3.4.If any power is absent, we treat it as present, but with

**coefficient**o.The binomial theorem gives a formula for writing down the

**coefficient**of any stated term in the expansion of any stated power of a given binomial.The first term is Abcde, in which all the letters are large; and the

**coefficient**of A 2 a 3 is therefore the number of terms which can be obtained from Abcde by changing three, and three only, of the large letters into small ones.Then, since nr rl is also a rational integral function of n of degree r, we can find a

**coefficient**c r, not containing n, and such as to make N-c r nr ri contain no power of n higher than n r - 1.The elementary idea of a differential

**coefficient**is useful in reference to the logarithmic and exponential series.He denotes quantities by the letters of the alphabet, retaining the vowels for the unknown and the consonants for the knowns; he introduced the vinculum and among others the terms

**coefficient**, affirmative, negative, pure and adfected equations.The

**coefficient**of expansion is constant for such metals only as crystallize in the regular system; the others expand differently in the directions of the different axes.With n=1, the re-entrant walls are given of Borda's mouthpiece, and the

**coefficient**of contraction becomes 2.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.Conversely, if the kinetic energy T is expressed as a quadratic function of x, x x3, y1, y2, y3, the components of momentum, the partial differential

**coefficient**with respect to a momentum component will give the component of velocity to correspond.The

**coefficient**of purity is increased and the viscosity of the juice diminished.Another steel containing 45% of nickel has, like platinum, the same

**coefficient**of expansion as glass.The

**coefficient**of expansion at constant pressure is equal to the**coefficient**of increase of pressure at constant volume.It is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the

**coefficient**d(pv)/dp is to a first approximation a function of the temperature only.The simplest assumption which suffices to express the small deviations of gases and vapours from the ideal state at moderate pressures is that the

**coefficient**a in the expression for the capillary pressure varies inversely as some power of the absolute temperature.C is a constant, equal to the

**coefficient**of viscosity in Helmholtz's theory, but less simple in Kirchhoff's theory.The short answer on leather is, leather has the perfect

**coefficient**of friction, and can achieve a very good balance between flex and protection.In the case of the inductive mode of exciting the oscillations an important quantity is the

**coefficient**of coupling of the two oscillation circuits.Viscosity increases with density, but oils of the same density often vary greatly; the

**coefficient**of expansion, on the other hand, varies inversely with the density, but bears no simple relation to the change of fluidity of the oil under the influence of heat, this being most marked in oils of paraffin base.We can calculate the heat of formation from its ions for any substance dissolved in a given liquid, from a knowledge of the temperature

**coefficient**of ionization, by means of an application of the well-known thermodynamical process, which also gives the latent heat of evaporation of a liquid when the temperature**coefficient**of its vapour pressure is known.The earliest formulation of the subject, due to Lord Kelvin, assumed that this relation was true in all cases, and, calculated in this way, the electromotive force of Daniell's cell, which happens to possess a very small temperature

**coefficient**, was found to agree with observation.Now by the theory of symmetric functions, any symmetric functions of the mn values which satisfy the two equations, can be expressed in terms of the

**coefficient**of those equations.Hence, finally, the resultant is expressed in terms of the coefficients of the three equations, and since it is at once seen to be of degree mn in the

**coefficient**of the third equation, by symmetry it must be of degrees np and pm in the coefficients of the first and second equations respectively.The number of partitions of a biweight pq into exactly i biparts is given (after Euler) by the

**coefficient**of a, z xPy Q in the expansion of the generating function 1 - ax.Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading

**Coefficient**Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the rotatory power, or rotational

**coefficient**.The strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the

**coefficient**of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).At barometric pressures such as exist between 18 and 36 kilometres above the ground the mobility of the ions varies inversely as the pressure, whilst the

**coefficient**of recombination a varies approximately as the pressure.The

**coefficient**of friction is a variable quantity depending upon the state of the rails, but is usually taken to be This is the fundamental equation between the forces acting, however the torque may be applied.But the temperature

**coefficient**of conductivity is now generally less than before; thus the effect of temperature on ionization must be of opposite sign to its effect on fluidity.In order to obtain the seminvari ants we would write down the (w; 0, n) terms each associated with a literal

**coefficient**; if we now operate with 52 we obtain a linear function of (w - I; 8, n) products, for the vanishing of which the literal coefficients must satisfy (w-I; 0, n) linear equations; hence (w; 8, n)-(w-I; 0, n) of these coefficients may be assumed arbitrarily, and the number of linearly independent solutions of 52=o, of the given degree and weight, is precisely (w; 8, n) - (w - I; 0, n).It is shown in the article on Combinatorial Analysis that (w; 0,n) is the

**coefficient**of a e z w in the ascending expansion of the fraction 1-a.The existence of such a relation, as 0-1+0-2+.,.+cr2=0, necessitates the vanishing of a certain function of the coefficients A2, A 3, ...A 9, and as a consequence one product of these coefficients can be eliminated from the expanding form and no seminvariant, which appears as a

**coefficient**to such a product (which may be the whole or only a part of the complete product, with which the seminvariant is associated), will be capable of reduction.The internal force F is opposite to the direction of the magnetization, and equal to NI, where N is a

**coefficient**depending only on the ratio of the axes.For small bodies other than spheres the

**coefficient**will be different, but its sign will always be negative for diamagnetic substances and positive for others; hence the forces acting on any small body will be in the same directions as in the case of a sphere' Directing Couple acting on an Elongated Body.If L and N are the inductances of any two circuits which have a

**coefficient**of mutual inductance M, then M/-/ (LN) is called the**coefficient**of coupling of the circuits and is generally expressed as a percentage.Two circuits are said to be closely coupled when this

**coefficient**is near unity and to be loosely coupled if it is very small.Suppose the

**coefficient**of association be n, i.e.The Partial Differential Equations.--It will be shown later that covariants may be studied by restricting attention to the leading

**coefficient**, viz.He proves, by means of the six linear partial differential equations satisfied by the concomitants, that, if any concomitant be expanded in powers of xi, x 2, x 3, the point variables-and of u 8, u 2, u3, the contragredient line variables-it is completely determinate if its leading

**coefficient**be known.Two of these show that the leading

**coefficient**of any covariant is an isobaric and homogeneous function of the coefficients of the form; the remaining two may be regarded as operators which cause the vanishing of the covariant.It is for this reason called a seminvariant, and every seminvariant is the leading

**coefficient**of a covariant.It is then possible to assign to each body a specific

**coefficient**of affinity.The temperature

**coefficient**of conductivity has approximately the same value for most aqueous salt solutions.