Defn: The ratio of onevector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another.
Note: In a triangle, either side is the vector sum of the other two sides taken in proper order; the process finding the vector sum of two or more vectors is vector addition (see under Addition).
Defn: A spiral whose polar equation is r2th = a; that is, a curve the square of whose radius vector varies inversely as the angle which the radius vector makes with a given line.
The areas swept over by a vector drawn from the sun to a planet are proportioned to the times of describing them.
Now the Soviet interceptors were on the Katsura radar, speeding toward Daedalus' last known vector coordinates.
Vance realized they were assuming a vector north by northeast, out over the ocean.
The area its radius vector sweeps out is therefore SAP, instead of what it would have been, SAB.
And the way it increases will be for the radius vector to lengthen, so as to sweep out a bigger area.
He also now answered quite satisfactorily, but too late, the question about the radius vector sent to him months before.
Now the area of the triangle CAD, swept out by the radius vector in unit time, is 1/2bh; h being the perpendicular height of the triangle from the base AC.
Leverrier the same old question as he had fruitlessly put to Mr. Adams: Did the new theory explain the errors of the radius vector or not?
The radius vector (or line joining sun and planet) sweeps out equal areas in equal times.
If it were a material substance, to which the law of gravitation applied, it must be moving in a conic section with the sun in one focus, and its radiusvector must sweep out equal areas in equal times.
The position of any particle of the system is defined by drawing a straight line or vector from the origin, or point of reference, to the given particle.
The latitude, longitude, and radius-vector of each planet are constantly varying, but they each have a determined value at each moment of time.
Hamilton of Dublin, as a geometry, primarily concerning itself with the operations by which one directed quantity or vector is changed into another.
Hansen, therefore, shows how the radius vector is corrected so as to give that of the true planet.
The angle QOP, which the radius vector makes with the fundamental plane.
This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.
The angle XOQ which the projection of the radius vector upon the fundamental plane makes with the initial line OX.
The third law enables us to compute the time taken by the radius vector to sweep over the entire area of the orbit, which is identical with the time of revolution.
Taking as the radiusvector of each body the line from the body to the common centre of gravity of all, the sum of the products formed by multiplying each area described, by the mass of the body, remains a constant.
The problem of constructing successive radii vectores, the angles of which are measured off from the radius vector of the body at the original given position, is then a geometric one, known as Kepler's problem.
Of the three co-ordinates, the radius vector does not admit of direct measurement, and must be inferred by a combination of indirect measurements and physical theories.
The speed of the latter may, therefore, be expressed as a function of its radius vector at the moment and of the major axis of its orbit without introducing any other elements into the expression.
The nightly vector resultants, on the other hand, are so consistent that they have the appearance of remarkable accuracy and tempt one to draw close correlations with the terrain.
In Figure 39, the direction of the over-all vector resultant, obtained from the sector vectors on the preceding map, is plotted to show the net trend at each station.
And, at Progreso, Yucatan, where the vectorresultants were 21 deg.
Nor do we know exactly what wind corresponds to the average or median flight level, which would otherwise be a good altitude at which to study the net trend or vector resultant.
Although the vector resultants show a net movement of birds to the northeast, there are important divergent components of the flights.
The process is repeated successively with each vector until all have been taken into consideration.
The arrows indicate direction only and their slants were obtained by vector analysis of the over-all sector densities.
Each sector vector is drawn in proportion to its percentage of the corresponding nightly station density; hence the vectors at each station are on an independent scale.
Each arrow is the vector resultant for a particular night, its length expressing the nightly density as a percentage of the total station density for the nights represented.
Each vector shown is the vector resultant for one particular night.
A solenoidal distribution of a vector is one corresponding to that of the velocity in an incompressible fluid.
Similarly, there is a vector quantity B (the "magnetic induction") intimately connected with the magnetic force H.
This state is represented by a vector D ("dielectric displacement") whose magnitude is measured by the quantity of electricity reckoned per unit area which has traversed an element of surface perpendicular to D itself.
I have before stated that I considered the establishment of this error of the radius vector of Uranus to be a very important determination.
But I should be very glad to know whether this assumed perturbation will explain the error of the radius vector of Uranus.
I therefore considered that the trial, whether the error of radius vector would be explained by the same theory which explained the error of longitude, would be truly an experimentum crucis.
Le Verrier then remarks, as one of the strong proofs of the correctness of the general theory, that the error of radiusvector is explained as accurately as the error of longitude.
I was, however, still desirous, as before, of learning whether the perturbation in radius vector was fully explained.
Airy made a mistake in regarding the question of the Radius Vector as of fundamental importance; Sir J.
The effective voltage between the external leads may in the same way be calculated by a vector diagram, and with the above star connexion the voltage between the outer pair of wires a and c is [root]2, or 1.
At any instant the value of the current in the third wire must be the vector sum of the two currents in the other wires, and if the shape of the curves of instantaneous E.
Centrifugal forces modify or reverse the directional vector of gravity.
It also can be increased by using a centrifuge which adds a radial acceleration vector to the 1 g of Earth.
Motion of the head in any direction not parallel to the centrifugal force vector would result in bizarre stimulation of the semicircular canals and consequent motion sickness.
Leverrier the same old question that he had fruitlessly put to Adams: Did the new theory explain the errors of the radius vector or not?
The reaction with the plane at P will be an equal parallel force; and its moment round G will provide the couple which causes the velocity of the vector of angular momentum appropriate to the steady motion; and this moment will be gM.
In the case of the steady motion of the top, the vector OH lies in the vertical plane COC', in OK suppose (fig.
In the general motion of the top the vector OH of resultant angular momentum is no longer compelled to lie in the vertical plane COC' (fig.
Plenty of time to kick-in vector and deceleration programs.
Reaching the taxi, Zolan and Hodak began to adjust its controls, vector and power instruments.
The computer adjusted thrust and vector to bring the ship to the 'fire' point and engage the countdown and sequence to launch, arm the warhead, and follow up.
The length of the vector must be proportional to the moment of the couple, and its sense must be such that the sum of the moments of the two forces of the couple about it is positive.
For, take any point O, and construct the vector [Sigma](m.
If we draw a vector OJ to represent the angular velocity, then J traces out a certain curve in the body, called the polhode, and a certain curve in space, called the herpolhode.
The momentum of a particle is the vector obtained by multiplying the velocity by the mass m.
The direction of tb, the third vector in the diagram, is also known, so that the problem is reduced to the condition that b is somewhere on the line tb.
In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.
If there are no extraneous forces, or if the extraneous forces have zero moment about any axis through G, the vector which represents the resultant angular momentum relative to G is constant in every respect.
The second method is based upon the vectorrepresentation of velocity, and may be illustrated by applying it to the four-bar chain.
Hence equal areas are swept over by the radius vector in equal times.
I wrote to Schumacher regarding the error in the tabular radius-vector of Uranus, which my mode of reducing the observations enabled me to see.
I wrote to him, enquiring whether his theory explained the irregularity of radius-vector (as well as that of longitude).
The imaginary line joining the earth and sun is called the earth's radius vector, and the pupil should note that the longitude and length of the radius vector taken together show the direction and distance of the earth from the sun--i.
The radius vector of each planet moves over equal areas in equal times.
In Kepler's form of stating the law the radius vector is supposed to travel with the planet and in each day to sweep over the same fractional part of the total area of the orbit.
This force is in a direction perpendicular to the radius vector and to the plane containing it and the element of current.
Maxwell also introduced in this connexion the notion of the vector potential.
Accordingly when we have an electric circuit or circuits in which there are simple periodic currents we can draw a vector diagram, the lines of which represent the relative magnitudes and phase differences of these currents.
Oblique tractions can always be resolved, by the vector law, into normal and tangential tractions.
The vector of change starts at the materiality and heads towards the abstract-that is, from objects to signs.
General protective measures are the same as for any infectious disease; specific protective measures are used once the vector or method of transmission has been identified.
They can be delivered directly (artillery or aircraft spray), or through a vector such as a flea or tick.
