Second-order Sentence Examples

As regards the polarization of the dispersed light as dependent on the angle at which it is emitted, we find that although, when terms of the second order are included, the scattered light no longer vanishes in the same direction as before, the peculiarity is not lost but merely transferred to another direction.

We then arrive at the second order Volucres, which is divided into two " series."

We will confine ourselves here to algebraic complex numbers - that is, to complex numbers of the second order taken in connexion with that definition of multiplication which leads to ordinary algebra.

The product of two complex numbers of the second order - namely, l e l +x 2 e 2 and y i e l +y 2 e 2, is in this case defined to mean the complex (x i y i - x 2 y 2)e i +(x i y 2 +x 2 y 1)e 2.

For the second order we may take Ob - I - A, 1 1 +A2, and the adjoint determinant is the same; hence (1 +A2)x1 = (1-A 2)X 1 + 2AX2, (l +A 2)x 2 = - 2AX1 +(1 - A2)X2.

He also showed that every equation of an even degree must have at least one real quadratic factor, reduced the solution of linear differential equations to definite integrals, and furnished an elegant method by which the linear partial differential equation of the second order might be solved.

He was also the first to consider the difficult problems involved in equations of mixed differences, and to prove that an equation in finite differences of the first degree and the second order might always be converted into a continued fraction.

The path of a ray from the wave-surface A 0 B 0 to the point A is changed; but in virtue of the minimum property the change may be neglected in calculating the optical distance,as it influences the result by quantities of the second order only in the changes of refrangibility.

But it is found not to vary at all, even up to the second order of the ratio of the earth's velocity to that of light.

The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium (.f',g',h') = c2(P,Q,R), because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order.

The shell-bearing forms belonging to this group which were known to Linnaeus were placed by him (in 1748) in the third order of his class Vermes under the name " Testacea," whilst the Echinoderms, Hydroids and Annelids, with the naked Mollusca, formed his second order termed " Zoophyta."

The Didache knows nothing of the presbyters; bishops and deacons are mentioned, but there is no reference to the second order.

The axis of the member xQ+x'Q' of the second-order complex Q, Q' (where Q=nq+wr, Q'=nq'+wr' and x, x' are scalars) is parallel to a fixed plane and intersects a fixed transversal, viz.

For example, in the case of a particle lying on a smooth curve, or on a smooth surface, if it be displaced along the curve, or on the surface, the virtual work of the normal component of the pressure may be ignored, since it is of the second order.

It is evident, in the first place, that in any displacement common to the two surfaces, the work of the two equal and opposite normal pressures will cancel; moreover if, one of the surfaces being fixed, an infinitely small displacement shifts the point of contact from A to B, and if A be the new position of that point of the sliding body which was at A, the pro jectior of AA on the normal at A is of the second order.

For the virtual work of two equal anc opposite forces will cancel in any displacement which is commor to the two surfaces; whilst, if one surface be fixed, the displace ment of that point of the rolling surface which was in contact with the other is of the second order.

The simplest case is that of a frame of three bars, when the three joints A, B, C fall into a straght line; a small displacement of the joint B at right angles to AC would involve changes in the lengths of AB, BC which are only of the second order of small quantities.

The distance between the planes of and of will be of the second order of small quantities, and the quadratic moments with respect to of and co will therefore be equal, to the first order.

The constant -r is called the modulus of decay of the oscillations; if it is large compared with 2irfa the effect of friction on the period is of the second order of small quantities and may in general be ignored.

To find the small oscillation about a state of steady precession in which the axis makes a constant angle a with the vertical, we write O=a+X, and neglect terms of the second order in x.

The effect of friction on the period is moreover of the second order.

The sea mussel (Mytilus edulis) belongs to the second order of the class Lamellibranchia, namely the Filibranchia, distinguished by the comparatively free condition of the gillfilaments, which, whilst adhering to one another to form gillplates, are yet not fused to one another by concrescence.

A curve of the second order is a conic, and is also called a quadric curve; and conversely every conic is a curve of the second order or quadric curve.

In general a cone consists of one or more single or twin-pair sheets, and if we consider the section of the cone by a plane, the curve consists of one or more complete branches, or say circuits, each of them the section of one sheet of the cone; thus, a cone of the second order is one twin-pair sheet, and any section of it is one circuit composed, it may be, of two branches.

And we then say that a curve consists of one or more circuits; thus the right line, or curve of the first order, consists of one circuit; a curve of the second order consists of one circuit; a cubic curve consists of one circuit or else of two circuits.

Moreover, the functions b'c" - b"c', b"c - bc", bc' - b'c used in the process are themselves the determinants of the second order l b",c"I?

Then the terms of the second order were found, and so on to any extent.

Poncelet, how all problems of the second order can be solved by aid of the straight-edge alone without the use of compasses, as soon as one circle is given on the drawing-paper.

This is shown by the fold bifurcation in the second order model.

My suggestion is a view which is more realistic than much second order cybernetics.

This is the land of second-order cybernetics, the joint share-holder in the concerns of this journal.

Bimolecular Elimination An elimination reaction which proceeds via second order kinetics.

Use of LT theory to solve a second order ode.

Did not distinguish analysis we focus second-order interactions par.

Sensitivity to stimuli of first and second order motion was measured, using a two alternative forced choice preferential looking procedure.

Reactions may commonly be zero order, first order or second order with respect to a particular reactant.

This is what is referred to as second-order signification.

Such an imprisonment does not operate as a satisfaction or extinguishment of the debt, and no second order of commitment can be made against him for the same debt, although where the court has made an order or judgment for the payment of the debt by instalments a power of committal arises on default of payment of each instalment.

The second order was that Poniatowski, moving to the village through the wood, should turn the Russian left flank.