text:
Page:Dictionary of spoken Russian (1945).djvu/387

 видит. He can't see any further than his own nose. • bow. Надо починить нос лодки. The bow of the boat needs repair. — На носу стоит складные кресла, пойдите лягте. There are folding chairs on the ship's bow; go and lie down. □ Что вы там бормочете под нос? What are you muttering there? • *Он последнее время чего-то стал нос задирать. He's been putting on airs lately. • *Зима уже на носу. Winter is right around the corner. • *Не пришли во-время, вот и остались с носом. You didn't come on time. That's why you were left out in the cold. • *Как ей не стыдно его за нос водить. She ought to be ashamed of herself for leading him on. • *Нечего вам совать нос не в своё дело. Mind your own business.

носилки (-лок P) stretcher. Вы двое понесёте его на носилках в автомобиль. You two take him to the car on a stretcher.

носильщик porter. Носильщик! Вы свободны? Porter! Are you busy? — Пошлите мне, пожалуйста, носильщика! Will you get me a porter, please! — Вы заметили номер вашего носильщика? Did you notice the number of your porter?

носить (ношу, носит; iter of нести) to carry. В этой сумке удобно носить книги. This case is very handy for carrying books. • to deliver. Эта женщина носит нам молоко. This woman delivers milk to us. • to wear. (iter only) Она всегда носит чёрное. She always wears black. □ (iter only) *Почему вы не носите фамилии мужа? Why don't you use your husband's name? • *Куда это вас носит? Вас никогда дома нет. What do you do with yourself all day? You're never at home. • (iter only) *Они меня прямо на руках носили. They made a big fuss over me.

носок (ска, gp носок or носков) sock. Вам шерстяные носки или нитяные? Do you want woolen or cotton socks? — Тут не хватает одной пары носков. There's a pair of socks missing. • toe. Эти ботинки слегка жмут в носке. These shoes pinch slightly in the toes. □ Он ловко поддал мяч носком. He kicked the ball skillfully.

нота note. На верхних нотах он всегда фальшивит. His high notes always sound flat. — Наш посол обратился с нотой протеста по этому поводу. Our ambassador submitted a note of protest on this matter. □ ноты score. Есть у вас ноты этой новой песни? Do you have the score for this new song? □ В её восторгах чувствуется какая-то фальшивая нота. Her enthusiasm sounds false. • Смотр физкультурников прошёл, как по нотам. The sports parade went off beautifully.

ночевать (both dur and pct) to spend a night. Ночевать нам придётся в поле. We'll have to spend the night out in the field. • to stay overnight. Я буду ночевать у знакомых. I'm staying overnight with my friends. □ Она у них днюет и ночует. She's at their house day and night.

ночной night. Поставьте мне стакан воды на ночной столик. Put a glass of water on my night table. — Он теперь работает в ночной смене. He's on the night shift now.

ночь (P ночи, ночей F) night. Спокойной ночи! Good night! □ белая ночь white night. Темное не станет — у нас в Ленинграде сейчас стоит белые ночи. It won't go any darker — we have white nights in Leningrad now. □ Это случилось в ночь под Новый Год. It happened New Year's Eve. • Мы приедем туда в два часа ночи. We'll get there at two o'clock in the morning.

ночью (is of ночь) at night. У него привычка работать ночью. It's his habit to work at night. — Ночью наша улица плохо освещена. Our street is badly lighted at night.

ношу See носить.

ною See ныть.

ноябрь (бря M) November.

нрав temper. Я боюсь его бешеного нрава. I'm afraid of his nasty temper. • disposition. У него кроткий нрав. He has a meek disposition. • nature. У неё простой весёлый нрав. She's a plain person with a cheerful nature. □ нравы customs. Вы, как видно, ещё не знаете наших нравов. Apparently you don't know our customs yet. □ Вам это, как видно, не по праву? Apparently this goes against your grain doesn't it? • Нравы у нас тут пуританские. We're very puritanical here.

нравиться to like. Мне это не нравится. I don't like this. — Им нравится подшучивать над ним. They like to poke fun at him. — Она мне нравится, но я в неё не влюблён. I like her but I'm not in love with her. — Вам нравится вид из этого окна? Do you like the view from this window? — Как вам это нравится? How do you like this?

ну come on. Ну, скорей! Come on, hurry up! • well. Ну, а дальше что? Well, and then what? — Ну, если так, то делать нечего. Well, if that's the way it is, then there's nothing to be done. — Ну, это уж дело ваше. Well, that's your business. • what a. Ну и денёк сегодня выдался. What a day this turned out to be! □ да ну? not really! "Он ей объяснился в любви". "Да ну?" "He told her he loved her." "Not really!" □ Ну так что? So what? • Ну, теперь я готов. Now I'm ready. • Да ну вас, чего пристали! Oh, cut it out, don't bother me. • Ну и угощение же у них, вое уйдут голодными. They set a fine table, I must say! Everybody will go home hungry. • Ну и ну! My, oh my!

нужда (P нужды) want. Нужда у нас после войны была большая. We were in great want after the war. • necessary. В случае нужды напишите мне. In case it's necessary, write me. • necessity. Нужда всему научит. Necessity is the mother of invention. — *Нужда пляшет, нужда скачет, нужда песенки поёт. Necessity will make you do anything. □ Без особой нужды я туда не пойду. I won't go there unless it's very important. • Нужды нет, что тесно, зато весело. We may be a bit crowded but we do have fun.

нуждаться to need. Мы нуждаемся в опытных инженерах. We need experienced engineers. — Он нуждается в деньгах? Does he need any money? □ Они, знаете, очень нуждаются. You know, they're pretty much up against it.

нужный (sh -жна/-ы/) necessary. Вы сделали все нужные распоряжения? Did you give all the necessary instructions? — Он не счёл нужным ответить мне на письмо. He didn't consider it necessary to answer my letter. • need. Эта книга мне больше не нужна. I don't need this book any more. — Сколько денег вам нужно? How much money do you need? □ Он у нас тут самый нужный человек. He's a key man


text: Appletons' Cyclopædia of American Biography/Graff, John Michael

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


text:
Page:Dictionary of spoken Russian (1945).djvu/388

 here. • *Он нам тут нужен, как пятая спица в колеснице. We need him like a fifth wheel on a cart. □ нужно necessary. Она говорит больше, чем нужно. She talks more than necessary. — Если нужно, я буду работать сверхурочно. If necessary, I'll work overtime. • to have to. Это нужно хорошо запаковать. This has to be packed well. • to want. Что вам здесь нужно? What do you want here? • must. Это нужно сделать сегодня. This must be done today.

ну-ка come on. Ну-ка, покажите, что это у вас? Come on, show me what you have here.

нуль (-ля M) zero (See also ноль).

нынешний this. Нынешнее лето жаркое. This summer has been very hot. • modern. Мне нынешние обычаи больше нравятся. I prefer modern customs. □ нынешние времена nowadays. По нынешним временам и такой материал будет хорош. Nowadays, even material like that will do. — В нынешние времена школьникам тоже приходится много работать. Nowadays schoolboys, too, have to work hard.

нынче today. Нынче холодно на дворе? Is it cold out today? • nowadays. Таких, как он, нынче немного. People like him are scarce nowadays.

нырнуть (pct of нырять) to dive. Он нырнул и выплыл далеко от берега. He dived and came up quite a way from the shore.

нырять (/pct нырнуть/) to dive. Плаваете вы хорошо, a нырять умеете? You swim well; can you dive too? — Смотрите, как этот самолёт ныряет! Look at that plane dive!

ныть (ною, ноет) to complain. Вечно он ноет. He's always complaining. • to ache. У меня что-то ноги ноют, верно, к дождю. I think it will rain; my feet ache.

НЭП (Новая экономическая политика) New Economic Policy.

нюхать to smell. Этого лекарства лучше не нюхать, глотайте сразу. You'd better swallow this medicine right away without smelling it. □ нюхать табак to take snuff. Мой дедушка нюхает табак. My grandfather takes snuff. □ *Он ещё молод, пороха не нюхал. He's such a youngster he's still wet behind the ears. • Он, как видно, техники и не нюхал. He evidently doesn't know the first thing about technical subjects.

няня nursemaid. В детстве няня была для меня самым близким человеком. When I was a child my nursemaid was my best friend. • matron. Мальчики бросили няне свой пальтишки и побежали в класс. The little boys threw their coats to the matron and ran into the classroom. • nurse's aid. Няня умыла больного. The nurse's aid washed the patient.

О
о (with a and l; before vowels, об; §31) over. Он споткнулся о порог. He stumbled over the doorstep. • against. Вы испачкались о стенку. You got dirty when you rubbed against the wall. • about. О чём это вы говорите? What is it you're talking about? — Что вы думаете о его работе? What do you think about his work? • on. Я иду на лекцию о Толстом. I'm going to a lecture on Tolstoy. □ Я прочла статью "О Задачах Комосомола." I've read an article called "The Tasks Before the Komsomols." • О нём все хорошо отзываются. He's well spoken of. • *Ну, знаете, это палка о двух концах. Well, you know, this can turn out either way. • *Что ты, о двух головах, что ли? What's the matter with you? Do you think you're leading a charmed life?

об (for о before vowels and in a few set phrases, §31) of. Я об этом не подумал. I didn't think of that. • on. Смотрите, не ударьтесь об угол. Be careful; don't bump yourself on that edge. • in. Мы шли рука об руку. We walked hand in hand. □ Вы слыхали об их отъезде? Have you heard that they left? • Просто хоть головой об стенку бейся. I just feel like throwing in the sponge.

оба (§22) both. Оба её сына погибли на войне. Both of her sons were killed in the war. — Я знакома с ними обоими. I know them both. □ смотреть в оба to watch closely. *За ним надо смотреть в оба. You've got to watch him closely.

обвинение charge. Против него выдвинуто обвинение в преступной небрежности. They brought suit against him on a charge of criminal negligence. • accusation. Это обвинение ни на чём не основано. This accusation is groundless. □ представитель обвинения prosecution. Представитель обвинения представил свой соображения. The prosecution presented its side. предъявить обвинение to indict. Ему предъявлено обвинение в растрате. He was indicted for embezzlement.

обвинитель (M) prosecutor. Кто обвинитель по этому делу? Who's the prosecutor in this case?

обвинить (pct of обвинять) to accuse. Я публично обвинил его во лжи. I publicly accused him of lying.

обвиняемый (prpp of обвинять) defendant. Уже начался допрос обвиняемых? Have they begun questioning the defendants yet?

обвинять (dur of обвинить) to charge. В чём его обвиняют? What is he charged with? • to blame. Я никого в этом не обвиняю, кроме себя самого. I blame no one but myself for this.

-ся to be charged. Он обвиняется в убийстве. He's charged with murder.

обгоню See обогнать.

обгонять (dur of обогнать) to outrun. Смотрите, наша лошадь всех обгоняет! Look, our horse is outrunning them all!

обдумать (pct of обдумывать) to think over. Давайте сперва обдумаем это хорошенько. Let's first think it over carefully. □ Это было убийство с заранее обдуманным намерением. It was premeditated murder.

обдумывать (dur of обдумать).


text:
Page:Memorials of a Southern Planter.djvu/276

 266 that we had for fishing. But that is the largest number that I ever caught in any one day. We always caught more than the family wanted, however; and Mrs. Harrison and Mrs. Smith were in the habit of supplying their neighbors with many a fine dish, for two to three of us would bring in a goodly pile of them."

He was at this time planning a trip to Pass Christian.

", 3d May, 1877.

",—I wrote to your brother last Sunday, but without mentioning your children. When such a letter comes from me, it may be considered as clean a 'bill of health' as can possibly be written. But I would have noticed them had I not expected Ida to stick in something. In all letters from me to any member of my family, if anything is the matter with another member, I always write the worst, not exaggerated, not extenuated, but precisely as the thing stands, leaning, if leaning at all, to the bad, but avoiding all leaning, if that be possible. But you know all this, and yet I find you as wretched as you can make yourself over imaginary sufferings of Emmeline. The child has not grunted once since my telegram to you, nor for four day's previously to the date of that telegram. There is no need of studying what she likes or dislikes, whether sweet milk or sour, bread or crackers, for she eats right and left four to five times during the day. The day before yesterday (1st May) the rectory children were all here, a May-party having been gotten up for them. They had various 'goodies' spread on a large table in the yard, the entertainment coming off late in the evening. After the children had satisfied themselves the grown folks partook. No long time afterwards, the company having left and Sue very tired, she said to Emmeline, 'Well, come along now and we will go to bed.' Whereupon Emmeline, with all the naivete imaginable, inquired if they were not going to have supper!


text:
Page:LorentzGravitation1916.djvu/15

 It is obvious that linear one-dimensional extensions can be called "straight lines", also it will be clear what is to be understood by a "prism" (or "cylinder"). This latter is bounded by two mutually parallel linear three-dimensional extensions $$\sigma_{1}$$ and $$\sigma_{s}$$ and by a lateral surface which may be extended indefinitely to both sides and in which mutually parallel straight lines ("generating lines") can be drawn.

We need not dwell upon the elementary properties of the prism.

§ 17. A vector may now be represented by a straight line of finite length; the quantities $$X_{1},\dots X_{4}$$, which have been introduced in § 10, are the changes of the coordinates caused by a displacement along that line. The magnitude of the vector, expressed in natural units, will be denoted by $$S$$. It is given by a formula similar to (1), viz. by

A vector may be regarded as being the same everywhere in the field-figure, if $$X_{1},\dots X_{4}$$ have constant values. In the same way a rotation $$\mathrm{R}$$ (§ 11) may be said to be the same everywhere, if it can be represented by two vectors of this kind.

If from a point $$P$$ two vectors $$PQ$$ and $$PR$$ issue, denoted by $$X'_{1},\dots X'_{4}$$, $$S'$$ and $$X_{1},\dots X_{4}$$, $$S''$$ resp., the angle between them (comp. (5)) is defined by

We remark here that $$X'_{a},\ X_{b}$$ are real, positive or negative quantities and that $$S'$$ and $$S$$ are expressed in the way indicated in § 5 ("absolute" values). It is to be understood that $$S$$ does not change when the signs of $$X_{1},\dots X_{4}$$ are reversed at the same time.

If $$S$$ is the value of the vector $$RQ$$ and if the angle between this vector and $$RP$$ is denoted by ($$S'', S$$), it follows further from (11) and (12) that

$S=S'\cos(S',S)+S\cos(S'',S)$

In the special case of a right angle $$R$$ we have

$S=S'\cos(S',S)$

an equation expressing the connexion between a vector $$PQ$$ and its "projection" on a line $$PR$$. The angle ($$S', S''$$) is the angle between the vector and its projection, both reckoned from the same point $$P$$.

§ 18. Let us now return to the prism $$R$$ mentioned in § 16. From a point $$A_{2}$$ of the boundary of the "upper face"$$\sigma_{2}$$, we can

title: Page:LorentzGravitation1916.djvu/15


text:
Page:LorentzGravitation1916.djvu/16

 draw a line perpendicular to $$\sigma_{2}$$ and $$\sigma_{1}$$. Let $$B_1$$ be the point, where it cuts thus last, plane, the "base", and $$A_{1}$$ the point where this plane is encountered by the generating line through $$A_{2}$$. If then $$\angle A_{1}A_{2}B_{1}=\vartheta$$, we have

The strokes over the letters indicate the absolute values of the distances $$A_{2}B_{1}$$ and $$A_{2}A_{1}$$.

It can be shown (§ 8) that, all quantities being expressed in natural units, the "volume" of the prism $$P$$ is found by taking the product of the numerical values of the base $$\sigma_{1}$$ and the "height" $$A_{2}B_{1}$$.

Let now linear three-dimensional extensions perpendicular to $$A_{1}A_{2}$$ be made to pass through $$A_1$$ and $$A_2$$. From these extensions the lateral boundary of the prism cuts the parts $$\sigma'_{1}$$ and $$\sigma'_{2}$$ and these parts, together with the lateral surface, enclose a new prism $$P'$$, the volume of which is equal to that of $$P$$. As now the volume of $$P'$$ is given by the product of $$\overline{A_{2}A_{1}}$$ and $$\sigma'_{1}$$, we have with regard to (13)

$\sigma'_{1}=\sigma{}_{1}\cos\vartheta$

If now we remember that, if a vector perpendicular to $$\sigma_{1}$$ is projected on the generating line, the ratio between the projection and the vector itself (viz. between their absolute values) is given by $$\cos\vartheta$$ and that a connexion similar to that which was found above between a normal section $$\sigma'_{1}$$ of the prism and $$\sigma_{1}$$, also exists between $$\sigma'_{1}$$ and any other oblique section, we easily find the following theorem:

Let $$\sigma$$ and $$\bar{\sigma}$$ be two arbitrarily chosen linear three-dimensional sections of the prism, $$\mathrm{N}$$ and $$\bar{\mathrm{N}}$$ two vectors, perpendicular to $$\sigma$$ and $$\bar{\sigma}$$ resp. and of the same length, $$S$$ and $$\bar{S}$$ the absolute values of the projections of $$\mathrm{N}$$ and $$\bar{\mathrm{N}}$$ on a generating line. Then we have

§ 19. After these preliminaries we can show that the left hand side of (10) is equal to 0, if the numbers $$g_{ab}$$ are constants and if moreover both the rotation $$\mathrm{R}_{e}$$ and the rotation $$\mathrm{R}_{h}$$ are everywhere the same. For the two parts of the integral the proof may be given in the same way, so that it suffices to consider the expression

Let $$X_{1},\dots X_{4}$$ be the components of the vector $$\mathrm{N}$$, expressed in $$x$$-units. From the distributive property of the vector product it then follows that each of the four components of

title: Page:LorentzGravitation1916.djvu/16


text:
Page:LorentzGravitation1916.djvu/17

 $\left[\mathrm{R}_{e}\cdot\mathrm{N}\right]_{x}$

is a homogeneous linear function of $$X_{1},\dots X_{4}$$. Under the special assumptions specified at the beginning of this § these are every where, the same functions. Let us thus consider a definite component of (15) e.g. that which corresponds to the direction of the coordinate $$x_{a}$$. We can represent it by an expression of the form

$\int\left(\alpha_{1}X_{1}+\dots+\alpha_{4}X_{4}\right)d\sigma$

where $$\alpha_{1},\dots\alpha_{4}$$ are constants. It will therefore be sufficient to prove that the four integrals

vanish.

In order to calculate $$\int X_{1}d\sigma$$ we consider an infinitely small prism, the edges of which have the direction $$x_1$$. This prism cuts from the boundary surface $$\sigma$$ two elements $$d\sigma$$ and $$\overline{d\sigma}$$. Proceeding along a generating line in the direction of the positive $$x_{1}$$ we shall enter the extension $$\Omega$$ bounded by $$\sigma$$ through one of these elements and leave it through the other. Now the vectors perpendicular to $$\sigma$$, which occur in (15) and which we shall denote by $$\mathrm{N}$$ and $$\bar{\mathrm{N}}$$ for the two elements, have the same value. If, therefore, $$S$$ and $$\bar{S}$$ are the absolute values of the projections of $$\mathrm{N}$$ and $$\bar{\mathrm{N}}$$ on a line in the direction $$x_1$$, we have according to (14)

Let first the four directions of coordinates be perpendicular to one another. Then the components of the vector obtained by projecting $$\mathrm{N}$$ on the above mentioned line are $$X_{1},0,0,0$$ and similarly those of the projection of $$\bar{\mathrm{N}}:\bar{X}_{1},0,0,0$$. But as, proceeding in the direction of $$x_1$$ we enter $$\Omega$$ through one element and leave it through the other, while $$\mathrm{N}$$ and $$\bar{\mathrm{N}}$$ are both directed outward, $$X_{1}$$ and $$\overline{X_{1}}$$, must have opposite signs. So we have

$S:\bar{S}=X_{1}:-\bar{X}_{1}$

and because of (17) we may now conclude that the elements $$X_{1}d\sigma$$

title: Page:LorentzGravitation1916.djvu/17


text:
Page:LorentzGravitation1916.djvu/18

 and $$\overline{X_{1}}\overline{d\sigma}$$ in the first of the integrals (16) annul each other. It will be clear now that the whole integral vanishes and that similar considerations may be applied to the other three.

So we have proved that under the special assumptions made the left hand side of (10) will vanish in the special case that the directions of the coordinates are perpendicular to each other. This conclusion likewise holds for an other set of coordinates if only the assumption made at the beginning of this § is fulfilled. This is obvious, as we can pass from mutually perpendicular coordinates $$x_{1},\dots x_{4}$$ to arbitrarily chosen other ones $$x'_{1},\dots x'_{4}$$ which fulfil this latter condition by linear transformation formulae with constant coefficients. The $$x$$- and the $$x'$$-components of the vector

$\left[\mathrm{R}_{e}\cdot\mathrm{N}\right]+\left[\mathrm{R}_{h}\cdot\mathrm{N}\right]$

are then connected by homogeneous linear formulae with coefficients which have the same value at all points of the surface $$\sigma$$. Hence if, as has been shown above, the four $$x$$-components of the vector

$\int\left\{ \left[\mathrm{R}_{e}\cdot\mathrm{N}\right]+\left[\mathrm{R}_{h}\cdot\mathrm{N}\right]\right\} d\sigma$

vanish, the four $$x'$$-components are now seen to do so likewise.

§ 20. The above considerations were intended to prepare a corollary which will be of use in the treatment of the integral on the left hand side of (10), if we now leave the special assumptions made above and suppose the quantities $$g_{ab}$$ to be functions of the coordinates while also the rotations $$\mathrm{R}_{e}$$ and $$\mathrm{R}_{h}$$ may change from point to point.

This corollary may be formulated as follows: If all dimensions of the limiting surface $$\sigma$$ are infinitely small of the first order, the integral

$\int\left\{ \left[\mathrm{R}_{e}\cdot\mathrm{N}\right]+\left[\mathrm{R}_{h}\cdot\mathrm{N}\right]\right\} _{x}d\sigma$

will be of the fourth order.

In order to make this clear let us suppose that in the calculation of the integral we confine ourselves to quantities of the third order. The surface $$\sigma$$ being already of that order we may then omit all infinitesimal values in the quantities by which $$d\sigma$$ is multiplied;

title: Page:LorentzGravitation1916.djvu/18


text:
Page:LorentzGravitation1916.djvu/19

 we may therefore neglect the infinitesimal changes of the quantities $$g_{ab}$$ over the extension considered, and also those of $$\mathrm{R}_{e}$$ and $$\mathrm{R}_{h}$$. By this we just come to the case considered in § 19. Thus it is evident, that as regards quantities of the third order the first part of (10) is 0. From this it follows that in reality it is at least of the fourth order.

§ 21. Let us now return to the general case that the extension $$\Omega$$ to which equation (10) refers, has finite dimensions. If by a surface $$\bar{\sigma}$$ this extension is divided into two extensions $$\Omega_{1}$$ and $$\Omega_{2}$$, the quantities on the two sides in (10) each consist of two parts referring to these extensions. For the right hand side this is immediately clear and as to the quantity on the left hand side, it follows from the consideration that the contributions of a to the integrals over the boundaries of $$\Omega_{1}$$ and $$\Omega_{2}$$ are equal with opposite signs. In the two cases namely we must take for $$\mathrm{N}$$ equal but opposite vectors.

Also, if the extension $$\Omega$$ is divided into an arbitrary number of parts, each term in (10) will be the sum of a number of integrals, each relating to one of these parts.

By surfaces with the equations $$x_{1}=\mathrm{const.},\dots x_{4}=\mathrm{const}.$$ we can divide the extension $$\Omega$$ into elements which we shall denote by $$\left(dx_{1},\dots dx_{4}\right)$$. As a rule there will be left near the surface $$\sigma$$ certain infinitely small extensions of a different form. From the preceding § it is evident that, in the calculation of the integrals, these latter extensions may be neglected and that only the extensions $$\left(dx_{1},\dots dx_{4}\right)$$ have to be considered. From this we can conclude that equation (10) is valid for any finite extension, as soon at it holds for each of the elements $$\left(dx_{1},\dots dx_{4}\right)$$.

§ 22. We shall now show what equation (10) becomes for one element $$\left(dx_{1},\dots dx_{4}\right)$$. Besides the infinitesimal quantities $$x_{1},\dots x_{4}$$, occurring in the equation

$F=\sum(ab)g_{ab}x_{a}x_{b}=\epsilon^{2}$

of the indicatrix we introduce four other quantities $$\xi_{1},\dots\xi_{4}$$, which we define by

or

{{MathForm2|(19)|$$\left.\begin{array}{c} \xi_{1}=g_{11}x_{1}+g_{12}x_{2}+\dots+g_{14}x_{4}\\ \cdots\cdots\cdots\cdots\cdots\cdots\\ \cdots\cdots\cdots\cdots\cdots\cdots\\ \xi_{4}=g_{41}x_{1}+g_{42}x_{2}+\dots+g_{44}x_{4} \end{array}\right\} $$}}

with the equalities $$g_{ba}=g_{ab}$$.

title: Page:LorentzGravitation1916.djvu/19


text:
Page:LorentzGravitation1916.djvu/20

 To each of these quantities corresponds a definite direction, viz. that in which we have to proceed in order to make the considered quantity change in positive sense while the other three remain constant. If we denote these directions by $$1^{*},2^{*},3^{*},4^{*}$$ and in the same way the directions of the coordinates $$x_{1},x_{2},x_{3}x_{4}$$ by 1, 2, 3, 4, it is evident that $$1^{*}$$ is conjugate with 2, 3 and 4, $$2^{*}$$ with 3, 1 and 4, and so on; inversely 1 with $$2^{*},3^{*},4^{*}$$; 2 with $$3^{*},1^{*},4^{*}$$, and so on. From what has been said above about the algebraic signs of $$g_{11},g_{22},g_{33},g_{44}$$ it follows further that, if directions opposite to 1, $$1^{*}$$ etc. are denoted by — 1, $$-1^{*}$$ etc., the directions — 1 and $$1^{*}$$ will point to the same side of an extension $$x_{1}=\mathrm{const}.$$. The same may be said of the directions —2 and$$2^{*}$$ or —3 and $$3^{*}$$ with respect to extensions $$x_{2}=\mathrm{const}.$$, or $$x_{3}=\mathrm{const}.$$, while with respect to an extension $$x_{4}=\mathrm{const}.$$, the directions 4 and $$4^{*}$$ point to the same side.

Finally, we shall fix (§11) as far as is necessary, which direction corresponds to three others. For that purpose we shall imagine the directions of coordinates $$1,\dots 4$$ to pass into mutually conjugate directions, which will also be called $$1,\dots 4$$, by gradual changes, in such a way that never three of them come to lie in one plane. We shall agree that after this change —4 corresponds to 1, 2, 3.

Let $$a,b,c,d$$ be the numbers 1, 2, 3, 4 in an order obtained from the natural one by an even number of permutations. Then the rule of § 11 teaches us that the direction $$-d$$ corresponds to $$a,b,c$$. It is clear that this would be the ease with $$d$$, if $$a,b,c,d$$ were obtained from 1, 2, 3, 4 by an odd number of permutations. If further it is kept in mind that, always in the new case, the directions $$1^{*},2^{*},3^{*},4^{*}$$ coincide with —1, —2, —3, 4, we come to the conclusion that the directions 1, 2, 3 and 4 correspond to the sets $$2^{*},3^{*},4^{*};3^{*},1^{*},4^{*};1^{*},2^{*},4^{*}$$ and $$1^{*},2^{*},3^{*}$$ respectively. The rule of gradual change (§11) involves that this holds also for the original case, in which 1, 2, 3, 4 were not yet mutually conjugate.

This is all that has to be said about the relations between the different directions. It must only be kept in mind, that whenever two of the first three directions are interchanged, the fourth must be reversed.

§ 23. In the neighbourhood of a point $$P$$ of the field-figure we may introduce as coordinates instead of $$x_{1},\dots x_{4}$$ the quantities $$\xi_{1},\dots\xi_{4}$$ defined by (19). Line-elements or finite vectors can be resolved in the directions of these coordinates, i.e. in the directions

title: Page:LorentzGravitation1916.djvu/20


text:
Page:LorentzGravitation1916.djvu/21

 $$1^{*},2^{*},3^{*},4^{*}$$. Their components and the magnitudes of different extensions can now be expressed in $$\xi$$-nits in the same way as formerly in $$x$$-units. So the volume of a three-dimensional parallelepiped with the positive edges $$d\xi_{1},d\xi_{2},d\xi_{3}$$ is represented by the product $$d\xi_{1}d\xi_{2}d\xi_{3}$$.

Solving $$x_{1},\dots x_{4}$$ from (19) we obtain expressions of the form

{{MathForm2|(20)|$$\left.\begin{array}{c} x_{1}=\gamma_{11}\xi_{1}+\gamma_{21}\xi_{2}+\dots+\gamma_{41}\xi_{4}\\ \cdots\cdots\cdots\cdots\cdots\cdots\\ \cdots\cdots\cdots\cdots\cdots\cdots\\ x_{4}=\gamma_{14}\xi_{1}+\gamma_{24}\xi_{2}+\dots+\gamma_{44}\xi_{4}\\ \gamma_{ba}=\gamma_{ab} \end{array}\right\} $$}}

If we use the coordinates $$\xi$$ the coefficients $$\gamma_{ab}$$ play the same part as the coefficients $$g_{ab}$$ when the coordinates $$x$$ are used. According to (18) and (20) we have namely

$F=\sum(a)\xi_{a}x_{a}=\sum(ab)\gamma_{ab}\xi_{a}\xi_{b}$

so that the equation of the indicatrix may be written

$\sum(ab)\gamma_{ba}\xi_{a}\xi_{b}=\epsilon^{2}$

§ 24. Let the rotations $$\mathrm{R}_{e}$$ and $$\mathrm{R}_{h}$$ of which we spoke in § 13 be defined by the vectors $$\mathrm{A^{I},A^{II}}$$ and $$\mathrm{A^{III},A^{IV}}$$ respectively, the resultants of the vectors $$\mathrm{A_{1^{*}}^{I},\dots A_{4^{*}}^{I}}$$, etc. in the directions $$1^{*},\dots4^{*}$$. Then, according to the properties of the vector product that were discussed in § 11,

$\begin{array}{ll} \left[\mathrm{R}_{e}\cdot\mathrm{N}\right] & =\left[\mathrm{\left(A_{1^{*}}^{I}+\dots+A_{4^{*}}^{I}\right)\cdot\left(A_{1^{*}}^{II}+\dots+A_{4^{*}}^{II}\right)\cdot N}\right]\\ & =\sum(\overline{ab})\left\{ \left[\mathrm{A}_{a^{*}}^{I},\ \mathrm{A}_{b^{*}}^{II}\cdot\mathrm{N}\right]-\left[\mathrm{A}_{a^{*}}^{II},\ \mathrm{A}_{b^{*}}^{I}\cdot\mathrm{N}\right]\right\} \end{array}$|undefined

where the stroke over $$ab$$ indicates that each combination of two different numbers $$a, b$$ contributes one term to the sum. For the vector product $$\left[\mathrm{R}_{h}\cdot\mathrm{N}\right]$$ we have a similar equation. Now two or more rotations in one and the same plane, e.g. in the plane $$a^{*}b^{*}$$, may be replaced by one rotation, which can be represented by means of two vectors with arbitrarily chosen directions in that plane, e.g. the directions $$a^{*}$$ and $$b^{*}$$. We may therefore introduce two vectors $$\mathrm{B}_{a^{*}}$$ and $$\mathrm{B}_{b^{*}}$$ directed along $$a^{*}$$ and $$b^{*}$$ resp., so that

Then we must substitute in (10)

Here it must be remarked that the magnitude and the sense of one of the vectors $$\mathrm{B}$$ may be chosen arbitrarily; when this has been done, the other vector is perfectly determined.

title: Page:LorentzGravitation1916.djvu/21


text:
Page:Chronological Table and Index of the Statutes.djvu/37

Rh


text:
Page:LorentzGravitation1916.djvu/22

 In the following calculations the vector $$\mathrm{N}$$ has one of the directions $$1^{*},\dots4^{*}$$. As this is also the case with the vectors $$\mathrm{B}_{a^{*}}$$ and $$\mathrm{B}_{b^{*}}$$, the vector product occurring in (22) can easily be expressed in $$\xi$$-units. After that we may pass to natural units and finally, as is necessary for the substitution in (10), to $$x$$-units.

In order to pass from $$\xi$$-units to natural units we have to multiply a vector in the direction $$a^{*}$$ by a certain coefficient $$\lambda_{a}$$, and a part of the extension $$a^{*},b^{*},c^{*}$$ by a coefficient $$\lambda_{abc}$$. These coefficients correspond to $$l_{a}$$ (§ 10) and $$l_{abc}$$ (§ 12). The factors $$\lambda_{abc}$$ e.g. can be expressed by means of the minors $$\Gamma_{ab}$$ of the determinant $$\gamma$$ of the quantities $$\gamma_{ab}$$. If this is worked out and if the equations

$\gamma_{ab}=\frac{G_{ab}}{g},\ g_{ab}=\frac{\Gamma_{ab}}{\gamma},\ g\gamma=1 $|undefined

are taken into consideration, we obtain the following corollary, which we shall soon use:

Let $$a, b, c, d$$ and also $$a', b', c', d'$$ be the numbers 1, 2, 3, 4 in any order, $$a'$$ being not the same as $$a$$, then we have, if none of the two numbers $$\alpha$$ and $$\alpha'$$ is 4,

and if one of the two is 4

§ 25. We shall now suppose (comp. § 24) that in $$\xi$$-units the vector $$\mathrm{B}_{a^{*}}$$ has the value +1, and we shall write $$\chi_{ab}$$ for the value that must then be given to $$\mathrm{B}_{b^{*}}$$. If the $$\xi$$-components of the vectors $$\mathrm{A^{I}}$$ etc. are denoted by $$\Xi_{1}^{I},\dots\Xi_{4}^{I}$$ etc., we find from (21)

This formula involves that

It may be remarked that $$\chi_{ba}$$ is the value that must be given to the vector $$\mathrm{B}_{a^{*}}$$ if $$\mathrm{B}_{b^{*}}$$ is taken to be 1.

The quantities $$\chi_{ab}$$ may be said to represent the rotations $$\left[\mathrm{B}_{a^{*}}\cdot\mathrm{B}_{b^{*}}\right]$$.

At the end of our calculations we shall introduce instead of $$\chi_{ab}$$ the quantities t$$\psi_{ab}$$ defined by

In the first of these equations $$a, b, a', b'$$ are supposed to be the numbers 1, 2, 3, 4, in an order obtained from 1, 2, 3, 4 by an even number of permutations.

title: Page:LorentzGravitation1916.djvu/22


text:
Page:LorentzGravitation1916.djvu/23

 § 26. We have now to calculate the left hand side of equation (10) for the case that $$\sigma$$ is the surface of an element $$\left(dx_{1},\dots dx_{4}\right)$$. For this purpose we shall each time take together two opposite sides, calculating for each pair the contributions due to the different terms on the right hand side of (22), or as we may say to the different rotations $$\chi_{ab}$$. It is convenient now to denote by $$a, b, c$$ the numbers 1, 2, 3 either in this order or in any other derived from it by a cyclic permutation, while the $$x$$-components of the vector we are calculating and which stands on the left hand side of (10) will be represented by $$X_{1},\dots X_{4}$$.

a. Let us first consider that one of the sides $$\left(dx_{a},dx_{b},dx_{c}\right)$$ which faces towards the side of the positive $$x_4$$. The vector $$\mathrm{N}$$ drawn outward has the direction $$4^{*}$$ and in $$\xi$$-units the magnitude $$\frac{1}{\lambda_{4}}$$. As the direction $$c$$ corresponds to $$a^{*},b^{*},4^{*}$$, the rotation $$\chi_{ab}$$ gives with $$\mathrm{N}$$ a vector product represented by a vector in the direction $$c$$. The magnitude of this vector is in $$\xi$$-units

$\frac{1}{\lambda_{4}}\chi_{ab}$|undefined

and in natural units

$\frac{\chi_{ab4}}{\lambda_{4}}\chi_{ab}$|undefined

This must be multiplied by $$l_{abc}dx_{a}dx_{b}dx_{c}$$, the magnitude of the side under consideration in natural units, and finally by $$\tfrac{1}{l_{c}}$$ to express the vector product in $$x$$-units. Because of (24) we may write for the result

$\chi_{abc}dx_{a}dx_{b}dx_{c}=\psi_{c4}dx_{a}dx_{b}dx_{c}$

The opposite side gives a similar result with the opposite sign ($$\mathrm{N}$$ having for that side the direction $$-4^{*}$$), so that together the sides contribute the term

$\frac{\partial\psi_{c4}}{\partial x_{4}}dW$|undefined

to the component $$X_{c}$$. For shortness sake we have put here

$dx_{1}dx_{2}dx_{3}dx_{4}=dW$

Finally we may take, $$c = 1, 2, 3$$.

b. Secondly we consider a side $$\left(dx_{a},dx_{b},dx_{4}\right)$$ facing towards the positive $$x_c$$. The vector $$\mathrm{N}$$ has now the direction $$-c^{*}$$. We consider the vector products of this vector with the rotations $$\chi_{b4}$$, $$\chi_{4a}$$ and $$\chi_{ba}$$, which vector products have the directions $$a, b$$ and 4. A calculation exactly similar to the one we performed just now gives the contributions to $$X_{a},X_{b},X_{4}$$. For these we thus find the products of $$dx_{a}dx_{b}dx_{4}$$ by

title: Page:LorentzGravitation1916.djvu/23


text:
Page:LorentzGravitation1916.djvu/24

 $\begin{array}{c} \frac{l_{ab4}\lambda_{bc4}}{l_{a}\lambda_{c}}\chi_{b4}=\chi_{4b}=\psi_{ac},\\ \\ \frac{l_{ab4}\lambda_{ac4}}{l_{b}\lambda_{c}}\chi_{4a}=\chi_{a4}=\psi_{bc},\\ \\ \frac{l_{ab4}\lambda_{abc}}{l_{4}\lambda_{c}}\chi_{ba}=\chi_{ba}=\psi_{4c}. \end{array}$|undefined

Taking also into consideration the opposite side $$\left(dx_{a},dx_{b},dx_{4}\right)$$ we find for $$X_{a},X_{b},X_{4}$$ the contributions

$\frac{\partial\psi_{ac}}{\partial x_{c}}dW,\ \frac{\partial\psi_{bc}}{\partial x_{c}}dW,\ \frac{\partial\psi_{4c}}{\partial x_{c}}dW.$|undefined

This may be applied to each of the three pairs of sides not yet mentioned under $$a$$; we have only to take for $$c$$ successively 1, 2, 3.

Summing up what has been said in this § we may say: the components of the vector on the left hand side of (10) are

$X_{a}=\sum(b)\frac{\partial\psi_{ab}}{\partial x_{b}}dW$|undefined

§ 27. For the components of the vector occurring on the right hand side of (10) we may write

$i\mathrm{q}_{a}d\Omega$

if $$\mathrm{q}_{a}$$ is the component of the vector $$\mathrm{q}$$ in the direction $$x_{a}$$ expressed in $$x$$-units, while $$d\Omega$$ represents the magnitude of the element $$\left(dx_{1},\dots dx_{4}\right)$$ in natural units. This magnitude is

$-i\sqrt{-g}dW$

so that by putting

we find for equation (10)

The four relations contained in this equation have the same form as those expressed by formula (25) in my paper of last year. We shall now show that the two sets of equations correspond in all respects. For this purpose it will be shown that the transformation formulae formerly deduced for $$w_{a}$$ and $$\psi_{ac}$$ follow from the way in which these quantities have been now defined. The notations from the former paper will again be used and we shall suppose the transformation determinant $$p$$ to be positive.

title: Page:LorentzGravitation1916.djvu/24


text:
Page:LorentzGravitation1916.djvu/25

 § 28. Between the differentials of the original coordinates $$x_{a}$$ and the new coordinates $$x'_{a}$$ which we are going to introduce we have the relations

and formulae of the same form (comp. § 10) may be written down for the components of a vector expressed in $$x$$-measure. As the quantities $$\mathrm{q}_{a}$$ constitute a vector and as

$\sqrt{-g'}=p\sqrt{-g}$

we have according to (28)

$\frac{1}{\sqrt{-g'}}w'_{a}=\frac{1}{\sqrt{-g}}\sum(b)\pi_{ba}w_{b}$|undefined

or

$w'_{a}=p\sum(b)\pi_{ba}w_{b}$

Further we have for the infinitely small quantities $$\xi_{a}$$ defined by (19)

$\xi'_{a}=\sum(b)p_{ba}\xi_{b}$

and in agreement with this for the components of a vector expressed in $$\xi$$-units

$\Xi'_{a}=\sum(b)p_{ba}\Xi_{b}$

so that we find from (25)

$\chi'_{ab}=\sum(cd)p_{ca}p_{db}\chi_{cd}$

Interchanging here $$c$$ and $$d$$, we obtain

$\chi'_{ab}=\sum(cd)p_{da}p_{cb}\chi_{dc}=-\sum(cd)p_{da}p_{cb}\chi_{cd}$

and

The quantity between brackets on the right hand side is a second order minor of the determinant $$p$$ and as is well known this minor

title: Page:LorentzGravitation1916.djvu/25


text:
Page:LorentzGravitation1916.djvu/26

 is related to a similar minor of the determinant of the coefficients $$\pi_{ab}$$. If $$a'b'$$ corresponds to $$ab$$ in the way mentioned in § 25, and $$c'd'$$ in the same way to $$cd$$, we have

$p_{ca}d_{db}-p_{da}p_{ch}=p\left(\pi_{c'a'}\pi_{d'b'}-\pi_{d'a'}\pi_{c'b'}\right)$

so that (31) becomes

$\chi'_{ab}=\frac{1}{2}p\sum(cd)\left(\pi_{c'a'}\pi_{d'b'}-\pi_{d'a'}\pi_{c'b'}\right)\chi_{cd}$

According to (27) this becomes

$\psi'_{a'b'}=\frac{1}{2}p\sum(cd)\left(\pi_{c'a'}\pi_{d'b'}-\pi_{d'a'}\pi_{c'b'}\right)\psi_{c'd'}$

for which we may write

$\psi'_{ab}=\frac{1}{2}p\sum(cd)\left(\pi_{ca}\pi_{db}-\pi_{da}\pi_{cb}\right)\psi_{cd}$

Interchanging $$c$$ and $$d$$ in the second of the two parts into which the sum on the right hand side can be decomposed, and taking into consideration that

$\psi_{dc}=-\psi_{cd}$

as is evident from (26) and (27), we find

$\psi'_{ab}=p\sum(cd)\pi_{ca}\pi_{db}\psi_{cd}$

§ 29. Finally it can be proved that if equation (10) holds for one system of coordinates $$x_{1},\dots x_{4}$$, it will also be true for every other system $$x'_{1},\dots x'_{4}$$, so that

To show this we shall first assume that the extension $$\Omega$$, which is understood to be the same in the two cases, is the element $$\left(dx_{1},\dots dx_{4}\right)$$.

For the four equations taken together in (10) we may then write

and in the same way for the four equations (32)

We have now to deduce these last equations from (33). In doing so we must keep in mind that $$u_{1},\dots u_{4}$$ are the $$x$$-components and $$u'_{1},\dots u'_{4}$$ the $$x$$-components of one definite vector and that the same may be said of $$v_{1},\dots v_{4}$$ and $$v'_{1},\dots v'_{4}$$.

Hence, at a definite point (comp. (30))

We shall particularly denote by $$\pi_{ba}$$ the values of these quantities belonging to the angle $$P$$ from which the edges $$dx_{1},\dots dx_{4}$$ issue

title: Page:LorentzGravitation1916.djvu/26


text:
Page:LorentzGravitation1916.djvu/27

 in positive directions. To the right hand sides of the equations (34) we may apply transformation (35) with these values of $$\pi_{ba}$$, $$d\Omega$$-being infinitely small of the fourth order and it being allowed to confine ourselves to quantities of this order.

On the left hand sides of (34), however, we must take into consideration, the surface being of the third order, that the values of $$\pi_{ba}$$ change from point to point. Let $$\mathrm{x}_{1},\dots\mathrm{x}_{4}$$ be the changes which $$x_{1},\dots x_{4}$$ undergo when we pass from $$P$$ to any other point of the surface. Then we must write for the value of the coefficient at this last point

$\pi_{ba}+\sum(c)\frac{d\pi_{ba}}{dx_{c}}\mathrm{x}_{c}$|undefined

We thus have

$\int u'_{a}d\sigma=\sum(b)\pi_{ba}\int u_{b}d\sigma+\sum(b)\int u_{b}\sum(c)\frac{\partial\pi{}_{ba}}{\partial x_{c}}\mathrm{x}_{c}d\sigma$|undefined

It will be shown presently that the last term vanishes. This being proved, it is clear that the relations (34) follow from (33); indeed, multiplying equations (33) by$$\pi_{1a},\dots\pi_{4a}$$ respectively and adding them we find

$\int u'_{a}d\sigma=v'_{a}d\Omega$

§ 30. The proof for

rests on the relations

which follow from

$\pi{}_{ba}=\frac{\partial x'_{b}}{\partial x_{b}},\ \pi{}_{ea}=\frac{\partial x'_{a}}{\partial x_{e}},$|undefined

The integral which occurs in (36) differs from

by the infinitely small factor under the sign of integration

$\sum(c)\frac{\partial\pi{}_{ba}}{\partial x_{c}}\mathrm{x}_{c}$|undefined

Now we have calculated in § 26 integrals like (38) by taking together each time two opposite sides, one of which $$\Sigma_{1}$$ passes through $$P$$ while the second $$\Sigma_{2}$$ is obtained from the first by a shift in the

title: Page:LorentzGravitation1916.djvu/27


text:
Page:LorentzGravitation1916.djvu/28

 direction of one of the coordinates e. g. of $$x_{e}$$ over the distance $$dx_{e}$$. We had then to keep in mind that for the two sides the values of $$u_{b}$$, which have opposite signs, are a little different; and it was precisely this difference that was of importance. In the calculation of the integral

however it may be neglected. Hence, when we express the components $$u_{b}$$ in terms of the quantities $$\psi_{ab}$$, we may give to these latter the values which they have at the point $$P$$.

Let us consider two sides situated at the ends of the edges $$dx_{e}$$ and whose magnitude we may therefore express in $$x$$-units $$dx_{j}dx_{k}dx_{l}$$ if $$j, k, l$$ are the numbers which are left of 1, 2, 3, 4 when the number $$e$$ is omitted. For the part contributed to (38) by the side $$\Sigma_{2}$$ we found in § 26

$\psi{}_{be}dx_{j}dx_{k}dx_{l}$

We now find for the part of (39) due to the two sides

$\psi{}_{be}\sum(c)\frac{\partial\pi{}_{ba}}{\partial x_{c}}\left[\int\limits _{2}\mathrm{x}_{c}d\sigma-\int\limits _{1}\mathrm{x}_{c}d\sigma\right]$|undefined

where the first integral relates to $$\Sigma_{2}$$ and the second to $$\Sigma_{1}$$. It is clear that but one value of $$c$$, viz. $$e$$ has to be considered. As everywhere in $$\Sigma_{1}:\mathrm{x}_{c}=0$$ and everywhere in $$\Sigma_{2}:\mathrm{x}_{c}=dx_{e}$$ it is further evident that the above expression becomes

$\psi{}_{eb}\frac{\partial\pi{}_{ba}}{\partial x_{c}}dW$|undefined

This is one part contributed to the expression (36). A second part, the origin of which will be immediately understood, is found by interchanging $$b$$ and $$e$$. With a view to (37) and because of

$\psi{}_{eb}=-\psi{}_{be}$

we have for each term of (36) another by which it is cancelled. This is what had to be proved.

§ 31. Now that we have shown that equation (32) holds for each element $$\left(dx_{1},\dots dx_{4}\right)$$ we may conclude by the considerations of § 21 that this is equally true for any arbitrarily chosen magnitude and shape of the extension $$\Omega$$. In particular the equation may be applied to an element $$\left(dx'_{1},\dots dx'_{4}\right)$$ and by considerations exactly similar to

title: Page:LorentzGravitation1916.djvu/28


text:
Page:LorentzGravitation1916.djvu/29

 those presented in § 26 we see that in the new coordinates as well as in the original ones we have equations of the form (29).

Whatever be our choice of the coordinates the part of the principal function indicated in § 14 can therefore be derived for a given current vector $$\mathrm{q}$$.

In a sequel to this paper some conclusions that may be drawn from 's principle will be considered.

title: Page:LorentzGravitation1916.djvu/29


text:
Page:Memorials of a Southern Planter.djvu/277

 Rh "So make yourself easy. I will never leave anything to your imagination about these dear little fellows; so, 'go 'long' and get yourself well as soon as you please."

", 6th July, 1877.

",—You can't know how much pleasure your eminently characteristic letter of the 20th ultimo gave me—gave all of us. It is so like you to remember a promise that I did not make, but which you chose to believe I did make because you wished to have it so. I was too fearful of being unable to visit you this summer to promise such a thing, and yet could not give expression to that doubt; and hence you were left to draw your own inference, and you only know one way of solving such problems as these. I now know that it is impossible for me to enjoy the hospitality of Cam and yourself this summer, as we are expecting my brother's family,—the whole tribe, consisting of himself and wife, Nanny, Mary Ware and her son Toby, and perhaps Martha, to spend the month of August with us. They are all together on Honey Island (except Martha), but they know that they can't stay there through the summer, and so they propose to divide about three months between Aggy, Colonel Porter, and myself. So you see, my dear, that I am nailed hard and fast right here for this summer, at least. But I don't relinquish the hope of seeing the inside of your new home some time or other, and will do it as soon as I can, for I wish to see you all very much. As you say nothing about gnats in your letter to me, I hope those vile pests left you quickly after your letter was written to Mrs. Douglas. They are a great deal worse than mosquitoes, I think, as they light on you in clouds—in your eyes, nose, and ears,—are not to be frightened off, bite like ——, and pass right through ordinary mosquito-bars. I fear your region is subject to them at certain seasons of the year.

"I don't know whether to congratulate Cam on his


text:
Page:Memorials of a Southern Planter.djvu/278

 268 elegant leisure or not. If he had much professional employment, you would probably have to burn the lamp o' nights.

"If your neighbors wish to see your old uncle, he is indebted to the kind words of his niece for that wish. But what is the use of having friends if they fail to show it on proper occasions!

"I am glad that you have some garden. I have had a scuffle to have even that, as it rained eternally during the spring, and then dropped off to no rain at all, and we are having the hottest summer I ever witnessed in Mississippi. I have to take the garden in broken doses, homœopathic at that, as I came near a sunstroke, or something worse, the other day, frightening the girls nearly out of their wits.

"Lelia, poor child, is very far from being well. I was in hopes of getting her off to the North, but could not make it out, and so she has gone to her kind friends in Brandon for a change of air and scene. If she is not improved by it, I must send her to New York when her brother returns to that place after his summer vacation terminates. Emmy has been in New York three to four months, but is expected to arrive at Terry to-morrow night. Her children have been with us during her absence, but she will have no fault to find when she sees them, as they are as hearty a trio as ever discussed bread and butter and sich.

"Charlie and Kate are as loving as ever, I believe, which is saying a good deal for this hot weather. The girls send any amount of love to you and Cam and the children. My love all round."

", 19th December, 1877.

",—I received, yesterday, a letter from Dr. Baird, giving the particulars of the dreadful calamity that has befallen you. I was waiting for that, or for something of the kind from some member of your family, being more than willing to postpone so mournful and difficult a task as writing a letter to you that could be satisfactory to me or in


text:
Page:Chronological Table and Index of the Statutes.djvu/38

20


text:
Page:Dictionary of spoken Russian (1945).djvu/389

 обе (/F of оба, § 22/) both. Обе книжки мой. Both books are mine. □ *Я ухватился за это предложение обеими руками. I jumped at the proposition.

обед dinner. Обед готов. Dinner's ready. — Мы об этом поговорим за обедом. We'll discuss it at dinner. — Надо их пригласить к обеду. We have to invite them to dinner. — Что это у вас сегодня — званый обед? Tell me, are you having a dinner party today? • lunch time. Поработаем до обеда! Let's work till lunch time. □ домашние обеды home-cooked meals. Здесь можно получать домашние обеды. Home-cooked meals are served here.

обедать (dur) to have dinner. Мы всегда обедаем в два часа. We always have dinner at two o'clock. — Вы уже обедали? Have you had dinner yet? • Пойдёмте сегодня обедать в ресторан. Let's dine in a restaurant today.

обезьяна monkey. В нашем зоопарке двенадцать обезьян. There are twelve monkeys in our zoo. — Смотрите, какой урод! настоящая обезьяна. Look at him; he's as ugly as a monkey. — Он всякого умеет передразнить — чистая обезьяна! He's a regular monkey: he can imitate anybody.

обернуть (pct of обёртывать and оборачивать) to wrap. Оберните книгу в газету. Wrap your book in a newspaper.

-ся to turn. Он обернулся в нашу сторону. He turned in our direction. • to turn out. Посмотрим, как это ещё обернётся! Let's see how it'll turn out.

обёртывать (dur of обернуть).

обеспечение insurance. Все граждане Советского Союза имеют право на обеспечение старости. All citizens of the Soviet Union have old-age insurance. □ социальное обеспечение social security.

обеспечивать (dur of обеспечить).

обеспечить (pct of обеспечивать) to provide for. Он хотел обеспечить семью. He wanted to provide for his family. • to insure. Необходимо обеспечить своевременное выполнение этой работы. It's necessary to insure the completion of the job on time. • to stock up. Мы на всю зиму обеспечены дровами. We've stocked up enough firewood for the whole winter.

обеспокоить (pct of беспокоить) to make uneasy. Его последнее письмо меня сильно обеспокоило. His last letter made me very uneasy. • to worry. Я очень обеспокоена его отсутствием. I'm very much worried about his absence.

обещание promise. Он сдержал своё обещание. He kept his promise. — Почему вы нарушили своё обещание? Why did you break your promise?

обещать (both dur and pct) to promise. Он обещал прийти. He promised to come. — Мне обещали путёвку в дом отдыха. I was promised a vacation in a rest home with all expenses paid. — Спектакль обещает быть интересным. The performance promises to be interesting.

обжечь (обожгу, -жжёт [-žj]; p обжёг, обожгла, -о, -и; ppp обожжённый [-žj-]; pct of обжигать) to burn. Где это вы так обожгли руку? Where did you burn your hand like that? — Мне крапивой все ноги обожгло. My legs burn from stinging nettles. □ Эта фигурка из обожжёной глины. This statuette is made of baked clay.

-ся to burn oneself. Я обжёгся о печку. I burned myself on the stove. • to burn. *Обжёгшись на молоке, будешь дуть и на воду. Once burned, twice shy.

обжигать (dur of обжечь).

обида insult. Я не скоро забуду эту обиду. I won't soon forget that insult. • offense. Не в обиду вам будь сказано, это была не очень удачная речь. No offense meant, but this speech was not so good. □ в обиде angry. Скажите правду, вы на меня не в обиде? Tell the truth; are you angry with me? □ Не бойтесь, я вас в обиду не дам. Don't worry, I won't let anyone take advantage of you. • Он сказал это с обидой в голосе. He said it in an injured tone of voice. • Ему пришлось проглотить обиду. He had to swallow his pride.

обидеть (-ижу, -идит, pct of обижать) to insult. Неужели вы не понимаете, что вы кровно обидели бедного профессора? Don't you understand that you've insulted this poor professor terribly? • to offend. Как-же! Его обидишь! You'll have a tough time trying to offend him. • to slight. Её не пригласили, и они очень обижена. She feels slighted because she wasn't invited. □ Его природа разумом обидела. He was left out when brains were passed out.

обидный offensive. Мне кажется, что в его предложении нет ничего обидного. I don't think there's anything offensive in his proposal. • insulting. Это очень обидное сравнение. That's a very insulting comparison. □ обидно it's a shame. Обидно, что это так случилось. It's a shame that it happened that way. □ Мне стало так обидно! I was awfully hurt.

обижать (dur of обидеть) to take advantage of. Не обижайте его — он тут совсем один, за него заступиться некому. Don't take advantage of him. He's here all alone with no one to take up for him. • to hurt. Я и не думала обижать его. I wouldn't think of hurting him.

обижу See обидеть.

обилие abundance. Какое обилие фруктов в этих краях! There certainly is an abundance of fruit in this part of the country!

обильный abundant. В прошлом году тут был обильный урожай яблок. Last year we had an abundant crop of apples. • hearty. После такого обильного обеда хорошо было бы вздремнуть. It'd be a good idea to take a nap after such a hearty meal.

обком obkom (committee of the Communist Party of an oblast). Идите в обком. Go to the obkom.

обкраду See обокрасть.

обкрадывать (dur of обокрасть).

облако (P облака, -ов) cloud. На небе сегодня только небольшие облака. There are only a few small clouds in the sky today. — За облаками пыли не видно было автомобиля. You couldn't see the car because of the clouds of dust. — *Она вечно в облаках витает. She's always up in the clouds. □ Всё небо в облаках, боюсь дождь пойдёт. I'm afraid it's going to rain; the sky is all cloudy.

областной oblast. На областном съезде советов было много делегатов. There were many delegates at the oblast convention of Soviets. • local. Это слово областное. This word is only used locally.

область (P -сти, -стёй F) oblast. (See Appendix 4). Эта


text:
Page:Memorials of a Southern Planter.djvu/279

Rh any way a comfort to you. To lose one's husband or wife I take to be the greatest calamity that can befall any one who may be happily married, and that you had that comfort in Cam I have every reason to be absolutely certain of. But, my dear child, it is among the inevitable laws of nature that these unions must be broken up at some time or other, and one or the other be left to mourn. It is therefore seemly that we should be grateful for such measure of happiness as we have been permitted to enjoy, and to bow our heads reverently and without a rebellious spirit when the All Wise sees fit to checker our path. I trust you may succeed, after a time, in schooling your mind to this necessity.

"Dr. Baird's letter to me shows him to be a very sincere friend of yours. He discusses your situation with a great deal of feeling, and exhorts me to go to see you, if possible, and, if not possible, to send some one on whose friendship you may be supposed to rely. . . . For myself, you may remember that I returned from the Pass a month or two ago (or were told that I did) so entirely indisposed as to make it doubtful whether or no I should ever get over it. I am unable now to undergo any extra exertion, and get to my garden with some difficulty, but force myself to go, as better than continuous inactivity. I never even go to Dry Grove if it can be avoided. It was therefore impossible for me to accede to Dr. Baird's suggestion by going to your house."

", 6th January, 1878.

"God bless my child and her children and her husband! And you thought of me in connection with the 4th, and your husband thought of me in connection with Christmas and oysters, and you forgot to write to me about it! But all is well that ends well, as you say; and I now know more about oysters than I ever did. I thought they must be lost, but I told Edward to bring them out unless they would knock a buzzard over. There were but two spoiled ones. The


text:
Category talk:New Jersey court decisions by topic

GUANGZHOU ROOQU IMPORT @ EXPORT TRADING CO., LIMITED <>Manufacturer, Trading Company] has been serving the worldwide market since 2010. High-quality and competitive price are the advantages of our rams, therefore, we have achieved good share of market in the business circle in and out of China. We manufacture products in Guangzhou, we are have products line on computer memory modules, memory cards; memory ram, DDR & DDR2 & DDR3 for Desktop & laptops. Most products have attained CE and FCC certification. We have a young and energetic professional work team to offer you excellent services. Our culture is based on a long-lasting commitment to customer satisfaction. We are determined to produce the most advanced products with absolutely the lowest rate of return for every customer to receive the quality, performance and dependability they deserve. Address:#422.Huangshixi Road.Baiyun.Guangzhou.510000.China Contact Person: Ms.Sophia Zheng Tel: 0086-20-87589060 Fax: 0086-20-87589060 Email: sales@rooqu.com & info@rooqu.com Website: www.rooqu.com


text:
Legal Analysis and Terminology

LEGAL ANALYSIS AND TERMINOLOGY Arthur L. Corbin Professor of Law, Yale University

Every student of the law must be equipped with certain fundamental concepts and with certain terms in which to express them. Let him read the federal Constitution or the opinion of any court or any legal treatise, or let him listen to the lecture of any law professor, and every sentence will be likely to bristle with rights and duties, powers, privileges, liabilities, and immunities. He will gradually realize also that these terms are frequently used loosely, each term often being used to express several distinct concepts, and he will find that our dictionaries merely record this wide and variable usage and aid little toward the clear expression essential to exact reasoning.

No doubt the beginner cannot be made to realize at once the disadvantages attendant upon variableness of terms and uncertainty of concept. But it is quite possible at the very outset to master a number of fundamental legal concepts and to acquire a single definite meaning for each of the terms used to express them. With such simple concepts and definite phraseology the student can more easily analyze a complex problem, arrive at a correct solution, and explain it clearly to others. He can thus be led to avoid much unnecessary obscurity and difficulty. As his experience increases he must test for himself the accuracy and usefulness of the analysis and terminology. The following definitions are offered, chiefly for the benefit of beginning students of the law, in order to assist in establishing an exact terminology and a definiteness and accuracy of mental concept. These definitions are in large part based upon the articles of Professor Wesley N. Hohfeld, referred to below.

I. : This is a world of facts. Physical existence and physical relations are facts. Our mental processes are facts. The existence of any legal relation is a fact. All changes and variations are facts. Facts include acts and events.

II. : An act is one of that class of facts manifest to the senses that consists of voluntary physical movements (muscular contractions that are willed) of human beings. A forbearance is a consciously willed absence of physical movement. Animals other than men can act or forbear, but they do not become parties to a legal relation.

III. : Any change in the existing totality of facts, including the acts of human beings.

IV. : Any fact the existence or occurrence of which will cause new legal relations between persons. A clear distinction should always be observed between the physical phenomena and the legal relations consequent thereon. The former are in the world of the senses, the latter are intellectual conceptions. Operative facts have also been described as “investitive,” “constitutive,” “causal,” and “dispositive.” The “extinguishment” of a legal relation is necessarily the creation of a new one.

V. : Any fact the existence or occurrence of which tends to prove the existence of some other fact. For example, a footprint on the sand is a fact from which we may infer the recent presence of a man.

Evidential facts may themselves be operative as well, but need not be. For example, if A strikes B this fact often creates a right to damages and at the same time it is evidence (not conclusive) of an intent in A’s mind.

VI. : A fact is material when it is either operative or evidential.

VII. : A relation perceivable by the senses, between two physical objects. This would include relations of space, time, weight, color, density, and the like.

VIII. : A law is a rule concerning human conduct, established by those agents of an organized society who have legislative power. When a rule of law has been reduced to words it is a statement of the legal effect of operative facts; i.e. it is a statement that certain facts will normally be followed by certain immediate or remote consequences in the form of action or non-action by the judicial and executive agents of society. Whenever any such operative facts exist the persons who will be affected by the stated consequences are said to have a legal relation each to the other. When we state that some particular legal relation exists we are impliedly asserting the existence of certain facts, and we are expressing our present mental concept of the societal consequences that will normally follow in the future. A statement that a legal relation exists between A and B is a prediction as to what society, acting through its courts or executive agents, will do or not do for one and against the other. If A invades B’s house, we are able to predict that the police will eject A, that a court will give judgment for damages, and that the sheriff will levy execution. We say that B had a right that A should not intrude and that A had a duty to stay out. But if B had invited A to enter, we know that those results would not occur. In such case we say that B had no right that A should stay out and that A had the privilege of entering.

The term “legal relation” should always be used with reference to two persons, neither more nor less. One does not have a legal relation to himself. Nor does one have a legal relation with two others; he has separate legal relations with each. A so-called legal relation to the State or to a corporation may always be reduced to many legal relations with the individuals composing the State or the corporation, even though for convenient discussion they may be grouped. There can be no such thing as a legal relation between a person and a thing. The relation of A to his house is a physical relation; but A has many legal relations to other persons with respect to his house.

Furthermore, the legal relations of any two persons are frequently numerous and complex, and it is of great service to analyze them into their simplest forms. Such terms of the law as “contract,” “trust,” “property” and “marriage” do not represent a single legal relation; they describe and represent complex and variable aggregates of legal relations. For clear thinking and for just and correct decision it is necessary to analyze these complex concepts into their simpler and invariable elements.

What then are these simple elements? Before attempting any formal definitions, they may first be indicated in a popular way. Assuming that we wish to determine the legal relations of A and B, we may ask ourselves the following questions:

(1) What may A (or B) do, without societal penalty assessed for the benefit of the other?

(2) What must A (or B) do, under threat of societal penalty assessed for the benefit of the other?

(3) What can A (or B) do, so as to change the existing legal relations of the other? (This has no reference to mere physical power.)

If we determine that A may conduct himself in a certain way he has a privilege with respect to B, and B has no-right that A shall not so conduct himself.

If we determine that A must conduct himself in a certain manner he has a duty to B, and B has a right against A.

If we determine that by his own voluntary act A can change B’s legal relations with A (or with X), A has a legal power and B has a liability.

If we determine that A cannot by his own voluntary act change the legal relations of B, then A has a disability and B has an immunity.

Having isolated these definite concepts and chosen these specific terms with which to express them—all being found in the actual decisions and usage of the courts —Professor Wesley N. Hohfeld then arranged them in the following pairs of opposites and correlatives:

Each pair of correlatives must always exist together; when some person (A) has one of the pair, another person (B) necessarily has the other. One of the terms expresses the relation of A to B; the other term expresses the relation of B to A.

No pair of opposites can exist together. That is, when a person has a right, he cannot have a no-right with respect to the same subject matter and the same person. When he has a privilege, he cannot have a duty.

The following grouping of terms may be useful:

Observe that when we assert that some fact or group of facts will operate to create a particular legal relation we are stating a rule of law. The mere statement that a certain legal relation exists is a statement of fact. Thus: (a) A owes B $100.—statement of fact. (b) C owns Blackacre—statement of fact. (c) An offer creates a power in the offeree—rule of law. (d) The delivery of a deed conveys title to land—rule of law. (e) The delivery of a release under seal discharges a debtor (creates privilege in place of duty)—rule of law.

Rules of law, enabling us to determine the operative effect of facts, 1 are not discovered by mere analysis; they are discovered rather by a study of history—by a knowledge of written statutes, of precedents, and of social mores. The terms and method of analysis here presented are merely to make possible a greater clearness of mental concept and a nicer accuracy of expression.

We may now proceed to the more formal definition of the eight named legal relations, and also of several varieties of rights.

(1) : A legal relation between two persons. The correlative of duty, and the opposite of no-right. An enforceable claim to performance (action or forbearance) by another. It is the legal relation of A to B when society commands action or forbearance by B and will at the instance of A in some manner penalize disobedience.

A, knowing that he has a particular right, can answer this question, “What must another do for me?” (The court will aid me by using compulsion if he does not do it.)

Examples: (a) B owes A $100.

(b) B has contracted for a consideration to deliver goods to or do labor for A. In each case A has a right and B has a correlative duty.

(c) A has a right that B shall not strike him, and B has a duty not to strike.

(2) : The correlative of the concept right, above defined, and the opposite of privilege. It is the legal relation of a person, B, who is commanded by society to act or to forbear for the benefit of another person, A, either immediately or in the future, and who will be penalized by society for disobedience.

B, knowing that he has a particular duty, can answer this question, “What must I do for another?” (A court will use compulsion against me if I do not do it.)

Examples: See examples under (1) above.

Rights and duties may be Primary or Secondary, Instant or Future, Conditional or Unconditional, In rem or In personam, Joint or Several.

(3) : The correlative of the legal concept no-right and the opposite of duty. The legal relation of A to B when A (with respect to B) is free or at liberty to conduct himself in a certain matter as he pleases; when his conduct is not regulated for the benefit of B by the command of society; and when he is not threatened with any penalty for disobedience, for the reason that society has made no command.

A, knowing that he has a particular privilege, can answer this question, “What may I do?” (A court will not prevent me or penalize me.)

Observe carefully that the concept privilege does not itself include a right to non-interference by another person, although such a privilege and such a right very commonly are found together. Being the opposite of duty, it is another name for no duty. If I am under no duty to A, I am with respect to A privileged.

Examples: (a) A assaults B. This gives B the legal privilege of striking back (commonly called the “right” of self-defence).

(b) B is sworn as a witness. He now has the privilege of saying words about another person that it was previously his legal duty not to say. What was previously slander is now a privileged statement.

(c) A neutral in war time has the privilege of shipping contraband to a belligerent. Other belligerents have no-right that he shall refrain, but they too are then privileged to seize the contraband. The neutral is privileged to run, when sighted, but if he disobeys a signal to heave to, the belligerent is then privileged to sink him.

(4) : The correlative of privilege, and the opposite of right. The legal relation of a person (A) in whose behalf society commands nothing of another (B). A has no control over B. A, knowing that he has no-right against B, can answer this question, “What may another person (B) do?” (A court will not prevent him or penalize him.)

Examples: A tells B that he may walk across A’s yard. This gives B a privilege and terminates A’s right that B shall not so walk, thus creating a relation of no-right in A. But B does not have a right, for A is privileged to lock B out. See also examples under (3) above.

(5) : The correlative of liability, and the opposite of disability (disability=no power). The legal relation of A to B when A’s own voluntary act will cause new legal relations either between B and A or between B and a third person.

A, knowing that he has a particular power, can answer this question, “What new legal relations can I create between B and myself or others?”

A sharp distinction must be drawn between legal power and physical power. Thus a person may have a legal power to make a will even though he is too weak physically to sign his name; i.e., he has the legal power but is physically unable to do the volitional act by which it is to be exercised.

Examples: (a) A’s voluntary act of picking up a shell on the seashore creates as against B a right of non-interference with possession. So A has a power to create such a right against B. (This new right is a constituent part of that aggregate of legal relations called ownership, title, or property.)

(b) A having made an offer to B, the latter has the power to create contractual rights, etc., by accepting.

(c) X writes to A that the latter may sell X’s land. A then has a power to make and accept offers. Distinguish sharply the following: (1) the physical acts of X; (2) the material document sent to A; (3) the legal relation of power in A, a mere mental concept.

(d) A has the legal power, by assaulting B, of creating a secondary right to damages in B.

Observe that legal power is not always accompanied by legal privilege; there may be a duty not to use it.

(6) : The correlative of power, and the opposite of immunity. (Immunity=no liability.) The relation of A to B when A may be brought into new legal relations by the voluntary act of B. A is liable to have new legal relations created for himself through the exercise by B of B’s power. The new relations may be with third, persons, or with B, or with both; but the liability-power relation is between A and B only.

A, knowing that he has a certain liability, can answer this question, “What new legal relations can B create between me and himself or others?”

Examples: (a) A having made an offer to B, A now has a liability that B will create contractual relations by accepting (the exercise of B’s power).

(b) A being the owner of Blackacre and having given to B the power to convey to X, A has a liability of being brought into property relations with X. Likewise every third person has the same liability of being brought into property relations with X. B’s exercise of his power, his voluntary act of conveyance, will give X rights against A and also against all third persons, each of whom will come under correlative duties to X. These duties they cannot avoid; for previously to B’s act of conveyance B has power to create these new relations, and each third party has the liability to their creation. Such is the law of property. B’s conveyance to X makes him the owner, creating between him and all other persons those innumerable relations of right, privilege, power, and immunity of which “property” or “ownership” consists.

(c) B having given A a privilege to cross B’s land, A has a liability to the extinguishment of his privilege by revocation, or in other words, to the creation of a duty not to cross.

Note carefully the distinction between liability and duty, inasmuch as one of the popular uses of this term is to describe the relation of duty. It is such double, triple, or quadruple meanings that make terms slippery, confuse thought, and cause erroneous and unjust decisions. Hence the necessity of adopting some one specific meaning, as is attempted here. A owes B $100: the legal relation particularly in mind is a duty to pay. There may no doubt also be a liability to the creation of new legal relations by a judgment.

Observe that liabilities are not always disadvantageous to the possessor, although it is the disadvantageous ones with which we are most often concerned. The correlative power in another person may be only to create valuable rights, privileges, powers and immunities. Thus where A’s debt to B has been barred by the statute of limitations B has a liability to the recreation of his right by a voluntary new promise by A (the exercise of a power by A).

(7) : The correlative of disability (no power), and the opposite of liability (no immunity). The relation of A to B when B has no legal power (has disability) to affect some one or more of the existing legal relations of A. As to that particular existing relation A has an immunity with respect to B.

A, knowing that he has a certain immunity, can answer this question, “Which one of my existing legal relations is safe from alteration by B?”

Examples: (a) A owns Blackacre. His right that B shall not enter cannot be extinguished by the voluntary act of B; so that with respect to B, A has immunity. At the same time A may have no such immunity with respect to C, for the latter may have been given the power to convey Blackacre to B and thus extinguish A’s right against B.

(b) The Constitution declares that no state shall impair the obligation of a contract. With respect to state legislatures, therefore, a contractor has an immunity.

(c) If a citizen of Connecticut has no land, goods, or business in New York he has an immunity from taxation there. The State of New York has a disability (no power) to tax in such a case.

(8) : The correlative of immunity, and the opposite of power. The relation of A to B when by no voluntary act of his own can A extinguish one (or more) of the existing legal relations of B.

A, knowing that he has a particular disability, can answer this question, “What existing legal relation of another person (B) is it impossible for me to extinguish?”

Examples: See the examples of immunity under (7) above, where B in the one case and the legislators in the other case have disabilities.

(9) in Rem: A right possessed by A against B when it happens to be one of innumerable similar rights possessed by A against all (or nearly all) other members of organized society, each one of whom is under a correlative duty to A (these innumerable duties being likewise similar). Professor Hohfeld has suggested as a substitute the term “multital right.”

Examples: (a) A owns Blackacre. He has a right against B that B shall not trespass, and similar rights against C, D, X, Y, etc. But if A has told M that he may walk across, he has no such right against M.

(b) A has a right that B shall not strike him. He has similar rights against C, D, X, Y, etc. But if A is M’s minor son, and has disobeyed, he has no such right against M.

(c) A patentee has a right that B shall not manufacture or sell, and similar rights against C, D, X, Y, etc. But he may have licensed M to manufacture and sell.

Observe that a right in rem is not a right in a thing or a right against a thing. Legal relations are relations between persons.

Observe also that a right in rem is not a right against the world or against all other persons.

The term “right in rem” is commonly used to include other legal relations in rem, viz., relations of privilege, power, and immunity. This must be avoided.

(10) in Personam: A right possessed by A against B, unaccompanied by similar rights against all (or nearly all) others. It may be accompanied by similar rights against certain specific other persons. If it is totally unaccompanied, Professor Hohfeld calls it a “unital” right; and if accompanied by similar rights against several specific persons, he calls it a “paucital” right.

Examples: (a) A holds B’s promissory note for $100. A’s right against B is unaccompanied or “unital.”

(b) B strikes A without justification. A has a right to damages from B, a secondary right, unaccompanied or “unital.”

(c) A holds the joint or joint and several promissory note of B, C, and D, for $100. A’s right against B is not in rem; it is a “paucital” right. He has exactly similar rights against C and D.

(11) : A right resulting from some operative fact that was not itself a violation of some precedent right. Primary rights may be either in rem or in personam, either multital or paucital or unital.

(12) : A right resulting from some operative fact that was a violation of some precedent right. So-called “remedial” rights are always secondary. Secondary rights are always in personam, paucital or unital.

(13) : See Right in rem, No. 9.

(14) : See Right in personam, No. 10.

(15) : See Right in personam, No. 10.

Observe that privileges, powers, immunities, duties, no-rights, disabilities, and liabilities, as well as rights, may all conceivably be multital, paucital, or unital.

(16) : The right of A may be that B shall act in a certain way at once, instantly, or that B shall so act at some future date. If it is the latter, we say that A has a right to future action by B. Such a right is not called a conditional right, even though the arrival of the date is a necessary operative fact, for the reason that it is certain to occur.

Example: A holds B’s promissory note for $100 payable on June 1 next. On June 1 A’s right to future payment becomes an instant right.

(17) : This is a right to a future performance that does not become instant by the mere arrival of a date, but becomes so only upon the occurrence of some uncertain operative fact. The creation of an instant right often requires the occurrence of several operative facts. If some of these have occurred but one has not, that one is a condition precedent to the existence of an instant right. Prior to the occurrence of this one fact we often describe the legal relations as a conditional right and a conditional duty.

Examples: (a) A pays B $100 and B promises to deliver a bale of goods on their arrival aboard the ship Peerless. This is a unilateral contract, and A has a conditional right.

(b) For a premium of $50 paid, an insurer agrees to pay A $10,000 if a house burns down.

(c) A agrees to work for B for $100 a week payable weekly. Here the completion of a week’s work is a condition precedent to A’s instant right. Meanwhile A has a conditional right; he may also be said to have a power, in case the condition is mere voluntary action by himself. The term unconditional right includes all instant rights and also all rights to future performance that depend on no fact other than the passage of time.

There is no need to discuss here such terms as “divine right” and “absolute right.” They have no proper place in a system of human justice.

(18) : A right may be a “joint” right either because there are (a) several obligees or (b) several obligors.

(a) If X gives his promissory note to A and B jointly, legal relations are created between A and X and between B and X (as well as between A and B). A has a right that X shall pay either A or B, and B has an exactly similar right against X. The character of these relations is not in the least affected by the rule that A’s secondary right to a judgment is conditional upon B’s joining as plaintiff.

Observe that A’s right against X is not a “paucital” right; it is unital, inasmuch as he has no similar right against any other person. Observe also that the relations between A and X are distinct from those between B and X. A and B are independent persons. They are not “one,” even in “the eye of the law.”

(b) If X and Y give their joint promissory note to A, he has two rights, one against X and an exactly similar one against Y, that the full sum shall be paid at maturity. In this case each of A’s rights is a “paucital” right. Here, too, A’s secondary right to a judgment is conditional upon his joining both as co-defendants; or, at least either X or Y when sued alone would have the power of depriving A of his right to a judgment by pleading in abatement.

In the above illustration it should be noted that the right to payment is quite different from the right to judgment. The first is against a party; the second is against the court.

(19) : The aggregate of the legal relations of a person with respect to some specific physical object or the physical relations of specific objects.

Examples: (a) A owns Blackacre. He has a legal interest, consisting of various rights, privileges, powers, and immunities. Here his interest is “property.” (The term property is often used to denote physical objects. Such use should be carefully distinguished.)

(b) A has contracted with B to employ B and to pay salary. A has here an interest consisting of contract rights, powers, etc., against B, and certain multital rights, powers, etc., against all other persons. Because of A’s multital rights, powers, etc., his interest is here also sometimes described as “property.”

(c) A has a legal interest in the physical safety of his wife, multital rights that she shall not be harmed, her affections alienated, etc.

Distinguish sharply between “legal interest” and the physical objects themselves with respect to which and for the enjoyment of which the legal relations are created.

Distinguish also between “legal interest” and that sort of “interest” that consists merely of an emotion or a state of mind.

Distinguish further the kind of “interest” that is a return or compensation for money loaned; the rate fixed by contract or by law is sometimes referred to as “legal interest.”

title: Legal Analysis and Terminology


text:
Page:Weird Tales volume 28 number 03.djvu/61

Rh land shaking on his gun-butt, and the breath rasped in his dry throat.

Why—he asked himself in a determined groping after steadiness—should the mere sight of a tree, even so fabulous a one as this, rouse that insane panic in the gazer? What peril could dwell invisibly in a tree so frightful that the living horror of it could drive a man mad with the very fact of its unseen presence? He clenched his teeth hard and stared resolutely at that terrible beauty in the clearing, fighting down the sick panic that rose in his throat as his eyes forced themselves to dwell upon the Tree.

Gradually the revulsion subsided. After a nightmare of striving he mustered the strength to force it down far enough to allow reason's entry once more. Sternly holding down that frantic terror under the surface of consciousness, he stared resolutely at the Tree. And he knew that this was Thag.

It could be nothing else, for surely two such dreadful things could not dwell in one land. It must be Thag, and he could understand now the immemorial terror in which the tree-folk held it, but he did not yet grasp in what way it threatened them physically. The inexplicable dreadfulness of it was a menace to the mind's very existence, but surely a rooted tree, however terrible to look at, could wield little actual danger.

As he reasoned, his eyes were seeking restlessly among the branches, searching for the answer to their dreadfulness. After all, this thing wore the aspect of an old pattern, and in that pattern there was nothing dreadful. The tree of life had made up the design upon that well-top in Illar through whose shadow he had entered here, and nothing in that bronze grille-work had roused terror. Then why——? What living menace dwelt invisibly among these branches to twist them into curves of horror?

A fragment of old verse drifted through his mind as he stared in perplexity:

And for the first time the true significance of a "fearful symmetry" broke upon him. Truly a more than human agency must have arched these subtle curves so delicately into dreadfulness, into such an awful beauty that the very sight of it made those atavistic terrors he was so sternly holding down leap in a gibbering terror.

A tremor rippled over the Tree. Smith froze rigid, staring with startled eyes. No breath of wind had stirred through the clearing, but the Tree was moving with a slow, serpentine grace, writhing its branches leisurely in a horrible travesty of voluptuous enjoyment. And upon their tips the blood-red flowers were spreading like cobra's hoods, swelling and stretching their petals out and glowing with a hue so eye-piercingly vivid that it transcended the bounds of color and blazed forth like pure light.

But it was not toward Smith that they stirred. They were arching out from the central trunk toward the far side of the clearing. After a moment Smith tore his eyes away from the indescribably dreadful flexibility of those branches and looked to see the cause of their writhing.

A blaze of luminous white had appeared among the trees across the clearing. The priestess had returned. He watched her pacing slowly toward the Tree, walking with a precise and delicate grace as liquidly lovely as the motion of the Tree. Her fabulous hair swung down about her in a swaying robe that rippled at every step away from the moon-white beauty of her body. Straight toward the Tree she paced, and all the blossoms glowed more vividly at her nearness, the


text:
Page:Weird Tales volume 28 number 03.djvu/62

328 branches stretching toward her, rippling with eagerness.

Priestess though she was, he could not believe that she was going to come within touch of that Tree the very sight of which roused such a panic instinct of revulsion in every fiber of him. But she did not swerve or slow in her advance, Walking delicately over the flowery grass, arrogantly luminous in the twilight, so that her body was the center and focus of any landscape she walked in, she neared her horribly eager god.

Now she was under the Tree, and its trunk had writhed down over her and she was lifting her arms like a girl to her lover. With a gliding slowness the flame-tipped branches slid round her. In that incredible embrace she stood immobile for a long moment, the Tree arching down with all its curling limbs, the girl straining upward, her head thrown back and the mantle of her hair swinging free of her body as she lifted her face to the quivering blossoms. The branches gathered her closer in their embrace. Now the blossoms arched near, curving down all about her, touching her very gently, twisting their blazing faces toward the focus of her moon-white body. One poised directly above her face, trembled, brushed her mouth lightly. And the Tree's tremor ran unbroken through the body of the girl it clasped.

HE incredible dreadfulness of that embrace was suddenly more than Smith could bear. All his terrors, crushed down with so stern a self-control, without warning burst all bounds and rushed over him in a flood of blind revulsion. A whimper choked up in his throat and quite involuntarily he swung round and plunged into the shielding trees, hands to his eyes in a futile effort to blot out the sight of lovely horror behind him whose vividness was burnt upon his very brain.

Heedlessly he blundered through the trees, no thought in his terror-blank mind save the necessity to run, run, run until he could run no more. He had given up all attempt at reason and rationality; he no longer cared why the beauty of the Tree was so dreadful. He only knew that until all space lay between him and its symmetry he must run and run and run.

What brought that frenzied madness to an end he never knew. When sanity returned to him he was lying face down on the flower-spangled sward in a silence so deep that his ears ached with its heaviness. The grass was cool against his cheek. For a moment he fought the back-flow of knowledge into his emptied mind. When it came, the memory of that horror he had fled from, he started up with a wild thing's swiftness and glared around pale-eyed into the unchanging dusk. He was alone. Not even a rustle in the leaves spoke of the tree-folk's presence.

For a moment he stood there alert, wondering what had roused him, wondering what would come next. He was not left long in doubt. The answer was shrilling very, very faintly through that aching quiet, an infinitesimally tiny, unthinkably far-away murmur which yet pierced his ear-drums with the sharpness of tiny needles. Breathless, he strained in listening. Swiftly the sound grew louder. It deepened upon the silence, sharpened and shrilled until the thin blade of it was vibrating in the center of his innermost brain.

And still it grew, swelling louder and louder through the twilight world in cadences that were rounding into a queer sort of music and taking on such an unbearable sweetness that Smith pressed his


text:
Page:Weird Tales volume 28 number 03.djvu/63

Rh hands over his ears in a futile attempt to shut the sound away. He could not. It rang in steadily deepening intensities through every fiber of his being, piercing him with thousands of tiny music-blades that quivered in his very soul with intolerable beauty. And he thought he sensed in the piercing strength of it a vibration of queer, unnamable power far mightier than anything ever generated by man, the dim echo of some cosmic dynamo's hum.

The sound grew sweeter as it strengthened, with a queer, inexplicable sweetness unlike any music he had ever heard before, rounder and fuller and more complete than any melody made up of separate notes. Stronger and stronger he felt the certainty that it was the song of some mighty power, humming and throbbing and deepening through the twilight until the whole dim land was one trembling reservoir of sound that filled his entire consciousness with its throbbing, driving out all other thoughts and realizations, until he was no more than a shell that vibrated in answer to the calling.

For it was a calling. No one could listen to that intolerable sweetness without knowing the necessity to seek its source. Remotely in the back of his mind Smith remembered the tree-folk's warning, "When Thag calls, you must answer." Not consciously did he recall it, for all his consciousness was answering the siren humming in the air, and, scarcely realizing that he moved, he had turned toward the source of that calling, stumbling blindly over the flowery sward with no thought in his music-brimmed mind but the need to answer that lovely, power-vibrant summoning.

Past him as he went on moved other shapes, little and dark-skinned and ecstatic, gripped like himself in the hypnotic melody. The tree-folk had forgotten even their inbred fear at Thag's calling, and walked boldly through the open twilight, lost in the wonder of the song.

Smith went on with the rest, deaf and blind to the land around him, alive to one thing only, that summons from the siren tune. Unrealizingly, he retraced the course of his frenzied flight, past the trees and bushes he had blundered through, down the slope that led to the Tree's hollow, through the thinning of the underbrush to the very edge of the last line of foliage which marked the valley's rim.

Y NOW the calling was so unbearably intense, so intolerably sweet that somehow in its very strength it set free a part of his dazed mind as it passed the limits of audible things and soared into ecstasies which no senses bound. And though it gripped him ever closer in its magic, a sane part of his brain was waking into realization. For the first time alarm came back into his mind, and by slow degrees the world returned about him. He stared stupidly at the grass moving by under his pacing feet. He lifted a dragging head and saw that the trees no longer rose about him, that a twilit clearing stretched away on all sides toward the forest rim which circled it, that the music was singing from some source so near that—that——

The Tree! Terror leaped within him like a wild thing. The Tree, quivering with unbearable clarity in the thick, dim air, writhed above him, blossoms blazing with bloody radiance and every branch vibrant and undulant to the tune of that unholy song. Then he was aware of the lovely, luminous whiteness of the priestess swaying forward under the swaying limbs, her hair rippling back from the loveliness of her as she moved.

Choked and frenzied with unreasoning terror, he mustered every; effort that was


text:
Page:Weird Tales volume 28 number 03.djvu/64

330 In him to turn, to run again like a madman out of that dreadful hollow, to hide himself under the weight of all space from the menace of the Tree. And all the while he fought, all the while panic drummed like mad in his brain, his relentless body plodded on straight toward the hideous loveliness of that siren singer towering above him. From the first he had felt subconsciously that it was Thag who called, and now, in the very center of that ocean of vibrant power, he knew. Gripped in the music's magic, he went on.

All over the clearing other hypnotized victims were advancing slowly, with mechanical steps and wide, frantic eyes as the tree-folk came helplessly to their god's calling. He watched a group of little, dusky sacrifices pace step by step nearer to the Tree's vibrant branches. The priestess came forward to meet them with outstretched arms. He saw her take the foremost gently by the hands. Unbelieving, hypnotized with horrified incredulity, he watched her lead the rigid little creature forward under the fabulous Tree whose limbs yearned downward like hungry snakes, the great flowers glowing with avid color.

He saw the branches twist out and lengthen toward the sacrifice, quivering with eagerness. Then with a tiger's leap they darted, and the victim was swept out of the priestess' guiding hands up into the branches that darted round like tangled snakes in a clot that hid him for an instant from view. Smith heard a high, shuddering wail ripple out from that knot of struggling branches, a dreadful cry that held such an infinity of purest horror and understanding that he could not but believe that Thag's victims in the moment of their doom must learn the secret of his horror. After that one frightful cry came silence. In an instant the limbs fell apart again from emptiness. The little savage had melted like smoke among their writhing, too quickly to have been devoured, more as if he had been snatched into another dimension in the instant the hungry limbs hid him. Flame-tipped, avid, they were dipping now toward another victim as the priestess paced serenely forward.

And still Smith's rebellious feet were carrying him on, nearer and nearer the writhing peril that towered over his head. The music shrilled like pain. Now he was so close that he could see the hungry flower-mouths in terrible detail as they faced round toward him. The limbs quivered and poised like cobras, reached out with a snakish lengthening, down inexorably toward his shuddering helplessness. The priestess was turning her calm white face toward his.

Those arcs and changing curves of the branches as they neared were sketching lines of pure horror whose meaning he still could not understand, save that they deepened in dreadfulness as he neared. For the last time that urgent wonder burned up in his mind why—why so simple a thing as this fabulous Tree should be infused with an indwelling terror strong enough to send his innermost soul frantic with revulsion. For the last time—because in that trembling instant as he waited for their touch, as the music brimmed up with unbearable, brain-wrenching intensity, in that one last moment before the flower-mouths seized him—he saw. He understood.

With eyes opened at last by the instant's ultimate horror, he saw the real Thag. Dimly he knew that until now the thing had been so frightful that his eyes had refused to register its existence, his brain to acknowledge the possibility of such dreadfulness. It had literally been too terrible to see, though his instinct knew the presence of infinite horror. But