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 Rh the lands lying upon and near the line of railroad from the city of Mexico to Vera Cruz, for the purpose of determining whether they were suited to American colonization. We are engaged at this time in the discharge of that duty. We find in the vicinity of this place the most beautiful and, all things considered, the best agricultural country that I have ever seen. The climate is delightful—never hot, never cold, always temperate, always pleasant; the soil richer and more productive than the best of the prairie lands of Mississippi in the Okolona country, yielding large crops of corn, barley, rice, tobacco, sugar-cane, and coffee, with all the fruits of the tropics, and the best that you ever tasted...

"In a calm review of the past I am glad to be able to say that I have nothing to regret but the failure of the revolution. My course was dictated by strong and clear convictions of duty. Had I faltered in following those convictions, it would 'have been at the sacrifice of principle and self-respect. It is better, far better, for me that I should have lost position, fortune, and home and stand here to-day a penniless exile than to have violated principle and forfeited self-respect for these miserable and paltry considerations. I thank God that I did not falter. . . . No; there are no terms or conditions upon which I could ever consent to live in that country, except the independence of the South..

"Where is Forrest, and what is he doing? And where and how is everybody else? for I have heard from hone of our friends since I left Mississippi.

"Give my kind regards to Mrs. Adair, Robbin, Jack, and Forrest, and kiss Mary for me and tell her that it would give me great pleasure to have a romp with her this evening.

"My health is excellent, and I feel that it can not be otherwise in this charming climate. Write me at Cordova, Mexico, and enclose to Henry Denis, Esq., at New Orleans. Denis will forward it to me."

The following paper in pencil manuscript has been preserved by Lieut. Col. S. G. Shepard, and was in his possession at the Nashville reunion. He commanded the Seventh Tennessee Regiment. Archer's Brigade: C. H., April 10, 1865. Agreement entered into this day in regard to the surrender of the Army of Northern Virginia to the United States authorities.

1. The troops shall march by brigades and detachments to a designated point, stack their arms, deposit their sabers, pistols, etc., and from thence march to their homes under charge of their officers, superintended by their respective divisions and corps commanders, officers retaining their side arms and their authorized number of private horses.

2. All public horses and public property of all kinds to be turned over to the staff officers designated by the United States authorities.

3. Such transportation as may be agreed upon as necessary for the transportation of the private baggage of officers will be allowed to accompany the officers, to be turned over at the end of the trip to the nearest United States quartermaster, receipt being taken for the same.

4. Couriers and mounted men of the artillery and cavalry whose horses are their own private property will be allowed to retain them.

5. The surrender of the Army of Northern Virginia shall be construed to include all the forces operating with that army on the 8th inst., the date of the commencement of negotiations for surrender, except such bodies of cavalry as actually [Here a line of the manuscript is not discernible] of artillery as were more than (20) twenty miles from Appomattox C. H. at the time of surrender, on the 9th inst.

Signed: J. Longstreet, Lieut-Gen.; John Gibbons, Maj.-Gen. Vols.; J. B. Gordon, Maj.-Gen.; Charles Griffin, Bvt. Maj.-Gen. Vols.; W. N. Pendleton Brig.-Gen. and Chief Artillery; W. Merrett, Bvt. Maj.-Gen.

A true copy. V. Latrobe, Lieut.-Col. and A. A. G.; R. H. Finney, A. A. G.

Official. Polk G. Johnson, A. A. A. G.

For Lieut.-Col. Shepard, Commanding Seventh Tennessee.

There was carelessness in direction, but experts traced out the men whose names were misspelled and whose regiments were confused with some other, etc., until finally the letter reached the right man.

The custom then was for a letter to be addressed to the company, regiment, brigade, and division of the army in which the soldier was supposed to be. Mail for a certain division went to the headquarters, was distributed to the brigades and regiments, and by the regimental headquarters to the companies, and by the company officers to the men. The government provided that all letters from the soldiers be forwarded without postage if they bore the frank of the adjutant or colonel. This was a great convenience to the men, because it was almost impossible for them to secure or carry postage-stamps. Packages of papers sent to the boys were more conscientiously delivered than they are in these times. In fact, the postal system of the army was a wonderful thing.

The pathetic side of the letter business occurred when the message of affection and love from sweethearts, sisters, and mothers came to the men who had been shot, maybe fatally wounded, or who were sick in the hospitals. The most trying duty of company or regimental officers was the handling of such correspondence. It required tact, sympathy, and understanding of human nature and a heart full of consideration and tenderness.

Joe Blankenship, Lake Como, Miss.: "I was a member of the Jeff Davis Artillery, from Selma. Ala., A. N. V. John Mitchell, of Tennessee, lieutenant of our company, was my friend. There was not a braver man in Stonewall Jackson's corps. He lost his right arm at Chancellorsville. I have not heard from him since the war. but would like to do so, or to hear from an other member of our battery."

At the suggestion of Comrade S. J. Corley it was declared to be the sense of his camp that the parades of Confederate Veterans heretofore practised at their annual reunions be hereafter abandoned, and that in place thereof a review of the Confederate veterans be arranged for at some convenient and accessible point.


text: Dictionary of National Biography, 1885-1900/Pritchard, William

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


text: Dictionary of National Biography, 1885-1900/Pritchett, James Pigott


text: Dictionary of National Biography, 1885-1900/Pritzler, Theophilus


text: Dictionary of National Biography, 1885-1900/Probert, William


text: Dictionary of National Biography, 1885-1900/Probus


text: Dictionary of National Biography, 1885-1900/Proby, Granville Leveson


text: Dictionary of National Biography, 1885-1900/Proby, John (1720-1772)


text: Dictionary of National Biography, 1885-1900/Proby, John Joshua


text: Dictionary of National Biography, 1885-1900/Probyn, Edmund


text: Dictionary of National Biography, 1885-1900/Proctor, Thomas (1753-1794)


text:
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 Jan. 6, 1834.]

" Simon Peter answered and said. Thou art the, the Son of the Living . And answered and said unto him. Blessed art thou, Simon Bar-jona: for flesh and blood hath not revealed it unto thee, but My  which is in heaven. And I say also unto thee, That thou art Peter; and upon this rock I will build My Church; and the gates of hell shall not prevail against it." Matt. xvi. 16–18.

The rock, then, upon which the Church is built, is the confession, that is the, the Son of the Living ; a truth set forth and shadowed by the Prophets, but openly and plainly taught by the Apostles. St. Paul uses a similar expression, when he speaks of the body of Christians being "built upon the foundation of the Apostles and Prophets;" (i. e. resting in the sound and true doctrine which they taught;) " Himself being the chief corner-stone," (Ephes. ii. 20.);—our very spiritual existence depending upon our adherence to this great truth, that was the anointed Son of  and Man, the promised  of the world;—He, who by taking man's nature upon Him in the womb of the Blessed Virgin, fulfilled the prophecy, that the  should be of the seed of Abraham, in whom "all the nations of the earth should be blessed," (Gen. xxii. 18.) and the seed of the woman, who should "bruise the serpent's head," (Gen. iii. 15.);—and who, inasmuch as He was "the Only-begotten  of, (John iii. 18.) " of ," "Very  of very ," (Nicene Creed,) fulfilled the prophecy, that the  should be "the mighty ," (Isaiah ix. 6.);—He, of whom it was said, "Let all the Angels of  worship Him,"


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 (Heb.i. 6.);—and of whom it was likewise said, "Thy throne, O God, is for ever and ever." Ps. xlv. 6.

I said, that our very spiritual existence depends upon our adhering to this great and fundamental truth; and this I said, not of us as individuals only, but as Members of the Church of, and of that portion of Church in this Kingdom which is usually called the Church of England. It is true of us individually, as appears by the words of St. John; "He that hath the, hath life; and he that hath not the of , hath not life," (1 John v. 12.); by which we learn, that as long as we slight or disbelieve, or deny this sacred truth, we have no spiritual life in us. It is also true of us, as Members of the Church of, and of that portion of Church in this Kingdom which is usually called the Church of England, as appears from the passage before us; "Upon this rock, (i. e. upon this firm confession of faith in  as the , the Son of the Living ,) "I will build My Church; and the gates of hell shall not prevail against it." For from this we learn, that the Church, and any given portion of that Church, is only then able to defy the assaults of the Devil, that she can only then look forward with confidence to get the victory, so long as she adheres firmly to this faith and belief in . When she departs from that foundation, then she ceases to have a claim for the continuance of the promised aid. This is a matter which it behoves Christians at all times to place before their eyes, and to keep in remembrance; but, especially, at the present time, does it behove us, who are Members of the Church of  in England, to do so; because of the unceasing endeavours which are being made by men who are either careless of religion altogether, or who have embraced false views of it, to overthrow our Church; endeavours, which we have reason to regard either with fear, or not, according as we have reason, or not, to suppose that the Members of the Church have departed from the true faith and fear of , and of the. If there is reason to believe that many or most of the Members of our Church are regardless of that true faith, and of the honour of Him in whom we believe, that by their lips, or by their lives, they set at nought His Majesty, neglect His Sacraments, despise His Word, forsake His Worship, obey not His


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 Voice, or look for redemption and salvation by any other means than by His Cross and Blood, then we have every reason to fear, that these endeavours of our enemies will be successful; that the light of presence will be withheld from us; and that, as He withdrew from the Jews, when they neglected, the Lord of Glory, so He will withdraw from our Nation also, and leave it to the wretchedness of its own chosen ways; to the enjoyment of those idols, the world, the flesh, and the Devil, for which it will have forsaken the  of Israel, and refused to hearken to the voice of the  of , who died to take away the sins of the world. But if not, if we have reason to hope that there are many true Servants of still to be found; that there are many who, not with their lips only, but in their hearts and with their lives acknowledge Him the only true, and  whom He has sent; acknowledge Him so as to obey His voice, and keep and do what He has commanded; then may we regard the attempts of our enemies without dismay; then may we have firm and stedfast hope, that the gates of Hell shall not prevail against us: that though it may please  that we should suffer for a while;—as we suffered, together with good King Charles, at the hands of the Dissenters; as we suffered, in the days of bloody Queen Mary, at the hands of the Roman Catholics; as we suffered during the first three hundred years after , at the hands of the Heathens and the Jews;—yet that eventually triumph will await us; that He will bring our Church out of the trial, like gold out of the fire, more pure and of greater worth, ("I will purely purge away thy dross, and take away all thy tin;" Is. i. 25.) that "all things will work together for good" to us; and that the purpose aimed at by the affliction is, that He "may present our Church to Himself as a glorious Church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish." Ephes. v. 27.

It will hence appear, that it is in the power of every individual, by a holy and religious life in the true faith and fear of and our, to promote not only his own salvation, but the welfare and stability of the Church of ; or by an unholy, careless, and irreligious life, not only to secure his own


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 damnation, but to assist the enemies of and man, who are purposed to overthrow that Church.

If times of confusion and trouble shall come, where can we seek for comfort but in the love of, in the love of to man for  sake? But how can we then take comfort in that love, if now we take no account of it? Let me entreat you, then, Christian Brethren, while the days of peace are vouchsafed to you, to give more and more heed to all religious duties. The days may come, when your Churches will be shut up, or only filled by men who will not teach the whole truth as it is in ; when you will be deprived of Ministers of Religion; or have only such as are destitute of Commission. Do not, I beseech you, by your neglect now, add to your misery then the bitterness of self-reproach, when you will have to say, "I had once the opportunity of worshipping aright, but I neglected it, and He now has withheld it from me. I had once the means of receiving the Body and Blood of my, at the hands of His own Minister; but I refused it, and now He has placed it out of my power."


text: Tracts for the Times/Tract 23

title: Tracts for the Times/Tract 23


text: Dictionary of National Biography, 1885-1900/Proud, Joseph


text:
Page:Dictionary of spoken Russian (1945).djvu/397

 ные окраины стали заселяться сравнительно недавно. Our northern border districts began to be settled only a relatively short time ago.

окрестность ([-sn-]; F) outskirts. Вы уже побывали в окрестностях города? Have you been to the outskirts of town? • vicinity. А здесь в окрестности доктор найдётся? Can you find a doctor here in the vicinity?

округ (P -а, -ов) okrug (a territorial administrative division comprising a national group).

окружать (dur of окружить) to surround. Её там окружали хорошие люди. She was surrounded by nice people there. □ Его окружали всеобщие любовь и уважение. He had everybody's love and respect.

окружить (pct of окружать) to surround. Девушки окружили американских лётчиков. The girls surrounded the American aviators. — Наш дом окружён забором. A fence surrounds our house.

октябрёнок oktiabrionok (child between the ages of seven and eleven, in the first stages of Communist training).

октябрь (-бря M) October. □ Октябрь (октябрьская революция) October revolution, 1917. Он произнёс эту речь в двадцать пятую годовщину Октября. He gave that speech on the twenty-fifth anniversary of the October revolution.

октябрьский October. Сегодня годовщина октябрьской революции. Today is the anniversary of the October revolution.

окурок (-рка) (cigarette) butt. Не бросайте окурков! Don't throw (cigarette) butts around!

оладья (/gp оладий or оладьев/) fritter.

олень (M) reindeer.

олово tin.

оловянный tin.

омлет omelette.

он (§18) he. Подождите заведующего, он вам покажет комнаты. Wait for the manager. He'll show you the rooms. — "Где Иван Иванович"? "Вот он". "Where's Ivan Ivanovich?" "Here he is." — Мы с ним большие друзья. He and I are good friends. — Он страшно ею увлечён. He's very much taken with her. • him. Вы его знаете? Do you know him? — Дайте ему сахару. Give him some sugar. — Предложите ему пойти с нами в театр. Ask him to go to the theater with us. — Я им недоволен. I'm not satisfied with him. — Его считали хорошим специалистом. They considered him an expert in his line. — О нём ходят разные слухи. There are all kinds of rumors about him. • his. Это его портфель. This is his brief case. — Это не его дело. It's none of his business. • it. "Где мой ключ"? "Вот он". "Where's my key?" "Here it is." — "Где карандаш?" "У меня его нет". "Where's my pencil?" "I don't have it." □ ему нужно he has to. Ему нужно пойти к врачу. He has to go to the doctor.

она (/nF of он/) she. Она не понимает вашего вопроса. She doesn't understand your question. • her. Не уходите без неё. Don't leave without her. — Я её видел вчера. I saw her yesterday. — Вы уже сказали ей, что уезжаете? Have you already told her that you're leaving? — Не ходите сейчас к ней, она занята. Don't go over to see her now; she's busy. — Вы говорили с ней? Did you speak to her? — Вы знаете её адрес? Do you know her address? • hers. Эта книга не моя, а её. This book isn't mine; it's hers. • it. "Где моя шапка?" "Я её не видал". "Where's my cap?" "I haven't seen it." — Я не читал этой книги, но о ней были очень хорошие отзывы в печати. I haven't read this book, but it received very good notices.

они (/np of он/) they. Они большие друзья. They're great friends. — Соседи ими недовольны — они очень шумят. They make so much noise that they annoy their neighbors. • them. Скажите им, что их тут кто-то спрашивал. Tell them that someone was asking for them here. — Что они мешкают, им пора ехать. Why don't they get a move on; it's time for them to leave. — Мы целый вечер проговорили с ними. We spent the whole evening talking to them. — Дайте ему попробовать блинов, он их никогда не ел. Give him some pancakes; he's never tasted them. — Вы видели наши музеи? Что вы о них скажете? Have you seen our museums? What do you think of them? • their. Вы видели их новую квартиру? Have you seen their new apartment? • theirs. Эта машина не наша, это их. This isn't our car; it's theirs.

оно (/nN of он/) it. "Закройте окно". "Да оно ведь закрыто". "Close the window." "But it's already closed." — Я прочитал это письмо и ничего обидного в нём не нашёл. I read the letter through and found nothing insulting in it. — Так оно и случилось, как вы говорили. It happened just as you said it would. — Вот то-то и оно, надо было быть осторожнее. That's just it; you should have been more careful. — Моё вечное перо испортилось, а я не могу без него обойтись. My fountain pen isn't working and I can't do without it. — Платье у вас красивое, но не мешало ему быть подлиннее. You have a pretty dress on; but it wouldn't hurt if it were a little longer. □ Дело было хорошо задумано, а исполняют его плохо. The work was well planned, but badly carried out.

опаздывать (dur of опоздать) to be late. Он вечно опаздывает. He's always late.

опасаться (dur) to be afraid of, to fear. Вот этого-то я и опасаюсь. This is what I'm afraid of. — Доктор опасался, что больной не перенесёт операции. The doctor feared that the patient couldn't stand the operation.

опасность (F) danger. Радист подал сигнал опасности. The radio operator sent out the danger signal. — Опасность ещё не миновала. The danger isn't over yet. • risk. Он вытащил её из огня с опасностью для собственной жизни. At the risk of his own life he pulled her out of the fire. □ вне опасности out of danger. Здесь мы уже вне опасности. We're out of danger here.

опасный dangerous. Это довольно опасное предприятие. This is a rather dangerous undertaking. — Будьте поосторожней, он опасный человек. Be careful with him; he's a dangerous person. □ опасно dangerously. Он опасно заболел. He became dangerously ill. • dangerous. Здесь купаться опасно. It's dangerous to swim here. — Это лекарство опасно принимать, не посоветовавшись с врачом. It's dangerous to take this medicine without a doctor's advice. • risky. По ночам тут ходить опасно. It's risky to walk here at night.

опера opera. Что сегодня дают в опере? What's being given at the opera today? □ *Ну, это совсем из другой оперы! That's a horse of another color!

операция operation. Вам необходима операция. You must


text: Dictionary of National Biography, 1885-1900/Prout, John (1810-1894)


text: Dictionary of National Biography, 1885-1900/Prout, John Skinner


text: Dictionary of National Biography, 1885-1900/Prout, Samuel


text:
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ER eyes," said Bill Brewster, "are like—like—what's the word I want?"

He looked across at Lucille and Archie. Lucille was leaning forward with an eager and interested face; Archie was leaning back with his finger-tips together and his eyes closed. This was not the first time since their meeting in Beale's Auction Rooms that his brother-in-law had touched on the subject of the girl he had become engaged to marry during his trip to England. Indeed, Brother Bill had touched on very little else: and Archie, though of a sympathetic nature and fond of his young relative, was beginning to feel that he had heard all he wished to hear about Mabel Winchester. Lucille, on the other hand, was absorbed. Her brother's recital had thrilled her.

"Like" said Bill. "Like"

"Stars?" suggested Lucille.

"Stars," said Bill gratefully. "Exactly the word. Twin stars shining in a clear sky on a summer night. Her teeth are like—what shall I say?"

"Pearls?"

"Pearls. And her hair is a lovely brown, like leaves in autumn. In fact," concluded Bill, slipping down from the heights with something of a jerk, "she's a corker. Isn't she, Archie?"

title: Page:Indiscretions of Archie.djvu/182


text: Dictionary of National Biography, 1885-1900/Prout, William


text:
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 Archie opened his eyes.

"Quite right, old top!" he said. "It was the only thing to do."

"What the devil are you talking about?" demanded Bill coldly. He had been suspicious all along of Archie's statement that he could listen better with his eyes shut.

"Eh? Oh, sorry! Thinking of something else."

"You were asleep."

"No, no, positively and distinctly not. Frightfully interested and rapt and all that, only I didn't quite get what you said.

"I said that Mabel was a corker."

"Oh, absolutely in every respect."

"There!" Bill turned to Lucille triumphantly. "You hear that? And Archie has only seen her photograph. Wait till he sees her in the flesh."

"My dear old chap!" said Archie, shocked. "Ladies present! I mean to say, what!"

"I'm afraid that father will be the one you'll find it hard to convince."

"Yes," admitted her brother gloomily.

"Your Mabel sounds perfectly charming, but—well, you know what father is. It is a pity she sings in the chorus."

"She hasn't much of a voice," argued Bill in extenuation.

"All the same"

Archie, the conversation having reached a topic on which he considered himself one of the greatest living authorities—to wit, the unlovable disposition of his father-in-law—addressed the meeting as one who has a right to be heard.

title: Page:Indiscretions of Archie.djvu/183


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180 "Lucille's absolutely right, old thing. Absolutely correct-o! Your esteemed progenitor is a pretty tough nut, and it's no good trying to get away from it. And I'm sorry to have to say it, old bird, but, if you come bounding in with part of the personnel of the ensemble on your arm and try to dig a father's blessing out of him, he's extremely apt to stab you in the gizzard."

"I wish," said Bill, annoyed, "you wouldn't talk as though Mabel were the ordinary kind of chorus-girl. She's only on the stage because her mother's hard-up and she wants to educate her little brother."

"I say," said Archie, concerned. "Take my tip, old top. In chatting the matter over with the pater, don't dwell too much on that aspect of the affair. I've been watching him closely, and it's about all he can stick, having to support me. If you ring in a mother and a little brother on him, he'll crack under the strain."

"Well, I've got to do something about it. Mabel will be over here in a week."

"Great Scot! You never told us that."

"Yes. She's going to be in the new Billington show. And, naturally, she will expect to meet my family. I've told her all about you."

"Did you explain father to her?" asked Lucille.

"Well, I just said she mustn't mind him, as his bark was worse than his bite."

"Well," said Archie, thoughtfully, "he hasn't bitten me yet, so you may be right. But you've got to admit that he's a bit of a barker."

Lucille considered.

"Really, Bill, I think your best plan would be to go straight to father and tell him the whole thing. You

title: Page:Indiscretions of Archie.djvu/184


text:
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Rh don't want him to hear about it in a roundabout way."

"The trouble is that, whenever I'm with father, I can't think of anything to say."

Archie found himself envying his father-in-law this merciful dispensation of Providence; for, where he himself was concerned, there had been no lack of eloquence on Bill's part. In the brief period in which he had known him, Bill had talked all the time and always on the one topic. As unpromising a subject as the tariff laws was easily diverted by him into a discussion of the absent Mabel.

"When I'm with father," said Bill, "I sort of lose my nerve, and yammer."

"Dashed awkward," said Archie, politely. He sat up suddenly. "I say! By Jove! I know what you want, old friend! Just thought of it!"

"That busy brain is never still," explained Lucille.

"Saw it in the paper this morning. An advertisement of a book, don't you know."

"I've no time for reading."

"You've time for reading this one, laddie, for you can't afford to miss it. It's a what-d'you-call-it book. What I mean to say is, if you read it and take its tips to heart, it guarantees to make you a convincing talker. The advertisement says so. The advertisement's all about a chappie whose name I forget, whom everybody loved because he talked so well. And, mark you, before he got hold of this book—The Personality That Wins was the name of it, if I remember rightly—he was known to all the lads in the office as Silent Samuel or something. Or it may have been Tongue-Tied Thomas. Well, one day he happened by good luck to blow in the necessary for the good old P.

title: Page:Indiscretions of Archie.djvu/185


text:
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182 that W.'s, and now, whenever they want someone to go and talk Rockefeller or someone into lending them a million or so, they send for Samuel. Only now they call him Sammy the Spell-Binder and fawn upon him pretty copiously and all that. How about it, old son? How do we go?"

"What perfect nonsense," said Lucille.

"I don't know," said Bill, plainly impressed. "There might be something in it."

"Absolutely!" said Archie. "I remember it said, 'Talk convincingly, and no man will ever treat you with cold, unresponsive indifference.' Well, cold, unresponsive indifference is just what you don't want the pater to treat you with, isn't it, or is it, or isn't it, what? I mean, what?"

"It sounds all right," said Bill.

"It is all right," said Archie. "It's a scheme! I'll go farther. It's an egg!"

"The idea I had," said Bill, "was to see if I couldn't get Mabel a job in some straight comedy. That would take the curse off the thing a bit. Then I wouldn't have to dwell on the chorus end of the business, you see."

"Much more sensible," said Lucille.

"But what a deuce of a sweat," argued Archie. "I mean to say, having to pop round and nose about and all that."

"Aren't you willing to take a little trouble for your stricken brother-in-law, worm?" said Lucille severely.

"Oh, absolutely! My idea was to get this book and coach the dear old chap. Rehearse him, don't you know. He could bone up the early chapters a bit and then drift round and try his convincing talk on me."

title: Page:Indiscretions of Archie.djvu/186


text: Dictionary of National Biography, 1885-1900/Prowse, William (1752?-1826)


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Rh "It might be a good idea," said Bill reflectively.

"Well, I'll tell you what I'm going to do," said Lucille. "I'm going to get Bill to introduce me to his Mabel, and, if she's as nice as he says she is, I'll go to father and talk convincingly to him."

"You're an ace!" said Bill.

"Absolutely!" agreed Archie cordially. "My partner, what! All the same, we ought to keep the book as a second string, you know. I mean to say, you are a young and delicately nurtured girl—full of sensibility and shrinking what's-its-name and all that—and you know what the jolly old pater is. He might bark at you and put you out of action in the first round. Well, then, if anything like that happened, don't you see, we could unleash old Bill, the trained silver-tongued expert, and let him have a shot. Personally, I'm all for the P. that W.'s."

"Me, too," said Bill.

Lucille looked at her watch.

"Good gracious! It's nearly one o'clock!"

"No!" Archie heaved himself up from his chair. "Well, it's a shame to break up this feast of reason and flow of soul and all that, but, if we don't leg it with some speed, we shall be late."

"We're lunching at the Nicholson's!" explained Lucille to her brother. "I wish you were coming too."

"Lunch!" Bill shook his head with a kind of tolerant scorn. "Lunch means nothing to me these days. I've other things to think of besides food." He looked as spiritual as his rugged features would permit. "I haven't written to Her yet to-day."

"But, dash it, old scream, if she's going to be over here

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184 in a week, what's the good of writing? The letter would cross her."

"I'm not mailing my letters to England," said Bill. "I'm keeping them for her to read when she arrives."

"My sainted aunt!" said Archie.

Devotion like this was something beyond his outlook.

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text: Indiscretions of Archie/Chapter 17

title: Indiscretions of Archie/Chapter 17


text: Dictionary of National Biography, 1885-1900/Prowse, William Jeffery


text: Dictionary of National Biography, 1885-1900/Prujean, Francis


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text: Dictionary of National Biography, 1885-1900/Inglis, Charles (1731?-1791)


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HERE are now before the public many Commentaries, written by British and American divines, of a popular or homiletical character. The Cambridge Bible for Schools, the Handbooks for Bible Classes and Private Students, The Speaker's Commentary, The Popular Commentary (Schaff), The Expositor's Bible, and other similar series, have their special place and importance. But they do not enter into the field of Critical Biblical scholarship occupied by such series of Commentaries as the Kurzgefasstes exegetisches Handbuch zum A. T.; De Wette's Kurzgefasstes exegetisches Handbuch zum N. T.; Meyer's Kritisch-exegetischer Kommentar; Keil and Delitzsch's Biblischer Commentar über das A. T.; Lange's Theologisch-homiletisches Bibelwerk; Nowack's Handkommentar zum A. T.; Holtzmann's Handkommentar zum N. T. Several of these have been translated, edited, and in some cases enlarged and adapted, for the English-speaking public; others are in process of translation. But no corresponding series by Britisn or American divines has hitherto been produced. The way has been prepared by special Commentaries by Cheyne, Ellicott, Kalisch, Lightfoot, Perowne, Westcott, and others; and the time has come, in the judgment of the projectors of this enterprise, when it is practicable to combine British and American scholars in the production of a critical, comprehensive Commentary that will be abreast of modern biblical scholarship and in a measure lead its van.


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42


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 Messrs. Charles Scribner's Sons of New York, and Messrs. T. & T. Clark of Edinburgh, propose to publish such a series of Commentaries on the Old and New Testaments, under the editorship of Prof. C. A., D.D., D.Litt., in America, and of Prof. S. R. , D.D., D.Litt., for the Old Testament, and the Rev. , D.D., for the New Testament, in Great Britain.

The Commentaries will be international and inter-confessional, and will be free from polemical and ecclesiastical bias. They will be based upon a thorough critical study of the original texts of the Bible, and upon critical methods of interpretation. They are designed chiefly for students and clergymen, and will be written in a compact style. Each book will be preceded by an Introduction, stating the results of criticism upon it, and discussing impartially the questions still remaining open. The details of criticism will appear in their proper place in the body of the Commentary. Each section of the Text will be introduced with a paraphrase, or summary of contents. Technical details of textual and philological criticism will, as a rule, be kept distinct from matter of a more general character; and in the Old Testament the exegetical notes will be arranged, as far as possible, so as to be serviceable to students not acquainted with Hebrew. The History of Interpretation of the Books will be dealt with, when necessary, in the Introductions, with critical notices of the most important literature of the subject. Historical and Archæological questions, as well as questions of Biblical Theology, are included in the plan of the Commentaries, but not Practical or Homiletical Exegesis. The Volumes will constitute a uniform series.


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interest and importance of the Book of Judges lie chiefly in the knowledge which it gives us of the state of society and religion in Israel in the early centuries of its settlement in Palestine, for which Judges and Samuel are our only sources. In addition to this, parts of the book are of preëminent historical value: in particular, ch. 1, which contains by far the oldest and most trustworthy account of the invasion of Canaan; and ch. 5, the Song of Deborah, the only contemporary monument of Israelitish history before the Kingdom. In the following commentary matters of history, antiquities, and especially the social and religious life of the people in this period, are properly given the largest place; not only for their intrinsic interest, but because the knowledge of these things is indispensable to any right understanding of the history of Israel and of its religion. The work of the prophets can only be comprehended in its relation to the national religion of Israel. But before there was a national religion, there was a common religion of the Israelite tribes which was one of the most potent forces in the making of the nation. What this religion was, which they brought with them into Canaan, and what changes it underwent in contact with Canaanite civilization and the religions of the land, we learn in no small part from the Book of Judges; while here and there, as in the Song of Deborah, we have glimpses of a remoter past, the adoption of the religion of Yahweh by the tribes at Horeb, the work of Moses.

To make such a use of the book, it is necessary to distinguish carefully between the work of the principal author, who wrote in


text:
Wardship Act 1235

 * Wardship Act 1235 (c.6)
 * Wardship Act 1235 (c.7)

title: Wardship Act 1235


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vi the 6th century B.C., separated from the times of the judges by as many centuries as lie between us and the crusades, and the much older sources from which the stories of the judges themselves are derived. We must also, as far as possible, define the age and character of these sources, which are not all of the same antiquity or historical value. Nor is it solely on historical grounds that this is required. The difficulties which the interpreter finds in the book are in considerable part of a kind for which exegesis and textual criticism have no solution. They have arisen from the changes and additions which the author made in transcribing his sources, or from the attempt to combine and harmonize two parallel but slightly different versions of the same story, and can be cleared up only by ascertaining how this was done. Criticism is thus not only obligatory upon the historian, it is an essential part of the work of the exegete. That the task is delicate and difficult, and in the nature of the case largely conjectural, cannot exempt the commentator from trying to solve these knotty questions. At the worst, the uncertainties of criticism are infinitely preferable to the exegetical violence which is the only alternative. In the commentary, especially in the introductions to the several stories, I have discussed the particular problems of criticism with such fulness as they seemed to demand; in the Introduction (§ 3–6) the reader will find set forth the general results to which these investigations lead.

The Hebrew text of Judges, with the exception of part of ch. 5, is comparatively well preserved; but in very many places the ancient versions have a better reading, or a variant which may not be neglected. The Greek translations of this book are of peculiar interest, and perhaps nowhere in the Old Testament can the difficult problems which this version presents be approached with more hope of illuminating results. I trust that the somewhat full registration of the readings of G in this commentary


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 (Communicated in the meeting of April 1916.)

§ 32. In the two preceding papers we have tried so far as possible to present the fundamental principles of the new gravitation theory in a simple form.

We shall now show how 's differential equations for the gravitation field can be derived from 's principle. In this connexion we shall also have to consider the energy, the stresses, momenta and energy-currents in that field.

We shall again introduce the quantities $$g_{ab}$$ formerly used and we shall also use the "inverse" system of quantities for which we shall now write $$g^{ab}$$. It is found useful to introduce besides these the quantities

$\mathfrak{g}^{ab}=\sqrt{-g}g^{ab}$

Differential coefficients of all these variables with respect to the coordinates will be represented by the indices belonging to these latter, e.g.

$g_{ab,p}=\frac{\partial g_{ab}}{\partial x_{p}},\ g_{ab,pq}=\frac{\partial^{2}g_{ab}}{\partial x_{q}\partial x_{p}}$|undefined

We shall use 's symbols

$\left[\begin{array}{c} ab\\ c \end{array}\right]=\frac{1}{2}\left(g_{ac,b}+g_{bc,a}-g_{ab,c}\right)$

and 's symbol

$\begin{array}{l} (ik,lm)=\frac{1}{2}\left(g_{im,lk}+g_{kl,im}-g_{il,km}-g_{km,il}\right)+\\ \\ \qquad+\sum(ab)g^{ab}\left\{ \left[\begin{array}{c} im\\ a \end{array}\right]\left[\begin{array}{c} kl\\ b \end{array}\right]-\left[\begin{array}{c} il\\ a \end{array}\right]\left[\begin{array}{c} km\\ b \end{array}\right]\right\} \end{array}$

Further we put

This latter quantity is a measure for the curvature of the field-figure. The principal function of the gravitation field is

title: Page:LorentzGravitation1916.djvu/30


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 $\frac{1}{2\varkappa}\int QdS$

where

$Q=\sqrt{-g}G$

In the integral $$dS$$, the element of the field-figure, is expressed in $$x$$-units. The integration has to be extended over the domain within a certain closed surface $$\sigma$$; $$\varkappa$$ is a positive constant.

§ 33. When we pass from the system of coordinates $$x_{1},\dots x_{4}$$ to another, the value of $$G$$ proves to remain unaltered; it is a scalar quantity. This may be verified by first proving that the quantities $$ik, lm$$ form a covariant tensor of the fourth order. Next, $$g^{kl}$$ being a contravariant tensor of the second order, we can deduce from (40) that $$\left(G_{im}\right)$$ is a covariant tensor of the same order. According to (41) $$G$$ is then a scalar. The same is true for $$Q dS$$.

We remark that $$g_{ba}=g_{ab}$$ and $$g_{ab,fe}=g_{ab,ef}$$. We shall suppose $$Q$$ to be written in such a way that its form is not altered by interchanging $$g_{ba}$$ and $$g_{ab}$$ or $$g_{ab,fe}$$ and $$g_{ab,ef}$$. If originally this condition is not fulfilled it is easy to pass to a "symmetrical" form of this kind.

It is clear that $$Q$$ may also be expressed in the quantities $$g_{ab}$$ and their first and second derivatives and in the same way in the $$\mathfrak{g}_{ab}$$ and first and second derivatives of these quantities.

If the necessary substitutions are executed with due care, these new forms of $$Q$$ will also be symmetrical.

§ 34. We shall first express the quantity $$Q$$ in the $$g_{ab}$$'s and their

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 derivatives and we shall determine the variation it undergoes by arbitrarily chosen variations $$\delta g_{ab}$$, these latter being continuous functions of the coordinates. We have evidently

$\delta Q=\sum(ab)\frac{\partial Q}{\partial g_{ab}}\delta g_{ab}+\sum(abe)\frac{\partial Q}{\partial g_{ab,e}}\delta g_{ab,e}+\sum(abef)\frac{\delta Q}{\partial g_{ab,ef}}\delta g_{ab,ef}$|undefined

By means of the equations

$\delta g_{ab,ef}=\frac{\partial}{\partial x_{f}}\delta g_{ab,e}$ and $\delta g_{ab,e}=\frac{\partial}{\partial x_{e}}\delta g_{ab}$|undefined

this may be decomposed into two parts

namely

The last equation shows that

if the variations $$\delta g_{ab}$$ and their first derivatives vanish at the boundary of the domain of integration.

§ 35. Equations of the same form may also be found if $$Q$$ is expressed in one of the two other ways mentioned in § 33. If e.g. we work with the quantities $$\mathfrak{g}^{ab}$$ we shall find

$(\delta Q)=\left(\delta_{1}Q\right)+\left(\delta_{2}Q\right)$

where $$\left(\delta_{1}Q\right)$$ and $$\left(\delta_{2}Q\right)$$ are directly found from (43) and (44) by replacing $$g_{ab}$$, $$g_{ab,e}$$, $$g_{ab,ef}$$, $$\delta g_{ab}$$ and $$\delta g_{ab,e}$$ etc. by $$\mathfrak{g}^{ab}$$, $$\mathfrak{g}^{ab,e}$$ etc. If the variations chosen in the two cases correspond to each other we shall have of course

$(dQ)=\delta Q$

Moreover we can show that the equalities

$\left(\delta_{1}Q\right)=\delta_{1}Q,\ \left(\delta_{2}Q\right)=\delta_{2}Q$

exist separately.

title: Page:LorentzGravitation1916.djvu/32


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 The decomposition of $$\delta Q$$ into two parts is therefore the same, whether we use $$g_{ab},g^{ab}$$ or $$\mathfrak{g}^{ab}$$.

It is further of importance that when the system of coordinates is changed, not only $$\delta QdS$$ is an invariant, but that this is also the case with $$\delta_{1}QdS$$ and $$\delta_{2}QdS$$ separately.

We have therefore

§ 36. For the calculation of $$\delta_{1}Q$$ we shall suppose $$Q$$ to be expressed in the quantities $$\mathfrak{g}^{ab}$$ and their derivatives. Therefore (comp. (43))

if we put

$M_{ab}=\frac{\partial Q}{\partial\mathfrak{g}^{ab}}-\sum(e)\frac{\partial}{\partial x_{e}}\frac{\partial Q}{\partial\mathfrak{g}^{ab,e}}+\sum(ef)\frac{\partial}{\partial x_{e}\partial x_{f}}\frac{\partial Q}{\partial\mathfrak{g}^{ab,ef}}$|undefined

Now we can show that the quantities $$M_{ab}$$ are exactly the quantities $$G_{ab}$$ defined by (40). To this effect we may use the following considerations.

We know that $$\left(\tfrac{1}{\sqrt{-g}}\mathfrak{g}^{ab}\right)$$ is a contravariant tensor of the second

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 order. From this we can deduce that $$\left(\frac{1}{\sqrt{-g}}\delta\mathfrak{g}^{ab}\right)$$ is also such a tensor.

Writing for it $$\epsilon^{ab}$$ we find according to (46) and (47) that

$\sum(ab)M_{ab}\epsilon^{ab}$

is a scalar for every choice of $$\left(\epsilon^{ab}\right)$$.

This involves that $$\left(M_{ab}\right)$$ is a covariant tensor of the second order and as the same is true for $$\left(G_{ab}\right)$$ we must prove the equation

$M_{ab}=G_{ab}$

only for one special choice of coordinates.

§ 37. Now this choice can be made in such a way that at the point $$P$$ of the field-figure $$g_{11}=g_{22}=g_{33}=-1$$, $$g_{44}=+1$$, $$g_{ab}=0$$ for $$a\neq b$$ and that moreover all first derivatives $$g_{ab,e}$$ vanish. If then the values $$g_{ab}$$ at a point $$Q$$ near $$P$$ are developed in series of ascending powers of the differences of coordinates $$x_{a}(Q)-x_{a}(P)$$ the terms directly following the constant ones will be of the second order. It is with these terms that we are concerned in the calculation both of $$M_{ab}$$ and of $$G_{ab}$$ for the point $$P$$. As in the results the coefficients of these terms occur to the first power only, it is sufficient to show that each of the above mentioned terms separately contributes the same value to $$M_{ab}$$ and to $$G_{ab}$$.

From these considerations we may conclude that

Expressions containing instead of $$\delta\mathfrak{g}^{ab}$$ either the variations $$\delta g^{ab}$$ or $$\delta g_{ab}$$ might be derived from this by using the relations between the different variations. Of these we shall only mention the formula

§ 38. In connexion with what precedes we here insert a consideration the purpose of which will be evident later on. Let the infinitely small quantity $$\xi$$ be an arbitrarily chosen continuous function of the coordinates and let the variations $$\delta g_{ab}$$ be defined by the condition that at some point $$P$$ the quantities $$g_{ab}$$ have after the change the values which existed before the change at the point $$Q$$, to which $$P$$ is shifted when $$x_{h}$$ is diminished by $$\xi$$, while the three other coordinates are left constant. Then we have

$\delta g_{ab}=-g_{ab,h}\xi$

and similar formulae for the variations $$\delta\mathfrak{g}^{ab}$$.

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 If for $$\delta_{1}Q$$ and $$\delta_{2}Q$$ the expressions (48) and (44) are taken, the equation

is an identity for every choice of the variations.

It will likewise be so in the special case considered and we shall also come to an identity if in (50) the terms with the derivatives of $$\xi$$ are omitted while those with $$\xi$$ itself are preserved.

When this is done $$\delta Q$$ reduces to

$-\frac{\partial Q}{\partial x_{h}}\xi$|undefined

and, taking into consideration (44) and (48), we find after division by $$\xi$$

In the second term of (44) we have interchanged here the indices $$e$$ and $$f$$.

If for shortness' sake we put, for $$e\ne h$$

and for $$e=h$$

we may write

The set of quantities $$\mathfrak{s}_{h}^{e}$$ will be called the complex $$\mathfrak{s}$$ and the set of the four quantities which stand on the left hand side of (54) in the cases $$h=1,2,3,4$$, the divergency of the complex. It will be denoted by $$div\mathfrak{s}$$ and each of the four quantities separately by $$div_{h}\mathfrak{s}$$.

The equation therefore becomes

title: Page:LorentzGravitation1916.djvu/35


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 If we take other coordinates the right hand side of this equation is transformed according to a formula which can be found easily. Hence we can also write down the transformation formula for the left hand side. It is as follows

§ 39. We shall now consider a second complex $$\mathfrak{s}_{0}$$, the components of which are defined by

Taking also the divergency of this complex we find that the difference

$div'_{h}\mathfrak{s}'_{0}-p\sum(m)p_{mh}div_{m}\mathfrak{s}_{0}$

has just the value which we can deduce from (56) for the corresponding difference

$div'_{h}\mathfrak{s}'-p\sum(m)p_{mh}div_{m}\mathfrak{s}$

It is thus seen that

$div'_{h}\mathfrak{s}'-div'_{h}\mathfrak{s}'_{0}=p\sum(m)p_{mh}\left(div_{m}\mathfrak{s}-div_{m}\mathfrak{s}_{0}\right)$

and that we have therefore

for all systems of coordinates as soon as this is the case for one system.

Now a direct calculation starting from (52), (53) and (57) teaches us that the terms with the highest derivatives of the quantities $$g_{ab}$$, (viz. those of the third order) are the same in $$div_{h}\mathfrak{s}$$ and $$div_{h}\mathfrak{s}_{0}$$. Further it is evident that in the system of coordinates introduced in § 37 these terms with the third derivatives are the only ones. This proves the general validity of equation (58). It is especially to be noticed that if $$\mathfrak{s}$$ and $$\mathfrak{s}_{0}$$ are determined by (52), (53) and (57) and if the function defined in § 32 is taken for $$G$$, the relation is an identity.

§ 40. We shall now derive the differential equations for the gravitation field, first for the case of an electromagnetic system. For the part of the principal function belonging to it we write

$\int\mathrm{L}dS$

where $$\mathrm{L}$$ is defined by (35) (1915). From $$\mathrm{L}$$ we can derive the stresses, the momenta, the energy-current and the energy of the

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 electromagnetic system; for this purpose we must use the equations (45) and (46) (1915) or in 's notation, which we shall follow here,

and for $$b\ne c$$

The set of quantities $$\mathfrak{T}_{c}^{b}$$ might be called the stress-energy-complex (comp. § 38). As for a change of the system of coordinates the transformation formulae for $$\mathfrak{T}$$ are similar to those by which tensors are defined, we can also speak of the stress-energy-tensor. We have namely

$\frac{1}{\sqrt{-g'}}\mathfrak{T}_{c}^{'b}=\frac{1}{\sqrt{-g}}\sum(kl)p_{kc}\pi lb\mathfrak{T}_{k}^{l}$|undefined

§ 41. The equations for the gravitation field are now obtained (comp. §§ 13 and 14, 1915) from the condition that

for all variations $$\delta g_{ab}$$ which vanish at the boundary of the field of integration together with their first derivatives. The index $$\psi$$ in the first term indicates that in the variation of $$\mathrm{L}$$ the quantities $$\psi_{ab}$$ must be kept constant.

If we suppose $$\mathrm{L}$$ to be expressed in the quantities $$g^{ab}$$ and if (42), (45) and (48) are taken into consideration, we find from (61) that at each point of the field-figure

If now in the first term we put

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and if for $$\partial g^{ab}$$ the value (49) is substituted, this term becomes

$\frac{1}{2}\sum(ab)T_{ab}\partial\mathfrak{g}^{ab}-\frac{1}{4}\sum(abcd)g^{ab}g_{cd}T_{ab}\delta\mathfrak{g}^{cd}$

or if in the latter summation $$a, b$$ is interchanged with $$c, d$$ and if the quantity

is introduced,

$\frac{1}{2}\sum(ab)\left(T_{ab}-\frac{1}{2}g_{ab}T\right)\delta\mathfrak{g}^{ab}$

Finally, putting equal to zero the coefficient of each $$\delta\mathfrak{g}^{ab}$$ we find from (62) the differential equation required

This is of the same form as 's field equations, but to see that the formulae really correspond to each other it remains to show that the quantities $$T_{ab}$$ and $$\mathfrak{T}_{c}^{b}$$ defined by (63), f59) and (60) are connected by 's formulae

We must have therefore

and for $$b\ne c$$

§ 42. This can be tested in the following way. The function $$\mathrm{L}$$ (comp. § 9, 1915) is a homogeneous quadratic function of the $$\psi_{ab}$$'s and when differentiated with respect to these variables it gives the quantities $$\bar{\psi}_{ab}$$. It may therefore also be regarded as a homogeneous quadratic function of the $$\bar{\psi}_{ab}$$. From (35), (29) and (32), 1915 we find therefore

Now we can also differentiate with respect to the $$g^{ab}$$'s, while not the $$\psi_{ab}$$'s but the quantities $$\bar{\psi}_{ab}$$ are kept constant, and we have e.g.

According to (69) one part of the latter differential coefficient is

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 obtained by differentiating the factor $$\sqrt{-g}$$ only and the other part by keeping this factor constant.

For the calculation of the first of these parts we can use the relation

and for the second part we find

$\frac{1}{2}\sqrt{-g}\sum(pq)g^{pq}\bar{\psi}_{ap}\bar{\psi}_{cq}$

If (32) 1915 is used (67) and (68) finally become

$\begin{array}{c} \sum(q)\psi_{cq}\bar{\psi}_{cq}+\sum\limits _{a\ne c}(a)\psi_{ac}^{*}\psi_{a'c'}=2\mathrm{L}\\ \\ \sum(q)\bar{\psi}_{cq}\psi_{bq}+\sum\limits _{a\ne c}(a)\psi_{ab}^{*}\psi_{a'c'}=0 \end{array}$

These equations are really fulfilled. This is evident from $$\psi_{aa}=0$$, $$\bar{\psi}_{aa}=0$$, $$\psi_{ba}=-\psi_{ab}$$ and $$\bar{\psi}_{ba}=-\bar{\psi}_{ab}$$, besides, the meaning of $$\psi_{ab}^{*}$$ (§ 11, 1915) and equation (35) 1915 must be taken into consideration.

§ 43. In nearly the same way we can treat the gravitation field of a system of incoherent material points; here the quantities $$w_{a}$$ and $$u_{a}$$ (§§ 4 and 5, 1915) play a similar part as $$\psi_{ab}$$ and $$\bar{\psi}_{ab}$$ in what precedes. To consider a more general case we can suppose "molecular forces" to act between the material points (which we assume to be equal to each other); in such a way that in ordinary mechanics we should ascribe to the system a potential energy depending on the density only. Conforming to this we shall add to the Lagrangian function $$\mathrm{L}$$ (§ 4, 1915) a term which is some function of the density of the matter at the point $$P$$ of the field-figure, such as that density is when by a transformation the matter at that point has been brought to rest. This can also be expressed as follows. Let $$d\sigma$$ be an infinitely small three-dimensional extension expressed in natural units, which at the point $$P$$ is perpendicular to the world-line passing through that point, and $$\bar{\varrho}d\sigma$$ the number of points where $$d\sigma$$ intersects world-lines. The contribution of an element of the field-figure to the principal function will then be found by multiplying the magnitude of that element expressed in natural units by a function of $$\bar{\varrho}$$. Further calculation teaches us that the term to be added to $$\mathrm{L}$$ must have the form

title: Page:LorentzGravitation1916.djvu/39


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 where $$P$$ is given by (15) 1915. As the Lagrangian function defined by (11) 1915 equally falls under this form and also the sum of this function and the new term, the expression (71) may be regarded as the total function $$\mathrm{L}$$. The function $$\varphi$$ may be left indeterminate. If now with this function the calculations of §§ 5 and 6, 1915 are repeated, we find the components of the stress-energy-tensor of the matter.

The equations for the gravitation field again take the form (65). $$T_{ab}$$ is defined by an equation of the form (63), where on the left hand side we must differentiate while the $$w_{a}$$'s are kept constant. Relation (66) can again be verified without difficulty.

We shall not, however, dwell upon this, as the following considerations are more general and apply e.g. also to systems of material points that are anisotropic as regards the configuration and the molecular actions.

§ 44. At any point $$P$$ of the field-figure the Lagrangian function $$\mathrm{L}$$ will evidently be determined by the course and the mutual situation of the world-lines of the material points in the neighbourhood of $$P$$. This leads to the assumption that for constant $$g_{ab}$$'s the variation $$\delta\mathrm{L}$$ is a homogeneous linear function of the virtual displacements $$\delta x_{a}$$ of the material points and of the differential coefficients

$\frac{\partial\delta x_{a}}{\partial x_{b}}$|undefined

these last quantities evidently determining the deformation of an infinitesimal part of the figure formed by the world-lines.

The calculation becomes most simple if we put

and for constant $$g_{ab}$$'s

Considerations corresponding exactly to those mentioned in §§ 4 — 6, 1915, now lead to the equations of motion and to the following expressions for the components of the stress-energy-tensor

and for $$b\ne c$$

The differential equations again take the form (65) if the quantities $$T_{ab}$$ are defined by

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 $\left(\frac{\partial\mathrm{L}}{\partial g^{ab}}\right)_{x}=\frac{1}{2}\sqrt{-g}T_{ab}$|undefined

in the differentiation on the left hand side the coordinates of the material points are kept constant. To show that $$T_{ab}$$ and $$\mathfrak{T}_{c}^{b}$$ satisfy equation (66) we must now show that

$-\mathrm{L}-\sqrt{-g}V_{c}^{c}=2\sum(a)g^{ac}\left(\frac{\partial L}{\partial g^{ac}}\right)_{x}$|undefined

and for $$b\ne c$$

$-\sqrt{-g}V_{c}^{b}=2\sum(a)g^{ab}\left(\frac{\partial\mathrm{L}}{\partial g^{ac}}\right)_{x}$|undefined

If here the value (72) is substituted for $$\mathrm{L}$$ and if (70) is taken into account, these equations say that for all values of $$b$$ and $$c$$ we must have

Now this relation immediately follows from a condition, to which $$\mathrm{L}$$ must be subjected at any rate, viz. that $$\mathrm{L}dS$$ is a scalar quantity. This involves that in a definite case we must find for $$H$$ always the same value whatever be the choice of coordinates.

§ 45. Let us suppose that instead of only one coordinate $$x_{c}$$ a new one $$x'_{c}$$ has been introduced, which differs infinitely little from $$x_{c}$$, with the restriction that if

$x'_{c}=x_{c}+\xi_{c}$

the term $$\xi_{c}$$ depends on the coordinate $$x_b$$ only and is zero at the point in question of the field-figure. The quantities $$g^{ab}$$ then take other values and in the new system of coordinates the world-lines of the material points will have a slightly changed course.

By each of these circumstances separately $$H$$ would change, but all together must leave it unaltered. As to the first change we remark that, according to the transformation formula for $$g^{ab}$$, the variation $$\delta g^{ab}$$ vanishes when the two indices are different from $$c$$, while

$\delta g^{cc}=2g^{cb}\frac{\partial\xi_{c}}{\partial x_{b}}$|undefined

and for $$a\ne c$$

$\delta g^{ac}=2g^{ca}=g^{ab}\frac{\partial\xi_{c}}{\partial x_{b}}$|undefined

The change of $$H$$ due to these variations is

$2\frac{\partial\xi_{c}}{\partial x_{b}}\sum(a)g^{ab}\left(\frac{\partial H}{\partial g^{ac}}\right)_{x}$|undefined

title: Page:LorentzGravitation1916.djvu/41


text:
Page:LorentzGravitation1916.djvu/42

 Further, in the new system of coordinates the figure formed by the world-lines differs from that figure in the old system by the variation $$\delta x_{c}=\xi_{c}$$ which is a function of $$x_{b}$$ only. Therefore according to (73) the second variation of $$H$$ is

$V_{c}^{b}=\frac{\partial\xi_{c}}{\partial x_{b}}$|undefined

By putting equal to zero the sum of this expression and the preceding one we obtain (76).

§ 46. We have thus deduced for some cases the equations of the gravitation field from the variation theorem. Probably this can also be done for thermodynamic systems, if the Lagrangian function is properly chosen in connexion with the thermodynamic functions, entropy and free energy. But as soon as we are concerned with irreversible phenomena, when e.g. the energy-current consists in a conduction of heat, the variation principle cannot be applied. We shall then be obliged to take 's field-equations as our point of departure, unless, considering the motions of the individual atoms or molecules, we succeed in treating these by means of the generalized principle of.

§ 47. Finally we shall consider the stresses, the energy etc. which belong to the gravitation field itself. The results will be the same for all the systems treated above, but we shall confine ourselves to the case of §§ 44 and 45. We suppose certain external forces $$K_{a}$$ to act on the material points, though we shall see that strictly speaking this is not allowed.

For any displacements $$\delta x_{a}$$ of the matter and variations of the gravitation field we first have the equation which summarizes what we found above

$\begin{array}{l} \delta\mathrm{L}+\frac{1}{2\varkappa}\delta Q+\sum(a)K_{a}^{*}\delta x_{a}=\sqrt{-g}\sum(a)U_{a}\delta x_{a}+\\ \\ \qquad+\sum(ab)\frac{\partial}{\partial x_{b}}\left(\sqrt{-g}V_{a}^{b}\delta x_{a}\right)-\sum(ab)\frac{\partial}{\partial x_{b}}\left(\sqrt{-g}V_{a}^{b}\right)\delta x_{a}+\\ \\ \qquad\qquad+\sum(ab)\left(\frac{\partial L}{\partial g^{ab}}\right)_{x}\delta g^{ab}+\frac{1}{2\varkappa}\delta_{1}Q+\frac{1}{2\varkappa}\delta_{2}Q+\sum(a)K_{a}\delta x_{a}. \end{array}$|undefined

In virtue of the equations of motion of the matter, the terms with $$\delta x_{a}$$ cancel each other on the right hand side and similarly, on account of the equations of the gravitation field, the terms with $$\delta g^{ab}$$ and $$\delta_{1}Q$$. Thus we can write

title: Page:LorentzGravitation1916.djvu/42


text:
Page:LorentzGravitation1916.djvu/43

Let us now suppose that only the coordinate $$x_{h}$$ undergoes an infinitely small change, which has the same value at all points of the field-figure. Let at the same time the system of values $$g_{ab}$$ be shifted everywhere in the direction of $$x_{h}$$ over the distance $$\delta x_{h}$$. The left hand side of the equation then becomes $$K_{h}\delta x_{h}$$ and we have on the right hand side

$\delta\mathrm{L}=-\frac{\partial\mathrm{L}}{\partial x_{h}}\delta x_{h},\ dQ=-\frac{\partial Q}{\partial x_{h}}\delta x_{h}$|undefined

After dividing the equation by $$\delta x_{h}$$ we may thus, according to (74) and (75), write

$-\sum(e)\frac{\partial\mathrm{T}h^{e}}{\partial x_{e}}=-div_{h}\mathfrak{T}$|undefined

By the same division we obtain from $$\delta Q-\delta_{2}Q$$ the expression occurring on the left hand side of (51), which we have represented by

$\sum(e)\frac{\partial\mathfrak{s}_{h}^{e}}{\partial x_{e}}=div_{h}\mathfrak{s}$|undefined

where the complex $$\mathfrak{s}$$ is defined by (52) and (53). If therefore we introduce a new complex $$\mathfrak{t}$$ which differs from $$\mathfrak{s}$$ only by the factor $$\tfrac{1}{2\varkappa}$$, so that

we find

The form of this equation leads us to consider $$\mathfrak{t}$$ as the stress-energy-complex of the gravitation field, just as $$\mathfrak{T}$$ is the stress-energy-tensor for the matter. We need not further explain that for the case $$K_{h}=0$$ the four equations contained in (79) express the conservation of momentum and of energy for the total system, matter and gravitation field taken together.

§ 48. To learn something about the nature of the stress-energy-complex $$\mathfrak{t}$$ we shall consider the stationary gravitation field caused by a quantity of matter without motion and distributed symmetrically around a point $$O$$. In this problem it is convenient to introduce for the three space coordinates $$x_{1},x_{2},x_{3}$$, ($$x_{4}$$ will represent the time) "polar" coordinates. By $$x_{3}$$ we shall therefore denote a quantity $$r$$

title: Page:LorentzGravitation1916.djvu/43


text:
Page:LorentzGravitation1916.djvu/44

 which is a measure for the "distance" to the centre. As to $$x_{1}$$ and $$x_{2}$$, we shall put $$x_{1}=\cos\vartheta$$, $$x_{2}=\varphi$$, after first having introduced polar coordinates $$\vartheta, \varphi$$ (in such a way that the rectangular coordinates are $$r\cos\vartheta$$, $$r\sin\vartheta\cos\varphi$$, $$r\sin\vartheta\sin\varphi$$). It can be proved that, because of the symmetry about the centre, $$g_{ab}=0$$ for $$a\ne b$$, while we may put for the quantities $$g_{aa}$$

where $$u, v, w$$ are certain functions of $$r$$. Ditferentiations of these functions will be represented by accents. We now find that of the complex $$\mathfrak{t}$$ only the components $$\mathfrak{t}_{1}^{1}$$, $$\mathfrak{t}_{3}^{3}$$ and $$\mathfrak{t}_{4}^{4}$$ are different from zero. The expressions found for them may be further simplified by properly choosing $$r$$. If the distance to the centre is measured by the time the light requires to be propagated from to the point in question, we have $$w = v$$. One then finds

{{MathForm2|(81)|$$\left.\begin{array}{l} \mathfrak{t}_{1}^{1}=\frac{1}{2\varkappa}\left(-\frac{u'^{2}}{2u}+2u-\frac{uv'^{2}}{v^{2}}+\frac{uv}{v}\right),\\ \\ \mathfrak{t}_{3}^{3}=\frac{1}{2\varkappa}\left(-2v+\frac{u'^{2}}{2u}+\frac{uv'}{v}\right),\\ \\ \mathfrak{t}_{4}^{4}=\frac{1}{2\varkappa}\left(-2v-\frac{u'^{2}}{2u}+2u+\frac{uv}{v}\right), \end{array}\right\}$$}}

§ 49. We must assume that in the gravitation fields really existing the quantities $$g_{ab}$$ have values differing very little from those which belong to a field without gravitation. In this latter we should have

$u=r^{3},\ v=w=1,$

and thus we put now

$u=r^{2}(1+\mu),\ v=w=1+\nu$

where the quantities $$\mu$$ and $$\nu$$ which depend on $$r$$ are infinitely small, say of the first order, and their derivatives too. Neglecting quantities of the second order we find from (81)

$\begin{array}{l} \mathfrak{t}_{1}^{1}=\frac{1}{2\varkappa}\left(2+2\mu+6r\mu'+2r^{2}\mu+r^{2}\nu\right),\\ \\ \mathfrak{t}_{3}^{3}=\frac{1}{\varkappa}\left(\mu-\nu+r\mu'+r\nu'\right),\\ \\ \mathfrak{t}_{4}^{4}=\frac{1}{2\varkappa}\left(2\mu-2\nu+6r\mu'+2r^{2}\mu+r^{2}\nu\right), \end{array}$

For our degree of approximation we may suppose that of the quantities $$T_{ab}$$ only $$T_{44}$$ differs from 0. If we put

title: Page:LorentzGravitation1916.djvu/44


text:
Page:LorentzGravitation1916.djvu/45

a quantity which depends on $$r$$ and which we shall assume to be zero outside a certain sphere, we find from the field equations

$\begin{array}{c} \mu=\varkappa\left\{ -\frac{2}{r}\int\limits _{0}^{r}\frac{dr}{r}\int\limits _{0}^{r}r^{2}\varrho dr-\frac{1}{r}\int\limits _{0}^{r}r^{2}\varrho dr+\int\limits _{\infty}^{r}r\varrho dr\right\} ,\\ \\ \nu=\varkappa\left\{ -\frac{1}{r}\int\limits _{0}^{r}r^{2}\varrho dr+\int\limits _{\infty}^{r}r\varrho dr\right\} \end{array}$

We thus obtain

§ 50. If first we leave aside the first term of $$\mathfrak{t}_{1}^{1}$$, which would also exist if no attracting matter were present, it is remarkable that the gravitation constant $$\varkappa$$ does not occur in the stress $$\mathfrak{t}_{1}^{1}$$ nor in the energy $$\mathfrak{t}_{4}^{4}$$; the same would have been found if we had used other coordinates. This constitutes an important difference between 's theory and other theories in which attracting or repulsing forces are reduced to "field actions". The pulsating spheres of e.g. are subjected to forces which, for a given motion, are proportional to the density of the fluid in which they are imbedded; and the changes of pressure and the energy in that fluid are likewise proportional to this density. In this case we shall therefore ascribe to the stress-energy-complex values proportional to the intensity of the actions which we want to explain. In 's theory such a proportionality does not exist. The value of $$\mathfrak{t}_{4}^{4}$$ is of the same order of magnitude as $$\mathfrak{T}_{4}^{4}$$ in the matter. To our degree of approximation we find namely from (82) $$\mathfrak{T}_{4}^{4}=r^{2}\varrho$$.

§ 51. If we had not worked with polar coordinates but with rectangular coordinates we should have had to put for the field without gravitation $$g_{11}=g_{22}=g_{33}=-1$$, $$g_{44}=1$$, $$g_{ab}=0$$ for $$a\ne b$$. Then we should have found zero for all the components of the complex. In the system of coordinates used above we found for the field without gravitation $$\mathfrak{t}_{1}^{1}=\tfrac{1}{\varkappa}$$; this is due to the complex $$\mathfrak{t}$$ being no tensor. If it were, the quantities $$\mathfrak{t}_{a}^{b}$$ would be zero in every system of coordinates if they had that value in one system.

title: Page:LorentzGravitation1916.djvu/45


text:
Page:LorentzGravitation1916.djvu/46

 It is also remarkable that in real eases the first term in (83) can be much larger than the following ones. If we consider e. g. a point $$P$$ outside the attracting sphere, we can prove that the ratio of the first term to the third is of the same order as the ratio of the square of the velocity of light to the square of the velocity with which a material point can describe a circular orbit passing through $$P$$.

The following must also be noticed. In the system of polar coordinates used above there will exist in the field without gravitation the stress $$\mathfrak{t}_{1}^{1}=\tfrac{1}{\varkappa}$$. If a stress of this magnitude were produced by means of actions which give rise to a stress-energy-tensor, the passage to rectangular coordinates would give us a stress which becomes infinite at the point $$O$$. In those coordinates we should namely have

$\mathfrak{t}_{1}^{'1}=\frac{\sin^{2}\vartheta}{r^{2}}\cdot\frac{1}{\varkappa}$|undefined

§ 52. Evidently it would be more satisfactory if we could ascribe a stress-energy-tensor to the gravitation field. Now this can really be done. Indeed, the quantities $$\mathfrak{s}_{0h}^{e}$$ determined by (57) form a tensor and according to (58), (79) may be replaced by

if $$\mathfrak{t}_{0}$$ is defined by a relation similar to (78), viz.

Equation (85) shows that, just as well as $$\mathfrak{t}_{h}^{c}$$, we may consider the quantities $$\mathfrak{t}_{0h}^{e}$$ as the stresses etc. in the gravitation field. This way of interpretation is very simple. With a view to (41) we can namely derive from the equations for the gravitation field (65)

$G=\varkappa T$

and

$T_{ab}=-\frac{1}{\varkappa}\left(G_{ab}-\frac{1}{2}g_{ab}G\right)$

Further we find from (66)

$\mathfrak{T}_{h}^{e}=\frac{1}{2\varkappa}G\sum(a)\mathfrak{g}^{ae}g_{ah}-\frac{1}{\varkappa}\sum(a)\mathfrak{g}^{ae}G_{ah}$

and from (57) and (86)

At every point of the field-figure the components of the stress-energy-tensor of the gravitation field would therefore be equal to

title: Page:LorentzGravitation1916.djvu/46


text:
Page:LorentzGravitation1916.djvu/47

 the corresponding quantities for the matter or the electro-magnetic system with the opposite sign. It is obvious that by this the condition of the conservation of momentum and energy for the whole system would be immediately fulfilled. It was in fact this circumstance that made me think of the tensor $$\mathfrak{t}_{0}=-\mathfrak{T}$$. The way in which $$\mathfrak{s}_{0}$$ was introduced in §§ 38 and 39 has only been chosen in order to lay stress on (58) being an identity, so that equation (85) is but another form of (79).

At first sight the relations (87) and the conception to which they have led, may look somewhat startling. According to it we should have to imagine that behind the directly observable world with its stresses, energy etc. there is hidden the gravitation field with stresses, energy etc. that are everywhere equal and opposite to the former; evidently this is in agreement with the interchange of momentum and energy which accompanies the action of gravitation. On the way of a light-beam e.g. there would be everywhere in the gravitation field an energy current equal and opposite to the one existing in the beam. If we remember that this hidden energy-current can be fully described mathematically by the quantities $$g_{ab}$$ and that only the interchange just mentioned makes it perceptible to us, this mode of viewing the phenomena does not seem unacceptable. At all events we are forcibly led to it if we want to preserve the advantage of a stress-energy-tensor also for the gravitation field. It can namely be shown that a tensor which is transformed in the same way as the tensor $$\mathfrak{t}_{0}$$ defined by (57) and (86) and which in every system of coordinates has the same divergency as the latter, must coincide with $$\mathfrak{t}_{0}$$.

Finally we may remark that (78), (86), (58), (87) give

$div\ \mathfrak{t}=div\ \mathfrak{t}_{0}=-div\ \mathfrak{T}$

so that we have, both from (79) and from (85), $$K_{h}=0$$.

The question is this, that, so long as the gravitation field is considered as given, we may introduce "external" forces, but that in the equations for the gravitation field itself we must also take into consideration the stress-energy-tensor of the system by which those forces are exerted.

title: Page:LorentzGravitation1916.djvu/47


text: Dictionary of National Biography, 1885-1900/Ironside, Edward


text:
Author:Ebenezer Howard

Works

 * Garden Cities of To-morrow (1902)
 * To-morrow: A Peaceful Path to Real Reform

title: Author:Ebenezer Howard


text:
Page:Chronological Table and Index of the Statutes.djvu/364

 ;
 * See ; ; ;, 1 (a); ; .; ;

 * Effect of, on actions in equity.
 * See (12).
 * See (12).

 * Royal assent to
 * 33 Hen. 8. c. 21.
 * Relating to Court of Request or Conscience to be public
 * (E.) 27 Geo. 2. c. 16. s. 2.
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 * 11 Geo. 4. & 1 Will. 4. c. 71.
 * 7 Will. 4 & 1 Vict. c. 60.
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 * 13 & 14 Vict. c. 21. s. 2.
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 * 56 Geo. 3. c. 98. s. 3.
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 * 6 Geo. 4. c. 68. s. 6.
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 * (E.) 7 & 8 Geo. 4. c. 28.
 * (I.) 9 Geo. 4. c. 54.
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 * 7 & 8 Geo.4. c.53. s. 3.
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 * See.
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 * (E.)7 Will. 4. & 1 Vict. c. 53. s. 7.
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 * 22 Vict. c. 26.
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 * 24 & 25 Vict. c. 47.
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 * (E.) 28 & 29 Vict. c. 37.
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 * (E.) 30 & 31 Vict. c. 142. s. 35.
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 * 32 & 33 Vict. c. 42. s. 69.
 * Interpretation of "Poor Law Board," "Secretary of State," and "Privy Council," in various Acts, &c., after establishment of Local Government Board, England
 * (E.) 34 & 35 Vict. c. 70. s. 7.
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 * (I.) 35 & 36 Vict. c. 69. s. 5.
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 * (E.) 36 & 37 Vict. c. 66. s. 76.
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 * (I.) 40 & 41 Vict. c. 57. s. 71.
 * Interpretation of Acts relating to attorneys.
 * See.
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 * See (17).
 * Citation of, and of Bills, in documents passed under Great Seal, Proclamation, &c.; enumeration of, in schedules to documents
 * 40 & 41 Vict. c. 41. s. 3.
 * See also, 3; ; ; ; ; ; (Generally);.
 * See also, 3; ; ; ; ; ; (Generally);.


text: Dictionary of National Biography, 1885-1900/Irving, David


text:
Page:Chronological Table and Index of the Statutes.djvu/365

 ;
 * No suit for goods in the Queen's Courts under 40 shillings (see also )
 * 6 Edw. 1. (Stat. Glouc.) c. 8.
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 * (E.) 16 & 16 Vict. c. 76. ss. 34–39.
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 * (E.) 15 & 16 Vict. c. 76.
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 * Of aliment, in what court brought, and proceedings therein
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 * 24 & 25 Vict. c. 86.
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 * See also ; and
 * See also ; and

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 * See also ; and ;  ;  ; ; ; ;
 * See also ; and ;  ;  ; ; ; ;

 * See.
 * See.

 * See.
 * See.

 * See ;
 * See ;

 * See ; ; ;
 * See ; ; ;

 * See ; ; ; ; ; ; ;; ;, 2 (f); ; ;
 * See ; ; ; ; ; ; ;; ;, 2 (f); ; ;

 * Appointment of, and who to be appointed
 * 31 Edw. 3. stat. 1. c. 11.
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 * (E.) 38 Geo. 3. c. 87.
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 * See.
 * Protection of
 * (E. I.) 23 & 24 Vict. c. 38. s. 13.
 * (E. I.) 23 & 24 Vict. c. 38. s. 13.


text: Index:Homes of the London Poor.djvu

title: Index:Homes of the London Poor.djvu


text: Index:Our Common Land (and other short essays).djvu


text:
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 * Administrator— :Solicitor to Treasury or Duchy of Lancaster to be, and account and application of property, where Crown entitled
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 * 22 & 23 Vict. c. 31. s. 18.
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 * 20 & 21 Vict. c. 79. ss. 86–8.
 * See also ; and ; ;
 * See also ; and ; ;

 * Jurisdiction of admiral and his deputy
 * 13 Ric. 2. stat. 1. c. 5.
 * 15 Ric.2.c. 3.
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 * 2 Will. & Mar. sess. 2. c. 2.
 * 7 & 8 Geo. 4. c. 66.
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 * 55 Geo. 3. c. 128.
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 * Geo. 2. c. 20. s. 14.
 * 2 & 3 Will. 4. c. 40.
 * 28 & 29 Vict. c. 124.
 * 31 & 32 Vict. c. 78.
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 * See.
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 * See.
 * See also .; ;, 3;.
 * See also .; ;, 3;.

 * Jurisdiction of, to be subject to Lord High Admiral of Great Britain
 * 6 Ann. c. 11.
 * 6 Ann. c. 11.

 * Jurisdiction of, over matters relating to the sea
 * 13 Ric. 2. stat. 1. c. 5.
 * 15 Ric. 2. c. 3.
 * 3 & 4 Vict. c. 65.
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 * 24 & 25 Vict. c. 10.
 * Jurisdiction as to offences against, and ships detained under, Foreign Enlistment Act
 * 33 & 34 Vict. c. 90.
 * Is a court of record, and effect of decrees of
 * 24 & 25 Vict. c. 10.
 * Dean of Arches to sit for judge of, in certain cases
 * 3 & 4 Vict. c. 65.
 * Salary and pension of judge of (see also (Members))
 * 3 & 4 Vict. c. 66. ss. 1, 7.
 * 38 & 39 Vict. c. 77. 8. 8.
 * Sitting by judge of, for judge of Probate Court, and vice versa
 * 21 & 22 Vict. c. 95. s. 1.
 * Barristers and attorneys allowed to practise in
 * 22 & 23 Vict. c. 6.
 * Practice and procedure in, examination of witnesses before, &c.
 * 3 & 4 Vict. c. 65.
 * 27 & 28 Vict. c. 25.
 * 24 & 25 Vict. c. 10.
 * 38 & 39 Vict. c. 77. ss. 16, 18. sch. 1.
 * Amount and payment by stamps of fees in, and annual account of receipts and expenditure
 * 30 & 31 Vict. c. 122.
 * 32 & 33 Vict. c. 91.
 * 32 & 33 Vict. c. 91.


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70 Hildeburh needed not hold in value her enemies’ honor! Innocent both were the loved ones she lost at the linden-play, bairn and brother; they bowed to fate, stricken by spears; ’twas a sorrowful woman! None doubted why the daughter of Hoc bewailed her doom when dawning came, and under the sky she saw them lying, kinsmen murdered, where most she had kenned of the sweets of the world! By war were swept, too,

support among scholars. Finn, a Frisian chieftain, who nevertheless has a “castle” outside the Frisian border, marries Hildeburh, a Danish princess; and her brother, Hnæf, with many other Danes, pays Finn a visit. Relations between the two peoples have been strained before. Something starts the old feud anew; and the visitors are attacked in their quarters. Hnæf is killed; so is a son of Hildeburh. Many fall on both sides. Peace is patched up; a stately funeral is held; and the surviving visitors become in a way vassals or liegemen of Finn, going back with him to Frisia. So matters rest a while. Hengest is now leader of the Danes; but he is set upon revenge for his former lord, Hnæf. Probably he is killed in feud; but his clansmen, Guthlaf and Oslaf, gather at their home a force of sturdy Danes, come back to Frisia, storm Finn’s stronghold, kill him, and carry back their kinswoman Hildeburh. The Finnsburg fragment, translated below, describes (so Bugge puts it, conforming, as he says, “to the common view”) the fight in which Hnæf fell, “that is to say, an event which precedes the story told in the Beowulf,” and is noted in these introductory lines (vv. 1069 f.).—In the Widsith, Hnæf is called ruler of the Hocings.—In v. 1142 it is assumed that Hengest is killed by the sword “Lafing” of a Frisian named Hun. In Widsith, v. 33, Hun ruled the Hætweras, a tribe of Franks now apparently subject to Finn the Frisian. Another reading makes Finn slay Hengest with a sword “Hunlafing.” Two other interpretations make either Finn lay this sword “Hunlafing,” or Hun lay “Lafing,” on Hengest’s lap, as a gift and a sign of allegiance on the part of the receiver. Of course, in this case, Hengest dissembles his real feelings to gain time and opportunity for the subsequent invasion.


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Removing the Barriers to State Government

State of New York Executive Chamber

No. 1 REMOVING THE BARRIERS TO STATE GOVERNMENT

No. 1

WHEREAS, it is essential to the maintenance of a democratic society that the government perform its business in an open and public manner;

WHEREAS, it is the responsibility of government to facilitate greater access and participation by its citizens;

WHEREAS, this access must include easier physical access to the government for members of the public;

WHEREAS, the New York State Capitol is the historic seat of government in New York State and a marvel of late 19th century architecture; and

WHEREAS, the barriers to access to the New York State Capitol have prevented this openness;

NOW, THEREFORE, I, Andrew M. Cuomo, Governor of the State of New York, by virtue of the authority vested in me by the Constitution and laws of the State of New York, do hereby order as follows:

Opening the Capitol

 * 1) Certain barriers erected around the perimeter of the Capitol shall be removed to allow for convenient loading and unloading of visitors to the Capitol.
 * 2) Access to the second floor of the Capitol, where the Governor’s office is located, shall hereafter be provided to members of the public during business hours except when restricted access is determined to be necessary to ensure the safety and security of those working in the Capitol.

Assistance

Every New York State department, division, board, bureau, commission, council and agency shall cooperate to effectuate this Executive Order and shall furnish such assistance as may be necessary for the accomplishment of the purposes of this Executive Order.

GIVEN under my hand and the Privy Seal of the                                                                                State in the City of Albany this first day of                                                                                January in the year two thousand eleven.

BY THE GOVERNOR


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 have an operation. — Обработка этой части распадается на четыре отдельные операции. This part is manufactured in four separate operations. • function. Какие операции производит Госбанк? What functions are carried on by the Gosbank? (See appendix 4).

опередить (pct of опережать) to get ahead of. Постарайтесь опередить эту машину. Try to get ahead of that car. • to leave behind. Мы их настолько опередили, что я их больше не вижу. We left them so far behind that I can't see them any more. — Он опередил весь класс. He left his whole class behind. □ Он дал мне опередить себя на десять минут. He gave me a ten-minute head start.

опережать (dur of опередить).

опережу See опередить.

оперетка operetta.

опереть (обопри, -прёт; p опёр, оперла; оперся, -рлась, ось, -ись; pap опёршийся, pger опершись; ppp опёртый, sh F оперта; pct of опирать).

-ся to lean on. Обопритесь о меня. Lean on me. — Он оперся локтями о подоконник. He leaned on the window sill with his elbows.

оперировать (both dur and pct) to operate. Его вчера оперировали. They operated on him yesterday. • to handle. Как он легко оперирует такими большими цифрами. He certainly handles large figures easily.

опечатка misprint.

опирать (dur of опереть).

-ся to lean on. Он опирался на палку. He was leaning on a stick. • to lean against. Не опирайтесь о стену, вы вымажетесь. Don't lean against the wall. You'll soil your clothes.

описание description.

описать (-пишу, -пишет; pct of описывать) to describe. Можете вы описать его? Can you describe him? □ *Она такая красавица, что ни в сказке сказать, ни пером описать! Her beauty defies description.

описывать (dur of описать) to describe. Я вам, кажется, описывал мою встречу с ним. I think I described how I met him.

опишу See описать.

оплата pay.

оплатить (-плачу, -платит pct of оплачивать) to pay. Вам оплатят расходы по поездке. They'll pay your expenses on the trip. — Этот счёт уже оплачен. This bill is already paid.

оплачивать (dur of оплатить) to pay.

оплачу See оплатить.

оплошность (F) blunder. Это непростительная оплошность. It's an unpardonable blunder. • slip. Как это вы допустили такую оплошность? How did you ever make such a slip?

оповестить (pct of оповещать) to let know, to notify. Оповестите всех о собрании. Let everyone know about the meeting.

оповещать (dur of оповестить) to let know, to notify.

оповещу See оповестить.

опоздание delay. Эти товары будут вам доставлены с некоторым опозданием. There'll be some delay in the delivery of this merchandise. □ Ещё два опоздания — и он попадёт на чёрную доску. He'll be put on the black list if he's late two more times. • Поезд приходит с опозданием. The train is coming in late.

опоздать (pct of опаздывать) to be late. Наш поезд опоздал на три часа. Our train was three hours late. — Вы сильно опоздали с отчётом. You're very late with your report. — Опоздавшие ждали у входа в зрительный зал. Those who were late waited at the entrance of the auditorium. • to be late for. Торопитесь, а то опоздаете на поезд. Hurry or you'll be late for the train.

оппозиция opposition.

оппортунизм opportunism.

оппортунист opportunist.

оправа frame. Он заказал себе очки в золотой оправе. He ordered a pair of glasses in a gold frame. • setting. Я хотел бы вставить этот камень в оправу. I'd like to have this stone put in a setting.

оправдание justification. Такому поступку не может быть оправдания! There's no justification for doing a thing like that! • excuse. Он приводил всевозможные оправдания. He offered all the excuses he could. • acquittal. Защитник требовал оправдания подсудимого. The attorney for the defense asked for an acquittal.

оправдать (pct of оправдывать) to acquit. Подсудимый был оправдан. The defendant was acquitted. • to justify. Он вполне оправдал наше доверие. He completely justified our confidence in him. • to excuse. Я никак не могу оправдать вашего поведения. I just can't excuse your conduct. □ Эта новая машина уже себя оправдала. This new machine has already paid for itself.

-ся to clear oneself. Вам никак не удастся оправдаться. You certainly won't be able to clear yourself. • to prove correct. Наши предположения оправдались. Our assumptions proved correct.

оправдывать (dur of оправдать) to find excuses for. Почему вы всегда его оправдываете? Why do you always find excuses for him?

-ся to justify oneself. Нечего оправдываться, мы вас ни в чём не обвиняем. Why are you trying to justify yourself? We're not accusing you of anything.

определённый (ppp of определить) definite. Когда же мы получим определённый ответ? When will we get a definite answer? — Неужели вы не понимаете, что его выступление имело определённый политический смысл. Don't you understand? His speech had a definite political meaning. • sure. Ну, это определённый провал. It's a sure flop. • steady. Теперь вы будете иметь определённый заработок. Now you'll have a steady income. • certain. Он может быть использован только в определённых условиях. He can be of use only under certain circumstances.

определить (pct of определить) to determine. Уже определили местонахождение судна? . Have they determined the location of the ship yet? • to fix. Давайте заранее определим день нашей встречи. Let's fix a date beforehand for meeting again. • to diagnose. Врач ещё не определил его болезни. The doctor still can't diagnose his illness. • to form. Я ещё не могу определить своего впечатления от нового сотрудника. I still haven't been able to form an opinion of the new employee.

определять (dur of определить) to define. Как вы определяете понятие "общество?" How do you define the term "society"?


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Rh Finn’s own liegemen, and few were left; in the parleying-place he could ply no longer weapon, nor war could he wage on Hengest, and rescue his remnant by right of arms from the prince’s thane. A pact he offered: another dwelling the Danes should have, hall and high-seat, and half the power should fall to them in Frisian land; and at the fee-gifts, Folcwald’s son day by day the Danes should honor, the folk of Hengest favor with rings, even as truly, with treasure and jewels, with fretted gold, as his Frisian kin he meant to honor in ale-hall there. Pact of peace they plighted further on both sides firmly. Finn to Hengest with oath, upon honor, openly promised that woful remnant, with wise-men’s aid, nobly to govern, so none of the guests by word or work should warp the treaty, or with malice of mind bemoan themselves as forced to follow their fee-giver’s slayer, lordless men, as their lot ordained. Should Frisian, moreover, with foeman’s taunt, that murderous hatred to mind recall.


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Sister Dolorosa had reached the summit of a low hill on her way to the convent she turned and stood for a while looking backward. The landscape stretched away in a rude, unlovely expanse of gray fields, shaded in places by brown stubble, and in others lightened by pale, thin corn—the stunted reward of necessitous husbandry. This way and that ran wavering lines of low fences, some worm-eaten, others rotting beneath over-clambering wild rose and blackberry. About the horizon masses of dense and rugged woods burned with sombre fires as the westering sun smote them from top to underbrush. Forth from the edge of one a few long-horned cattle, with lowered heads, wound meekly homeward to the scant milking. The path they followed led towards the middle background of the picture, where the weather-stained and sagging roof of a farm house rose above the tops of aged cedars. Some of the branches, broken by the sleet and snow of winters, trailed their burdens from the thinned and desolated crests—as sometimes the highest hopes of the mind, after being beaten down by the tempests of the world, droop around it as memories of once transcendent aspirations.

Where she stood in the dead autumn fields few sounds broke in upon the pervasive hush of the declining day.