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potential

potential

potential Sentence Examples

  • What is the potential impact of the costs of future technologies?

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  • I am eager to do what I can to help the children of our Province reach full potential.

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  • Her earning potential is higher in a private home, around $60,000.

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  • We looked for any potential hazards at each step of the process.

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  • Potential buyers are looking for a property that they can see themselves living in.

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  • In our opinion the business offers tremendous potential for further increase in the right hands.

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  • Commercial interest in the area is growing very rapidly due to its huge market potential.

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  • There will be potential tax benefits depending on your individual circumstances.

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  • Because its meaning has to be imputed, we have tended to describe it in terms of prior technologies—which, in many cases, understates its potential by many orders of magnitude.

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  • These few were given the tools to achieve their maximum potential, to live that dream.

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  • In dry weather the electric potential in the atmosphere is normally positive relative to the earth, and increases with the height.

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  • The site was seen to have considerable potential for drawing in innovative products for the construction industry.

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  • The key to unlocking the untapped potential within cities is to build an environment that is conducive to creativity.

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  • For migratory species on the verge of stock collapse, we must now aim to maximize the potential to recover.

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  • What is the potential threat to us humble bloggers arising from France's recent problems?

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  • We heard from potential customers in some of the earlier replies in this thread.

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  • The play really worked with the natural elements of the Magdalen College school grounds to realize the potential of open-air theater.

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  • Eventually, the pea was as large as its genetic potential allowed it to be.

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  • Some have questioned whether Friedman's thesis is 100 percent true, mentioning NATO air strikes against Yugoslavia as a potential exception.

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  • I am delighted that the Scottish Higher Education Funding Council and Scotland's medical schools are leading the way in exploring this huge potential.

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  • How much potential is there in millions of discoveries like that?

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  • That there was enormous potential for development in the staging of the event was undeniable; how to realize it was a problem.

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  • These jobs can be market jobs that have the potential to make a person vastly richer, creating more and more wealth on the planet.

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  • But doing so also meant sacrificing her independence and the risk of losing everything that meant something to her, a potential lifetime of pain.

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  • It really demonstrates the true potential of an iPod using peripheral speakers.

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  • The potential candidate was able to deflect some of the harder questions by flattering the interviewer.

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  • To be accepted to this program, students must excel academically, as well as show leadership potential.

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  • I, Ben Gustefson, collated boring statistical figures while locked in a cramped cubical of a company that offered me no future potential.

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  • Yet, in spite of the obstacles, it seemed utterly sinful to ignore the potential.

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  • Suppose now that the sphere's earth connexion is broken and that it is carried without loss of charge inside a building at zero potential.

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  • In the earliest the conductor was represented by long metal wires, supported by silk or other insulating material, and left to pick up the air's potential.

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  • When rain or snow is falling, the potential frequently changes rapidly.

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  • - Annual Variation Potential Gradient.

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  • Above the level plain of absolutely smooth surface, devoid of houses or vegetation, the equipotential surfaces under normal conditions would be strictly horizontal, and if we could determine the potential at one metre above the ground we should have a definite measure of the potential gradient at the earth's surface.

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  • In an ordinary climate a building seems to be practically at the earth's potential; near its walls the equipotential surfaces are highly inclined, and near the ridges they may lie very close together.

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  • The potential gradient near the ground varies with the season of the year and the hour of the day, and is largely dependent on the weather conditions.

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  • The large difference between the means obtained at Potsdam and Kremsmtinster, as compared to the comparative similarity between the results for Kew and Karasjok, suggests that the mean value of the potential gradient may be much more dependent on local conditions than on difference of latitude.

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  • At any single station potential gradient has a wide range of values.

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  • Kew At Batavia the Potential 100, -?

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  • The two last curves in the diagram contrast the diurnal variation at Kew in potential gradient and in barometric pressure for the year as a whole.

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  • In the potential curves of the diagram the ordinates represent the hourly values expressed - as in Tables II.

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  • The first line gives the mean value of the potential gradient, the second the mean excess of the largest over the smallest hourly value on individual days.

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  • It will be noticed that the difference between the greatest and least hourly values is, in all but three winter months, actually larger than the mean value of the potential gradient for the day; it bears to the range of the regular diurnal inequality a ratio varying from 2.0 in May to 3.6 in November.

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  • In this table, unlike Table IV., amplitudes are all expressed as decimals of the mean value of the potential gradient for the corresponding season.

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  • The potential gradient is in all cases lower in summer than winter, and thus the reduction in c 1 in summer would appear even larger than in Table V.

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  • The potential difference between the two is recorded, and the potential gradient is thus found.

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  • Thus at 4000 metres the potential seems of the order of 150,000 volts.

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  • At most stations a negative potential gradient is exceptional, unless during rain or thunder.

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  • During rain the potential is usually but not always negative, and frequent alternations of sign are not uncommon.

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  • In some localities, however, negative potential gradient is by no means uncommon, at least at some seasons, in the absence of rain.

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  • The proportion of occurrences of negative potential under a clear sky was much above its average in autumn.

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  • At Sodankyla rain or snowfall was often unaccompanied by change of sign in the potential.

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  • Lenard, Elster and Geitel, and others have found the potential gradient negative near waterfalls, the influence sometimes extending to a considerable distance.

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  • Linss (6) found that an insulated conductor charged either positively or negatively lost its charge in the free atmosphere; the potential V after time t being connected with its initial value Vo by a formula of the type V = Voe - at where a is constant.

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  • A cylinder condenser has its inner surface insulated and charged to a high positive or negative potential.

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  • The charge given up to the inner cylinder is known from its loss of potential.

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  • in diameter, charged to a negative potential of at least 2000 volts, is supported between insulators in the open, usually at a height of about 2 metres.

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  • The radioactivity is denoted by A, and A = signifies that the potential of the dissipation apparatus fell I volt in an hour per metre of wire introduced.

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  • The Different Elements Potential Gradient, Dissipation, Ionization And Radioactivityare Clearly Not Independent Of One Another.

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  • will give a general idea of the relations of potential gradient to dissipation and ionization.

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  • Table Potential, Dissipation, Ioniz If we regard the potential gradient near the ground as representing a negative charge on the earth, then if the source of supply of that charge is unaffected the gradient will rise and become high when the operations by which discharge is promoted slacken their activity.

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  • A diminution in the number of positive ions would thus naturally be accompanied by a rise in potential gradient.

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  • No distinct relationship has yet been established between potential gradient and radioactivity.

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  • If V be the potential, p the density of free electricity at a point in the atmosphere, at a distance r from the earth's centre, then assuming statical conditions and neglecting variation of V in horizontal directions, we have r2 (d/dr) (r 2 dV/dr) - - 4.rp = o.

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  • There is a difficulty in reconciling observed values of the ionization with the results obtained from balloon ascents as to the variation of the potential with altitude.

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  • Wilson supposes that by the fall to the ground of a preponderance of negatively charged rain the air above the shower has a higher positive potential than elsewhere at the same level, thus leading to large conduction currents laterally in the highly conducting upper layers.

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  • I've drawn up a potential plan for reorganizing.

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  • In most mechanical systems the working stresses acting between the parts can be determined when the relative positions of all the parts are known; and the energy which a system possesses in virtue of the relative positions of its parts, or its configuration, is classified as "potential energy," to distinguish it from energy of motion which we shall presently consider.

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  • The word potential does not imply that this energy is not real; it exists in potentiality only in the sense that it is stored away in some latent manner; but it can be drawn upon without limit for mechanical work.

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  • A simple example of the transformation of kinetic energy into potential energy, and vice versa, is afforded by the pendulum.

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  • When work is done against these forces no full equivalent of potential energy may be produced; this applies especially to frictional forces, for if the motion of the system be reversed the forces will be also reversed and will still oppose the motion.

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  • Mayer made an assumption the converse of that of Seguin, asserting that the whole of the work done in compressing the air was converted into heat, and neglecting the possibility of heat being consumed in doing work within the air itself or being produced by the transformation of internal potential energy.

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  • When the key is released the condensers and cables at once begin to return to zero potential, and if the key is depressed and released several times in rapid succession the cable is divided into sections of varying potential, which travel rapidly towards the receiving end, and indicate their arrival there by producing corresponding fluctuations in the charge of the condenser C3.

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  • The electrical condition of the cable was then excellent, but unfortunately the electrician in charge, Wildman Whitehouse, conceived the wrong idea that it should be worked by currents of high potential.

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  • 38 6), the insulated wires or plates being upheld by masts, its operation is as follows: - When the key in the primary circuit of the induction coil is pressed the transmitting antenna wire is alternately charged to a high potential and discharged with the production of high frequency oscillations in it.

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  • If these spark balls are set at the right distance, then when the potential difference accumulates the antenna will be charged and at some stage suddenly discharged by the discharge leaping across the spark gap. This was Marconi's original method, and the plan is still used under the name of the direct method of excitation or the plain antenna.

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  • These wave-detecting devices may be divided into two classes: (i) potential operated detectors, and (ii) current operated detectors.

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  • He showed that in a simple Marconi antenna the variations of potential are a maximum at the insulated top and a minimum at the base, whilst the current amplitudes are a maximum at the top earthed end and zero at the top end.

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  • He therefore saw that it was a mistake to insert a potential-affected detector such as a coherer in between the base of the antenna and the earth because it was then subject to very small variations of potential between its ends.

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  • The oscillations set up in the vertical antenna excited sympathetic ones in the lateral circuit provided this was of the proper length; and the coherer was acted upon by the maximum potential variations possible.

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  • Increase in the voltage acting upon a solid conductor increases the current through it, but in the case of the electric arc an increase in current is accompanied by a fall in the difference of potential of the carbons, within certain limits, and the arc has therefore been said to possess a negative resistance.'

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  • When this is the case the amplitude of the potential difference of the surfaces of the tubular condenser becomes a maximum, and this is indicated by connecting a vacuum tube filled with neon to the surfaces of the condenser.

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  • Varley, who proposed to make use of it in a telegraphic receiving instrument.4 In Dolbear's instrument one plate of a condenser was a flexible diaphragm, connected with the telephone line in such a way that the varying electric potential produced by the action of the transmitting telephone caused an increased or diminished charge in the condenser.

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  • The single-wire earthed circuits used in the early days of telephony were subject to serious disturbances from the induction caused by currents in neighbouring telegraph and electric light wires, and from the varying potential of the earth due to natural or artificial causes.

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  • This requirement is usually met by connecting a third or " test " wire to each of the jacks associated with a subscriber's line, and by making the circuit arrangements such that this wire is either disconnected or at earth potential when the line is not in use, and at some potential above or below that of the earth, when the circuit is engaged.

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  • (histocytes) and germinal cells, actual or potential (archaeocytes), amongst the constituent cells of the animal body.

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  • The assimilation of complex foods consequently may be regarded as supplying the protoplasm with a potential store of energy, as well as building tip its substance.

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  • This energy is obtained especially by the chioroplastids, and part of it is at once devoted to the construction of carbohydrate material, being thus turned from the kinetic to the potential condition.

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  • The other constructive processes, which arc dependent partly upon the oxidation of the carbohydrates so formed and therefore upon an expenditure of part of such energy, also mar]~ the storage of energy in the potential form.

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  • This is the absorption of elaborated compounds from their environment, by whose decomposition the potential energy expended in their construction can be liberated.

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  • Respiration, indeed, is the expression of the liberation of the potential energy of the protoplasm itself.

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  • In such cells as are capable of absorbing it, by virtue oi their chlorophyll apparatus, the greater part of it is converted int< the potential form, and by the transport from cell to cell of th compounds constructed every part of the plant is put into possessiol of the energy it needs.

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  • The growth of such a cell will be found to depend mainly upon five conditions: (I) There must be a supply of nutritive or plastic materials, at the expense of which the increase of its living substance can take place, and which supply the needed potential energy.

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  • This is clearly the same process in essence as that of the formation of a vitellogenous gland from part of the primitive ovary, or of the feeding of an ovarian egg by the absorption of neighbouring potential eggs; but here the period at which the sacrifice of one egg to another takes place is somewhat late.

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  • to his own, the royalists began to compass the death of the man whom they had at first naively looked on as a potential General Monk to their Charles II.

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  • So long as these remain potential or ideal, they form the motive of action; motive consisting always in the idea of some "end" or "good" which man presents to himself as an end in the attainment of which he would be satisfied, that is, in the realization of which he would find his true self.

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  • Precosmically the Will is potential and the Reason latent, and the Will is void of reason when it passes from potentiality to actual willing.

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  • The potential difference of the ends of the low resistance is at the same time measured on the potentiometer, and the quotient of this potential difference by the known value of the low resistance gives the true value of the current passing through the ammeter.

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  • Claus maintained that Baeyer's view was identical with his own, for as in Baeyer's formula, the fourth valencies have a different function from the peripheral valencies, being united at the centre in a form of potential union.

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  • When applied to benzene, a twofold conjugated system is suggested in which the partial valencies of adjacent atoms neutralize, with the formation of a potential double link.

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  • In general, therefore, it may be considered that the double linkages are not of exactly the same nature as the double linkage present in ethylene and ethylenoid compounds, but that they are analogous to the potential valencies of benzene.

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  • Hence the absolute velocities of the two ions can be determined, and we can calculate the actual speed with which a certain ion moves through a given liquid under the action of a given potential gradient or electromotive force.

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  • The phenomena of polarization are thus seen to be due to the changes of surface produced, and are correlated with the differences of potential which exist at any surface of separation between a metal and an electrolyte.

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  • The ions carry their charges with them, and, as a matter of fact, it is found that water in contact with a solution takes with respect to it a positive or negative potential, according as the positive or negative ion travels the faster.

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  • As we have seen above, when a solution is placed in contact with water the water will take a positive or negative potential with regard to the solution, according as the cation or anion has the greater specific velocity, and therefore the greater initial rate of diffusion.

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  • The difference of potential between two solutions of a substance at different concentrations can be calculated from the equations used to give the diffusion constants.

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  • The contact differences of potential at the interfaces of metals and electrolytes have been co-ordinated by Nernst with those at the surfaces of separation between different liquids.

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  • On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself.

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  • Sometimes the metal is deposited in a pulverulent form, at others as a firm tenacious film, the nature of the deposit being dependent upon the particular metal, the concentration of the solution, the difference of potential between the electrodes, and other experimental conditions.

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  • The vats for depositing may be of enamelled iron, slate, glazed earthenware, glass, lead-lined wood, &c. The current densities and potential differences frequently used for some of the commoner metals are given in the following table, taken from M ` Millan's Treatise on Electrometallurgy.

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  • The magnetic potential at any point in a magnetic field is the work which would be done against the magnetic fdrees in bringing a unit pole to that point from the boundary of the field.

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  • The line through the given point along which the potential decreases most rapidly is the direction of the resultant magnetic force, and the rate of decrease of the potential in any direction is equal to the component of the force in that direction.

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  • If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.

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  • The potential due to a single pole of strength m at the distance r from the pole is V = m/ r, (7) the equipotential surfaces being spheres of which the pole is the centre and the lines of force radii.

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  • The potential due to a thin magnet at a point whose distance from the two poles respectively is r and r' is V =m(l/r=l/r') (8) When V is constant, this equation represents an equipotential surface.

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  • The equipotential surfaces are two series of ovoids surrounding the two poles respectively, and separated by a plane at zero potential passing perpendicularly through the middle of the axis.

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  • The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is r, is V=M cos 0/r 2, (io) where 0 is the angle between r and the axis of the magnet.

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  • The potential at any point due to a magnetic shell is the product of its strength into the solid angle w subtended by its edge at the given point, or V = Fu.

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  • For a given strength, therefore, the potential depends solely upon the boundary of the shell, and the potential outside a closed shell is everywhere zero.

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  • The potential due to a uniformly magnetized sphere of radius a for an external point at a distance r from the centre is V =:I ra 3 I cos 0/r 22, (23) 0 being the inclination of r to the magnetic axis.

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  • Forces acting on a Small Body in the Magnetic Field.-If a small magnet of length ds and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are V 1 and the work done upon the magnet, and therefore its potential energy, will be W =m(V2-Vi) =mdV, which may be written W =m d s- = M d v= - MHo = - vIHo, ds ds where M is the moment of the magnet, v the volume, I the magnetization, and Ho the magnetic force along ds.

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  • Suppose the switches to be adjusted so that the effective number of turns in the variable coil is loo; the magnetizing forces in the two coils will then be equal, and if the test rod is of the same quality as the standard, the flow of induction will be confined entirely to the iron circuit, the two yokes will be at the same magnetic potential, and the compass needle will not be affected.

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  • But the application of a magnetic field at right angles to the plane of the metal causes the equipotential lines to rotate through a small angle, and the points at] which the galvanometer is connected being no longer at the same potential, a current is indicated by the galvanometer.'

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  • A transverse difference of electric potential (Hall effect).

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  • electric potential (Nernst effect).

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  • This double cultivation of his scientific powers had the happiest effect on his subsequent work; for the greatest achievements of Riemann were effected by the application in pure mathematics generally of a method (theory of potential) which had up to this time been used solely in the solution of certain problems that arise in mathematical physics.

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  • Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.

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  • Hungary herself was now directly menaced, and the very circumstances which had facilitated the advance of the Turks, enfeebled the potential resistance of the Magyars.

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  • " him," " her," " the man," &c.), ldtok, " I see " (indefinite); the insertion of the causative, frequentative, diminutive and potential syllables after the root of the verb, e.g.

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  • These researches derive additional importance from having introduced two powerful engines of analysis for the treatment of physical problems, Laplace's coefficients and the potential function.

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  • Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light from Clerk Maxwell's interpretation of harmonics with reference to poles on the sphere.

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  • A mass of living protoplasm is simply a molecular machine of great complexity, the total results of the working of which, or its vital phenomena, depend - on the one hand, Life con- of this water is absolutely incompatible with either moister by a ctual or potential life.

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  • 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.

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  • 2wr { a 0, dt2WE+2UC+ dz = o, dw dt - 2un+2v+ dH = 0, where H = fdp/p +V +1q 2, (7) 2 2 +v 2 2 (8) and the three terms in H may be called the pressure head, potential head, and head of velocity, when the gravitation unit is employed and Zq 2 is replaced by 1q 2 1 g.

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  • Calling the sum of the pressure and potential head the statical head, surfaces of constant statical and dynamical head intersect in lines on H, and the three surfaces touch where the velocity is stationary.

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  • Irrotational Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.

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  • In some cases the value of this electromotive force between two points or conductors is independent of the precise path selected, and it is then called the potential difference (P.D.) of the two points or conductors.

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  • We may define the term potential difference otherwise by saying that it is the work done in carrying a small conductor charged with one unit of electricity from one point to the other in a direction opposite to that in which it would move under the electric forces if left to itself.

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  • In the next place we may consider the charged body to be surrounded by a number of closed surfaces, such that the potential difference between any point on one surface and the earth is the same.

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  • These surfaces are called "equipotential" or "level surfaces," and we may so locate them that the potential difference between two adjacent surfaces is one unit of potential; that is, it requires one absolute unit of work (I erg) to move a small body charged with one unit of electricity from one surface to the next.

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  • These enclosing surfaces, therefore, cut up the space into shells of potential, and divide up the tubes of force into electric cells.

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  • We arbitrarily call the potential of the earth zero, since all potential difference is relative and there is no absolute potential any more than absolute level.

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  • We call the difference of potential between a charged conductor and the earth the potential of the conductor.

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  • Hence when a body is charged positively its potential is raised above that of the earth, and when negatively it is lowered beneath that of the earth.

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  • Potential in a certain sense is to electricity as difference of level is to liquids or difference of temperature to heat.

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  • It must be noted, however, that potential is a mere mathematical concept, and has no objective existence like difference of level, nor is it capable per se of producing physical changes in bodies, such as those which are brought about by rise of temperature, apart from any question of difference of temperature.

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  • Electricity tends to flow from places of high to places of low potential, water to flow down hill, and heat to move from places of high to places of low temperature.

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  • Returning to the case of the charged body with the space around it cut up into electric cells by the tubes of force and shells of potential, it is obvious that the number of these cells is represented by the product QV, where Q is the charge and V the potential of the body in electrostatic units.

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  • An electrified conductor is a store of energy, and from the definition of potential it is clear that the work done in increasing the charge q of a conductor whose potential is v by a small amount dq, is vdq, and since this added charge increases in turn the potential, it is easy to prove that the work done in charging a conductor with Q units to a potential V units is z QV units of work.

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  • (i) Electrical Equilibrium and Potential.

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  • For since electricity tends to move between points or conductors at different potentials, if the electricity is at rest on them the potential must be everywhere the same.

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  • Another corollary of the fact that there is no electric force in the interior of a charged conductor is that the potential in the interior is constant and equal to that at the surface.

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  • For by the definition of potential it follows that the electric force in any direction at any point is measured by the space rate of change of potential in that direction or E = + dVldx.

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  • Hence if the force is zero the potential V must be constant.

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  • The potential of a conductor has already been defined as the mechanical work which must be done to bring up a very small body charged with a unit of positive electricity from the earth's surface or other boundary taken as the place of zero potential to the surface of this conductor in question.

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  • The mathematical expression for this potential can in some cases be calculated or predetermined.

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  • It is a fundamental theorem in attractions that a thin spherical shell of matter which attracts according to the potential law of the inverse square acts on all external points as of a if it were concentrated at its centre.

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  • having a charge Q repels a unit charge placed at a distance x from its centre with a force Q/x 2 dynes, and therefore the work W in ergs expended in bringing the unit up to that point from an infinite distance is given by the integral W = Q x 2 dx = Hence the potential at the surface of the sphere, and therefore the potential of the sphere, is Q/R, where R is the radius of the sphere in centimetres.

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  • The quantity of electricity which must be given to the sphere to raise it to unit potential is therefore R electrostatic units.

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  • The capacity of a conductor is defined to be the charge required to raise its potential to unity, all other charged conductors being at an infinite distance.

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  • Since the potential of a small charge of electricity dQ at a distance r is equal to dQ/r, and since the potential of all parts of a conductor is the same in those cases in which the distribution of surface density of electrification is uniform or symmetrical with respect to some point or axis in the conductor, we can calculate the potential by simply summing up terms like rdS/r, where dS is an element of surface, o- the surface density of electricity on it, and r the distance from the symmetrical centre.

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  • The capacity is then obtained as the quotient of the whole charge by this potential.

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  • Accordingly the potential at the centre is Q/R.

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  • But this must be the potential of the Capacity sphere, since all parts are at the same potential V.

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  • Since of a the capacity C is the ratio of charge to potential, the sphere.

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  • 21rry/dx units, and the potential V at a point on the axis at a distance x from the annulus due to this elementary charge is ll2 2?rrc V=2 j o (r2+x2) dx=47rrvj log e (2l+1,/ r2 +412 ') - loge'} If, then, r is small compared with 1, we have V =47rry log e llr.

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  • It must be such a potential distribution that the potential in the interior will be to constant, since the electric force must be zero.

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  • The potential of such a shell at any internal point is constant, and the equi-potential surfaces for external space are ellipsoids confocal with the ellipsoidal shell.

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  • Let a charge +Q be f t the ellipsoid a similar and slightly larger one, that distribution will be in equilibrium and will produce a constant potential throughout the interior.

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  • Hence the density v is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS V f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2) V (x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).

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  • Hence the electric force E in the interspace 1dRccor the potential V at any point in the interspace is given by varies inversely E = as - the distance distance =A/R from or V the - axis.

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  • If then the outer cylinder be at zero potential the potential V of the inner one is V =A log (R 2 /R 1), and its capacity C =1/2 log R2/R1.

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  • The outer larger plate in which the hole is cut is called the " guard plate," and must be kept at the same potential as the smaller inner or " trap-door plate."

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  • Hence the potential V at the centre of the inner sphere is given by V =Q/R1 - Q/R2+Q/R3.

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  • Then when the inner cylinder is at potential V 1 and the outer one kept at of two potential V 2 the lines of electric force between the cylinders Q (4).

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  • In the absolute determination of capacity we have to measure the ratio of the charge of a condenser to its plate potential difference.

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  • If a condenser of capacity C is charged to potential V, and discharged n times per second through a galvanometer, this series of intermittent discharges is equivalent to a current nCV.

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  • Cavendish and subsequently Faraday discovered this fact, and the latter gave the name " specific inductive capacity," or " dielectric constant," to that quality of an insulator which determines the charge taken by a conductor embedded in it when charged to a given potential.

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  • Since then they are all charged with the same quantity of electricity, and the total over all potential difference V is the sum of each of the individual potential differences V1, V2, V3, &c., we have Q=C I V I =C 2 V 2 =C 3 V 3 =&c., and V=V1-FV2+V3+&c. The resultant capacity is C = Q/V, and C= I/(I/C1 +I /C2+1/C3+&c) = I/Z(I /C) (15).

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  • For if C l and C2 are the capacities and Q i and Q2 are the charges after contact, then Qi/CI and Q2/C2 are the potential differences of the coatings and must be equal.

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  • It depends on the principle that if two condensers of capacity C I and C2 are respectively charged to potentials V I and V2, and then joined in parallel with terminals of opposite charge together, the resulting potential difference of the two condensers will be V, such that V = (C,V 2 -CiV2) /(C1+C2) (16); and hence if V is zero we have C I: C2 = V2 The method is carried out by charging the two condensers to be compared at the two sections of a high resistance joining the ends of a battery which is divided into two parts by a movable contact.'

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  • If a charged condenser is suddenly discharged and then insulated, the reappearance of a potential difference between its coatings is analogous to the reappearance of a torque In the case of a glass fibre which has been twisted, released suddenly, and then gripped again at the ends.

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  • It has been shown above that the potential due to a charge of q units placed on a very small sphere, commonly called a point-charge, at any distance x is q/x.

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  • The mathematical importance of this function called the potential is that it is a scalar quantity, and the potential at any point due to any number of point charges ql, q2, q3, &c., distributed in any manner, is the sum of them separately, or qi/xl+q2/x2+q3/x3+&c. =F (q/x) =V (17), where xi, x2, x 3, &c., are the distances of the respective point charges from the point in question at which the total potential is required.

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  • We may describe, through all the points in an electric field which have the same potential, surfaces called equipotential surfaces, and these will be everywhere perpendicular or orthogonal to the lines of electric force.

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  • Let V be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d xl and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx.

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  • It defines the condition which must be fulfilled by the potential at any and every point in an electric field, through which p is finite and the electric force continuous.

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  • An exactly similar expression holds good in hydrokinetics, provided that for the electric potential we substitute velocity potential, and for the electric force the velocity of the liquid.

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  • Since the potential of a conductor is defined to be the work required to move a unit of positive electricity from the surface of the earth or from an infinite distance from all electricity to the surface of the conductor, it follows that the work done in putting a small charge dq into a conductor at a potential v is v dq.

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  • Let us then suppose that a conductor originally at zero potential has its potential raised by administering to it small successive doses of electricity dq.

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  • The first raises its potential to v, the second to v' and so on, and the nth to V.

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  • Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.

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  • 4.4), and hence the work done in charging the conductor with quantity Q to final potential V is zQV, or since Q=CV, where C is its capacity, the work done is represented by 1CV 2 or by 2Q2/C.

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  • We can deduce a remarkable expression for the energy stored up in an electric field containing electrified bodies as follows:' Let V denote the potential at any point in the field.

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  • Hence that distribution of potential which is neces 1 See Maxwell, Electricity and Magnetism, vol.

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  • sary to satisfy Laplace's equation is also one which makes the potential energy a minimum and therefore the energy stable.

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  • 5) a point-charge of positive electricity +q _q/ +q and an infinite conducting plate PO, shown in section, connected to earth and therefore at zero potential.

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  • yet by any means can keep the identical surface occupied by it a plane of zero potential, the boundary conditions will remain the same, and therefore the field of force to the left of PO will remain unaltered.

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  • Then the potential at any point P in this ideal plane PO is equal to q/AP-q/BP=0, whilst the resultant force at P due to the two point charges is 2gAO/AP 3, and is parallel to AB or normal to PO.

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  • So the potential distribution in the space due to the electric point-charge +q as A together with -q at B is the same as that due to +q at A and the negative induced charge erected on the infinite plane (earthed) metal sheet placed half-way between A and B.

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  • If then we put a negative point-charge -qr/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24).

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  • It is then a zero potential surface, and every point outside is at zero potential as far as concerns the electric charge on the conductors inside.

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  • Then if U is the potential outside the surface due to this electric charge inside alone, and V that due to the opposite charge it induces on the inside of the metal surface, we must have U+V =O or U = - V at all points outside the earthed metal surface.

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  • This function is also called the " thermodynamic potential at constant volume " from the analogy with the condition of minimum potential energy as the criterion of stable equilibrium in statics.

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  • The condition of stable equilibrium is that G should be a minimum, for which reason it has been called the " thermodynamic potential at constant pressure."

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  • The simplest application of the thermodynamic potential is to questions of change of state.

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  • Although the value of G in any case cannot be found without that of 0, and although the consideration of the properties of the thermodynamic potential cannot in any case lead to results which are not directly deducible from the two fundamental laws, it affords a convenient method of formal expression in abstract thermodynamics for the condition of equilibrium between different phases, or the criterion of the possibility of a transformation.

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  • G, J, Thermodynamic potential functions.

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  • apart (or more with pure solutions), and are on the multiple system, and the potential difference at the terminals of the bath is I volt.

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  • Such a riper analysis of the mystery of his own personality enabled him to arrive at a clearer conception of the idea of divine personality, " whose triunity has nothing potential or unrealized about it; whose triune elements are eternally actualized, by no outward influence, but from within; a Trinity in Unity."

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  • Though the cavalry were freely engaged, the training of both was so far beneath the standard of the present day that the most that can be credited to them in respect of results is that they from time to time averted imminent disaster, but failed altogether to achieve such a decision as was well within their potential capacities.

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  • Besides this the atom is endowed with potential force, that is to say, that any two atoms attract or repel each other with a force depending on their distance apart.

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  • originally impinged on that at rest is now represented by the energy, kinetic and potential, of the small motions of the individual molecules.

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  • In terms of the molecular theory this indicates that the total energy of the gas is the sum of the separate energies of its different molecules: the potential energy arising from intermolecular forces between pairs of molecules may be treated as negligible when the matter is in the gaseous state.

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  • Now if the atoms are regarded as points or spherical bodies oscillating about positions of equilibrium, the value of n+3 is precisely six, for we can express the energy of the atom in the form (9 2 v a 2 v a2v E = z(mu 2 +mv 2 +mw 2 +x 2 ax2 + y2ay2-fz2az2), where V is the potential and x, y, z are the displacements of the atom referred to a certain set of orthogonal axes.

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  • These two quadrants are interconnected by the high resistance to be measured, and, therefore, themselves differ in potential.

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  • The exact position taken up by the needle is therefore determined by the potential difference (P.D.) of the quadrants and the P.D.

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  • Thus man's spirit, ever largely but potential, can respond actively to the historic Jesus, because already touched and made hungry by the all-actual Spirit-God who made that soul akin unto Himself.

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  • We shall show that if we sum these up for a whole wave the potential energy is equal to the kinetic energy.

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  • During the quarter swing ending with greatest nodal pressure, the kinetic energy is changed to potential energy manifested in the increase of pressure.

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  • This becomes again kinetic in the second quarter swing, then in the third quarter it is changed to potential energy again, but now manifested in the decrease of pressure.

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  • The pressure is further increased and the potential energy is also increased.

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  • But if the heat is given at the instant of greatest rarefaction, the increase of pressure lessens the difference from the undisturbed pressure, and lessens the potential energy, so that during the return less kinetic energy is formed and the vibration tends to die away.

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  • In his Nobel address he said: "In any community of any size the authority of the courts rests upon actual potential force; on the existence of a police or on the knowledge that the able-bodied men of the country are both ready and willing to see that the decrees of judicial and legislative bodies are put into effect;" and he expressed the opinion that until a recognized international supreme court was firmly established, every nation must be prepared to defend itself, and when it was established all the nations must be prepared to maintain its decrees against any recalcitrant nation.

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  • Sovereignty is also used in a wider sense, as the equivalent of the power, actual or potential, of the whole nation or society (Gierke, 3.568).

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  • Its principle is as follows: Suppose there are two pendulum clocks, one having an ordinary pendulum and the other having a pendulum consisting of a fine coil of wire through which a current is passed proportional to the potential difference of the supply mains - in other words, a shunt current.

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  • The current in the shunt coil lags 90 degrees behind the impressed electromotive force of the circuit to be measured; hence if the main current is in step with the potential difference of the terminals of the supply mains, which is the case when the supply is given wholly to electric lamps, then the field due to the main coil differs from that due to the shunt coil by 90 degrees.

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  • If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving finite velocity of matter.

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  • In this memoir also the function which is now called the potential was, at the suggestion of Laplace, first introduced.

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  • POTENTIOMETER, an instrument for the measurement of electromotive force and also of difference of electric potential between two points.

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  • The term potentiometer is usually applied to an instrument for the measurement of steady or continuous potential difference between two points in terms of the potential difference of the terminals of a standard voltaic cell of some kind, such as a Clark or Weston cell.

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  • In principle the modern potentiometer consists of an arrangement by means of which any potential difference not exceeding a certain assigned value can be compared with that of a standard cell having a known electromotive force.

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  • We then know that the fall of potential down the 2000 divisions of the fine wire must be exactly 2 volts.

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  • The scale reading then indicates directly the electromotive force of this second source of potential.

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  • Instead of adjusting in this manner the electromotive force of any form of cell, if we pass any constant current through a known resistance and bring wires from the extremities of that resistance into connexion with the slider and the galvanometer terminal, we can in the same way determine the fall of potential down the above resistance in terms of the electromotive force of the standard cell and thus measure the current flowing through the standard resistance.

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  • By such an arrangement the potential difference can be measured of any amount from o to 1.5 volts.

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  • We may employ such a potentiometer to measure large potential difference greater than the electromotive force of the working battery, as follows: The two points between which the potential difference is required are connected by high resistance, say of 100,000 ohms or more, and from the extremities of a known fraction of this resistance, say, 'Roo or I/1000 or I/Io,000 wires are brought to the potentiometer and connected in between the slider and the corresponding galvanometer terminal.

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  • We can thus measure as described the drop in volts down a known fraction of the whole high resistance and therefore calculate the fall in potential down the whole of the high resistance, which is the potential difference required.

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  • The potentiometer and the divided resistance constitute a sort of electrical scaleyard by means of which any electromotive force or difference of potential can be compared with the electromotive force of a standard cell.

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  • In practical work, the low resistances take the form of certain strips of metal which have on them two pairs of terminals, one termed " current terminals," and the other " potential terminals."

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  • These resistance strips, as they are called, are carefully adjusted so that the resistance between the potential terminals has a known low value.

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  • From the potential terminals of the strip, wires are brought to the potentiometer so as to determine their potential difference in terms of the electromotive force of the standard Clark cell.

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  • Supposing that the potential fall down the strip is found to be.

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  • In electrical measurements connected with incandescent electric lamps the potentiometer is of great use, as it enables us to make accurately and nearly simultaneously two measurements, one of the current through the lamp and the other of the potential difference of the terminals.

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  • For this purpose a resistance, say, of one ohm is placed in series with the lamp and a resistance of 100,000 ohms placed across the terminals of the lamp; the latter resistance is divided into two parts, one consisting of loon ohms and the other of 99,000 ohms. The potentiometer enables us to measure therefore the current through the lamp by measuring the drop in volts down a resistance in series with it and the potential difference of the terminals of the lamp by measuring the drop in volts down the tooth part of the high resistance of 100,000 ohms connected across the terminals of the lamp.

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  • The fixed coil is called the current coil, and the movable coil is called the potential coil, and each of these coils has its ends brought to separate terminals on the base of the instrument.

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  • The principle on which the instrument works is as follows: Suppose any circuit, such as an electric motor, lamp or transformer, is receiving electric current; then the power given to that circuit reckoned in watts is measured by the product of the current flowing through the circuit in amperes and the potential difference of the ends of that circuit in volts, multiplied by a certain factor called the power factor in those cases in which the circuit is inductive and the current alternating.

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  • The torque required to hold the coils in their normal position is proportional to the mean value of the product of the currents flowing through two coils respectively, or to the mean value of the product of the current in the power-absorbing circuit and the potential difference at its ends, that is, to the power taken up by the circuit.

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  • Sumpner in 1891, an electrostatic voltmeter is employed to measure the fall of potential V 1 down any inductive circuit in which it is desired to measure the power absorption, and also the volt-drop V2 down an inductionless resistance R in series with it, and also the volt-drop V3 down the two together.

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  • Soc. (1891), 49, 424; Id., "Alternate Current and Potential Difference Analogies in the Method of Measuring Power," Phil.

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