Word Finder - differential

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The differential gear in an automobile etc

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A qualitative or quantitative difference between similar or comparable things

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An infinitesimal change in a variable, or the result of differentiation

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One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.

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A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.

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Of, or relating to a difference

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differential characteristics

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Dependent on, or making a difference; distinctive

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Having differences in speed or direction of motion

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Of, or relating to differentiation, or the differential calculus

Suppose the key to be depressed, then a current flows through one winding of the differential relay to line and through the other winding and rheostat to earth.

This arrangement can be duplexed in the way already explained, by providing differential relays and arranging for the outgoing currents to divide differentially through the two relays at each end.

Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular linear and higher transformations connected with analysis and geometry.

The series of equations of the type (3) is then replaced by a single linear partial differential equation, or by a set of two or three such equations, according to the number of dependent variables.

Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.

The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

Expressed as a differential relation, with the value of c-TKL ai,G+2 (a 2 +A) a d ?

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.

This is mathematically expressed by the statement that dE is an exact differential of a function of the co-ordinates defining the state of the body, which can be integrated between limits without reference to the relation representing the path along which the variations are taken.

This inequality holds in all cases, but cannot in general be applied to an irreversible change, because Od4 is not a perfect differential, and cannot be evaluated without a knowledge of the path or process of transformation.

The value of Od4 is then the same as d(64), which is a perfect differential, so that the condition may be written d(46-E) =dW.

In this case dW=pdv=d(pv), a perfect differential, so that the external work done is known from the initial and final states.

Meanwhile the study of mathematics was not neglected, as appears not only from his giving instruction in geometry to his younger brother Daniel, but from his writings on the differential, integral, and exponential calculus, and from his father considering him, at the age of twenty-one, worthy of receiving the torch of science from his own hands.

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.

If we divide throughout by T, we obtain d 2 (n+3)RN T +RNd v, showing that dQ/T is a perfect differential.

In what follows it will be assumed that the conditions of continuity (which imply the continuity not only of u but also of some of its differential coefficients) are satisfied, subject to the small errors in the values of u actually given; the limits of these errors being known.

The most simple case is that in which the trapezette tapers out in such a way that the curve forming its top has very close contact, at its extremities, with the base; in other words, the differential coefficients u', u", u"',.

The following are the results (for the formulae involving chordal areas), given in terms of differential coefficients and of central differences.

At the same time the differential duty on refined sugar, which operated as protection to the sugar trust, was not abolished, as the ardent tariff reformers had proposed, but kept in substance not greatly changed.

He published a memoir on the integration of partial differential equations and a few others, which have not been noticed above, but they relate to subjects with which his name is not especially associated.

Pfaff's researches bore chiefly on the theory of series, to which he applied the methods of the so-called combinatorial school of German mathematicians, and on the solution of differential equations.

The other method starts from the observed values of the periods, and establishes a differential equation from which these periods may be derived.

Riecke, 3 who deduced a differential equation of the 10th order.

It should be added that the differential treatment of the various classes was by no means confined to the case of wergilds.

His primary aim has been declared to be the advancement and elaboration of the theory of differential equations, and it was with this end in view that he developed his theory of transformation groups, set forth in his Theorie der Transf ormationsgruppen (3 vols., Leipzig, 1888-1893), a work of wide range and great originality, by which probably his name is best known.

Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.

These have often been mistaken for nuclei and have to be carefully distinguished by differential stains.

The total power developed is 600 H.P., and though the load factor varies very greatly in this case, the differential type of governor used secures perfect control of the running of the wheels.

We thus obtain the differential equation gk(d 2 0/dx 2) =cgdo/dt+hpo, which is satisfied by terms of the type =c" sin where a 2 -b 2 = hp/qk, and ab = urnc/k.

The differential equation for the distribution of temperature in this case includes the majority of the methods already considered, and may be stated as follows.

There has been some discussion as to the fairness of the treatment accorded by Pascal to his rivals, but no question of the fact that his initiative led to a great extension of our knowledge of the properties of the cycloid, and indirectly hastened the progress of the differential calculus.

A third form of selection, which may affect the composition of the next generation without of necessity involving a differential death-rate or a differential fertility, is assortative mating, or the tendency of those members of one sex which exhibit a particular character to mate only with members of the other sex which exhibit the same or some other definite character.

Differential fertility may be induced in either of two ways.

For an attempt to treat the whole problem of differential fertility and assortative mating numerically, see Pearson, The Grammar of Science, 2nd edition, London, 1900.

His well-known correction of Laplace's partial differential equation for the potential was first published in the Bulletin de la societe philomatique (1813).

Where accurate differential observations or photographs involving other than instantaneous exposures have to be made, the additional condition is required that the optical axis of the telescope shall accurately and automatically follow the object under observation in spite of the apparent diurnal motion of the heavens, or in some cases even of the apparent motion of the object relative to neighbouring fixed stars.

The thermal capacity of the scale-pan, &c., can be determined by a separate experiment., or, still better, eliminated by the differential method of counterpoising with an exactly similar arrangement on the other arm of the balance.

If in this we put r= I/u, and eliminate t by means of (15), we obtain the general differential equation of central orbits, viz.

Required the relation between the velocity of translation 02 of W and the angular velocity af of the differential barrel.

This combination, called Hunters or the differential screw, combines the strength of a large thread with the slowness of motion due to a small one.

A conspicuous feature of the New Mexican landscape is the mesa, a flat-topped hill created by differential erosion and projecting above the surrounding country like a table.

Electric attractions and repulsions were, however, regarded as differential actions in which the mutual repulsion of the particles of electricity operated, so to speak, in antagonism to the mutual attraction of particles of matter for one another and of particles of electricity for matter.

The chief piece of mechanism in the roving frame is the gearing known as the "differential motion."

He also developed the theory of differential and of summational tones.

The aberrations can also be expressed by means of the "characteristic function " of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order.

Everywhere are evidences of water and wind erosion, of desiccation and differential weathering.

The differential diagnosis is of the highest importance, but very frequently time alone will furnish a sufficient criterion.

Freedom of navigation of the Congo and all its affluents was also secured, and differential dues on vessels and merchandise were forbidden.

Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the parallax, or the inclination of the lunar orbit.