## Coefficient Sentence Examples

- 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. - 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. - 6 1.86 3.01 o 88 1.03 Since at the boiling-point under atmospheric pressure liquids are in corresponding states, the additive nature of the critical
**coefficient**should also be presented by boiling-points. - Arrhenius has pointed out that the
**coefficient**of affinity of an acid is proportional to its electrolytic ionization. - 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. - 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. - 1 2 3 We have found above that the
**coefficient**of (x 1 1 x 12 x 13...) i n the product XmiXm2X m3 ... - It is for this reason called a seminvariant, and every seminvariant is the leading
**coefficient**of a covariant. - 1 -az 74 - 2.1 -azn-4....1 - azn+4.1 - az n+2.1 - az-n in which we have to take the
**coefficient**of aezne-2', the expansion. - In general the
**coefficient**, of any product A n A m A 7, 3 ..., will have, as**coefficient**, a seminvariant which, when expressed by partitions, will have as leading partition (preceding in dictionary order all others) the partition (Tr1lr2lr3ï¿½..). - The existence of such a relation, as 0-1+0-2+.,.+cr2=0, necessitates the vanishing of a certain function of the
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**coefficients****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. - 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 Number Of Linearly Independent Seminvariants Of The Given Type Will Then Be Denoted By (W; 0, P; 0', Q) (W; 0, P; 0', Q); And Will Be Given By The
**Coefficient**Of A E B E 'Z W In L Z 1 A. - 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. - This ratio, termed by Guye the critical
**coefficient**, has the following approximate values: C. H. - Ramsay and Shields found from investigations of the temperature
**coefficient**of the surface energy that Tin the equation y(Mv) 3 = KT must be counted downwards from the critical temperature T less about 6°. - Suppose the
**coefficient**of association be n, i.e. - 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. - 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. - ï¿½ Oxl d 2x 77n If we have new variables z such that zs=4s(yl, Y2,...yn), we have also z s =1 Y 8(x1, x2,ï¿½ï¿½ï¿½xn), and we may consider the three determinants which i s 7xk, the partial differential
**coefficient**of z i, with regard to k . - Hence, finally, the resultant is expressed in terms of the
of the three equations, and since it is at once seen to be of degree mn in the**coefficients****coefficient**of the third equation, by symmetry it must be of degrees np and pm in theof the first and second equations respectively.**coefficients** - = ...+O(s i s 2 s 3 ...)xl1x12x13...+..., where 0 is a numerical
**coefficient**, then also O ?2 0.3 P1 P2 P3 Al A2 A3 +. - It is definied as having four elements, and is written the
**coefficient**of a0 o a1 a2 2 ... - 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. - And the weight' of the
**coefficient**of the leading term xi +Q+T+.ï¿½ï¿½ is equal to i+j+k+.... - The orders of the quantic and covariant, and the degree and weight of the leading
**coefficient**; calling these 'n, e,' 0, w respectively we can see that they are not independent integers, but that they are invariably connected by a certain relation n9 -2w = 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 theof the form; the remaining two may be regarded as operators which cause the vanishing of the covariant.**coefficients** - Let a covariant of degree e in the variables, and of degree 8 in the
(the weight of the leading**coefficients****coefficient**being w and n8-2w = ï¿½), be Coxl -}- ec l l 1 x 2 -{-... - 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.