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Runo XXV]

“It was in this very winter,

In the summer just passed over,

That the pathways had been sighing

For the sweeper of the pathways,

And the cowsheds nearer drawing

To the cleanser of the cowsheds;

Songs and dances were abandoned,

Till should sing and dance our duckling.

“On this very day already,

And upon the day before it,

Early has the cow been lowing,

And her morning hay expecting,

And the foal has loud been neighing

That his truss of hay be cast him,

And the lamb of spring has bleated,

That its food its mistress bring it.

“On this very day already,

And upon the day before it,

Sat the old folks at the windows,

On the beach there ran the children,

By the wall there stood the women,

In the porch-door youths were waiting,

Waiting for the youthful mistress,

And the bride they all awaited.

“Hail to all within the household,

Likewise hail to all the heroes,

Hail, O barn, and all within thee,

Barn, and all the guests within thee,

Hail, O hall, and all within thee,

Birchbark roof, and all thy people,

Hail, O room, and all within thee,

Hundred-boards, with all thy children!

Hail, O moon, to thee, O monarch,

And the bridal train so youthful!

Never was there here aforetime,

Never yesterday nor ever,

Was a bridal train so splendid:

Never were such handsome people.

“Bridegroom, O my dearest brother,

Let the red cloths now be loosened,

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 ficiary has not utilised or received the benefit from the said administrative order and failure to revoke it would damage the public interest;

there might be serious damage to the public interest or to the people, which needs to be prevented or eliminated.

In the case that an administrative order is revoked for the cause under paragraph 2(3), (4), or (5), the beneficiary has the right to be compensated for the damage accruing from the honest belief in the continued existence of the administrative order, and section 52 shall apply mutatis mutandis.

In the following cases, a lawful administrative order which provides for money or for divisible property or benefit may be revoked in whole or in part, whether with or without retroactive effect or with effect for the future up to any time as may be designated:

the objectives of the administrative order have not been implemented or have been implemented in a delayed manner;

the beneficiary failed to fulfil the conditions of the administrative order or fulfilled them in a delayed manner.

In this respect, the dispositions of section 51 shall apply mutatis mutandis.

In the following cases, the authority may, upon application by a participant, revoke or amend an administrative order which has gone over the time limit for appeal according to Part 5:

new evidence is obtained which would cause a material change to the facts conclusively established;

the actual participants have not joined the administrative proceedings or have joined the previous proceedings but were unfairly deprived of the opportunity to participate therein;

the authority has no power to make the administrative order in question;

if the administrative act has been issued by virtue of any fact or law and the material parts of such fact or law have subsequently changed in a manner likely to favour the participant.

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

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text: Graffiti d'Italia/Persica

title: Graffiti d'Italia/Persica


text: The Painted Veil/Chapter 23

title: The Painted Veil/Chapter 23


text: The Painted Veil/Chapter 24

title: The Painted Veil/Chapter 24


text: The Painted Veil/Chapter 25

title: The Painted Veil/Chapter 25


text: Graffiti d'Italia/Snowdrop

title: Graffiti d'Italia/Snowdrop


text: The Painted Veil/Chapter 26

title: The Painted Veil/Chapter 26


text: The Painted Veil/Chapter 27

title: The Painted Veil/Chapter 27


text: The Painted Veil/Chapter 28

title: The Painted Veil/Chapter 28


text: The Painted Veil/Chapter 29

title: The Painted Veil/Chapter 29


text: The Painted Veil/Chapter 30

title: The Painted Veil/Chapter 30


text: The Painted Veil/Chapter 31

title: The Painted Veil/Chapter 31


text: The Painted Veil/Chapter 32

title: The Painted Veil/Chapter 32


text: The Painted Veil/Chapter 33

title: The Painted Veil/Chapter 33


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Page:Kalevala (Kirby 1907) v1.djvu/326

306

Laid aside the veils all silken;

Let us see thy cherished marten,

Whom for five long years thou wooed’st,

And for eight years thou hast longed for.

“Hast thou brought whom thou hast wished for,

Hast thou brought with thee the cuckoo,

From the land a fair one chosen,

Or a rosy water-maiden?

“But I see without my asking,

Comprehend without inquiry,

Thou has really brought the cuckoo,

Hast the blue duck in thy keeping;

Greenest of the topmost branches,

Thou hast brought from out the greenwood,

Freshest of the cherry-branches,

From the freshest cherry-thickets.”

On the floor there sat an infant,

From the floor spoke out the infant:

“O my brother, what thou bringest,

Is a tar-stump void of beauty,

Half as long as a tar-barrel,

And as tall as is a bobbin.

“Shame, O shame, unhappy bridegroom,

All thy life thou hast desired,

Vowed to choose from hundred maidens,

And among a thousand maidens,

Bring the noblest of the hundred,

From a thousand unattractive;

From the swamp you bring a lapwing,

From the hedge you bring a magpie,

From the field you bring a scarecrow,

From the fallow field a blackbird.

“What has she as yet accomplished,

In the summer just passed over,

If the gloves she was not weaving,

Nor begun to make the stockings?

Empty to the house she cometh,

To our household brings no presents,

Mice are squeaking in the baskets,

Long-eared mice are in the coppers.”

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text: The Painted Veil/Chapter 34

title: The Painted Veil/Chapter 34


text: The Painted Veil/Chapter 35

title: The Painted Veil/Chapter 35


text: The Painted Veil/Chapter 36

title: The Painted Veil/Chapter 36


text:
Lorelei's Song

If there's reason, I can't recall it, Why I feel sick and tense. A fable demands I tell it, An old tale without sense.

The heavens are cool and dark now And quiet flows the Rhine; The peak of the Rock is a spark now Of summer eveningshine.

In glory amid the last light There sits a maid most fair. Her garment and jewels shine bright As she combs her golden hair

With a golden comb; and she's singing The most marvellous song to me. Even piercing my drums could not bring Escape from that melody.

In my skiff I am a captive Of each melodious note, Caring nothing for the rapids That wait to sink my boat.

The waves will be devouring, Too soon, both skiff and I; And I will die still hearing The song of Lorelei.

title: Lorelei's Song


text: The Painted Veil/Chapter 37

title: The Painted Veil/Chapter 37


text: The Painted Veil/Chapter 38

title: The Painted Veil/Chapter 38


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Page:The Necromancer, or, The Tale of the Black Forest Vol. 2.djvu/116

 thing else. I soon was infected with an ardent desire to become his pupil, and, after a few months instruction, was as great a fool as himself."

"It would be too tedious if I was to relate all our fruitless endeavours to effect the apparition of a spirit, and I was soon convinced that it lay not in the power of man to lord over these bodiless beings: My master, however, continued his mysterious operations day and night with an indefatigable ardour."

"It is very natural, that it at length came into my head to profit by his superstitious enthusiasm, and that I eagerly seized every opportunity to impose upon a man, who promised to fall an easy sacrifice to art and cunning, having great reason to expect that such an attempt would ensure me his affection, and promote my fortune rapidly."

"One night as he was conjuring up his guardian angel with much impatience, I en-


text: The Painted Veil/Chapter 39

title: The Painted Veil/Chapter 39


text: The Painted Veil/Chapter 40

title: The Painted Veil/Chapter 40


text: The Painted Veil/Chapter 41

title: The Painted Veil/Chapter 41


text: The Painted Veil/Chapter 42

title: The Painted Veil/Chapter 42


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Page:Alexander Jonas - Reporter and Socialist (1885).djvu/65

 velop it, instead of being, as they now are, crushed into uniformity and stupidity by the necessity for haste and ceaseless dull work; the scientist, the artist, the man of letters would no longer have to sell himself at auction for the pleasure of the idle and incapable, but sure of his livelihood, not driven to earn special profits by the exercise of his talents, would be able to devote himself deliberately to science and the arts, and satisfy all the requirements of his genius; nor can we doubt that under these happier conditions the number of people able and willing to exercise special talents for the good of the community would much increase, so that the destruction of the so-called individualist system would result in a prodigious development of individuality."

And then, it would seem to me that in the communistic society the liberty of the individual would be less restrained than in any other social organization ever in existence heretofore?

Undoubtedly it would. Only imagine the situation as it would really be: Everybody is given a chance to make his or her living, according to taste and choice in any industrial, agricultural or commercial pursuit; and all the facilities and opportunities to make that choice and to successfully work in any branch of business and trade would be guaranteed by the institutions of that society of the future. Every one may avail himself, or herself, of these facilities and opportunities according to the respective individual's own free will and pleasure. There will be no compulsion of any kind except that of the laws of reason and individual disposition, the latter to be restrained only so far as is necessary to avoid the violation of the rights of others, or of society as a whole. This is true liberty, and the sole freedom really agreeing with the organization of the nature of mankind.

I might ask a great many questions more; the subject is really interesting me a good deal. For instance: will there be any taxes in your society, and how are the tax-payers to be assessed; what will be the position of woman, and how about the family question which, it seems, the public at large does not very well understand


text: The Painted Veil/Chapter 44

title: The Painted Veil/Chapter 44


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 (interrupting): Hold on, Sir! I know what you are about to say. You are going to voice the common prejudices and slanders of the wealthy populace whose ruling propensities are threatened by the advent of victorious socialism. But, I shall answer you immediately. To-day, my dear Sir, the overwhelming majority of mankind does not enjoy the real blessings of matrimony and family-life. For, matrimony to-day is an institution for the support of some of our female population, while hundreds of thousands of women and children are compelled to work for a living in order to satisfy the dire wants of their bodies. In our society all this will be different. Woman will be equal to man. If she be married her existence will be guaranteed on account of the labor she performs as a mother and a teacher of her young children. And no woman will be compelled to take a husband merely to be supported; her work will support her under all circumstances, and children will, of course, be expected to participate in the process of production considerably later in life than at present, after having been fitted thereto by a thorough scientific and practical education. You may ask, whether society will have the means thus to educate the growing generation? Indeed, it will. The work of assessing and collecting taxes, if you chose to call it so, will be very simple and practical. The necessary amount to be raised for public purposes will be estimated, and regulated according to the demands of the time; and from every certificate for labor produced, or certificate of wages, if you please, a certain percentage will be deducted, and the amount of the deduction will be according to the amount of the wages, which may also be affected by the number of members in each family. You see that it will not be very difficult to solve all these questions. But now let me tell you one thing: we might sit here till to-morrow morning to talk over all these minor arrangements and yet we would not get through; therefore, let us speak about them at some other time when you are at leisure. May it suffice at present that I have shown you by what the Socialists propose to replace the present system of production which brings misery and starvation to the masses of the people. Consequently, if it be impossible to attack the principle upon which the entire socialistic structure is based, it would be reasonable to suppose


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Author:David Fleischer

Director

 * The Einstein Theory of Relativity (1923)

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text: The Painted Veil/Chapter 43

title: The Painted Veil/Chapter 43


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 that the aspirations of the Socialists are rational, practicable. If they are carried out in practice, a society will be organized in which every one will have the means to live like a human being, and to participate in the comforts and enjoyments of life brought forth and produced by a society whose members are all contributing their best efforts to the common welfare. In such a society the interests of one are the concern of all, and vice versa, while the economic institutions will be so regulated that no individual can live upon the labor of others, i. e. that no one can rob the rest. I now ask you whether any intelligent human being could doubt that such a society with such noble aims and objects would not easily solve all the minor questions of matrimony, family, education, elections, taxation, etc.?! For, and I have to repeat it, upon a communistic-economic basis humanity would be afforded, for the first time in its history the possibility, I might even say the necessity, of an harmonious development. Who would doubt that such an harmonious development will take place?

(after reflecting for a short while): I shall leave this question to be answered by the learned gentlemen of our editorial staff, for I, on my part, have no longer any objections.

But I have one more, and a very momentous question to ask you: How are you going to bring about that great, enormous revolution which is to replace the present society by the socialistic one?

This is one of the commonly occurring questions which—allow me to say so—are generally asked mostly by thoughtless people who know nothing of history. No revolution has ever been "made," but a radical change of social systems where one principle is substituted for one of totally different tendency—and this is what I mean by revolution—has always been effected according to the natural development of society itself without the possibility for any one to arrest or materially accelerate its course, and therein lies the certainty with which we expect the victory of our ideas that they are not idle speculations, but that they are based upon facts, and that they must necessarily, according to natural development, once become a reality.


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title: The Painted Veil/Chapter 45


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 It seems to me, to the contrary that, as you have said it yourself, the present economic development is continually strengthening and fortifying monopolism?

Just so. This is one side of the development: but the other one, going hand in hand with this, is the enormous decrease of the middle classes whose elements are sinking to the level of the proletarian, of the non-possessing class, very fast. With every new factory smoke-stack part of the old system of producing by hand is being replaced by a new branch of the modern system of production, by steam and machinery; the opening of every new store and emporium of gigantic proportions means ruin and bankruptcy to hundreds of small business men and shop keepers; whenever a capitalist buys up several hundreds of thousands of acres of land for the purpose of modern farming upon a grand scale, hundreds of farmers who cannot compete with the gigantic monopolist are doomed; every new invention by which more workmen are made superfluous, ruins so many more manufacturers who are unable to acquire the new machines; the great monopolies like the Standard Oil Co., the Telegraph and Railroad Companies, are continually confiscating the labor and the property of the smaller capitalists, and in this way the army of the disinherited ones, of the wage-slaves, of those who have an interest in seeing the present system destroyed is constantly increased, while the number of those in whose interest the preservation of the system would be, must necessarily decrease. And finally—as the mass of the people will no longer tolerate such a state of affairs—the crash must inevitably come; and, as the entire economic organization is evolving towards co-operative production at an immense scale, as the victorious revolutionists will find it, so to speak, ready made for them to take possession of—as I have already described it to you in the instance of that great factory—there is no doubt but that not alone that revolution will take place, but that its tendency also, that the way in which it will shape things in the future, will be clearly defined.

 * Then, the Socialists refrain from influencing the development of society altogether?

 * Not at all! I told you that we could not materially accelerate the development toward a sudden social crash


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 as the nature of things has this tendency already. Yet there is plenty of room for wholesome revolutionary agitation and action, among which we consider as very important the organization of the workmen, and of all who have the same class interest as the workmen, in order to enable them to resist at least somewhat any further economic degradation. We also believe that all phases and occurrences of public life should be utilized for the purpose of preparing the way for the great change to come. I mean, that whenever opportunity offers we should introduce measures of relief like the reduction of the hours of labor, the prohibition of child-labor, the organization of bureaus of labor statistics, the payment of equal wages for men and women, if the task and the quality of the labor be equal, etc. etc. For the purpose of accomplishing our aims and objects we recommend all expedient means that may be in the reach of those who are suffering from the effects of the evil system of these days. We make use of the legal institutions of the country we live in; we take part in elections whenever we think best to do so; we agitate in public and in private by the means of meetings, by publishing newspapers and tracts, and whomsoever we come in contact with we try to convince that we are teaching what is true and rational. And those whom we have convinced see it clearly before them that a lasting improvement of their condition can only be brought about by the total destruction of the present social system. A man who has once become a Socialist knows but one more object in life: To devote himself to the noble work of liberating the laboring people; and then comes the second part of the duty of Socialists: To show to those whom they have converted by what the old system which they endeavor to destroy, is to be replaced? They soon understand what we want—better than all the learned gentlemen who profess to possess the secret of solving the great social question. They see that our propositions are sensible and practical. To enlighten the workmen in this respect is as necessary as to make them act in common with us, in order to avoid that after the last battle of the revolution chaos should prevail; to enable them to assist in rebuilding society according to a real and rational social order, and to make any reaction in favor of the old system an im-


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STORY XVI.]. ALI'S FORBEARANCE. 59 I should root up the mountains from their bases,

And lay bare the secrets of a hundred Adams,

And convert a hundred fresh Iblises into Musulmans."

Adam answered, "I repent me of my scornful looks;

Such arrogant thoughts shall not be mine again.

O Lord, pardon this rashness in Thy slave;

I repent; chastise me not for these words!"

O Aider of aid-seekers, guide us,

For there is no security in knowledge or wealth;

"Lead not our hearts astray after Thou hast guided us," [1]

And avert the evil that the "Pen" has written.

Turn aside from our souls the evil written in our fates,

Repel us not from the tables of purity!

O God, Thy grace is the proper object of our desire;

To couple others with Thee is not proper.

Nothing is bitterer than severance from Thee,

Without Thy shelter there is naught but perplexity.

Our worldly goods rob us of our heavenly goods,

Our body rends the garment of our soul.

Our hands, as it were, prey on our feet;

Without reliance on Thee how can we live?

And if the soul escapes these great perils,

It is made captive as a victim of misfortunes and fears,

Inasmuch as when the soul lacks union with the Beloved,

It abides for ever blind and darkened by itself.

If Thou showest not the way, our life is lost;

A life living without Thee esteem as dead!

If Thou findest fault with Thy slaves,

Verily it is right in Thee, O Blessed One!

If Thou shouldst call sun and moon obscure,

If Thou shouldst call the straight cypress crooked,

If Thou shouldst declare the highest heaven base,

Or rich mines and oceans paupers,

All this is the truth in relation to Thy perfection!

Thine is the dominion and the glory and the wealth! 1 Koran iii. 6.

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 possibility. This kind of agitation is what the organized Socialists of all countries—in the United States the "Socialistic Labor Party"—are actively engaged in.

 * So you believe that in spite of the peaceable means you propose to employ, a violent revolution will come in the end?

 * In order to best answer this question I will read to you what the "Socialistic Labor Party" of this country have said in a Manifesto, adopted at their congress convened at Baltimore in December, 1883":

 * Then you are aiming at bringing about a violent revolution notwithstanding?


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 : Will you please look out of this window?

 * What do you mean?

 * Do you see those clouds?

 * I see they are quite black, and from their general aspect I apprehend we shall soon have a tremendous thunderstorm.

 * Are you sure of it?

 * Indeed, I am. There—did you see the lightning?

 * Then, my dear Sir, you are "aiming" at bringing about a thunderstorm?

 * What do you mean? I have nothing to do with it—it is coming, it is there already!

 * Now then, my young friend: This is the way we are aiming at bringing about the violent revolution. We see it approaching—it is almost there, and we are preparing to meet its consequences.


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 tered his room, telling him, that all his efforts would be in vain, because he was not acquainted with the proper means of forcing the inhabitants of the other world to make their appearance."

"Gazing at me with wonder and surprise, he inquired whether I had improved so much in the occult sciences that I could effect what he so eagerly desired. I neither denied nor confirmed his question, but told him, that I would give him the next day, a specimen of my skill in Necromancy."

"It was an easy task to impose on my credulous enthusiastic Count, having secured the assistance of a fellow servant. We resided at a country seat his mother had left him, which was the fittest place in the world for the execution of our design. Having succeeded better than I at first expected, I made him my dupe above a twelvemonth, and grew at last so bold and impudent, that the Count could not


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text: The Child's Own Music Book/The Song of the Moon


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 but perceive my juggling tricks, and instantly sent me away.

"The good credulous man has certainly been convinced afterwards, that the lesson I gave him by my cheats deserved the warmest gratitude."

"I had saved a pretty sum of money during my stay with the Count, and, being used to an idle life, had not the least thought of looking about for another master. I went back to H, where I abandoned myself to gambling, drinking, and all sorts, of dissipation, until all my money was spent, and no other means of getting an honest livelihood left, than to try my fortune in the army."

"A recruiting officer paid me a hundred dollars for my liberty, and I cheerfully enlisted under the banner of Mars."

"I had received the promise to be made a serjeant, but saw myself at first very much


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 An application can be made in accordance with paragraph 1(1), (2), or (3) only when the participant was not aware of such cause during the previous proceedings without fault on his part.

An application for resumption of proceedings must be made within ninety days from the time the person in question becomes aware of the cause which may ground the application.

Administrative execution shall not be applied by one authority to another, save where the law otherwise designates.

The authority making an administrative order has the power to consider and apply measures for administrative execution according to the provisions of this Part so as to implement his order, save where a stay of the execution has been ordered by such authority himself, by the person having the power to consider appeals, or by the person having the power to consider and rule upon the correctness of such administrative order.

The authority under paragraph 1 may authorise a subordinate authority or other authority to do so according to the criteria and procedure designated by ministerial regulations.

The authority under paragraph 1 or paragraph 2 shall apply the measures for administrative execution only to the extent necessary for the administrative order to achieve its objectives, so that the person subjected to the administrative order would be affected as least as possible.

As regards an administrative order that requires any person to make a monetary payment, if the payment has not been made correctly and completely despite having been due, the authority shall warn such person in writing in order that he would make the payment within a period of time designated, which must not be less than seven days. If the warning has not been complied with, the authority may apply a measure for administrative execution by seizing or attaching his property and selling it at public auction to completely satisfy the payment.

The procedure for the seizure, attachment, and sale of property shall follow the Civil Procedure Code mutatis mutandis, whilst the person having the power to order the seizure, or attachment, or sale shall be designated by a ministerial regulation.

As regards an administrative order that requires an act to be done or omitted, if the person subjected to the administrative order violates or fails to comply with the order, the authority may apply any of the following measures for administrative execution:

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6 to desire that it should be conducted without any fear of unpleasant consequences. Rarely, indeed, may one find the most genuine champion of free thought entirely consistent. Milton, for example, could hardly be accused of advocating the root and branch destruction of contemporary persecution; for indeed he defended elsewhere the persecution of Catholics. But he certainly did plead, in theory, for the extension of free discussion from the region of politics to that of theology.

To hold that toleration need not be consciously sceptical is not equivalent to admitting that it has ever existed without a sceptical foundation. In an ideal society no opinions will be condemned without an exhaustive discussion of their merits; but as human nature is at present and always seems to have been constituted, men find no time for this; and were one to traverse the country preaching the duty of parricide on evolutionary or other grounds (and it might be preached as plausibly as any other doctrine), one would not meet with retorts either syllogistic or courteous. In fact the law would treat such an apostle as a disturber of the peace. Quite recently a magistrate declared that the sight of a lady publicly smoking a cigarette was calculated to promote a breach of the peace.

A perfect toleration could no doubt exist in a Spencerian millennium; but, as yet, we must reckon with our own kind, and men, as we know them,

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Rh speedily exhaustible means, so that the walls of their system blend to their eye in the remote horizon within the walls of the universe. . . They cannot imagine how you aliens have any right to see,. . . . how you can see! "

Perhaps the best analogy to the attitude of the persecutor is the spontaneous yet blind abhorrence felt for acts and opinions which are probably connected with a certain amount of mental aberration, e.g. anarchism or sexual abnormality.

Such an attitude, however, has been still more characteristic of many heretics, in so far as they have hopelessly exaggerated a side issue at the expense of the whole; nor have they usually advocated toleration for others—especially when they were themselves in power.

But, just as the persecuting spirit may be largely bound up with an absence of very definitely formulated convictions, so, in the same way, it would be obviously absurd to classify all advocates of toleration as sceptics; for this would involve putting men like Socrates, Milton and Diderot into the same category as Pyrrho, Hobbes and Montaigne. The latter class of men are, on the whole, indifferent to abstract truth, and therefore not inclined to quarrel about it, whereas the former class are enthusiastic enough to welcome disputation in all its forms, and 1 Essays (Eversley edition), Macmillan, 1899, pp. 64, 65.

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20 Seeley, in his book on "Natural Religion," invariably used the word to express his own meaning, but this often makes his opinions obscure to the general reader. I consider it necessary to make this foregoing explanation, because otherwise the whole trend of the following chapters might be open to grave misunderstanding.

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 of Church and State in the newly founded States of America.

In European civilisation, however, there has always been a gradual advance to the separation, real or nominal, of Church and State. This separation was never at all durable before the existence of medieval Europe, when Jews and other aliens were allowed certain rights of citizenship. The ' medieval Pope was an offshoot from the Roman Emperor, who had himself exercised the functions of Pontifex Maximus amongst many others. Up to this time there could be no such separation, for the simple reason that the Church was the State and the State was the Church; for example, the kings in Sparta and in the earlier Jewish

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first step to any kind of religious toleration in Europe was taken by Rome with the sole object of establishing a political compromise which should unite the heterogeneous elements of the Roman Empire. This achievement was rudely disturbed by Christianity, which implicitly and explicitly opposed the imperial system by creating in this world, and projecting into the next, an ideal and a society for which no sort of niche could be found in the State as then understood. But the advance of Christianity brought it into such close association with the Empire that for the time being the distinctive theory of its independence of political society was merged in the Roman theory of a state-religion. After a period of unstable equilibrium, in which the Empire attempted to preserve a neutral attitude, the old system revived, with the result that the pagans were persecuted just as the Christians had been. Not till the end of the eighteenth century did the Christian idea realise its true self on a large scale in the complete separation

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Rh ligious bodies ; in Spain the bishops are constantly urging the extirpation of Freemasons and Agnostics; across the Atlantic the Mormons have been stringently repressed, and in England legal penalties are enforced against Christian scientists. " Conscientious scruples" cannot excuse crimes against the State or society at large. We do not all of us subscribe to the wisdom of the legislation of 1898 on vaccination.

Our own country is probably now one of the most tolerant in the world— especially in regard to those aspects of religion in which continental countries are most intolerant. Since 1880 secularist lectures gain a very fair hearing, and their meetings are rarely interrupted, though it is hardly a hundred years since Dr Priestley, the Unitarian, had his library burnt in Birmingham by the mob for being an atheistic revolutionary. But no greater measure of tolerance was accorded to the pro-Boer meetings of 1899 and 1900 than to the orations of Mr Holy-oake fifty years before, and a policy of intolerance was deliberately sanctioned by some of the authorities at the time.

Moreover, although the violence of the clerical and anti-clerical parties on the Continent seems inconsistent with the existence of a widespread

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Rh of government are no longer avowedly religious, because modern men have become stolid and unimaginative. On the contrary, I believe that modern democracies are more strongly swayed in politics by appeals to the imagination than the communities of past times, and that statesmen consciously use this leverage on a larger scale than before. In the United States politicians use more rhetorical and sentimental language every year, and the same tendency is apparent in Europe. The Jubilee procession of 1897, and the coronation of Queen Wilhelmina in 1898, aroused extraordinary outbursts of enthusiasm in nations conventionally considered more phlegmatic than the Latin or the Slav peoples.

On all these grounds it seems probable that modern toleration is intimately bound up with the sceptical or inquiring spirit, and that there is some historical continuity in the process. The primitive tribe and the ancient city-state were theocracies pure and simple; even the Greek city was a "parochial Sinai." To some extent Christianity reinforced, and was helped by the universality of Stoic philosophy in revolting against this, and set up the individual conscience as the supreme arbiter for men. It substituted an otherworldly jurisdiction for that of the State. "My kingdom is not of this world" is the key-note of Christ's teaching. The partial success of this new idea is

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16 seen in the birth of the Papacy, as it were, out of the rib of the Empire. The imperial and papal jurisdictions had many points of contact, but they were far from coinciding. The attempted revivals of a Judaic theocracy under Calvin, and of a Roman theocracy under Henry VIII. and the German Protestants, were in course of time diverted into purely political channels, and in the seventeenth and eighteenth centuries the State came to insist on outward conformity in religious matters only for the sake of political and civic unity. The genuinely religious energies of the Reformation movement were ultimately absorbed in laying the foundations of modern democracy on the fundamental principle of the congregational unit in England, Scotland and France, and in exalting the authority of the magistrate at the expense of the priestly office in the North German and Scandinavian countries. The net result was that most of these States in the seventeenth and eighteenth centuries emphasised the merely legal aspect of religious conformity, and endowed their churches with the idea of thus economising their expenditure on police. The establishment of a religious neutral commonwealth across the Atlantic by the Federation Act of 1783, and the subjection of the Church to the State in France by Napoleon I., marked a new era. In the English-speaking world of to-day (with the present

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26 will show how in the Greek State the details of individual conduct also are exhaustively mapped out. In his ideal State citizens dine in public, are restricted in regard to the age of marriage, and have their whole existence arranged for them. Yet the Greek City did indeed teem with sceptical philosophies and burned with the zeal of the scientific spirit, which vented itself in keen intellectual discussion. Such disputations were, however, for the most part academic and were regarded rather as exercises in dialectic. When, however, Socrates tried to bring philosophy down to earth and set up an individual standard of conduct, he could no longer be tolerated.

Mr Gilbert Murray in his "History of Greek Literature" puts forward the theory that the accuser of Socrates had probably a genuine grievance, since the son of the accuser, intellectually emancipated from the old sanctions of conduct, had not constructed new sanctions for himself. Such risks few parents will approve, and least of all would an Athenian father have done so. But the main issue of the trial was that no citizen should be allowed to stand apart from the State or criticise the ethics of the State, which were entirely bound up with the State religion.

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Rh We are accustomed to think of the Greeks as the least superstitious and most tolerant of ancient peoples; we are sometimes told that we stretch hands across the gulf of the Dark Ages to them. But men like Anaxagoras (whose philosophy somewhat resembled that of modern idealism) were not hailed as harbingers of light, and probably escaped being condemned to death only because their speculations were never really understood except by a small circle of philosophers.

Again, it must be remembered that one of the greatest mistakes made by Athens in the Peloponnesian War was that of driving Alcibiades into the Lacedaemonian camp, because he and his friends were, though without much reason, suspected of having mutilated the Hermae, which would bring down the wrath of the gods on the whole city. The gods of the Greek City State were to a certain extent Pan-Hellenic, but they were also taken to represent the city alone. The State-gods and State-ideals were the gods and ideals of the individual. Even Socrates assented to this, if the " Crito" have any foundation in fact.

The most cursory perusal of Aristotle's politics

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Rh community were virtually priests, or else had the priests in a close alliance that bordered on subjection. Again, in Egypt, where the priests themselves had great power, they were, like other functionaries, appointed by the king, who also initiated fresh ritual; for example, under the second dynasty Khaicehos Kahan introduced the worship of bulls at Memphis.

The later history of the Jewish theocracy shows a rivalry between king and priest as exponents of the divine will; but, in spite of the royal power, the kings depended very greatly on the approval of priest and prophet, who often seem to have had a greater hold on public opinion.

As in all primitive states, the religious code is the basis of all law and minutely regulates the conduct of the individual. The Israelite who

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BAILEY - COLEMAN


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User talk:Breslevjoy

Belated welcome
I see that you have been around for some months, but as no-one has done this yet -

Welcome
Welcome

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Again, welcome! -- Beardo (talk) 20:49, 23 January 2024 (UTC)

Translation:Likutei Moharan/14
The line:

"L’hamshikh shalom'' (To draw peace) into the world it is necessary to elevate the Holy One’s glory to its source—i.e., to fear. As it is written (Deuteronomy 28:58), “To fear the glorious name.”"

has unmatched italics. -- Beardo (talk) 02:13, 31 March 2024 (UTC)

 * Thanks, just changed it. Breslevjoy (talk) 19:17, 31 March 2024 (UTC)

title: User talk:Breslevjoy


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Translation:Theorematis fundamentalis in doctrina de residuis quadraticis demonstrationes et ampliationes novae

The fundamental theorem of quadratic residues, which is said to be among the most beautiful truths of higher arithmetic, was easily discovered by induction, but it is much more difficult to demonstrate. It often happens in this subject that the simplest truths, which offer themselves spontaneously to the inquirer by induction, have demonstrations which are hidden in the deepest depths, which can only be brought to light after many fruitless attempts, and quite possibly by a different path than that by which they were sought. Then, when at first one path has been discovered, it happens not infrequently that several more appear from time to time, with some being shorter and more direct, and others arising obliquely and from very different principles, which one would have thought to be nearly unrelated to the proposed question. Strange connections of this kind between abstruse truths not only give a certain charm to these contemplations, but also deserve to be diligently investigated and analyzed, because they frequently lead to new resources or advances in science.

Therefore, although the arithmetic theorem which is to be discussed here may seem to be fully completed by previous efforts, which provided four entirely different demonstrations, I nonetheless return again to the same theme, and add two more demonstrations, which will certainly shed new light on this matter. The first is in a certain way related to the third, as it proceeds from the same lemma; afterwards, however, it follows a different course, so that it can well be considered a new proof, whose elegance will be seen to be, if not superior, then at least not inferior to that of the third. On the other hand, the sixth demonstration is based on a completely different and more subtle principle and provides a new example of an astonishing connection between arithmetic truths that, at first glance, appear to be very far removed from each other. To these two demonstrations, a very simple new algorithm is added to determine whether a given integer is a quadratic residue modulo a given prime or not.

There was yet another reason, which prompted me to publish the new demonstrations at this particular moment, although they had been promised nine years ago. In 1805, when I began to investigate the theory of cubic and biquadratic residues, which is a much more difficult subject, I experienced almost the same fate as I once had in the theory of quadratic residues. Indeed, those theorems, which entirely exhaust these questions, and in which a remarkable analogy with the theorems pertaining to quadratic residues shines forth, were immediately discovered by induction as soon as a suitable approach had been found. However, all efforts to obtain them, with their demonstrations perfected in every aspect, remained fruitless for a long time. This was the incentive for me to add more and more demonstrations concerning quadratic residues to those already known, supported by the hope that among the many diverse methods, one or another might do something to reveal an analogous line of reasoning. This hope was by no means in vain, and tireless labor was finally followed by prosperous success. It will soon be possible to bring the fruits of this vigilance to public light; but before embarking on this arduous task, I decided to return once more to the theory of quadratic residues, to complete all that still remained of that agenda, and thus to bid farewell to this sublime part of arithmetic.

1.
In the introduction, we have already stated that the fifth and third proof proceed from the same lemma. As a matter of convenience, it seems appropriate to repeat it in this place, with notation adapted to the present discussion.

Let $m$ be a prime number (positive odd), and let $M$  be an integer not divisible by $m.$  Consider the minimal positive residues of the numbers

$$M, 2 M, 3 M, 4 M, \ldots \frac{1}{2}(m-1) M$$

modulo $m.$ Some of these will be less than $\frac{1}{2} m$  and some will be greater; let the multitude of the latter $=n.$  Then $M$  will be a quadratic residue or non-residue modulo $m,$  depending on whether $n$  is even or odd.

Let those residues which are less than $\frac{1}{2} m$ be denoted by $a,$  $b,$  $c,$  $d$  etc. , and let the rest, which are greater than $\frac{1}{2} m,$ be denoted by $a^{\prime},$  $b^{\prime},$  $c^{\prime},$  $d^{\prime}$  etc. The complements modulo $m$ of the latter, $m-a^{\prime},$  $m-b^{\prime},$  $m-c^{\prime},$  $m-d^{\prime}$  etc. , will evidently all be less than $\frac{1}{2} m,$ and they will be distinct both among themselves and from the residues $a,$  $b,$  $c,$  $d,$  etc. Thus they will be identical, albeit in a different order, to the numbers $1,$ $2,$  $3,$  $4 \dots \frac{1}{2}(m-1).$  So, if we set

$$1 \times 2 \times 3 \times 4 \ldots \frac{1}{2}(m-1)=P$$

then

$$P=a b c d \ldots \times(m-a^{\prime})(m-b^{\prime})(m-c^{\prime})(m-d^{\prime}) \ldots$$

and thus

$$(-1)^{n} P=a b c d \ldots \times(a^{\prime}-m)(b^{\prime}-m)(c^{\prime}-m)(d^{\prime}-m) \ldots$$

Furthermore, we have

$$P M^{\frac{1}{2}(m-1)} \equiv a b c d \ldots \times a^{\prime} b^{\prime} c^{\prime} d^{\prime} \ldots \equiv a b c d \ldots \times(a^{\prime}-m)(b^{\prime}-m)(c^{\prime}-m)(d^{\prime}-m) \ldots$$

modulo $m,$ so

$$P M^{\frac{1}{2}(m-1)} \equiv P(-1)^{n}$$

Hence $M^{\frac{1}{2}(m-1)} \equiv \pm 1,$ where the sign is positive if $n$  is even and negative if $n$  is odd. Therefore, with the help of the theorem proved in Disquisitiones Arithmeticae art. 106, the truth of the lemma is immediately apparent.

2.
Let $m,$ $M$  be positive odd relatively prime integers, and let $n$  be the multitude of numbers in the sequence

$$M, 2 M, 3 M \ldots \frac{1}{2}(m-1) M$$

whose minimal positive residues modulo $m$ are greater than $\frac{1}{2} m.$  Similarly, let $N$  be the multitude of numbers in the sequence

$$m, 2 m, 3 m \ldots \frac{1}{2}(M-1) m$$

whose minimal positive residues modulo $M$ are greater than $\frac{1}{2} M.$  Then the three numbers $n,$  $N,$  $\frac{1}{4}(m-1)(M-1)$  will either be all even, or one will be even and the other two will be odd.

Let us denote

by $f$ the complex of numbers $1, 2, 3 \ldots \frac{1}{2}(m-1)$

by $f^{\prime}$ the complex of numbers $m-1, m-2, m-3 \ldots \frac{1}{2}(m+1)$

by $F$ the complex of numbers $1,2,3 \ldots \frac{1}{2}({M}-1)$

by $F^{\prime}$ the complex of numbers $M-1, M-2, M-3 \ldots \frac{1}{2}(M+1)$

Thus $n$ will indicate how many numbers $M f$  have their least positive residues modulo $m$  in the complex $f^{\prime},$  and similarly $N$  will indicate how many numbers $m F$  have their least positive residues modulo $M$  in the complex $F^{\prime}.$  Finally, let us denote

by $\varphi$ the of numbers $1, 2, 3 \ldots \frac{1}{2}(m M-1)$ by $\varphi^{\prime}$ the complex of numbers $m M-1, m M-2, m M-3 \ldots \frac{1}{2}(m M+1)$

Since every integer not divisible by $m$ must be congruent, modulo $m,$  to a residue from the complex $f$  or from the complex $f^{\prime},$  and similarly every integer not divisible by $M$  must be congruent to a residue from the complex $F$  or from the complex $F^{\prime},$  it follows that all the numbers $\varphi,$  among which obviously no one is divisible by both $m$  and $M,$  can be distributed into eight classes in the following way.

 * I. In the first class there will be those numbers which are congruent to some number from $f$ modulo $m,$  and congruent to some number from $F$  modulo $M.$  We will denote the multitude of these numbers by $\alpha.$

 * II. Numbers congruent to numbers from $f,$ $F^{\prime}$  modulo $m,$  $M,$  respectively, the multitude of which we set $=\beta.$

 * III. Numbers congruent to numbers from $f^{\prime},$ $F$  modulo $m,$  $M,$  respectively, the multitude of which we set $=\gamma.$

 * IV. Numbers congruent to numbers from $f^{\prime},$ $F^{\prime}$  modulo $m,$  $M,$  respectively, the multitude of which shall be $=\delta.$

 * V. Numbers divisible by $m,$ and congruent to one of the residues from $F$  modulo $M.$

 * VI. Numbers divisible by $m,$ and congruent to one of the residues from $F^{\prime}$  modulo $M.$

 * VII. Numbers divisible by $M,$ congruent to one of the residues from $f$  modulo $m.$

 * VIII. Numbers divisible by $M,$ congruent to one of the residues from $f^{\prime}$  modulo $m.$

Clearly, classes V and VI taken together will include all of the numbers $mF.$ The multitude of numbers contained in VI will be $=N,$  and hence the multitude of numbers contained in V will be $\frac{1}{2}(M-1)-N.$  Similarly, classes VII and VIII taken together will contain all numbers $Mf,$  in class VIII there will be $n$  numbers, and in class VII there will be $\frac{1}{2}(m-1)-n.$

Similarly, all the numbers $\varphi^{\prime}$ will be distributed into eight classes IX - XVI. If we maintain the same order, then it is easy to see that the numbers in the classes

IX, X, XI, XII, XIII, XIV, XV, XVI

are the complements modulo $mM$ of the numbers in the classes

IV, III, II, I, VI, V, VIII, VII

respectively, so that in class IX there will be $\delta$ numbers; in class X, there will be $\gamma,$  and so on. Now, it is clear that if all the numbers of the first class are joined with all the numbers of the ninth class, one will have all the numbers below $m M$ which are congruent to some number from $f$  modulo $m$ , and to some number from $F$  modulo $M.$  It is easily seen that the multitude of these is equal to the multitude of all combinations of one individual from $f$  and one individual from $F.$  Therefore,

$$\alpha+\delta=\frac{1}{4}(m-1)(M-1)$$

and by a similar argument

$$\beta+\gamma=\frac{1}{4}(m-1)(M-1)$$

By joining all numbers of classes II, IV, VI, we will clearly have all numbers below $\frac{1}{2} m M,$ which are congruent to some residue from $F^{\prime}$  modulo $M.$  Moreover, these same numbers can also be presented as follows:

$$F^{\prime}, M+F^{\prime}, 2 M+F^{\prime}, 3 M+F^{\prime} \ldots \frac{1}{2}(m-3) M+F^{\prime}$$

from which the total number of them will be $=\frac{1}{4}(m-1)(M-1),$ or in other words we will have

$$\beta+\delta+N=\frac{1}{4}(m-1)(M-1)$$

Similarly, by joining the classes III, IV, VIII, it follows that

$$\gamma+\delta+n=\frac{1}{4}(m-1)(M-1)$$

From this the following four equations arise:

$$\begin{aligned} &2 \alpha=\frac{1}{4}(m-1)(M-1)+n+N \\ &2 \beta=\frac{1}{4}(m-1)(M-1)+n-N \\ &2 \gamma=\frac{1}{4}(m-1)(M-1)-n+N \\ &2 \delta=\frac{1}{4}(m-1)(M-1)-n-N \end{aligned}$$

each of which demonstrates the truth of the theorem.

3.
If we now assume that $m$ and $M$  are prime numbers, the combination of the previous theorem with the lemma of article 1 immediately yields the fundamental theorem. For it is clear that,

 * I. Whenever one or both of $m,$ $M$  is of the form $4k+1,$  the number $\frac{1}{4}(m-1)(M-1)$  will be even, and therefore $n$  and $N$  will either be both even or both odd, and thus either $m$  and $M$  are both quadratic residues modulo each other, or both are quadratic non-residues modulo each other.

 * II. Whenever $m,$ $M$  are both of the form $4k+3,$  the number $\frac{1}{4}(m-1)(M-1)$  will be odd, hence one of the numbers $n,$  $N$  will be even and the other odd, and therefore one of the numbers $m,$  $M$  will be a quadratic residue modulo the other, and the other will be a quadratic non-residue modulo the one. Q. E. D.

1.
''Let $p$ be a prime number (odd positive), let $n$  be a positive integer not divisible by $p,$  and let $x$  be an indeterminate quantity. Then the function''

$$1+x^{n}+x^{2 n}+x^{3 n}+\text{etc.}+x^{n p-n}$$

will be divisible by

$$1+x+x x+x^{3}+\text{etc.}+x^{p-1}$$

Let $g$ be a positive integer such that $g n \equiv 1\pmod{p},$  and let $g n=1+h p.$  Then we have

$$\begin{aligned} \frac{1+x^{n}+x^{2 n}+x^{3 n}+\text{etc.}+x^{n p-n}}{1+x+x x+x^{3}+\text{etc.}+x^{p-1}}=\frac{(1-x^{n p})(1-x)}{(1-x^{n})(1-x^{p})} & =\frac{(1-x^{n p})(1-x^{g n}-x+x^{h p+1})}{(1-x^{n})(1-x^{p})} \\ & =\frac{1-x^{n p}}{1-x^{p}} \cdot \frac{1-x^{g n}}{1-x^{n}}-\frac{x(1-x^{n p})}{1-x^{n}} \cdot \frac{1-x^{h p}}{1-x^{p}} \end{aligned}$$

and therefore the function is clearly integral. Q. E. D.

It follows that any integral function of $x$ which is divisible by $\frac{1-x^{n p}}{1-x^{n}},$  will also be divisible by $\frac{1-x^{p}}{1-x}.$

2.
Let $\alpha$ denote a positive primitive root modulo $p,$  i. e. , let $\alpha$ be a positive integer such that the minimal positive residues of the powers $1,$  $\alpha,$  $\alpha \alpha,$  $\alpha^{3},$  $\ldots,$  $\alpha^{p-2}$  modulo $p$  are identical (without regard to order) to the numbers $1,$  $2,$  $3,$  $4,$  $\ldots,$  $p-1.$   Furthermore, denoting the function

$$x+x^{\alpha}+x^{\alpha \alpha}+x^{\alpha^{3}}+\ldots+x^{\alpha^{p-2}}+1$$

by $f(x),$ it is clear that $f(x)-1-x-x x-x^{3}-\ldots-x^{p-1}$  will be divisible by $1-x^{p},$  and therefore a fortiori by $\frac{1-x^{p}}{1-x}=1+x+x x+x^{3}+\ldots+x^{p-1}.$  From this it follows, since $x$  is an indeterminate quantity, that $f(x^{n})$  will also be divisible by $\frac{1-x^{n p}}{1-x^{n}}$  and consequently (by the previous article) also by $\frac{1-x^{p}}{1-x},$  as long as $n$  is an integer not divisible by $p.$  Conversely, whenever $n$  is an integer divisible by $p,$  each part of the function $f(x^{n}),$  reduced by unity, will be divisible by $1-x^{p}.$  Therefore in this case, $f(x^{n})-p$  will also be divisible by $1-x^{p},$  and consequently also by $\frac{1-x^{p}}{1-x}.$

3.
If we set

$$x-x^{\alpha}+x^{\alpha \alpha}-x^{\alpha^{3}}+x^{\alpha^{4}}-\text{etc.}-x^{\alpha^{p-2}}=\xi$$

then $\xi \xi \mp p$ will be divisible by $\frac{1-x^{p}}{1- x},$  if we take the upper sign whenever $p$  is of the form $4k+1$  and the lower sign whenever $p$  is of the form $4k+3.$

It can easily be seen that, of the $p-1$ functions

$$\begin{aligned} & +x \xi-x x+x^{\alpha+1}-x^{\alpha \alpha+1}+\text{etc.}+x^{\alpha^{p-2}+1} \\ & -x^{\alpha} \xi-x^{2 \alpha}+x^{\alpha \alpha+\alpha}-x^{\alpha^{3}+\alpha}+\text{etc.}+x^{\alpha^{p-1}+\alpha} \\ & +x^{\alpha \alpha} \xi-x^{2 \alpha \alpha}+x^{\alpha^{3}+\alpha \alpha}-x^{\alpha^{4}+\alpha \alpha}+\text{etc.}+x^{\alpha^{p}+\alpha \alpha} \\ & -x^{\alpha^{3}} \xi-x^{2 \alpha^{3}}+x^{\alpha^{4}+\alpha^{3}}-x^{\alpha^{5}+\alpha^{3}}+\text{etc.}+x^{\alpha^{p+1}+\alpha^{3}} \end{aligned}$$

etc. up to

$$-x^{\alpha^{p-2}} \xi-x^{2 \alpha^{p-2}}+x^{\alpha^{p-1}+\alpha^{p-2}}-x^{\alpha^{p}+\alpha^{p-2}}+\text{etc.}+x^{\alpha^{2 p-4}+\alpha^{p-2}}$$

the first will be $=0,$ and each of the others will be divisible by $1-x^{p}.$  Therefore, the sum of all these will also be divisible by $1-x^{p}.$  This sum is

$$\begin{aligned} &=\xi \xi-(f(x x)-1)+(f(x^{\alpha+1})-1)-(f(x^{\alpha \alpha+1})-1)+(f(x^{\alpha^{3}+1})-1)-\text{etc.}+(f(x^{\alpha^{p-2}+1})-1)\\ &=\xi \xi-f(x x)+f(x^{\alpha+1})-f(x^{\alpha \alpha+1})+f(x^{\alpha^{3}+1})-\text{etc.}+f(x^{\alpha^{p-2}+1})=\Omega \end{aligned}$$

Therefore, this expression $\Omega$ will also be divisible by $\frac{1-x^{p}}{1-x}.$  Now among the exponents $2,$  $\alpha+1,$  $\alpha \alpha+1,$  $\alpha^{3}+1 \ldots \alpha^{p-2}+1,$  the only one divisible by $p$  will be $\alpha^{\frac{1}{2}(p-1)}+1,$  and so by the previous article, the individual parts of the expression $\Omega,$

$$f(x x), f(x^{\alpha+1}), f(x^{\alpha \alpha+1}), f(x^{\alpha^{3}+1}) \text{ etc.}$$

except for the term $f(x^{\alpha^{\frac{1}{2}(p-1)}+1}),$ will be divisible by $\frac{1-x^{p}}{1-x}.$  It is therefore permissible to delete those parts, and the remaining function

$$\xi \xi \mp f(x^{\alpha^{\frac{1}{2}(p-1)}+1})$$

will still be divisible by $\frac{1-x^{p}}{1-x}.$ Above the sign will be positive or negative, depending on whether $p$  is of the form $4k+1$  or $4k+3.$  And since $f(x^{\alpha^{\frac{1}{2}(p-1)}+1})-p$  is divisible by $\frac{1-x^{p}}{1-x},$  it follows that $\xi \xi \mp p$  will also be divisible by $\frac{1-x^{p}}{1-x}.$  Q.E.D.

To avoid any ambiguity from the double sign, we will denote by $\varepsilon$ the number $+1$  or $-1,$  according to whether $p$  is of the form $4k+1$  or $4k+3.$  Therefore,

$$\frac{(1-x)(\xi \xi-\varepsilon p)}{1-x^{p}}$$

will be an integral function of $x,$ which we will denote by $Z.$

4.
Let $q$ be a positive odd number, so that $\frac{1}{2}(q-1)$  an integer. Then $(\xi \xi)^{\frac{1}{2}(q-1)}-(\varepsilon p)^{\frac{1}{2}(q-1)}$ will be divisible by $\xi \xi-\varepsilon p,$  and therefore also by $\frac{1-x^{p}}{1-x}.$  If we set $\varepsilon^{\frac{1}{2}(q-1)}=\delta,$  and

$$\xi^{q-1}-\delta p^{\frac{1}{2}(q-1)}=\frac{1-x^{p}}{1-x} \cdot Y$$

then $Y$ will be an integral function of $x,$  and we will have $\delta=+1$  whenever one of the numbers $p,$  $q,$  or both, is of the form $4k+1;$  on the other hand, we will have $\delta=-1$  whenever both $p,$  $q$  are of the form $4k+3.$

5.
Now, let us assume that $q$ is also a prime number (different from $p$ ). Then it is clear from the theorem proven in Disquisitiones Arithmeticae, art. 51, that

$$\xi^{q}-(x^{q}-x^{q \alpha}+x^{q \alpha \alpha}-x^{q \alpha^{3}}+\text{etc.}-x^{q \alpha^{p-2}})$$

is divisible by $q,$ or of the form $qX,$  where $X$  is an integral function of $x,$  even with respect to its numerical coefficients (which also applies to the other integral functions occurring here, $Z,$  $Y,$  $W$ ). Let us denote by $\mu$ the index of the number $q$  with respect to the primitive root $\alpha$  modulo $p,$  i. e. let $q \equiv \alpha^{\mu}\pmod{p}.$ Then the numbers $q,$  $q \alpha,$  $q \alpha \alpha,$  $q \alpha^{3}\ldots q \alpha^{p-2}$  will be congruent to $\alpha^{\mu},$  $\alpha^{\mu+1},$  $\alpha^{\mu+2}\ldots \alpha^{p-2},$  $1,$  $\alpha,$  $\alpha \alpha\ldots \alpha^{\mu-1}$  modulo $p,$  and thus

$$\begin{aligned} &x^{q}-x^{\alpha^{\mu}} \\ &x^{q \alpha}-x^{\alpha^{\mu+1}} \\ &x^{q \alpha \alpha}-x^{\alpha^{\mu+2}} \\ &x^{q \alpha^{3}}-x^{\alpha^{\mu+3}}\\ &\quad \vdots \\ &x^{q \alpha^{p-\mu-2}}-x^{\alpha^{p-2}}\\ &x^{q \alpha^{p-\mu-1}}-x\\ &x^{q \alpha^{p-\mu}}-x^{\alpha}\\ &x^{q \alpha^{p-\mu+1}}-x^{\alpha \alpha}\\ &\quad \vdots\\ &x^{q\alpha^{p-2}}-x^{\alpha^{\mu-1}} \end{aligned}$$

will all be divisible by $1-x^{p}.$ Taking these quantities alternately positively and negatively, and adding them all up, it is clear that the function

$$x^{q}-x^{q \alpha}+x^{q \alpha \alpha}-x^{q \alpha \alpha^{3}}+\text{etc.}-x^{q \alpha^{p-2}}\mp \xi$$

will be divisible by $1-x^{p},$ provided that the sign is taken to be positive or negative depending on whether $\mu$  is even or odd, i.e. depending on whether $q$ is a quadratic residue or non-residue modulo $p.$  Therefore, let us set

$$x^{q}-x^{q \alpha}+x^{q \alpha}-x^{q \alpha^{3}}+\text{etc.}-x^{q \alpha^{p-2}}-\gamma \xi=(1-x^{p})W$$

where $\gamma=+1$ or $\gamma=-1$  depending on whether $q$  is a quadratic residue or non-residue modulo $p.$  Then it is clear that $W$  will be an integral function.

6.
Having made these preparations, we deduce by combining the preceding equations that

$$q \xi {X}=\varepsilon p(\delta p^{\frac{1}{2}(q-1)}-\gamma)+\frac{1-x^{p}}{1-x} \cdot(Z(\delta p^{\frac{1}{2}(q-1)}-\gamma)+Y \xi \xi-W \xi(1-x))$$

Suppose that upon dividing the function $\xi X$ by

$$x^{p-1}+x^{p-2}+x^{p-3}+\text{etc.}+x+1$$

we obtain a quotient $U$ and remainder $T,$  or in other words we have

$$\xi X=\frac{1-x^{p}}{1-x} \cdot U+T$$

where $U$ and $T$  are integral functions, even with respect to their numerical coefficients, and the degree of $T$  is lower than the divisor. Then we will have

$$q T-\varepsilon p(\delta p^{\frac{1}{2}(q-1)}-\gamma)=\frac{1-x^{p}}{1-x} \cdot(Z(\delta p^{\frac{1}{2}(q-1)}-\gamma)+Y \xi \xi-W \xi(1-x)-q U)$$

which is obviously false unless the left member and the right member both vanish individually. Thus $\varepsilon p(\delta p^{\frac{1}{2}(q-1)}-\gamma)$ will be divisible by $q,$  and also $\delta p^{\frac{1}{2}(q-1)}-\gamma,$  and therefore, because $\delta \delta=1,$  the number $p^{\frac{1}{2}(q-1)}-\gamma \delta$  will be divisible by $q.$

Now if $\beta$ denotes a positive or negative unit, depending on whether $p$  is a quadratic residue or non-residue modulo $q,$  then $p^{\frac{1}{2}(q-1)}-\beta$  will be divisible by $q,$  and therefore so will be $\beta-\gamma \delta,$  which cannot happen unless $\beta=\gamma \delta.$  Hence, the fundamental theorem follows automatically. Namely,

 * I. Whenever both $p,$ $q,$  or one of them alone, is of the form $4 k+1,$  and consequently $\delta=+1,$  we will have $\beta=\gamma,$  and thererfore either $q$  is a quadratic residue mduloo $p,$  and $p$  is simultaneously a quadratic residue modulo $q,$  or $q$  is a quadratic non-residue modulo $p,$  and simultaneously $p$  is a quadratic non-residue modulo $q.$

 * II. Whenever both $p,$ $q$  are of the form $4 k+3,$  and consequently $\delta=-1,$  we will have $\beta=-\gamma,$  and therefore either $q$  is a quadratic residue modulo $p,$  and simultaneously $p$  is a quadratic non-residue modulo $q,$  or $q$  is a non-residue modulo $p,$  and simultaneously $p$  is a residue modulo $q.$  Q. E. D.

1.
Before we present a new solution to this problem, we will briefly repeat the solution given in Disquisitiones Arithmeticae, which was accomplished quite expediently with the help of the fundamental theorem and the following well-known theorems:

 * I. The relation of a number $a$ to a number $b$  (insofar as the former is a quadratic residue or non-residue modulo the latter) is the same as the relation of a number $c$  to $b,$  if $a \equiv c\pmod{b}.$

 * II. If $a$ is a product of factors $\alpha,$  $\beta,$  $\gamma,$  $\delta,$  etc ., and $b$  is a prime number, then the relation of $a$  to $b$  will depend on the relation of these factors to $b,$  so that $a$  will be a quadratic residue or non-residue depending on whether there is an even or odd number of such factors which are quadratic non-residues modulo $b.$  Thus, whenever any factor is a square, it will not be considered at all in this examination; and if any factor is a power of an integer with an odd exponent, it can be replaced with that integer instead.

 * III. The number 2 is a quadratic residue modulo any prime number of the form $8m+1$ or $8m+7,$  and a non-residue modulo any prime number of the form $8m+3$  or $8m+5.$

Therefore, given a number $a$ whose relation to the prime number $b$  is sought, we first substitute the minimal positive residue of $a$  modulo $b$  in place of $a.$  Then, after resolving this residue into its prime factors, the problem is reduced by theorem II to the determination of the relations of each of these factors to $b.$  The relation of the factor 2 (if it is present an odd number of times) to $b$  is known by theorem III. The relations of the remaining factors to $b$  known by the fundamental theorem. Thus instead of the relation of the given number to the prime number $b,$ we must now investigate the relations of $b$  to certain other odd primes smaller than $b$, and these problems will be reduced in the same way to smaller moduli, and it is clear that these successive reductions will eventually be exhausted.

2.
To illustrate this solution by an example, let us seek the relation of the number $103$ to $379.$  Since $103$  is already less than $379,$  and is itself a prime number, the fundamental theorem must be applied immediately, which tells us that the relation we seek is the opposite of the relation of the number $379$  to $103.$  This in turn is equal to the relation of the number $70$  to $103,$  which depends on the relations of the numbers $2,$  $5,$  $7$  to $103.$  The first of these relations is revealed by theorem III. The second, by the fundamental theorem, depends on the relation of the number $103$ to $5,$  which by theorem I is equal to the relation of the number $3$  to $5;$  this, in turn, by the fundamental theorem, depends on the relation of the number $5$  to $3,$  which by theorem I is equal the relation of the number $2$  to $3,$  which is known by theorem III. Likewise, the relation of the number $7$ to $103$  depends, by the fundamental theorem, on the relation of the number $103$  to $7,$  which by theorem I is equal to the relation of the number $5$  to $7;$  this, in turn, by the fundamental theorem, depends on the relation of the number $7$  to $5,$  which is equal, by theorem I, to the relation of the number $2$  to $5,$  which is known by theorem III. If one prefers to transform this analysis into a synthesis, the decision of the question will be referred to the fourteen points, which we present here in full, so that the greater concision of the new solution may be the more clearly understood.

 * 1) The number $2$  is a quadratic residue modulo $103$  (theorem III).
 * 2) The number $2$  is a quadratic non-residue modulo $3$  (theorem III).
 * 3) The number $5$  is a quadratic non-residue modulo $3$  (by 1 and 2).
 * 4) The number $3$  is a quadratic non-residue modulo $5$  (fund . theorem and 3).
 * 5) The number $103$  is a quadratic non-residue modulo $5$  (1 and 4).
 * 6) The number $5$  is a quadratic non-residue modulo $103$  (fund . theorem and 5).
 * 7) The number $2$  is a quadratic non-residue modulo $5$  (theorem III).
 * 8) The number $7$  is a quadratic non-residue modulo $5$  (1 and 7).
 * 9) The number $5$  is a quadratic non-residue modulo $7$  (fund . theorem and 8).
 * 10) The number $103$  is a quadratic non-residue modulo $7$  (1 and 9).
 * 11) The number $7$  is a quadratic residue modulo $103$  (fund . theorem and 10).
 * 12) The number $70$  is a quadratic non-residue modulo $103$  (II, 1, 6, 11).
 * 13) The number $379$  is a quadratic non-residue modulo $103$  (1 and 12).
 * 14) The number $103$  is a quadratic residue modulo $379$  (fund . theorem and 13).

In the following, for the sake of brevity, we will use the notation introduced in ''Comment. Gotting. Vol.'' XVI. Namely, by $[x]$ we will denote the quantity $x$  itself, if $x$  is an integer, or the greatest integer smaller than $x,$  if $x$  is a fractional quantity, so that $x-[x]$  is always a non-negative quantity less than unity.

3.
If $a$ and $b$  are positive integers which are relatively prime to each other, and $\left[\frac{1}{2} a\right]=a^{\prime},$  evaluate the sum

$$\left[\frac{b}{a}\right]+\left[\frac{2 b}{a}\right]+\left[\frac{3 b}{a}\right]+\left[\frac{4 b}{a}\right]+\text{etc.}+\left[\frac{a^{\prime} b}{a}\right]$$

For the sake of brevity, let us denote the sum in question by $\varphi(a, b),$ so that

$$\varphi(b, a)=\left[\frac{a}{b}\right]+\left[\frac{2 a}{b}\right]+\left[\frac{3 a}{b}\right]+\text{etc.}+\left[\frac{b^{\prime} a}{b}\right]$$

if we set $\left[\frac{1}{2} b\right]=b^{\prime}.$ It was shown in the demonstration of the third fundamental theorem that in the case where $a$  and $b$  are both odd, we have

$$\varphi(a, b)+\varphi(b, a)=a^{\prime} b^{\prime}$$

As we already mentioned there, the truth of this proposition can also be extended to the case where only one of the numbers $a,$ $b$  is odd, by following the same method. Let $a$ be divided by $b$  in a manner analogous to the method by which the greatest common divisor of two integers is investigated, let $\beta$  be the quotient, and let $c$  be the remainder; then divide $b$  by $c$  and so on in a similar manner, so as to obtain equations

$$\begin{aligned} & a=\beta b+c \\ & b=\gamma c+d \\ & c=\delta d+e \\ & d=\varepsilon e+f \text{ etc.} \end{aligned}$$

In this way, through a series of continually decreasing numbers $b,$ $c,$  $d,$  $e,$  $f$  etc. , we shall eventually arive at unity, since by hypothesis $a$ and $b$  are coprime. Then the final equation will be

$$k=\lambda l+1$$

We clearly have

$$\begin{aligned} & {\left[\frac{a}{b}\right]=\left[\beta+\frac{c}{b}\right]=\beta+\left[\frac{c}{b}\right]} \\ & {\left[\frac{2 a}{b}\right]=\left[2 \beta+\frac{2 c}{b}\right]=2 \beta+\left[\frac{2 c}{b}\right]} \\ & {\left[\frac{3 a}{b}\right]=\left[3 \beta+\frac{3 c}{b}\right]=3 \beta+\left[\frac{3 c}{b}\right]} \end{aligned}$$

etc., so

$$\varphi(b, a)=\varphi(b, c)+\frac{1}{2} \beta (b^{\prime} b^{\prime}+b^{\prime})$$

and therefore

$$\varphi(a, b)=a^{\prime} b^{\prime}-\frac{1}{2} \beta (b^{\prime} b^{\prime}+b^{\prime})-\varphi(b, c)$$

By similar reasoning, if we set $\left[\frac{1}{2} c\right]=c^{\prime},$ $\left[\frac{1}{2} d\right]=d^{\prime},$  $\left[\frac{1}{2} e\right]=e^{\prime}$  etc. , then

$$\begin{aligned} & \varphi(b, c)=b^{\prime} c^{\prime}-\frac{1}{2} \gamma(c^{\prime} c^{\prime}+c^{\prime})-\varphi(a, d) \\ & \varphi(c, d)=c^{\prime} d^{\prime}-\frac{1}{2} \delta(d^{\prime} d^{\prime}+d^{\prime})-\varphi(d, e) \\ & \varphi(d, e)=d^{\prime} e^{\prime}-\frac{1}{2} \varepsilon(e^{\prime} e^{\prime}+e^{\prime})-\varphi(e, f) \end{aligned}$$

etc. up to

$$\varphi(k, l)=k^{\prime} l^{\prime}-\frac{1}{2} \lambda(l^{\prime} l^{\prime}+l^{\prime})-\varphi(l, 1)$$

Therefore, since it is obvious that $\varphi(l, 1)=0,$ we obtain the formula

$$\begin{aligned} \varphi(a, b)=&a^{\prime} b^{\prime}-b^{\prime} c^{\prime}+c^{\prime} d^{\prime}-d^{\prime} e^{\prime}+\text{etc.} \pm k^{\prime} l^{\prime} \\ &-\frac{1}{2} \beta (b^{\prime} b^{\prime}+b^{\prime})+\frac{1}{2} \gamma(c^{\prime} c^{\prime}+c^{\prime})-\frac{1}{2} \delta(d^{\prime} d^{\prime}+d^{\prime})+\frac{1}{2} \varepsilon(e^{\prime} e^{\prime}+e^{\prime})-\text{etc.} \mp \frac{1}{2} \lambda(l^{\prime} l^{\prime}+l^{\prime}) \end{aligned}$$

4.
It is easily concluded from what was set forth in the third proof, that the relation of the number $b$ to $a,$  whenever $a$  is a prime number, is automatically known from the value of the sum $\varphi(a, 2 b).$  Namely, $b$  will be a quadratic residue or non-residue modulo $a$  according to whether this sum is an even or odd number. The sum $\varphi(a, b)$ itself can be used for the same purpose, but with the restriction that the case where $b$  is odd must be distinguished from the case where it is even. Specifically,

 * I. Whenever $b$ is odd, $b$  will be a quadratic residue or non-residue modulo $a,$  depending on whether $\varphi(a, b)$  is even or odd.

 * II. Whenever $b$ is even, the same rule will hold, if in addition $a$  is of the form $8n+1$  or of the form $8n+7.$  If however, for an even value of $b$  the modulus $a$  is of the form $8n+3$  or $8n+5,$  the opposite rule must be applied, namely that $b$  will be a quadratic residue modulo $a$  if $\varphi(a, b)$  is odd, but it will be a non-residue if $\varphi(a, b)$  is even.

All of this is very easily derived from article 4 of the third proof.

5.
Example. If the ratio of the number 103 to the prime number 379 is sought, then to find the sum $\varphi(379,103),$ we first compute

$$\begin{array}{r|r|r} a= 379 & a^{\prime}=189 & \\ b= 103 & b^{\prime}=\phantom{0}51 & \beta=3 \\ c= \phantom{0}70 & c^{\prime}=\phantom{0}35 & \gamma=1 \\ d= \phantom{0}33 & d^{\prime}=\phantom{0}16 & \delta=2 \\ e= \phantom{00}4 & e^{\prime}=\phantom{00}2 & \varepsilon=8 \end{array}$$

hence

$$\varphi(379,103)=9639-1785+560-32-3978+630-272+24=4786$$

and thus $103$ is a quadratic residue modulo $379.$  If we want to use the sum $\varphi(379,206)$  for the same purpose, we have the following pattern,

$$ \begin{array}{r|r|r} 379&189&\\ 206&103&1\\ 173&86&1\\ 33&16&5\\ 8&4&4\end{array}$$

from which we deduce

$$\varphi(379,206)=19467-8858+1376-64-5356+3741-680+40=9666$$

and thus 103 is a quadratic residue modulo 379.

6.
Since in order to determine the relation of $b$ to $a,$  it is not necessary to compute each part of the aggregate $\varphi(a, b),$  but rather it is sufficient to know how many of them are odd, our rule can also be expressed as follows:

Let $a = \beta b+c,$ $b = \gamma c+d,$  $c = \delta d+e$  etc. , until the series of numbers $a,$ $b,$  $c,$  $d,$  $e$  etc. reaches unity. Set $\left[\frac{1}{2} a\right]=a^{\prime},$ $\left[\frac{1}{2} b\right]=b^{\prime},$  $\left[\frac{1}{2} c\right]=c^{\prime}$  etc. , and let $\mu$ be the multitude of odd numbers in the series $a^{\prime},$  $b^{\prime},$  $c^{\prime}$  etc. which are immediately followed by an odd number; further, let $\nu$ be the multitude of odd numbers in the series $\beta,$  $\gamma,$  $\delta$  etc. , such that the corresponding number in the series $b^{\prime},$ $c^{\prime},$  $d^{\prime}$  etc. is of the form $4n+1$ or $4n+2.$  With this being done, $b$  will be a quadratic residue or non-residue modulo $a,$  depending on whether $\mu + \nu$  is even or odd, except in the case where $b$  is even and $a$  is of the form $8n+3$  or $8n+5,$  in which case the opposite rule holds.

In our example, the sequence $a^{\prime},$ $b^{\prime},$  $c^{\prime},$  $d^{\prime},$  $e^{\prime}$  has two consecutive pairs of odd numbers, hence $\mu =2,$  and in the series $b^{\prime},$  $c^{\prime},$  $d^{\prime},$  $e^{\prime},$  there are two odd numbers, but the corresponding numbers in $b^{\prime},$  $c^{\prime},$  $d^{\prime},$  $e^{\prime}$  are of the form $4n+3,$  hence $\nu = 0.$  Therefore, $\mu + \nu$  is even, and it follows that 103 is a quadratic residue modulo 379.


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I came to myself again, my hands were full of young grass and mould, and a little girl kneeling at my side was rubbing my forehead tenderly with a dock-leaf and a handkerchief.

"Oh, I am so glad," she whispered softly, as I opened my eyes and looked at her; "now you will try to be better, won't you?"

I had never heard so sweet a sound as came from between her bright red lips, while there she knelt and gazed at me; neither had I ever seen anything so beautiful as the large dark eyes intent upon me, full of pity and wonder. And then, my nature being slow, and perhaps, for that matter, heavy, I wandered with my hazy eyes down the black shower of her hair, as to my jaded gaze it seemed; and where it fell on the turf, among it (like an early star) was the first primrose of the season. And since that day, I think of her, through all the rough storms of my life, when I see an early primrose. Perhaps she liked my countenance, and indeed I know she did, because she said so


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 afterwards; although at the time she was too young to know what made her take to me. Not that I had any beauty, or ever pretended to have any, only a solid healthy face, which many girls have laughed at.

Thereupon I sate upright, with my little trident still in one hand, and was much afraid to speak to her, being conscious of my country-brogue, lest she should cease to like me. But she clapped her hands, and made a trifling dance around my back, and came to me on the other side, as if I were a great plaything.

"What is your name?" she said, as if she had every right to ask me; "and how did you come here, and what are these wet things in this great bag?"

"You had better let them alone," I said; "they are loaches for my mother. But I will give you some, if you like."

"Dear me, how much you think of them! Why they are only fish. But how your feet are bleeding! oh, I must tie them up for you. And no shoes nor stockings! Is your mother very poor, poor boy?"

"No," I said, being vexed at this; "we are rich enough to buy all this great meadow, if we chose; and here my shoes and stockings be."

"Why they are quite as wet as your feet; and I cannot bear to see your feet. Oh, please to let me manage them; I will do it very softly."

"Oh, I don't think much of that," I replied; "I shall put some goose-grease to them. But how you are


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Author:Otto Bonnell

Works

 * Turkey in the Straw (1899 ragtime arrangement)

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 necked people—a foolish nation:—as were your fathers, so are ye."

As was the country, so the people:—the country, geographically, was embraced within the circuit of the East; nevertheless, in climate and productions it was European more than it was Asiatic. And so the people—Orientals by origin, by physiognomy, by usages, and yet in many points of mental constitution, and by its restless energy, it was more European than Oriental. Toward the trans-Euphratean races—the ultra-Orientals—the Israelite showed a decisive contrariety or alienation: he refused his sympathies toward the sun-rising; or, if in some instances amalgamation in that direction took place, the sure and speedy consequence was loss of nationality in every sense—physical, ritual, social. The captive tribes, when carried eastward, forgot their institutions—forgot their very name.

But toward the people of the "Islands of the sea"—the European races—the Jew, while maintaining a sullen antagonism, and continuing to rebut scorn with scorn, has done so in a manner that gave proof of his consciousness of what might be called—intellectual and moral consanguinity. By his sympathies, by his intellectual range, by his moral intensity, by his religious depth, and even by his tastes, the Jew has made good his claim to be numbered with those that constitute the commonwealth of western civilization. Intimately consorted with European nations, this integrate people has


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8 Beside the path the unburied carcass lay; The shepherd, by the fountains of the glen, Fled, while the robber swept his flock away, And slew his babes. The sick, untended then, Languished in the damp shade, and died afar from men.

But misery brought in love; in passion's strife Man gave his heart to mercy, pleading long, And sought out gentle deeds to gladden life; The weak, against the sons of spoil and wrong, Banded, and watched their hamlets, and grew strong; States rose, and, in the shadow of their might, The timid rested. To the reverent throng, Grave and time-wrinkled men, with locks all white, Gave laws, and judged their strifes, and taught the way of right;

Till bolder spirits seized the rule, and nailed On men the yoke that man should never bear, And drave them forth to battle. Lo! unveiled The scene of those stern ages! What is there! A boundless sea of blood, and the wild air Moans with the crimson surges that entomb Cities and bannered armies; forms that wear The kingly circlet rise, amid the gloom, O'er the dark wave, and straight are swallowed in its womb.

Those ages have no memory, but they left A record in the desert—columns strown On the waste sands, and statues fallen and cleft, Heaped like a host in battle overthrown;


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 the authority carries out the action himself or authorises another person to do so on his behalf, with the person subjected to the administrative order being obliged to pay the authority the costs and a surcharge at the rate of twenty-five per cent per year of the said costs;

an administrative fine is imposed in an amount appropriate for the situation, but not over twenty thousand baht per day.

The authorities at which level shall have the power to impose administrative fines in what amount and for what cases shall be designated by ministerial regulations.

In the case that urgent execution is required for prevention of a breach of a law which carries a criminal punishment or prevention of damage to the public interest, the authority may apply the measure for administrative execution without having to issue an administrative order requiring an act to be done or omitted first. However, this must be done to the extent appropriate for the situation and not beyond the scope of his powers and duties.

Prior to applying a measure for administrative execution according to section 58, the authority must issue written warning requiring the act according to the administrative order to be done or omitted within a period of time designated as appropriate for the case. The said warning may be issued together with the administrative order.

Such warning must specify—

the measure for administrative execution clearly, but no more than one measure shall be designated on the same occasion;

the costs of the actions carried out by the authority himself or through another person as may be authorised, or the amount of the administrative fine, as the case may be.

The costs designated in the warning shall not prejudice the right to demand additional costs, if more costs than those designated are actually incurred.

The authority must apply the measure for administrative execution designated in the warning under section 59. The measure may be changed only when it appears that the measure so designated cannot achieve its objectives.

If the person subjected to the administrative order offers resistance or obstruction to the administrative execution, the authority may employ forces to implement the measure for administrative execution, but this must be done to the extent appropriate for the case. In the case of necessity, the authority may seek assistance from police officers.

In the case of nonpayment of an administrative fine, the authority shall proceed with it in accordance with section 57.

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 A person to whom a measure for administrative execution is applied may file an appeal against such administrative execution.

An appeal against administrative execution shall follow the same criteria and procedure as those for an appeal against an administrative order.

If any provision of law has established a specific measure for administrative execution but an authority finds that such measure is likely to bring about less effect than any measure under this Chapter, the authority may apply a measure under this Chapter instead.

When a time limit is designated in days, weeks, months, or years, the first day thereof shall not be included in calculation, save where the act in question is commenced on that very day or an authority otherwise designates.

In the case that an authority has the duty to carry out any act within a designated period of time, the last day thereof shall be included in calculation, even though it is his holiday.

In the case that any person has to do anything within a period of time designated by the law or by an order of an authority, if the last day is a holiday for an authority or is a conventional holiday for the recipient of the order, the period of time shall be deemed to conclude on the working day that follows such holiday, save where the law or an order of an authority otherwise designates.

A period of time designated in an order of an authority may be extended, and if the period of time has already concluded, the authority may also give it a retroactive extension when it would be unfair to let it conclude as it originally would.

In the case that any person is prevented, by necessary circumstances arising not out of his fault, from doing anything within a period of time designated by the law, an authority may, upon his application, extend the period of time and renew any action which has already lapsed. In this respect, the application must be filed within fifteen days from the conclusion of those circumstances.

When an appeal has been made in accordance with the provisions of Part 5 of Chapter 2 of this Act or an application has been filed with a commission for ruling of disputes or with the Commission for Ruling of Petitions under the law

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