Force Sentence Examples

The sun was trying to force its way through the curtains.

I wouldn.t force a human to do anything.

What mysterious force guided the seedling from the dark earth up to the light, through leaf and stem and bud, to glorious fulfilment in the perfect flower?

There is a band of thieves in our district who ought to be arrested by a strong force--October 11.

He doesn't force me to do what he wants.

He pulled back, having to exert considerable force against her surprising strength.

He.d serve on the Council and force it to stay together.

She was going to have to force it.

Only the deities can force another deity to resign.

If any part of you cared about him, you'd want him to be happy, not force him to love you!

She acts like you should spank her and force her admit to doing something she considers really bad.

Public opinion is a powerful force, and if it is generally a force for peace, then the web magnifies it.

So we're in force, it seems....

Of all the coddling he'd accused Sofi and Bianca of doing, he'd been working hard to protect Darian from anything that might force him to grow into his powers.

And this is a force for peace.

What force made men act so?

Darkyn didn't appear to force her to return.

And truth is a force for peace.

What force moves the nations?

They'd been right to use force over reason with the Council, a lesson he'd learned almost too late.

Dean said, trying to force a tone of normalcy into his strained voice.

This force was hemmed in by the enemy.

We have a police force and a court system to apply the laws equally to all.

I shall not attempt to conquer her by force alone; but I shall insist on reasonable obedience from the start.

To get her to do the simplest thing, such as combing her hair or washing her hands or buttoning her boots, it was necessary to use force, and, of course, a distressing scene followed.

What force has a multitude?

Apparently she had forgotten her age and by force of habit employed all the old feminine arts.

Exploding at the word intriguer, Nicholas, raising his voice, told his mother he had never expected her to try to force him to sell his feelings, but if that were so, he would say for the last time....

This city was evidently living with the full force of its own life.

But dazed by the force of the movement, it was long before people understood this.

The feel of the planet's life force through his body was staggering, the sensation similar to what he felt the first time he'd met his nishani.

Order was maintained by a mounted native police force.

First, the web promotes access to information, a huge force for peace.

Enabling people to communicate in a method with which their governments cannot interfere is a force for freedom and peace.

The recognition of man's free will as something capable of influencing historical events, that is, as not subject to laws, is the same for history as the recognition of a free force moving the heavenly bodies would be for astronomy.

Had he brought her all the way out here to force himself on her?

Our work concerns electrostatic forces; force fields that surround us everywhere.

I tried to force from my memory the mayhem and violence Grasso had wrought across the country.

Two had helped force feed him, before he knew kiri loved him.

Deidre had never seen him like this, as a quietly commanding figure, capable of lethal force one moment and gentle kisses the next.

His powers were back in full force, without her to steady his control.

Perhaps it will give Edith enough time to go to the authorities and force him to stay away.

Josh hit the floor with enough force to take the breath out of the average man.

Don't let him force you into a decision you're not ready to make.

During the war of 1812 a British force occupied Bangor for several days (in September 1814), destroying vessels and cargoes.

In March 1650 Montrose landed in the Orkneys to take the command of a small force which he had sent on before him.

No unnecessary force is permitted, and no stoppage must occur during the operation.

Induction is an effect of the field of force associated with a magnet.

The moment of a small magnet may be resolved like a force.

When the saturation value of I has been reached, the relation of magnetic induction to magnetic force may be expressed by B = H +constant.

The provincial force consists of a militia, fully equipped and armed with modern weapons.

There is also an armed and mounted police force of 870 Europeans.

In fact, they were a police force as well as an army.

On 1st January 1900 a new criminal code, thoroughly modern in spirit, was put in force; and in 1901 a Civil Code Bill, to replace the old Hungarian customary system, was introduced.

By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single function, Laplace laid the foundations of the mathematical sciences of heat, electricity and magnetism.

It was held by a British force for five days in September 1814.

Kruger's force called itself the Staatsleger or Army of the State.

In 1807 an unsuccessful attack was made upon the city by an English force.

The hill was frequently occupied in attacks on Syracuse by the besieging force.

After an arduous campaign, the Natal force (about 5000 strong) being commanded by Col.

A military force entered Zululand, and Dinizulu surrendered without opposition.

Two of these (UBI, L B 15) were attached to the Austrian submarine force.

A British force was stationed at Bamian beyond it in 1840, with an outpost at Saighan.

The struggle, however, soon revived with increased force.

We no longer force prisoners to kill each other for our amusement.

No such system of laws controls relations among nations, no significant world police force exists, and the world court system is very weak.

But at the time the doctrine was in force, MAD was effective (or at least, not proven ineffective).

However, if it were stigmatized, and public opinion dramatically and pervasively changed, that would force policy change.

Some might argue this is not in and of itself a force for peace.

Very seldom is that, "I should go to war to force others to my will."

The web is a force for truth, connectedness, understanding, and communication—all things whose absence can trigger war.

Sure, it isn't as big a force as Democratic Peace Theory or Mutually Assured Poverty.

Still I could not shut my eyes to the force and weight of their arguments, and I saw plainly that I must abandon--'s scheme as impracticable.

Although I try very hard not to force issues, I find it very difficult to avoid them.

Helen resisted, and Viney tried to force it out of her hand, and I suspect that she slapped the child, or did something which caused this unusual outburst of temper.

Also, as we are masters of Ulm, we cannot be deprived of the advantage of commanding both sides of the Danube, so that should the enemy not cross the Lech, we can cross the Danube, throw ourselves on his line of communications, recross the river lower down, and frustrate his intention should he try to direct his whole force against our faithful ally.

General Buxhowden was all but attacked and captured by a superior enemy force as a result of one of these maneuvers that enabled us to escape him.

To favor revolutions, overthrow everything, repel force by force?...

Once, when in a room with a lamp dimly lit before the icon Theodosia was talking of her life, the thought that Theodosia alone had found the true path of life suddenly came to Princess Mary with such force that she resolved to become a pilgrim herself.

The whole expression of his face told her that he had not forgotten the morning's talk, that his decision remained in force, and only the presence of visitors hindered his speaking of it to her now.

If I don't sleep for three nights I'll not leave this passage and will hold her back by force and will and not let the family be disgraced, thought she.

No one was or is able to foresee in what condition our or the enemy's armies will be in a day's time, and no one can gauge the force of this or that detachment.

He said the peasants were obdurate and that at the present moment it would be imprudent to "overresist" them without an armed force, and would it not be better first to send for the military?

The moral force of the attacking French army was exhausted.

But though I do not know what causes the cold winds to blow when the oak buds unfold, I cannot agree with the peasants that the unfolding of the oak buds is the cause of the cold wind, for the force of the wind is beyond the influence of the buds.

But the face remained before him with the force of reality and drew nearer.

In the corporal's changed face, in the sound of his voice, in the stirring and deafening noise of the drums, he recognized that mysterious, callous force which compelled people against their will to kill their fellow men--that force the effect of which he had witnessed during the executions.

To fear or to try to escape that force, to address entreaties or exhortations to those who served as its tools, was useless.

Pierre felt that that fatal force which had crushed him during the executions, but which he had not felt during his imprisonment, now again controlled his existence.

It was terrible, but he felt that in proportion to the efforts of that fatal force to crush him, there grew and strengthened in his soul a power of life independent of it.

Each of them desired nothing more than to give himself up as a prisoner to escape from all this horror and misery; but on the one hand the force of this common attraction to Smolensk, their goal, drew each of them in the same direction; on the other hand an army corps could not surrender to a company, and though the French availed themselves of every convenient opportunity to detach themselves and to surrender on the slightest decent pretext, such pretexts did not always occur.

I see a force producing effects beyond the scope of ordinary human agencies; I do not understand why this occurs and I talk of genius.

But she had to force herself to attend, for what he was saying did not interest her at all.

History seems to assume that this force is self-evident and known to everyone.

Biographical historians and historians of separate nations understand this force as a power inherent in heroes and rulers.

The answers given by this kind of historian to the question of what force causes events to happen are satisfactory only as long as there is but one historian to each event.

As soon as historians of different nationalities and tendencies begin to describe the same event, the replies they give immediately lose all meaning, for this force is understood by them all not only differently but often in quite contradictory ways.

According to this view the power of historical personages, represented as the product of many forces, can no longer, it would seem, be regarded as a force that itself produces events.

To find component forces equal to the composite or resultant force, the sum of the components must equal the resultant.

This condition is never observed by the universal historians, and so to explain the resultant forces they are obliged to admit, in addition to the insufficient components, another unexplained force affecting the resultant action.

A third class of historians--the so-called historians of culture-- following the path laid down by the universal historians who sometimes accept writers and ladies as forces producing events--again take that force to be something quite different.

The only conception that can explain the movement of the locomotive is that of a force commensurate with the movement observed.

The only conception that can explain the movement of the peoples is that of some force commensurate with the whole movement of the peoples.

But in that case, if the force that moves nations lies not in the historic leaders but in the nations themselves, what significance have those leaders?

Vital force is only an expression for the unknown remainder over and above what we know of the essence of life.

She pushed his chin aside with more force and kissed his neck before closing her eyes and letting her fangs sink into him.

He said it but he couldn't force the appropriate accompanying tone to sound enthusiastic.

She raced forward through the men, not caring what they thought, and flung herself into Mansr's arms with enough force to drive him back a step.

The logarithmic formulae for these concentration cells indicate that theoretically their electromotive force can be increased to any extent by diminishing without limit the concentration of the more dilute solution, log c i /c 2 then becoming very great.

Now a force under Sir Duncan McKenzie entered Zululand.

On the 1st of August 1907 the Belgian minister in London transmitted to Sir Edward Grey a draft, additional act prepared by the commission for carrying out the proposal of His Britannic Majesty's government, and on the 28th of August following an additional act was signed at Brussels by the plenipotentiaries of the contracting parties, by which they undertook to maintain the convention of the 5th of March 1902 in force for a fresh period of five years.

If he failed in his wider schemes of reform, this was only one more illustration of a truth of which other " enlightened " sovereigns besides himself had experienced the force, namely, that it is impossible to impose any system, however admirable, from above on a people whose deepest convictions and prejudices it offends.

As in the last days of the Roman empire the poor landowner had found his only refuge from the exactions of the government in the protection of the senator, who could in some way obtain exemptions, so the poor Frank could escape the ruinous demands of military service only by submitting himself and his lands to the count, who did not hesitate on his side to force such submission.

He explained how an army, ninety thousand strong, was to threaten Prussia so as to bring her out of her neutrality and draw her into the war; how part of that army was to join some Swedish forces at Stralsund; how two hundred and twenty thousand Austrians, with a hundred thousand Russians, were to operate in Italy and on the Rhine; how fifty thousand Russians and as many English were to land at Naples, and how a total force of five hundred thousand men was to attack the French from different sides.

The spy reported that the French, after crossing the bridge at Vienna, were advancing in immense force upon Kutuzov's line of communication with the troops that were arriving from Russia.

Part of the Russian force had already descended into the valley toward the ponds and lakes and part were leaving these Pratzen Heights which he intended to attack and regarded as the key to the position.

Thoughts of home grew stronger the nearer he approached it--far stronger, as though this feeling of his was subject to the law by which the force of attraction is in inverse proportion to the square of the distance.

Her throat quivered with convulsive sobs and, afraid of weakening and letting the force of her anger run to waste, she turned and rushed headlong up the stairs.

But he also knew (or rather felt at the bottom of his heart) that by resigning himself now to the force of circumstances and to those who were guiding him, he was not only doing nothing wrong, but was doing something very important--more important than anything he had ever done in his life.

He knew he was in these men's power, that only by force had they brought him there, that force alone gave them the right to demand answers to their questions, and that the sole object of that assembly was to inculpate him.

So the historians of this class, by mutually destroying one another's positions, destroy the understanding of the force which produces events, and furnish no reply to history's essential question.

In their exposition, an historic character is first the product of his time, and his power only the resultant of various forces, and then his power is itself a force producing events.

Man's free will differs from every other force in that man is directly conscious of it, but in the eyes of reason it in no way differs from any other force.

And as the undefinable essence of the force moving the heavenly bodies, the undefinable essence of the forces of heat and electricity, or of chemical affinity, or of the vital force, forms the content of astronomy, physics, chemistry, botany, zoology, and so on, just in the same way does the force of free will form the content of history.

But just as the subject of every science is the manifestation of this unknown essence of life while that essence itself can only be the subject of metaphysics, even the manifestation of the force of free will in human beings in space, in time, and in dependence on cause forms the subject of history, while free will itself is the subject of metaphysics.

Under the influence of an applied electric force, he imagined that the B part of the first molecule was liberated at the anode, and that the A part thus isolated united with the B part of the second molecule, which, in its turn, passed on its A to the B of the third molecule.

The conductivity gives us the amount of electricity conveyed per second under a definite electromotive force.

The concentration is known, and the conductivity can be measured experimentally; thus the average velocity with which the ions move past each other under the existent electromotive force can be estimated.

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.

Clausius extended to electrolysis the chemical ideas which looked on the opposite parts of the molecule as always changing partners independently of any electric force, and regarded the function of the current as merely directive.

In accordance with the principles of energetics, any change which involves a decrease in the total available energy of the system will tend to occur, and thus the necessary and sufficient condition for the production of electromotive force is that the available energy of the system should decrease when the current flows.

In order that the current should be maintained, and the electromotive force of the cell remain constant during action, it is necessary to ensure that the changes in the cell, chemical or other, which produce the current, should neither destroy the difference between the electrodes, nor coat either electrode with a non-conducting layer through which the current cannot pass.

Let an electromotive force exactly equal to that of the cell be applied to it in the reverse direction.

When the applied electromotive force is diminished by an infinitesimal amount, the cell produces a current in the usual direction, and the ordinary chemical changes occur.

If the external electromotive force exceed that of the cell by ever so little, a current flows in the opposite direction, and all the former chemical changes are reversed, copper dissolving from the copper plate, while zinc is deposited on the zinc plate.

The cell, together with this balancing electromotive force, is thus a reversible system in true equilibrium, and the thermodynamical reasoning applicable to such systems can be used to examine its properties.

During a small electric transfer through the cell, the external work done is Ee, where E is the electromotive force.

It will be noticed that when dE/dT is zero, that is, when the electromotive force of the cell does not change with temperature.

The earliest formulation of the subject, due to Lord Kelvin, assumed that this relation was true in all cases, and, calculated in this way, the electromotive force of Daniell's cell, which happens to possess a very small temperature coefficient, was found to agree with observation.

For cells in which the electromotive force varies with temperature, the full equation given by Gibbs and Helmholtz has also been confirmed experimentally.

As stated above, an electromotive force is set up whenever there is a difference of any kind at two electrodes immersed in electrolytes.

In ordinary cells the difference is secured by using two dissimilar metals, but an electromotive force exists if two plates of the same metal are placed in solutions of different substances, or of the same substance at different concentrations.

An electromotive force is therefore set up in this direction, and, if we can calculate the change in available energy due to the processes of the cell, we can foretell the value of the electromotive force.

Nernst, to whom this theory is due, determined the electromotive force of this cell experimentally, and found the value 0.055 volt.

The result is that a high electromotive force is set up, which has been calculated as o.

It is now evident that the electromotive force of an ordinary chemical cell such as that of Daniell depends on the concentration of the solutions as well as on the nature of the metals.

In ordinary cases possible changes in the concentrations only affect the electromotive force by a few parts in a hundred, but, by means such as those indicated above, it is possible to produce such immense differences in the concentrations that the electromotive force of the cell is not only changed appreciably but even reversed in direction.

Once more we see that it is the total impending change in the available energy of the system which controls the electromotive force.

The effective electromotive force of the common lead accumulator is less than that required to charge it.

This drop in the electromotive force has led to the belief that the cell is not reversible.

If, instead of using a single Daniell's cell, we employ some source of electromotive force which can be varied as we please, and gradually raise its intensity, we shall find that, when it exceeds a certain value, about 1.7 volt, a permanent current of considerable strength flows through the solution, and, after the initial period, shows no signs of decrease.

These phenomena are explained by the existence of a reverse electromotive force at the surface of the platinum plates.

Only when the applied electromotive force exceeds this reverse force of polarization, will a permanent steady current pass through the liquid, and visible chemical decomposition proceed.

It seems that this reverse electromotive force of polarization is due to the deposit on the electrodes of minute quantities of the products of chemical decomposition.

Differences between the two electrodes are thus set up, and, as we have seen above, an electromotive force will therefore exist between them.

To pass a steady current in the direction opposite to this electromotive force of polarization, the applied electromotive force E must exceed that of polarization E', and the excess E - E' is the effective electromotive force of the circuit, the current being, in accordance with Ohm's law, proportional to the applied electromotive force and represented by (E - E')/ R, where R is a constant called the resistance of the circuit.

The opposing force of polarization is about 1.7 volt, but, when the plates are disconnected and used as a source of current, the electromotive force they give is only about 1.07 volt.

If secondary effects are eliminated, the deposition of metals also is a reversible process; the decomposition voltage is equal to the electromotive force which the metal itself gives when going into solution.

Since zinc goes into solution and copper comes out, the electromotive force of the cell will be the difference between the two effects.

By both these methods the single potential-differences found at the surfaces of the zinc and copper have opposite signs, and the effective electromotive force of a Daniell's cell is the sum of the two effects.

There must, then, be a relation between the rate of change of the concentration and the osmotic pressure gradient, and thus we may consider the osmotic pressure gradient as a force driving the solute through a viscous medium.

This process will go on until the simultaneous separation of electric charges produces an electrostatic force strong enough to prevent further separation of ions.

The living force of development in the Latin Church was symbolized in her garments; the stereotyped orthodoxy of the Greek Church in hers.

In 1303 it withstood for twenty days a siege in force by the English under Edward I., surrendering only when its governor, Sir Thomas Maule, had been slain.

His subjects at length grew weary of the heavy expense of maintaining a large military force on the Belgian frontier and in 1839 the king gave way.

On the 29th of September a Greek naval force, commanded by an English Philhellene, Captain Frank Abney Hastings, had destroyed some Turkish vessels in Salona Bay, on the north side of the Gulf of Corinth.

By general agreement among the powers the command was entrusted to Codrington, and the allied force consisted of three British, four French and four Russian sail of the line, if the French admiral's flagship the "Sirene" (60), which was technically "a double banked frigate," be included.

The almost uninterrupted series of victories of the Hussites now rendered vain all hope of subduing them by force of arms. Moreover, the conspicuously democratic character of the Hussite movement caused the German princes, who were afraid that such views might extend to their own countries, to desire peace.

On the other hand, it is not too much to say that, from the end of 1759 to the end of 1761, the unshakable firmness of the Russian empress was the one constraining political force which held together the heterogeneous, incessantly jarring elements of the anti-Prussian combination.

King Stanislaus was at first inclined to mediate between the confederates and Russia; but finding this impossible, sent a force against them under the grand hetmen Ksawery Branicki and two generals, who captured Bar.

It must be remembered, however, that variations in conditions modify the electromotive force required for any given process.

This solution, being an inferior conductor of electricity, requires a much higher electromotive force to drive the current through it, and is therefore more costly in use.

As a war-goddess, she is the embodiment of prudent and intelligent tactics, entirely different from Ares, the personification of brute force and rashness, who is fitly represented as suffering defeat at her hands.

Ulm is the basis of operations for the German army behind the Black Forest, and can easily shelter a force of ioo,000 men; its peace garrison is 5600.

When the struggle between the colonies and the mother country began, although he felt much sympathy for the former, his opposition to any form of obstruction to the Stamp Act and other measures, and his denunciation of a resort to force created a breach between him and his parish, and in a fiery farewell discourse preached after the opening of hostilities he declared that no power on earth should prevent him from praying and shouting "God save the King."

The regions of greatest attraction have received the name of poles, and the line joining them is called the axis of the magnet; the space around a magnet in which magnetic effects are exhibited is called the field of magnetic force, or the magnetic field.

It follows that between two neighbouring magnets, the poles of which are regarded as centres of force, there must always be four forces in action.

Hence it is not very easy to determine experimentally the law of magnetic force between poles.

Coulomb, who by using very long and thin magnets, so arranged that the action of their distant poles was negligible, succeeded in establishing the law, which has since been confirmed by more accurate methods, that the force of attraction or repulsion exerted between two magnetic poles varies inversely as the square of the distance between them.

Other conditions remaining unchanged, the force between two poles is proportional to the product of their strengths; it is repulsive or attractive according as the signs of the poles are like or unlike.

Magnetic force has not merely the property of acting upon magnetic poles, it has the additional property of producing a phenomenon known as magnetic induction, or magnetic flux, a physical condition which is of the nature of a flow continuously circulating through the magnet and the space outside it.

Outside the magnet the direction of the magnetic induction is generally the same as that of the magnetic force.

A map indicating the direction of the force in different parts of the field due to a magnet may be constructed in a very simple manner.

A line of force may be defined as an imaginary line so drawn that its direction at every point of its course coincides with the direction of the magnetic force at that point.

Through any point in the field one such line can be drawn, but not more than one, for the force obviously cannot have more than one direction; the lines therefore never intersect.

A line of force is regarded as proceeding from the north pole towards the south pole of the magnet, its direction being that in which an isolated north pole would be urged along FIG.

A south pole would be urged oppositely to the conventional " direction " of the line; hence it follows that a very small magnetic needle, if placed in the field, would tend to set itself along or tangentially to the line of force passing through its centre, as may be approximately verified if the compass be placed among the filings on the cardboard.

In the internal field of a long coil of wire carrying an electric current, the lines of force are, except near the ends, parallel to the axis of the coil, and it is chiefly for this reason that the field due to a coil is particularly well adapted for inductively magnetizing iron and steel.

Where the lines are crowded together, as in the neighbourhood of the poles, the force is greater (or the field is stronger) than where they are more widely separated; hence the strength of a field at any point can be accurately specified by reference to the concentration of the lines.

It is however easy to demonstrate by means of the compass that the force is much greater in some parts of the field than in others.

When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square root of the magnetic force at the spot.

If the inductively magnetized body lies in a part of the field which happens to be uniform there will be no resulting force tending to move the body, and it will not be " attracted."

If however there is a small variation of the force in the space occupied by the body, it can be shown that the body will be urged, not necessarily towards a magnetic pole, but towards places of stronger magnetic force.

It will not in general move along a line of force, as would an isolated pole, but will follow the direction in which the magnetic force increases most rapidly, and in so doing it may cross the lines of force obliquely or even at right angles.

It is by the horizontal component of the earth's total force that the compass-needle is directed.

Let a magnetic pole be drawn several times around a uniform steel ring, so that every part of the ring may be successively subjected to the magnetic force.

The process of magnetization consists in turning round the molecules by the application of magnetic force, so that their north poles may all point more or less approximately in the direction of the force; thus the body as a whole becomes a magnet which is merely the resultant of an immense number of molecular magnets.

In every magnet the strength of the south pole is exactly equal to that of the north pole, the action of the same magnetic force upon the two poles being equal and oppositely directed.

This may be shown by means of the uniform field of force due to the earth's magnetism.

A unit magnetic pole is that which acts on an equal pole at a distance of one centimetre with a force of one dyne.

If m, and m 2 are the strengths of two poles, d the distance between them expressed in centimetres, and f the force in dynes, f=ml m2/d2 (I) The force is one of attraction or repulsion, according as the sign of the product m l m 2 is negative or positive.

The poles at the ends of an infinitely thin uniform magnet, or magnetic filament, would act as definite centres of force.

Any space at every point of which there is a finite magnetic force is called a field of magnetic force, or a magnetic field.

The strength or intensity of a magnetic field at any point is measured by the force in dynes which a unit pole will experience when placed at that point, the direction of the field being the direction in which a positive pole is urged.

A line of force is a line drawn through a magnetic field in the direction of the force at each point through which it passes.

A uniform magnetic field is one in which H has everywhere the same value and the same direction, the lines of force being, therefore, straight and parallel.

The field at the centre of a circular conductor of radius r through which current is passing is H = 27ri/r, (3) the direction of the force being along the axis and related to the direction of the current as the thrust of a corkscrew to its rotation.

The direction of the force is parallel to the axis of the coil, and related to the direction of the current as the thrust of a corkscrew to its rotation.

The direction of the magnetization is that of the magnetic axis of the element;'in isotropic substances it coincides with the direction of the magnetic force at the point.

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.

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.

The resultant magnetic force at every point of such a surface is in the direction of the normal (n) to the surface; every line of force therefore cuts the equipotential surfaces at right angles.

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.

If r and r' make angles 0 and 0 with the axis, it is easily shown that the equation to a line of force is cos 0 - cos B'= constant.

If F T is the force along r and F t that along t at right angles to r, F r =X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = - r 3 sin 0.

If a small magnet of moment M is placed in the sensibly uniform field H due to a distant magnet, the couple tending to turn the small magnet upon an axis at right angles to the magnet and to the force is MH sin 0, (17) where 0 is the angle between the axis of the magnet and the direction of the force.

Since 7ra'I is the moment of the sphere (=volume X magnetization), it appears from (10) that the magnetized sphere produces the same external effect as a very small magnet of equal moment placed at its centre and magnetized in the same direction; the resultant force therefore is the same as in (14).

The internal force F is opposite to the direction of the magnetization, and equal to NI, where N is a coefficient depending only on the ratio of the axes.

Magnetic induction, like other fluxes such as electrical, thermal or fluid currents, is defined with reference to an area; it satisfies the same conditions of continuity as the electric current does, and in isotropic media it depends on the magnetic force just as the electric current depends on the electromotive force.

In the case of a straight uniformly magnetized bar the direction of the magnetic force due to the poles of the magnet is from the north to the south pole outside the magnet, and from the south to the north inside.

Lines of induction are frequently but inaccurately spoken of as lines of force.

Magnetization is usually regarded as the direct effect of the resultant magnetic force, which is therefore often termed the magnetizing force.

The magnetic susceptibility expresses the numerical relation of the magnetization to the magnetizing force.

The total magnetic induction or flux corresponds to the current of electricity (practically measured in amperes); the induction or flux density B to the density of the current (number of amperes to the square centimetre of section); the magnetic permeability to the specific electric conductivity; and the line integral of the magnetic force, sometimes called the magnetomotive force, to the electro-motive force in the circuit.

Steel, which is well suited for the construction of permanent magnets, is said to possess great " coercive force."

The coercive force, or coercivity, of a material is that reversed magnetic force which, while it is acting, just suffices to reduce the residual induction to nothing after the material has been temporarily submitted to any great magnetizing force.

A metal which has great retentiveness may at the same time have small coercive force, and it is the latter quality which is of chief importance in permanent magnets.

Demagnetizing Force.-It has already been mentioned that when a ferromagnetic body is placed in a magnetic field, the resultant magnetic force H, at a point within the body, is compounded of the force H o, due to the external field, and of another force, Hi, arising from the induced magnetization of the body.

Since H, generally tends to oppose the external force, thus making H less than H o, it may be called the demagnetizing force.

Except in the few special cases when a uniform external field produces uniform magnetization, the value of the demagnetizing force cannot be calculated, and an exact determination of the actual magnetic force within the body is therefore impossible.

An important instance in which the calculation can be made is that of an elongated ellipsoid of revolution placed in a uniform field H o, with its axis of revolution parallel to the lines of force.

Since I =KH, we have KH I-KNI =KHo, (30) or H =Ho-NI, NI being the demagnetizing force H i.

Equations (33) and (34) show that when, as is generally the case with ferromagnetic substances, the value of is considerable, the resultant magnetic force is only a small fraction of the external force, while the numerical value of the induction is approximately three times that of the external force, and nearly independent of the permeability.

The demagnetizing force inside a cylindrical rod placed longitudinally in a uniform field Ho is not uniform, being greatest at the ends and least in the middle part.

Hence the difficulty of imparting any considerable permanent magnetization to a short thick bar not possessed of great coercive force.

The magnetization retained by a long thin rod, even when its coercive force is small, is sometimes little less than that which was produced by the direct action of the field.

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.

It can be shown 3 that in a uniform field an elongated piece of any non-crystalline material is in stable equilibrium only when its length is parallel to the lines of force; for diamagnetic substances, however, the directing couple is exceedingly small, and it would hardly be possible to obtain a uniform field of sufficient strength to show the effect experimentally.

At a point whose distance from the axis of the wire is r the tangential magnetic force is H = 21r /a 2 (39) it therefore varies directly as the distance from the axis, where it is zero.'

If the wire consists of a ferromagnetic metal, it will become " circularly magnetized by the field, the lines of magnetization being, like the lines of force, concentric circles.

The action of a hollow magnetized shell on a point inside it is always opposed to that of the external magnetizing force, 6 the resultant interior field being therefore weaker than the field outside.

If a hollow sphere 7 of which the outer radius is R and the inner radius r is placed in a uniform field Ho, the field inside will also be uniform and in the same direction as Ho, and its value will be approximately 3 i - R 3 For a cylinder placed with its axis at right angles to the lines of force, 2 = Ho (41) 2 +4(-2)(i - R2) These expressions show that the thicker the screen and the greater its permeability o, the more effectual will be the shielding action.

In anisotropic bodies, such as crystals, the direction of the magnetization does not in general coincide with that of the magnetic force.

There are, however, always three principal axes at right angles to one another along which the magnetization and the force have the same direction.

If each of these axes successively is placed parallel to the lines of force in a uniform field H, we shall have = 12 = 13=K3H, the three susceptibilities being in general unequal, though in some cases two of them may have the same value.

The body (or each element of it) will tend to set itself with its axis of greatest susceptibility parallel to the lines of force, while, if the field is not uniform, each volume-element will also tend to move towards places of greater or smaller force (according as the substance is paramagnetic or diamagnetic), the tendency being a maximum when the axis of greatest susceptibility is parallel to the field, and a minimum when it is perpendicular to it.

Gauss, which gives the value not only of M, but also that of H, the horizontal component of the earth's force.

A compass having a very short needle is placed on the line which bisects the axis of the magnet at right angles, and is moved until a neutral point is found where the force due to the earth's field H is balanced by that due to the magnet.

The suspended needle is, in the absence of disturbing causes, directed solely by the horizontal component of the earth's field of magnetic force H E, and therefore sets itself approximately north and south.

The magnetized body which is to be tested should be placed in such a position that the force H P due to its poles may, at the spot occupied by the suspended needle, act in a direction at right angles to that due to the earth - that is, east and west.

The direction of the resultant field of force will then make, with that of H E, an angle 0, such that Hp/H E tan 0, and the suspended needle will be deflected through the same angle.

Denoting the distance AM by d 1, BM by d2, and AB by 1, we have for the force at M due to the magnetism of the rod H P =d 12 - horizontal component (dla - d 2 3).

If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q=SBns R, where SB is the increment or decrement of induction per square centimetre, s is the area of the coil, n the number of turns of wire, and R the resistance of the circuit.

The ballistic method is largely employed for determining the relation of induction to magnetizing force in samples of the iron and steel used in the manufacture of electrical machinery, and especially for the observation of hysteresis effects.

With these arrangements there is no demagnetizing force to be considered, for the ring has not any ends to produce one, and the force due to the ends of a rod 400 or 500 diameters in length is quite insensible at the middle portion; H therefore is equal to Ho.

The downward course of the curve is, owing to hysteresis, strikingly different from its upward course, and when the magnetizing force has been reduced to zero, there is still remaining an induction of 7500 units.

Hopkinson pointed out that the greatest dissipation of energy which can be caused by a to-and-fro reversal is approximately represented by Coercive force X maximum induction fir.

The reversing key K having been put over to the left side, the short-circuit key S is suddenly opened; this inserts the resistance R, which has been suitably adjusted before hand, and thus reduces the current and therefore the magnetizing force to a known value.

The distinguishing feature of the first is the steepness of its outlines; this indicates that the induction increases rapidly in relation to the magnetic force, and hence the metal is well suited for the construction of dynamo magnets.

On the other hand, the form of the third curve, with its large intercepts on the axes of H and B, denotes that the specimen to which it relates possesses both retentiveness and coercive force in a high degree; such a metal would be chosen for making good permanent magnets.

During the first stage, when the magnetizing force is small, the magnetization (or the induction) increases rather slowly with increasing force; this is well shown by the nickel curve in the diagram, but the effect would be no less conspicuous in the iron curve if the abscissae were plotted to a larger scale.

During the second stage small increments of magnetizing force are attended by relatively large increments of magnetization, as is indicated by the steep ascent of the curve.

Then the curve bends over, forming what is often called a " knee," and a third stage is entered upon, during which a considerable increase of magnetizing force has little further effect upon the magnetization.

Under increasing magnetizing forces, greatly exceeding those comprised within the limits of the diagram, the magAetization does practically reach a limit, the maximum value being attained with a magnetizing force of less than 2000 for wrought iron and nickel, and less than 4000 for cast iron and cobalt.

When it is mechanically hardened by hammering, rolling or wire-drawing its permeability may be greatly diminished, especially under a moderate magnetizing force.

An experiment by Ewing showed that by the operation of stretching an annealed iron wire beyond the limits of elasticity the permeability under a magnetizing force of about 3 units was reduced by as much as 75%.

The permeability of a soft iron wire, which was tapped while subjected to a very small magnetizing force, rose to the enormous value of about 80,000 (Magnetic Induction, § 85).

The actual experiment to which it relates was carried only as the point marked X, corresponding to a magnetizing force of 65, and an induction of nearly 17,000.

It has, however, been shown that, if the magnetizing force is carried far enough, the curve always becomes convex to the axis instead of meeting it.

The full line shows the result of an experiment in which the magnetizing force was carried up to 585,1 FIG.

With this arrangement it is possible to find the actual value of the magnetizing force, corrected for the effects of joints and other sources of error.

If H l and H2 be the values of 47rinll and 47ri' - 'Z/ l for the 2 2 same induction B, it can be shown that the true magnetizing force is H = H l - (H 2 - H 1).

The induction of the magnetization may be measured by observing the force required to draw apart the two portions of a divided rod or ring when held together by their mutual attraction.

Thus the whole force, when the two portions of the bar are surrounded by a loosely-fitting magnetizing coil, is.

If each portion of the bar has an independent magnetizing coil wound tightly upon it, we have further to take into account the force due to, the mutual action of the two magnetizing coils, which assists.

In the case supposed therefore the total force per square centimetre is H2 F =2712-f-HI+B ?r (4 7r I +H)2 8?r B2 =87r.

The values assigned to H were calculated from H= 2ni/r, and ranged from 3.9 to 585, but inasmuch as no account was taken of any 2 Since in most practicable experiments H 2 is negligible in comparison with B 2, the force may be taken as B 2 /87r without sensible= error.

The instrument exhibited by Thompson would, without undue heating, take a current of 30 amperes, which was sufficient to produce a magnetizing force of woo units.

Ewing has described an arrangement in which the test bar has a soft-iron pole piece clamped to each of its ends; the pole pieces are joined by a long well-fitting block of iron, which is placed upon them (like the " keeper " of a magnet), and the induction is measured by the force required to detach the block.

In all such measurements a correction should be made in respect of the demagnetizing force due to the joint, and unless the fit is very accurate the demagnetizing action will be variable.

In the magnetic balance of du Bois (Magnetic Circuit, p. 346) the uncertainty arising from the presence of a joint is avoided, the force measured being that exerted between two pieces of iron separated from each other by a narrow air-gap of known width.

The actual magnetizing force H is of course less than that due to the coil; the corrections required are effected automatically by the use of a set of demagnetization lines drawn on a sheet of celluloid which is supplied with the instrument.

The standard force H =20 was selected as being sufficiently low to distinguish between good and bad specimens, and at the same time sufficiently high to make the order of merit the same Ss it would be under stronger forces.

For simplicity of calculation, the clear length of each rod between the yokes is made 12.56 (=47r) centimetres, while the coil surrounding the standard bar contains 100 turns; hence the magnetizing force due to a current of n amperes will be ion C.G.S.

But a balance may still be obtained by altering the effective number of turns in the test coil, and thus increasing or decreasing the magnetizing force acting on the test rod, till the induction in the two rods is the same, a condition which is fulfilled when reversal of the current has no effect on the compass needle.

A small coil of fine wire, connected in series with a ballistic galvanometer, is placed in the field, with its windings perpendicular to the lines of force, and then suddenly reversed or withdrawn from the field, the integral electromotive force being twice as great in the first case as in the second.

The intensity of a field may be measured by the rotation of the plane of polarization of light passing in the direction of the magnetic force through a transparent substance.

On the 26th of August a force of 5000 Highlanders suddenly appearing, Cleland posted his men in the church and behind the wall of the earl of Atholl's mansion.

Kassala was captured from the dervishes by an Italian force under Colonel Baratieri on the 17th of July 1894 and by the Italians was handed over on Christmas day 1897 to Egypt.

In 1368 the adversaries of the twelve succeeded in driving them by force from the public palace, and substituting a government of thirteen - ten nobles and three noveschi.

But this concession, grudgingly made, only remained in force for a few years, and on the death of the pope (1464) was revoked altogether, save in the case of members of the Piccolomini house, who were decreed to be popolani and were allowed to retain all their privileges.

There the Prussians defeated the Austrians in May 1745, and in June 1760 the Prussians were routed by a greatly superior force of Austrians.

Suraj Mall raised the Jat power to its highest point; and Colonel Dow, in 1770, estimated the raja's revenue (perhaps extravagantly) at £2,000,000 and his military force at 60,000 or 70,000 men.

A dispute as to the right of the succession again led to a war in 1825, and Lord Combermere captured Bharatpur with a besieging force of 20,000 men, after a desperate resistance, on the 18th of January 1826.

A Scab Act is in force, and is stringently carried out by government inspectors with most satisfactory results.

In a desperate fight (April 17) with a strong force of the enemy the English were overwhelmed and only four Europeans escaped to the bay.

Public opinion of the hour in each section of the community was the only force in the land" (History of South Africa 1834 - 1854, chap. xliv.).

Having at length received an intimation from London that the queen " could not acknowledge the independence of her own subjects, but that the trade of the emigrant farmers would be placed on the same footing as that of any other British settlement, upon their receiving a military force to exclude the interference 1 Commonly called the Republic of Natalia or Natal.

C. Smith with a force of 263 men left his camp at the Umgazi,on the eastern frontier of Cape Colony, and marching overland reached Durban without opposition, and encamped, on the 4th of May, at the base of the Berea hills.

While dependent on the Cape, ordinances had been passed establishing Roman-Dutch law as the law of Natal, and save where modified by legislation it remained in force.

On the 12th Laing's Nek was occupied by the Boer forces, who were moved in considerable force over the Natal border.

Brigadier-General Yule then took command, and an overwhelming force of Boers rendering the further occupation of Dundee dangerous, he decided to retire his force to Ladysmith.

On the 21 st of October General Sir George White and General (Sir John) French defeated at Elandslaagte a strong force of Boers, who threatened to cut off General Yule's retreat.

Albert and no doubt stood on a higher level than Anselm and Abelard, not merely by their wider range of knowledge but also by the intellectual massiveness of their achieve ments; but it may be questioned whether the earlier writers did not possess a greater force of originality and a keener talent.

And when relations with America were becoming critical and menacing in consequence of the depredations committed on American commerce by vessels issuing from British ports, he brought the question before the House of Commons in a series of speeches of rare clearness and force.

In addition to this, a reserve force called the telekkatonasag was recruited from among the lesser gentry according to their teleks or holdings, every thirty-three teleks being held responsible for a mounted and fully equipped archer.

It was with a small force of mercenaries, raised at his own expense, that the young king won his first Turkish victories, and expelled the Czechs from his northern and the Habsburgs from his western provinces.

This force, formed in 1459, was generally known as the Fekete Sereg, or "Black Brigade," from the colour of its armour.

Ferdinand at once asserted his rights by force of arms, and attacked Buda in May 1541, despite the urgent remonstrances of Martinuzzi, who knew that the Turk would never suffer the emperor to reign at Buda.

The despatch of a large force of militia to the assistance of the Viennese was, in fact, the first act of open rebellion of the Hungarians.

But a nation that for a thousand years had maintained its individuality in the midst of hostile and rival races could not be expected to allow itself without a struggle to be sacrificed to the force of mere numbers, and the less so if it were justified in its claim that it stood for a higher ideal of culture and civilization.

Marie zealously pushed her favourite towards office, and had gone so far as to absent herself from court for three months on account of the king's persistent refusal, when Charles, duc de La Vieuville, then head of the council, in need of her aid in his negotiations with reference to the marriage of her daughter Henriette Marie, finally agreed to force Richelieu's appointment to office upon the king, Louis XIII.

The nobility and clergy favoured the League, and urged the king to force his subjects to profess the Catholic religion.

Its real motive force was supplied by Ljudevit Gaj, who combined to a remarkable degree the qualities of author, philologist and political agitator.

The signatories were careful to disclaim all idea of a pact or treaty, and to define the declaration as a mere statement of ideals and principles which could not acquire binding force until ratified by elected representatives of the nation as a whole.

This arrangement, however, never really came into force, for the simple reason that telegraphic communications between the West and Serbia were hopelessly irregular, and that events continued to move, with the advance of the Serbian army and civil authorities from the South and of the Italians from the West.

Under his weaker but more neutral guidance, and aided by the unifying force of the Adriatic crisis, the parties reached agreement upon a new parliamentary franchise, based on universal suffrage.

From time to time efforts were made by those who believed that the Creator must have followed a symmetrical system in his production of animals to force one or other artificial, neatly balanced scheme of classification upon the zoological world.