text:
The American Journal of Sociology/Reviews

Volume 1

 * "Reviews", Vol. 1, No. 2 (Sep., 1895), pp. 218–230
 * Annales de l'Institut International de Sociologie.—A. W. Small
 * (Editor). Aspects of the Social Problem.—W. I. Thomas.
 * . The Evolution of Industry.—A. W. Small
 * . The Evolution of Modern Capitalism.—A. W. Small
 * . Trusts, or Industrial Combinations in the United States.—A. W. Small
 * . Industrial Evolution of the United States. —Edw. W. Bemis

 * "Reviews", Vol. 1, No. 4 (Jan., 1896), pp. 492–508
 * . Social Theory. A Grouping of Social Facts and Principles.—A. W. Small
 * . Social Regeneration.—C. R. Henderson
 * . Practical Christian Sociology. A series of special lectures before Princeton Theological Seminary and Marietta College, with supplemental notes and appendixes.—A. W. Small
 * . Ruling Ideas of the Present Age.—A. W. Small
 * . Anarchy or Government? An Inquiry in Fundamental Politics.—A. W. Small
 * . Primitive Civilizations.—W. I. Thomas
 * . Statistics and Sociology.—E. R. L. Gould
 * . Punishment and Reformation.—C. R. Henderson

 * "Reviews", Vol. 1, No. 5 (Mar., 1896), pp. 633–642
 * . Ethnology.—Merton L. Miller
 * . The Theory of Social Forces.—Lester F. Ward

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text: Index:MinkowskiRaumZeit

title: Index:MinkowskiRaumZeit


text:
Page:Metamorphoses (Ovid, 1567).djvu/29

Rh

For when that of this wicked Age once opened was the veyne Therein all mischief rushed forth: then Fayth and Truth were faine And honest shame to hide their heades: for whom crept stoutly in, Craft, Treason, Violence, Envie, Pride and wicked Lust to win. The shipman hoyst his sailes to wind, whose names he did not knowe: And shippes that erst in toppes of hilles and mountaines had ygrowe, Did leape and daunce on uncouth waves: and men began to bound With dowles and diches drawen in length the free and fertile ground, Which was as common as the Ayre and light of Sunne before. Not onely corne and other fruites, for sustnance and for store, Were now exacted of the Earth: but eft they gan to digge, And in the bowels of the ground unsaciably to rigge, For Riches coucht and hidden deepe, in places nere to Hell, The spurres and stirrers unto vice, and foes to doing well. Then hurtfull yron came abrode, then came forth yellow golde, More hurtfull than the yron farre, then came forth battle bolde, That feightes with bothe, and shakes his sword in cruell bloudy hand. Men live by ravine and by stelth: the wandring guest doth stand In daunger of his host: the host in daunger of his guest: And fathers of their sonne in lawes: yea seldome time doth rest, Betweene borne brothers such accord and love as ought to bee. The goodman seekes the goodwifes death, and his againe seeks shee. The stepdames fell their husbandes sonnes with poyson do assayle. To see their fathers live so long the children doe bewayle. All godlynesse lies under foote. And Ladie Astrey, last Of heavenly vertues, from this earth in slaughter drowned past. And to thintent the earth alone thus should not be opprest, And heaven above in slouthfull ease and carelesse quiet rest, Men say that Giantes went about the Realme of Heaven to win To place themselves to raigne as Gods and lawlesse Lordes therein. And hill on hill they heaped up aloft into the skie, Till God almighty from the Heaven did let his thunder flie, The dint whereof the ayrie tops of high Olympus brake, And pressed Pelion violently from under Ossa strake. When whelmed in their wicked worke those cursed Caitives lay, The Earth their mother tooke their bloud yet warme and (as they say) Did give it life. And for bicause some ympes should still remaine

title: Page:Metamorphoses (Ovid, 1567).djvu/29


text:
Page:Metamorphoses (Ovid, 1567).djvu/30

 Of that same stocke, she gave it shape and limmes of men againe. This offspring eke against the Gods did beare a native spight, In slaughter and in doing wrong was all their whole delight. Their deedes declared them of bloud engendred for to bee. The which as soone as Saturns sonne from Heaven aloft did see, He fetcht a sigh, and therwithall revolving in his thought The shamefull act which at a feast Lycaon late had wrought, As yet unknowne or blowne abrode: He gan thereat to storme And stomacke like an angry Ioue. And therfore to reforme Such haynous actes, he sommonde streight his Court of Parliament, Whereto resorted all the Gods that had their sommons sent. Highe in the Welkin is a way apparant to the sight In starrie nights, which of his passing whitenesse Milkie hight: It is the streete that to the Court and Princely Pallace leades, Of mightie Jove whose thunderclaps eche living creature dreades. On both the sides of this same waye do stand in stately port The sumptuous houses of the Peeres. For all the common sort Dwell scattring here and there abrode: the face of all the skie The houses of the chiefe estates and Princes doe supplie. And sure and if I may be bolde to speake my fancie free I take this place of all the Heaven the Pallace for to bee. Now when the Goddes assembled were, and eche had tane his place, Ioue standing up aloft and leaning on his yvorie Mace, Right dreadfully his bushie lockes did thrise or four times shake, Wherewith he made both Sea and Land and Heaven it self to quake, And afterward in wrathfull wordes his angrie minde thus brake: I never was in greater care nor more perplexitie, How to maintaine my soveraigne state and Princelie royaltie, When with their hundreth handes apiece the Adderfooted rout, Did practise for to conquere Heaven and for to cast us out. For though it were a cruell foe: yet did that warre depende Upon one ground, and in one stocke it had his finall ende. But now as farre as any sea about the worlde doth winde, I must destroy both man and beast and all the mortall kinde. I sweare by Styxes hideous streames that run within the ground, All other meanes must first be sought: but when there can be found No helpe to heale a festred sore, it must away be cut,

title: Page:Metamorphoses (Ovid, 1567).djvu/30


text:
Page:Metamorphoses (Ovid, 1567).djvu/31

 Lest that the partes that yet are sound, in daunger should be put. We have a number in the worlde that mans estate surmount, Of such whom for their private Gods the countrie folkes account, As Satyres, Faunes, and sundry Nymphes, with Silvanes eke beside, That in the woods and hillie grounds continually abide. Whome into Heaven since that as yet we vouch not safe to take, And of the honour of this place copartners for to make, Such landes as to inhabite in, we erst to them assignde, That they should still enjoye the same, it is my will and minde. But can you thinke that they in rest and safetie shall remaine When proud Lycaon laye in waite by secret meanes and traine To have confounded me your Lorde, who in my hand doe beare The dreadfull thunder, and of whom even you doe stand in feare? The house was moved at his words and earnestly requirde, The man that had so traiterously against their Lord conspirde. Even so when Rebels did arise to stroy the Romane name, By shedding of our Cesars bloud, the horror of the same Did pierce the heartes of all mankinde, and made the world to quake. Whose fervent zeale in thy behalfe (O August) thou did take, As thankfully as Jove doth heare the loving care of his, Who beckning to them with his hand, forbiddeth them to hisse. And therewithall through all the house attentive silence is. As soone as that his majestie all muttring had alayde, He brake the silence once againe, and thus unto them sayde: Let passe this carefull thought of yours: for he that did offende, Hath dearely bought the wicked Act, the which he did entende. Yet shall you heare what was his fault and vengeance for the same. A foule report and infamie unto our hearing came Of mischiefe used in those times: which wishing all untrew I did descend in shape of man, th'infamed Earth to vew. It were a processe overlong to tell you of the sinne, That did abound in every place where as I entred in. The bruit was lesser than the truth, and partiall in report. The dreadfull dennes of Menalus where savage beastes resort And Cyllen had I overpast, with all the Pynetrees hie Of cold Lyceus, and from thence I entred by and by The herbroughlesse and cruell house of late th'Arcadian King,

title: Page:Metamorphoses (Ovid, 1567).djvu/31


text: The American Journal of Sociology/Volume 01/Number 2/Reviews


text:
Page:South Carolina Declaration and Ordinance of Secession.djvu/7

 "Article 1.—His Britannic Majesty acknowledges the said United States, viz: New Hampshire, Massachusetts Bay, Rhode Island and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, South Carolina and Georgia, to be FREE, SOVEREIGN AND INDEPENDENT STATES; that he treats them as such; and for himself, his heirs and successors, relinquishes all claims to the government, propriety and territorial rights of the same and every part thereof."

Thus were established the two great principles asserted by the Colonies, namely: the right of a State to govern itself; and the right of a people to abolish a Government when it becomes destructive of the ends for which it was instituted. And concurrent with the establisement of these principles, was the fact, that each Colony became and was recognized by the mother Country as a FREE, SOVEREIGN AND INDEPENDENT STATE.

In 1787, Deputies were appointed by the States to revise the Articles of Confederation, and on 17th September, 1787, these Deputies recommended, for the adoption of the States, the Articles of Union, known as the Constitution of the United States.

The parties to whom this Constitution was submitted, were the several sovereign States; they were to agree or disagree, and when nine of them agreed, the compact was to take effect among those concurring; and the General Government, as the common agent, was then to be invested with their authority.

If only nine of the thirteen States had concurred, the other four would have remained as they then were—separate, sovereign States, independent of any of the


text:
Page:Dictionary of National Biography. Sup. Vol II (1901).djvu/40

  in the ‘Heir at Law,’ and other parts. After reappearing in America he was again at the Strand as Dr. Ollapod in the ‘Poor Gentleman,’ following it up with Paul Pry and Robert Tyke in the ‘School of Reform.’ In November 1872 he opened the Charing Cross theatre, enacting Bob Acres in the ‘Rivals,’ and on 4 April 1874 he opened at the Holborn as Phineas Pettiephogge in Byron's ‘Thumbscrew.’ In the autumn of 1878 he assumed the management of the Haymarket, where he produced the ‘Crisis,’ Albery's adaptation of ‘Les Fourchambault.’ Wills's ‘Ellen, or Love's Cunning,’ 14 April 1879, was a failure, and enjoyed no better fortune when rewritten and produced on 12 June as ‘Brag.’ Clarke then transferred the theatre to the Bancrofts and appeared, 11 July 1885, at the Strand, which he purchased, as Cousin Johnny in a piece by Messrs. Rae and Nisbet so named. After acting in country theatres he retired eventually in 1887, and never made a reappearance, though he often discussed it. He died on 24 Sept. 1899 at his house in Surbiton-on-Tharnes, and was buried the Thursday following at Teddington. He married, in 1859, Asia Booth, daughter of Junius Brutus Booth and sister of Edwin Booth, and left two sons on the stage. A likeness appears in the ‘Era’ for 30 Sept. 1899.

Clarke was an excellent actor in old comedy, in which his principal successes were made. He was a ‘mugger’ of the Liston type, but had more intensity than his predecessor. His new creations were neither very successful nor very important. A portion of his method was due to American actors unknown in this country.

 CLARKE, MARY VICTORIA COWDEN- (1809–1898), miscellaneous writer and compiler of a concordance to Shakespeare, the eldest daughter of eleven children of [q. v.] and his wife, Mary Sabilla Hehl, was born at 240 Oxford Street, London, on 22 June 1809. She was called Victoria after her father's friend the Rev. Victor Fryer. During her early years she made at her father's house the acquaintance of many men distinguished in art and letters. Varley, Copley Fielding, Havell, and Cristall among artists, and Charles and Mary Lamb, Leigh Hunt, and Keats among writers, were included in the circle of her father's most intimate friends, and she acquired much of her taste for literature from Mary Lamb, who gave her lessons in Latin and poetical reading. She is mentioned as ‘Victoria’ in several of Lamb's letters to Vincent Novello; and Leigh Hunt and the Lambs maintained throughout their lives most affectionate relations with her and her husband. Her education was entrusted subsequently to the care of a M. Bonnefoy, who kept a school at Boulogne. On her return to England she acted for a short time as governess in a family named Purcell residing at Cranford, but she was compelled to abandon this employment owing to ill-health. On 1 Nov. 1826 she was affianced to [q. v.], who had been for many years a close friend of the Novellos, and two years later, on 5 July 1828, they were married, spending their honeymoon at the ‘Greyhound’ at Enfield. The marriage was celebrated by Lamb in a playful ‘Serenata, for two Voices,’ which he sent to Vincent Novello in a letter dated 6 Nov. 1828. Charles and Mary Cowden-Clarke continued to live with the Novello family.

Mrs. Cowden-Clarke had already published ‘My Arm Chair,’ under the initials M. H., in Hone's ‘Table Book’ in 1827. This contribution was followed by others of a similar nature and a paper on ‘The Assignats in currency at the time of the French Republic of 1792.’ In 1829 she began her most important work, ‘The Complete Concordance to Shakespeare, being a Verbal Index to all the Passages in the Dramatic Works of the Poet.’ The compilation occupied twelve years, a further four years being devoted to seeing it through the press. It originally appeared in eighteen monthly parts, 1844-5, and in the latter year was issued in one volume. Douglas Jerrold noticed it in ‘Punch,’ breaking the rule then observed against reviews there (Notes and Queries, 6th ser. viii. 479, 8th ser. xi. 313). It was by far the most complete work of its kind which had hitherto been produced, and was a remarkable advance on similar compilations by [q. v.] in 1790 and by [q. v.], 1805-7. It was, however, superseded in 1894 by John Bartlett's ‘New and Complete Concordance’ (Cambridge, Mass. U.S.A.)

In November 1847 and January 1848 Mrs. Cowden-Clarke played Mrs. Malaprop in three amateur productions of ‘The Rivals.’ These private theatricals led to an introduction through Leigh Hunt to Charles Dickens, who persuaded her to perform in the amateur company which, under his direction, gave representations in London and several provincial towns in aid of the establishment of a perpetual curatorship of Shakespeare's birthplace at Stratford-on-Avon (Recollections of


text:
Page:De Raum Zeit Minkowski 010.jpg

 By in Göttingen.

Gentlemen! The concepts about time and space, which I would like to develop before you today, have grown on experimental physical grounds. Herein lies their strength. Their tendency is radical. Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence.

I

I would like to show you at first, how we can arrive – from mechanics as currently accepted – at the changed concepts about time and space, by purely mathematical considerations. The equations of ian mechanics show a twofold invariance. First, their form remains unaltered when we subject the underlying spatial coordinate system to any change of position, second, when we change the system in its state of motion, i. e., when we impress upon it any uniform motion of translation; also the null-point of time plays no role. We are accustomed to look upon the axioms of geometry as settled, when we feel ready for the axioms of mechanics, and therefore the two invariants certainly are seldom mentioned in the same breath. Each one of these denotes a certain group of transformations in itself for the differential equations of mechanics. We look upon the existence of the first group as a fundamental characteristics of space. We always prefer to punish the second group with content, so as to get over the fact with a light heart, that we can never decide from physical considerations whether the space, which is supposed to be at rest, may not finally be in uniform motion. So these two groups have quite separate existences besides each other. Their totally heterogeneous character may scare us away from the attempt to compound them. Yet it is the whole compounded group which as a whole gives us occasion for thought.

We wish to picture to ourselves the whole relation graphically. Let x, y, z be the rectangular coordinates of space, and t denote the time. Subjects of our perception are always places and times connected. No one has observed a place except

title: Page:De Raum Zeit Minkowski 010.jpg


text:
Page:De Raum Zeit Minkowski 011.jpg

 at a particular time, or has observed a time except at a particular place. Yet I still respect the dogma that time and space have independent existences each. I will call a space-point at a time-point, i.e., a system of values x, y, z, t, as a world-point. The manifold of all possible value systems of x, y, z, t, shall be denoted as the world. I boldly could draw four world-axes with a chalk upon a table. Even one axis drawn consists of nothing but quickly vibrating molecules, and besides, takes part in all the journeys of the earth in the universe; and therefore gives us plenty occasions for abstractions. The greater abstraction connected with the number of 4 does not cause the mathematician any trouble. In order not to allow any yawning gap to exist, we shall suppose that at every place and time, something perceptible exists. In order not to say either matter or electricity, we shall simply use the word substance for this something. We direct our attention to the substantial point located at world-point x, y, z, t, and suppose that we are in a position to recognize this substantial point at any other time. Let dt be the time element corresponding to the changes dx, dy, dz of space coordinates of this substantial point. Then we obtain (as a picture, so to speak, of the perennial life-career of the substantial point), a curve in the world, the world-line, whose points can unambiguously be connected to the parameter t from $$+\infty$$ to $$-\infty$$. The whole world appears to be resolved in such world-lines, and I may just anticipate, that according to my opinion the physical laws would find their most perfect expression as mutual relations among these world-lines.

By concepts of time and space, the x, y, z manifold $$t = 0$$ and its two sides $$t<0$$ and $$t>0$$ fall apart. If, for the sake of simplicity, we keep the null-point of time and space fixed, then the first mentioned group of mechanics signifies that at $$t=0$$ we can give the x, y, z-axes an arbitrary rotation about the null-point, corresponding to the homogeneous linear transformation of the expression

$x^{2}+y^{2}+z^{2}\,$

in itself. Yet the second group denotes that – also without changing the expression for the mechanical laws – we can substitute

x, y, z, t by $$ x - \alpha t ,\, y - \beta t ,\, z - \gamma t, t$$

with any constants $$\alpha, \beta, \gamma$$. According to this we can give the time-axis any possible direction in the upper half of the world $$t>0$$. Now, what has the demand of orthogonality

title: Page:De Raum Zeit Minkowski 011.jpg


text:
Author:Horace Porter

Works

 * Campaigning with Grant (1897)
 * “Ulysses S. Grant” in The Presidents of the United States, 1789-1914, 1914.
 * “Ulysses S. Grant” in The Presidents of the United States, 1789-1914, 1914.

title: Author:Horace Porter


text:
Page:South Carolina Declaration and Ordinance of Secession.djvu/8

 of the Constitution. In fact, two of the States did not accede to the Constitution until long after it had gone into operation among the other eleven; and during that interval, they each exercised the functions of an independent nation.

By this Constitution, certain duties were imposed upon the several States, and the exercise of certain of their powers were restrained, which necessarily implied their continued existence as sovereign States. But, to remove all doubt, an amendment was added, which declared that the powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States, respectively, or to the people. On 23d May, 1788, South Carolina, by a Convention of her people, passed an Ordinance assenting to this Constitution, and afterwards altered her own Constitution, to conform herself to the obligations she had undertaken.

Thus was established, by compact between the States, a Government, with defined objects and powers, limited to the express words of the grant. This limitation left the whole remaining mass of power subject to the clause reserving it to the States or to the people, and rendered unnecessary any specification of reserved rights.

We hold that the Government thus established is subject to the two great principles asserted in the Declaration of Independence; and we hold further, that the mode of its formation subjects it to a third fundamental principle, namely: the law of compact. We maintain that in every compact between two or more parties, the obligation is mutual; that the failure of one of the contracting parties to perform a material part of the agreement, entirely releases the obligation of the other; and that where no


text:
Page:De Raum Zeit Minkowski 012.jpg

 in space to do with this perfect freedom of the time-axis towards the upper direction?

To establish this connection, let us take a positive parameter c, and let us consider the figure

$c^{2}t^{2}-x^{2}-y^{2}-z^{2}=1.\,$

According to the analogy of the hyperboloid of two sheets, this consists of two sheets separated by $$t=0$$. Let us consider the sheet in the region of $$t>0$$, and let us now conceive the transformation of x, y, z, t into four new variables x', y', z', t', and the expression of this sheet in the new variables will be equivalent. Clearly the rotations of space round the null-point belongs to this group of transformations. We can already have a complete idea of the transformations, when we look upon one of them, in which y and z remain unaltered. Let us draw the cross section of that sheet with the plane of the x-and t-axes, i.e., the upper branch of the hyperbola $$c^{2}t^{2}-x^{2}=1$$, with its asymptotes (Fig. 1). Then let us draw an arbitrary radius vector $$OA'$$ of that hyperbola branch from the origin O, the tangent in $$A'$$ at the hyperbola to the cutting $$B'$$ with the asymptote given at the right, and completing $$OA'B'$$ to the parallelogram $$OA' B'C'$$; at last for what follows, $$B' C'$$ is drawn to meet the x-axis at $$D'$$. Let us now take $$OC'$$ and $$OA'$$ as axes for the parallel coordinates $$x', t'$$ with measuring rods $$OC'=1$$, $$OA'=1/c$$; then that hyperbola branch is again expressed in the form $$c^2t'^2-x'^2=1, t'> 0$$ and the transition from x, y, z, t to x' y z t' is one of the transitions in question. Let us add to those characteristic transformations an arbitrary displacement of the space- and time-nullpoints; by the we form a group of transformations still depending on the parameter c, which I may denote by $$G_c$$.

Now let us increase c to infinity, thus $$1/c$$ converges to zero, and it appears from the above figure, that the branch of the hyperbola gradually approaches the x-axis, the asymptotic angle extends becomes more obtuse, that the special transformation in the limit changes into one where the t-axis can have any direction upwards, and $$x'$$ more and more approaches x. With respect to this it is clear that the

title: Page:De Raum Zeit Minkowski 012.jpg


text:
Page:De Raum Zeit Minkowski 013.jpg

 group $$G_{c}$$ in the limit for $$c = \infty$$, i.e. as group $$G_{\infty}$$, exactly becomes the full group belonging to ian Mechanics. In this state of affairs, and since $$G_{c}$$ is mathematically more intelligible than $$G_{\infty}$$, a mathematician may, by a free play of imagination, hit upon the thought that natural phenomena actually possess an invariance, not for the group $$G_{\infty}$$, but rather for a group $$G_{c}$$, where c is definitely finite, and only exceedingly large using the ordinary measuring units. Such a preconception would have been an extraordinary triumph for pure mathematics. Now, although mathematics only shows irony at this place, still the satisfaction remains for it, that thanks to its fortunate antecedents by its senses sharpened in free remote-view, it is instantly able to grasp the deep consequences of such a modification of our view of nature.

At the same time I shall remark about which value of c we eventually will arrive. For c, we shall substitute the propagation velocity of light in free space. In order to avoid speaking either of space or of vacuum, we again may take this quantity as the ratio between the electrostatic and electromagnetic units of the quantity of electricity.

We could form an idea of the invariant character of natural laws for the corresponding group $$G_{c}$$ in the following manner:

Out of the totality of natural phenomena, we can, by successive higher approximations, deduce with increased precision a coordinate system x, y, z, and t, space and time, by means of which we can represent the phenomena according to definite laws. This system of reference, however, is by no means uniquely determined by the phenomena. ''We can change the system of reference in any possible manner corresponding to the transformation of the above mentioned group $$G_{c}$$, but the expressions for natural laws will not be changed thereby. ''

For example, corresponding to the figure described above, we also can denote $$t'$$ as time, but in connection with this, we must necessarily define the space by the manifoldness of the three parameters x' y z. The physical laws are now expressed by means of x', y, z, t', — and the expressions are exactly the same as in the case of x, y, z, t. According to this, we shall have, not one space, but an infinite number of spaces in the world, — analogous to the case that the three-dimensional space consists of an infinite number of planes. The three-dimensional geometry becomes a chapter of four-dimensional physics. Now you perceive, why I said in the beginning that time and space shall reduce to mere shadows and we shall have only one world itself.

title: Page:De Raum Zeit Minkowski 013.jpg


text:
Page:De Raum Zeit Minkowski 014.jpg

 II.

Now the question may be asked, — what circumstances forces upon us these changed views about time and space, are they actually never in contradiction with observed phenomena, do they finally guarantee us advantages for the description of natural phenomena?

Before we enter into the discussion, a very important point must be noticed. Suppose we have individualized time and space in any manner; then a substantial point as a world-line corresponds to a line parallel to the t-axis; a uniformly moving substantial point corresponds to a world-line inclined to the t-axis; and non-uniformly moving substantial point will correspond to a somehow curved world-curve. Let us consider the world-line passing through any world point x, y, z, t; now if we find the world-line parallel to any radius vector $$OA'$$ of the hyperboloidal sheet mentioned before, then we can introduce $$OA'$$ as a new time-axis, and then according to the new conceptions of time and space the substance in the corresponding world point will appear to be at rest. We shall now introduce this fundamental axiom:

The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably.

The axiom means, that in a world-point the expression

$c^{2}dt^{2}-dx^{2}-dy^{2}-dz^{2},\,$

shall always be positive or what is equivalent to the same thing, every velocity v should always be smaller than c. c shall therefore be the upper limit for all substantial velocities and exactly herein lies a deep significance for the quantity c. At the first impression, the axiom in this different form seems to be rather unsatisfactory. However, it is to be remembered that a modified mechanics will hold now, in which the square root of this differential combination takes is included, so that cases in which the velocity is greater than c will only play a role in a similar way as figures with imaginary coordinates in geometry.

The impulse and real cause for accepting the group $$G_{c}$$, came from the fact that the differential equation for the propagation of light in vacant space possesses that group $$G_{c}$$. On the other hand, the idea of rigid bodies has any sense only in a system mechanics with the group $$G_{\infty}$$. Now if we have an optics with $$G_{c}$$, and on the other hand if there

title: Page:De Raum Zeit Minkowski 014.jpg


text:
Page:De Raum Zeit Minkowski 015.jpg

 were rigid bodies, it is easy to see that one t-direction is preferred by the two hyperboloidal shells belonging to the groups $$G_{\infty}$$, and $$G_{c}$$, which would have got the further consequence, that by means of suitable rigid instruments in the laboratory, we can perceive a change in natural phenomena, in case of different orientations with regard to the direction of progressive motion of the earth. But all efforts directed towards this goal, and even the celebrated interference-experiment of have given negative results. In order to supply an explanation for this result, formed a hypothesis whose success lies exactly in the invariance of optics for the group $$G_{c}$$. According to every body in motion, shall suffer a contraction in the direction of its motion, namely at velocity v in the ratio

$1:\sqrt{1-\frac{v^{2}}{c^{2}}}$|undefined

This hypothesis sounds rather fantastical. For the contraction is not to be thought of as a consequence of resistances in the ether, but purely as a gift from above, as a condition accompanying the state of motion.

I shall show in our figure, that 's hypothesis is fully equivalent to the new conceptions about time and space, by which it becomes more intelligible. Let us now, for the sake of simplicity, neglect y and z and imagine a spatially two dimensional world, in which upright strips parallel to the t-axis represent a state of rest and another parallel strip inclined to the t-axis represent a state of uniform motion for a body (see fig. 1). If $$OA'$$ is parallel to the second strip, we can take $$t'$$ as time and $$x'$$ as the space coordinate, then the second body will appear to be at rest, and the first body in uniform motion. We shall now assume that the first body supposed to be at rest, has the length l, i.e., the cross section PP of the first strip upon the x-axis $$=l\cdot OC$$, where OC is the unit measuring rod upon the x-axis — and that on the other hand, the second body also, when supposed to be at rest, has the same length l, this means that the cross section is $$Q'Q'=l\cdot OC'$$ when measured parallel to the $$x'$$-axis. In these two bodies, we have now images of two equal -electrons, one of which is at rest and the other moves uniformly. Now if we stick to our original coordinates, then the extension of the second electron is given by the cross section QQ of the corresponding strip is to be given parallel to the x-axis. Now it is clear, since $$Q'Q'=l\cdot OC'$$, that

title: Page:De Raum Zeit Minkowski 015.jpg


text:
Page:De Raum Zeit Minkowski 016.jpg

 $$QQ=l\cdot OD'$$. If $$\frac{dx}{dt}=v$$ for the second strip, a simple calculation gives $$OD'=OC\sqrt{1-\frac{v^{2}}{c^{2}}}$$, therefore also $$PP:QQ=1:\sqrt{1-\frac{v^{2}}{c^{2}}}$$. This, however, is the sense of 's hypothesis about the contraction of electrons in motion. On the other hand, if we conceive the second electron to be at rest, and therefore adopt the system $$x', t'$$, then the cross-section $$P'P'$$ of the strip of the electron parallel to $$OC'$$ is to be regarded as its length and we shall find the first electron shortened with reference to the second in the same proportion, for it is in the figure

$P'P':Q'Q'=OD:OC'=OD':OC=QQ:PP\,$

denoted the combination $$t'$$ of (t and x) as the local time (Ortszeit) of the uniformly moving electron, and used a physical construction of this idea for a better comprehension of the contraction-hypothesis. But to perceive clearly that the time of an electron is as good as the time of any other electron, i.e., that t and $$t'$$ are to be treated equivalently, has been the service of. By that, the concept of time was shown to be unambiguously established by natural phenomena. But the concept of space was not altered, either by or, probably because in the case of the above-mentioned spatial transformations, where the $$x', t'$$ plane coincides with the x, t plane, the interpretation is possible as if the x-axis of space somehow remains conserved in its position. To step over the concept of space in a corresponding manner, is certainly only to assess as the boldness of mathematical culture. After this inevitable step for the true understanding of the group Gc, however, the word "Relativity-Postulate" for the demands of invariance in the group Gc, seems to be rather weak to me. Because the sense of the postulate is that the four-dimensional world is given in space and time by phenomena only, but the projection in time and space can be handled with a certain freedom, and therefore I would rather like to give to this assertion the name "The Postulate of the Absolute World", (or shortly World-Postulate).

III.

By the world-postulate a similar treatment of the four determining parts x, y, z, t becomes possible. Thereby the forms

title: Page:De Raum Zeit Minkowski 016.jpg


text:
Page:De Raum Zeit Minkowski 017.jpg

 under which the physical laws come forth, gain in intelligibility, as I shall presently show. Above all, the idea of acceleration becomes much more striking and clear.

I shall again use the geometrical method of expression, which presents itself by tacitly neglecting x from the triple x, y, z. Let us call any world-point O as a space-time-null-point. The cone

$c^{2}t^{2}-x^{2}-y^{2}-z^{2}=0\,$

consists of two parts with O as apex, one part having $$t < 0$$, the other having $$t > 0$$ (Vide fig. 2).. The first, the fore-cone consists of all those points which "send light towards O", the second, the aft-cone, consists of all those points which "receive their light from O". The region bounded by the fore-cone may be called the "fore-side of O", and the region bounded by the aft-cone may be called the "aft-side of O". On the aft-side of O we have the already considered hyperboloidal shell

$F=c^{2}t^{2}-x^{2}-y^{2}-z^{2}=l,\ t>0$.

The region between the cones will be occupied by the hyperboloid forms of one sheet

$-F=x^{2}+y^{2}+z^{2}-c^{2}t^{2}=k^2\,$,

to all constant positive values $$k^2$$. The hyperbolas which lie upon this figure with O as center, are important for us. For the sake of shortness the individual branches of this hyperbola will be called the interhyperbola to center O. Such a hyperbolic branch, when thought of as a world-line of a substantial point, would represent a motion which for $$t = -\infty$$ and $$t = +\infty$$ asymptotically approaches the velocity of light c.

If, by way of analogy to the idea of vectors in space, we call any directed length in the manifoldness x, y, z, t a vector, then we have to distinguish between a time-like vector directed from O towards the sheet $$+F = 1$$, $$t > O$$ and a space-like vector directed from O towards the sheet $$-F = 1$$. The time-axis can be parallel to any vector of the first kind. Any world-point between the fore and aft cones of O, may by means of the system of reference be regarded either as synchronous with O, as well as later or earlier than O. Every world-point on the fore-side of O is necessarily

title: Page:De Raum Zeit Minkowski 017.jpg


text:
Page:De Raum Zeit Minkowski 018.jpg

 always earlier, every point on the aft side of O, necessarily later than O. The limit $$c = \infty$$ corresponds to a complete folding up of the wedge-shaped cross-section between the cones in the plane manifoldness $$t = 0$$. In the figure drawn, this cross-section has been intentionally drawn with a different breadth.

Let us decompose a vector drawn from O towards x, y, z, t into its four components x, y, z, t. If the directions of the two vectors are respectively the directions of the radius vector OR of O at one of the surfaces $$\pm F = 1$$, and additionally a tangent RS at the point R of the relevant surface, then the vectors shall be called normal to each other. Accordingly

$c^{2}tt_{1}-xx_{1}-yy_{1}-zz_{1}=0,\,$

which is the condition that the vectors with the components x, y, z, t and $$\left(x_{1}\ y_{1}\ z_{1}\ t_{1}\right)$$ are normal to each other.

For the sums of vectors in different directions, the unit measuring rods are to be fixed in the following manner; — a space-like vector from to $$-F = 1$$ is always to have the sum 1, and a time-like vector from O to $$+F = 1$$, $$t>0$$ is always to have the sum $$1/c$$.

Let us now fix our attention upon the world-line of a substantial point running through the world-point P(x, y, z, t); then as we follow the progress of the line, the quantity

$d\tau=\frac{1}{c}\sqrt{c^{2}dt^{2}-dx^{2}-dy^{2}-dz^{2}},$|undefined

corresponds to the time-like vector-element dx, dy, dz, dt.

The integral $$\tau=\int d\tau$$ of this sum, taken over the world-line from any fixed initial point $$P_{0}$$ to any variable endpoint P, may be called the "proper-time" of the substantial point in P. Upon the world-line, we may regard x, y, z, t, i.e., the components of the vector OP, as functions of the "proper-time" $$\tau$$; let $$\left(\dot{x},\ \dot{y},\ \dot{z},\ \dot{t}\right)$$ denote their first differential-quotients with respect to $$\tau$$, and $$\left(\ddot{x},\ \ddot{y},\ \ddot{z},\ \ddot{t}\right)$$ their second differential quotients with respect to $$\tau$$, and denote the corresponding vectors, i.e. the derivation of the vector OP with respect to $$\tau$$ the motion-vector in P, and the derivation of this motion-vector with respect to $$\tau$$ the acceleration-vector in P. There we have

{{Center|$$\left.\begin{array}{l} c^{2}\dot{t}^{2}-\dot{x}^{2}-\dot{y}^{2}-\dot{z}^{2}=c^{2}\\ c^{2}\dot{t}\ddot{t}-\dot{x}\ddot{x}-\dot{y}\ddot{y}-\dot{z}\ddot{z}=0\end{array}\right\} $$}}

i.e., the motion-vector is the time-like vector in the direction of the world-line at P of sum 1, the acceleration-vector at P is normal to the motion-vector at P, and is in any case a space-like vector.

title: Page:De Raum Zeit Minkowski 018.jpg


text:
Page:De Raum Zeit Minkowski 019.jpg

 Now there is, as can be easily seen, a certain hyperbola, which has three infinitely contiguous points in common with the world-line at P, and of which the asymptotes are the generators of a fore-cone and an aft-cone. This hyperbola may be called the hyperbola of curvature at P (vide fig. 3). If M be the center of this hyperbola, then we have to deal here with an inter-hyperbola with center M. Let $$\varrho$$ be the sum of the vector MP, then we perceive that the acceleration-vector at P is a vector of magnitude $$c^{2}/\varrho$$ in the direction of MP.

If $$\ddot{x},\ \ddot{y},\ \ddot{z},\ \ddot{t}$$ are nil, then the hyperbola of curvature at P reduces to the straight line touching the world-line at P, and $$\varrho=\infty$$.

IV.

In order to demonstrate that the assumption of the group $$G_{c}$$ for the physical laws does not possibly lead to any contradiction, it is inevitable to undertake a revision of the whole of physics on the basis of the assumptions of this group. The revision has, to a certain extent, already been successfully made in the case of thermodynamics and tadiation," for electromagnetic phenomena", and finally for Mechanics with the maintenance of the idea of mass.

For the latter area, the question may be asked: if there is a force with the components X, Y, Z (with respect to the space-axes) at a world-point P(x, y, z, t), where the motion-vector is $$\left(\dot{x},\ \dot{y},\ \dot{z},\ \dot{t}\right)$$, then how are we to regard this force when the system of reference is changed in any possible manner? Now, certain well-tested theorems about the ponderomotive force in electromagnetic fields exist, where the group $$G_{c}$$ is undoubtedly permissible. These theorems lead us to the following simple rule; if the system of reference be changed, then the supposed force is to be put as a force in the new space-coordinates in such a manner, that the corresponding vector with the components

$\dot{t}X,\ \dot{t}Y,\ \dot{t}Z,\ \dot{t}T,$

where

$T=\frac{1}{c^{2}}\left(\frac{\dot{x}}{\dot{t}}X+\frac{\dot{y}}{\dot{t}}Y+\frac{\dot{z}}{\dot{t}}Z\right)$|undefined

is the work of the force divided by $$c^2$$ at the world-point, remains unaltered. This vector is always normal to the motion-vector at P. Such a force-vector belonging to a force at P, may be called a moving force-vector at P.

title: Page:De Raum Zeit Minkowski 019.jpg


text:
Page:De Raum Zeit Minkowski 020.jpg

 Now the world-line passing through P will be described by a substantial point with the constant mechanical mass m. Let us call m-times the velocity-vector at P as the momentum-vector, and m-times the acceleration-vector at P as the force-vector of motion at P. According to these definitions, the law telling us how the motion of a point-mass takes place under a given moving force-vector :

''The force-vector of motion is equal to the moving force-vector. ''

This enunciation comprises four equations for the components in the four directions, of which the fourth can be deduced from the first three, because both of the above-mentioned vectors are perpendicular to the velocity-vector from the outset. From the above-mentioned definition of T, we see that the fourth certainly expresses the energy-law. Accordingly, $$c^2$$-times the component of the momentum-vector in the direction of the t-axis is to be defined as the kinetic-energy of the point-mass. The expression for this is

$mc^{2}\frac{dt}{d\tau}=mc^{2}/\sqrt{1-\frac{v^{2}}{c^{2}}}$|undefined

i.e., if we deduct from this the additive constant $$mc^2$$, we obtain the expression $$\tfrac{1}{2}mv^2$$ of ian-mechanics up to magnitudes of the order of $$1/c^2$$. Hence it illustratively appears that the energy depends upon the system of reference. But since the t-axis can be laid in the direction of any time-like axis, however, the energy-law formed for any possible system of reference, therefore comprises already the whole system of equations of motion. This fact retains its significance for the axiomatic construction of Newtonian mechanics, even in the considered passage to the limit $$c = \infty$$, as has already been recognized out by.

From the very beginning, we can establish the ratio between the units of length and time in such a manner, that the natural limiting velocity becomes $$c=1$$. If we now write $$\sqrt{-1}t=s$$, in the place of t, then the quadratic differential expression

$d\tau^{2}=-\left(dx^{2}+dy^{2}+dz^{2}+ds^{2}\right),$

becomes symmetrical in x, y, z, s; this symmetry then enters into each law, which does not contradict the world-postulate. We can clothe the essential nature of this postulate in the mystical, but mathematically significant formula

3·105 km = $$\sqrt{-1}$$ Sec.

title: Page:De Raum Zeit Minkowski 020.jpg


text:
Page:De Raum Zeit Minkowski 021.jpg

 V. The advantages arising from the formulation of the world-postulate are illustrated by nothing so strikingly as by giving the expressions for the reactions exerted by a point-charge moving in any manner according to the theory. Let us conceive the world-line of such a point-like electron with the charge e, and let us introduce upon it the proper-time $$\tau$$ reckoned from any initial point. In order to obtain the field caused by the electron at any world-point $$P_{1}$$, let us construct the fore-cone belonging to $$P_{1}$$ (vide fig. 4). Evidently this cuts the unlimited world-line of the electron at a single point P, because these directions are all time-like vectors. At P, let us draw the tangent to the world-line, and let us draw from $$P_{1}$$ the normal $$P_{1}Q$$ to this tangent. Let r be the sum of $$P_{1}Q$$. According to the definition of a fore-cone, $$r/c$$ is to be reckoned as the sum of PQ. Now at the world-point $$P_{1}$$, the vector with respect to PQ of magnitude $$e/r$$ in its components along the x-, y-, z-axes, is represented by the vector-potential of the field multiplied by c; the component along the t-axis is represented by the scalar-potential of the field excited by e. This is the elementary law found out by, and.

In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect.

I shall now describe the ponderomotive force which is exerted by a point-charge moving in an arbitrary way, to another point-charge moving in an arbitrary way. Let us suppose

title: Page:De Raum Zeit Minkowski 021.jpg


text:
Page:South Carolina Declaration and Ordinance of Secession.djvu/9

 arbiter is provided, each party is remitted to his own judgment to determine the fact of failure, with all its consequences.

In the present case, that fact is established with certainty. We assert, that fourteen of the States have deliberately refused for years past to fulfil their constitutional obligations, and we refer to their own Statutes for the proof.

The Constitution of the United States, in its 4th Article, provides as follows:

"No person held to service or labor in one State, under the laws thereof, escaping into another, shall, in consequence of any law or regulation therein, be discharged from such service or labor, but shall be delivered up, on claim of the party to whom such service or labor may be due."

This stipulation was so material to the compact, that without it that compact would not have been made. The greater number of the contracting parties held slaves, and they had previously evinced their estimate of the value of such a stipulation by making it a condition in the Ordinance for the government of the territory ceded by Virginia, which now composes the States north of the Ohio river.

The same article of the Constitution stipulates also for rendition by the several States of fugitives from justice from the other States.

The General Government, as the common agent, passed laws to carry into effect these stipulations of the States. For many years these laws were executed. But an increasing hostility on the part of the non-slaveholding States to the Institution of Slavery has led to a disregard of their obligations, and the laws of the General Government have


text:
Page:De Raum Zeit Minkowski 022.jpg

 that the world-line of a second point-electron passes through the world-point $$P_{1}$$. Let us determine P, Q, r as before, construct the middle-point of the hyperbola of curvature at P, and finally the normal MN from M upon a line through P which is parallel to $$QP_{1}$$. With P as the initial point, we shall establish a system of reference in the following way: the t-axis will be laid along PQ, the x-axis in the direction of $$QP_{1}$$; the y-axis in the direction of MN, then the direction of the z-axis is automatically determined as normal to the t-,x-,y--axes. Let $$\ddot{x},\ \ddot{y},\ \ddot{z},\ \ddot{t}$$ be the acceleration-vector at $$P$$, $$\dot{x}_{1},\ \dot{y}_{1},\ \dot{z}_{1},\ \dot{t}_{1}$$ be the motion-vector at $$P_{1}$$. Then the force-vector exerted by the first electron e (moving in any possible manner) upon the second electron $$e_1$$ (likewise moving in any possible manner) at $$P_{1}$$ is represented by

$-ee_{1}\left(\dot{t}_{1}-\frac{\dot{x}_{1}}{c}\right)\mathfrak{K}$|undefined

For the components $$\mathfrak{K}_{x},\ \mathfrak{K}_{y},\ \mathfrak{K}_{z},\ \mathfrak{K}_{t}$$ of the vector $$\mathfrak{K}$$ the three relations hold: —

$c\mathfrak{K}_{t}-\mathfrak{K}_{x}=\frac{1}{r^{2}},\ \mathfrak{K}_{y}=\frac{\ddot{y}}{c^{2}r},\ \mathfrak{K}_{z}=0$|undefined

''and fourthly this vector $$\mathfrak{K}$$ is normal to the motion-vector $$P_{1}$$, and through this circumstance alone, its dependence on this latter motion-vector arises. ''

If we compare with this expression the previous formulations giving the same elementary law about the ponderomotive action of moving electric point-charges upon each other, then we cannot but admit, that the relations which occur here only reveal the inner essence of full simplicity first in four dimensions; but upon a space of three dimensions that is forced upon them from the outset, they cast very complicated projections.

In the mechanics reformed according to the world-postulate, the disharmonies which have disturbed the relations between ian mechanics and modern electrodynamics automatically disappear. I still shall consider the position of the ian law of attraction to this postulate. I will assume that when two point-masses m and $$m_{1}$$ describe their world-lines, a moving force-vector is exerted by m upon $$m_{1}$$, and the expression is just the same as in the case of the electron previously discussed; we only have to write $$+mm_{1}$$ instead of $$-ee_{1}$$. We shall consider now the special case in which the acceleration-vector of m is constantly zero; then t may be introduced in such a manner that m may be regarded as fixed, the motion of $$m_{1}$$

title: Page:De Raum Zeit Minkowski 022.jpg


text:
Page:De Raum Zeit Minkowski 023.jpg

 is now subjected to the moving force-vector of m alone. If we now modify this given vector, first by writing $$\dot{t}^{-1}=\sqrt{1-\frac{v^{2}}{c^{2}}}$$, which = 1 up to magnitudes of the order $$1/c^2$$, then it is shown that 's laws hold good for the positions $$x_{1}, y_{1}, z_{1}$$ of $$m_{1}$$ at any time, except that in place of the times $$t_{1}$$ we have to write the proper times $$\tau_{1}$$ of $$m_{1}$$. On the basis of this simple remark, it can be seen that the proposed law of attraction in combination with new mechanics is not less suited for the explanation of astronomical phenomena than the ian law of attraction in combination with ian mechanics.

Also the fundamental equations for electromagnetic processes in ponderable bodies are in accordance with the world-postulate throughout. I shall also show on a later occasion that even the deduction of these equations, as taught by on the basis of the concepts of electron theory, are by no means to be given up.

The validity of the world-postulate without exception is, I would like to believe, the true core of an electromagnetic picture of the world; this core was first hit upon by, further carved out by , bringing it completely to daylight. In course of further developing the mathematical consequences, enough suggestions will be forthcoming for the experimental verification of the postulate; in this way even those, who find it unsympathetic or even painful to give up the old, time-honoured concepts, will be reconciled by idea of a pre-established harmony between pure mathematics and physics.

title: Page:De Raum Zeit Minkowski 023.jpg


text:
Page:South Carolina Declaration and Ordinance of Secession.djvu/10

 ceased to effect the objects of the Constitution. The States of Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York, Pennsylvania, Illinois, Indiana, Michigan, Wisconsin and Iowa, have enacted laws which either nullify the Acts of Congress or render useless any attempt to execute them. In many of these States the fugitive is discharged from the service or labor claimed, and in none of them has the State Government complied with the stipulation made in the Constitution. The State of New Jersey, at an early day, passed a law in conformity with her constitutional obligation; but the current of anti-slavery feeling has led her more recently to enact laws which render inoperative the remedies provided by her own law and by the laws of Congress. In the State of New York even the right of transit for a slave has been denied by her tribunals; and the States of Ohio and Iowa have refused to surrender to justice fugitives charged with murder, and with inciting servile insurrection in the State of Virginia. Thus the constitutional compact has been deliberately broken and disregarded by the non-slaveholding States, and the consequence follows that South Carolina is released from her obligation.

The ends for which this Constitution was framed are declared by itself to be "to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defence, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity."

These ends it endeavored to accomplish by a Federal Government, in which each State was recognized as an equal, and had separate control over its own institutions. The right of property in slaves was recognized by giving to free persons distinct political rights, by giving them


text:
Page:South Carolina Declaration and Ordinance of Secession.djvu/11

 the right to represent, and burthening them with direct taxes for three-fifths of their slaves; by authorizing the importation of slaves for twenty years; and by stipulating for the rendition of fugitives from labor.

We affirm that these ends for which this Government was instituted have been defeated, and the Government itself has been made destructive of them by the action of the non-slaveholding States. Those States have assumed the right of deciding upon the propriety of our domestic institutions; and have denied the rights of property established in fifteen of the States and recognized by the Constitution; they have denounced as sinful the institution of Slavery; they have permitted the open establishment among them of societies, whose avowed object is to disturb the peace and to eloign the property of the citizens of other States. They have encouraged and assisted thousands of our slaves to leave their homes; and those who remain, have been incited by emissaries, books and pictures to servile insurrection.

For twenty-five years this agitation has been steadily increasing, until it has now secured to its aid the power of the Common Government. Observing the forms of the Constitution, a sectional party has found within that article establishing the Executive Department, the means of subverting the Constitution itself. A geographical line has been drawn across the Union, and all the States north of that line have united in the election of a man to the high office of President of the United States whose opinions and purposes are hostile to slavery. He is to be entrusted with the administration of the Common Government, because he has declared that that "Government cannot endure permanently half slave, half free," and that the public mind must rest in the belief that Slavery is in the course of ultimate extinction.


text:
Page:South Carolina Declaration and Ordinance of Secession.djvu/12

 This sectional combination for the subversion of the Constitution, has been aided in some of the States by elevating to citizenship, persons, who, by the Supreme Law of the land, are incapable of becoming citizens; and their votes have been used to inaugurate a new policy, hostile to the South, and destructive of its peace and safety.

On the 4th March next, this party will take possession of the Government. It has announced, that the South shall be excluded from the common Territory; that the Judicial Tribunals shall be made sectional, and that a war must be waged against slavery until it shall cease throughout the United States.

The Guaranties of the Constitution will then no longer exist; the equal rights of the States will be lost. The slaveholding States will no longer have the power of self-government, or self-protection, and the Federal Government will have become their enemy.

Sectional interest and animosity will deepen the irritation, and all hope of remedy is rendered vain, by the fact that public opinion at the North has invested a great political error with the sanctions of a more erroneous religious belief.

We, therefore, the people of South Carolina, by our delegates, in Convention assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, have solemnly declared that the Union heretofore existing between this State and the other States of North America, is dissolved, and that the State of South Carolina has resumed her position among the nations of the world, as a separate and independent State; with full power to levy war, conclude peace, contract alliances, establish commerce, and to do all other acts and things which independent States may of right do.