text:
The Encyclopedia Americana (1920)/Johnson, Owen

JOHNSON, Owen, American author: b. New York, 27 Aug. 1878. He is a son of Robert Underwood Johnson and was graduated at Yale in 1901. His story of school life ‘The Varmint’ (1910), with its boyish high spirits, cleverness and wholesomeness, is perhaps his best work. ‘Stover at Yale’ (1911), a college story, frank in its criticisms of certain phases of life at Yale, aroused a storm of controversy. He has also written ‘Arrows of the Almighty’ (1901); ‘In the Name of Liberty’ (1905); ‘Max Fargus’ (1906); ‘The Eternal Boy’ (1909); ‘The Humming Bird’ (1910); ‘Tennessee Shad’ (1911); ‘The Sixty-first Second’ (1912); ‘The Salamander’ (1914), later dramatized; ‘Murder in Any Degree’ (1914); ‘Making Money’ (1914); ‘The Woman Gives’ (1915). He also wrote the plays ‘The Comet’ (1908); ‘Comedy for Wives’ (1912), and an adaptation from the French, ‘The Return from Jerusalem’ (1912); ‘Virtuous Wives’ (1918).


text:
Collier's New Encyclopedia (1921)/MacKaye, Percy

MACKAYE, PERCY, dramatist and poet; born in 1875 in New York, graduated from Harvard in 1897, and became a student at Leipsic, after traveling in Europe, he taught privately in New York and from 1904 has been engaged in dramatic work. His works include “The Canterbury Pilgrims,” a comedy (1903); “A Modern Rendering into Prose of Chaucer's Tales” (1904); “Fenris the Wolf,” a tragedy (1905); “Jeanne d'Arc,” a tragedy (1906); “Sappho and Phaon” (1907); “The Scarecrow: a tragedy of the Ludicrous” (1908); “The Playhouse and the Play” (1909); “The Civic Theater” (1912); “The Present Hour” (1914); “Caliban” (1916); “Christmas Masque” (1917); “George Washington” (1920).

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


text:
The New International Encyclopædia/Mackaye, James Steele

MACKAYE,, (1842-94). An American dramatist, born in Buffalo. He studied dramatic expression in Paris under François Delsarte, and on his return to America lectured in New York City and Boston. His two plays, Monaldi and Marriage, written about this time, were produced at the Saint James Theatre in New York City. He afterwards toured in England as an actor, and played Hamlet in London, where he collaborated in several well-known plays. His other works include: The Twins (1876); Won at Last (1877); Through the Dark (1878, later called Money Mad); Hazel Kirke (1880); and Anarchy (1887, later called Paul Kauvar).


text:
The New International Encyclopædia/Johnson, Samuel William

JOHNSON, (1830—). An American agricultural chemist, born at Kingsboro, N. Y. He was educated at the Scientific School of Yale College, and studied at the universities of Leipzig and Munich. He was made professor of analytical chemistry at the Yale Scientific School in 1856, taught agricultural chemistry there from 1857 to 1875, and after 1875 acted as professor of theoretical and agricultural chemistry. From 1877 to 1900 he was also director of the Connecticut Agricultural Experiment Station. In 1866 he became a member

of the Connecticut State Board of Agriculture and of the National Academy of Sciences. His publications include: Essays on Manures (1859); Peat and Its Uses (1866); How Crops Grow (1868); How Crops Feed (1870); Chemical Notation and Nomenclature (1870).


text: Our American Holidays - Christmas/A Merry Christmas to You


text:
1922 Encyclopædia Britannica/Mackaye, Percy

MACKAYE, PERCY (1875-), American poet and playwright, was born in New York City March 16 1875. He graduated from Harvard in 1897 and later was a student in the university of Leipzig. From 1900 to 1904 he was a teacher in private schools in New York, and in the latter year became a member of the Cornish (N.H.) colony of artists and writers. He was made a member of the National Institute of Arts and Letters in 1914.


text:
User:Prosody/textinputs standalone.js

/** * @license Rangy Text Inputs, a cross-browser textarea and text input library

* Part of Rangy, a cross-browser JavaScript range and selection library * http://code.google.com/p/rangy/ * * This file is standalone. * * Copyright 2010, Tim Down * Licensed under the MIT license. * Version: %%build:version%% * Build date: %%build:date%% */ var rangyTextInputs; (function {   var UNDEF = "undefined";    var getSelection, setSelection, deleteSelectedText, deleteText, insertText;    var replaceSelectedText, surroundSelectedText, extractSelectedText, collapseSelection;    var initialized = false;

// Trio of isHost* functions taken from Peter Michaux's article: // http://peter.michaux.ca/articles/feature-detection-state-of-the-art-browser-scripting function isHostMethod(object, property) { var t = typeof object[property]; return t === "function" || (!!(t == "object" && object[property])) || t == "unknown"; }

function isHostProperty(object, property) { return typeof(object[property]) != UNDEF; }

function isHostObject(object, property) { return !!(typeof(object[property]) == "object" && object[property]); }

function fail(reason) { if (window.console && window.console.log) { window.console.log("Rangy Text Inputs not supported in your browser. Reason: " + reason); }   }

function adjustOffsets(el, start, end) { if (start < 0) { start += el.value.length; }       if (typeof end == UNDEF) { end = start; }       if (end < 0) { end += el.value.length; }       return { start: start, end: end }; }

function makeSelection(el, start, end) { return { start: start, end: end, length: end - start, text: el.value.slice(start, end) };   }

function getBody { return isHostObject(document, "body") ? document.body : document.getElementsByTagName("body")[0]; }

function init { var testTextArea = document.createElement("textarea"); getBody.appendChild(testTextArea);

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setSelection = function(el, startOffset, endOffset) { var offsets = adjustOffsets(el, startOffset, endOffset); el.selectionStart = offsets.start; el.selectionEnd = offsets.end; };

collapseSelection = function(el, toStart) { if (toStart) { el.selectionEnd = el.selectionStart; } else { el.selectionStart = el.selectionEnd; }           };        } else if (isHostMethod(testTextArea, "createTextRange") && isHostObject(document, "selection") &&                   isHostMethod(document.selection, "createRange")) {

getSelection = function(el) { var start = 0, end = 0, normalizedValue, textInputRange, len, endRange; var range = document.selection.createRange;

if (range && range.parentElement == el) { len = el.value.length;

normalizedValue = el.value.replace(/\r\n/g, "\n"); textInputRange = el.createTextRange; textInputRange.moveToBookmark(range.getBookmark); endRange = el.createTextRange; endRange.collapse(false); if (textInputRange.compareEndPoints("StartToEnd", endRange) > -1) { start = end = len; } else { start = -textInputRange.moveStart("character", -len); start += normalizedValue.slice(0, start).split("\n").length - 1; if (textInputRange.compareEndPoints("EndToEnd", endRange) > -1) { end = len; } else { end = -textInputRange.moveEnd("character", -len); end += normalizedValue.slice(0, end).split("\n").length - 1; }                   }                }

return makeSelection(el, start, end); };

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setSelection = function(el, startOffset, endOffset) { var offsets = adjustOffsets(el, startOffset, endOffset); var range = el.createTextRange; var startCharMove = offsetToRangeCharacterMove(el, offsets.start); range.collapse(true); if (offsets.start == offsets.end) { range.move("character", startCharMove); } else { range.moveEnd("character", offsetToRangeCharacterMove(el, offsets.end)); range.moveStart("character", startCharMove); }               range.select; };

collapseSelection = function(el, toStart) { var range = document.selection.createRange; range.collapse(toStart); range.select; };       } else { getBody.removeChild(testTextArea); fail("No means of finding text input caret position"); return; }

// Clean up       getBody.removeChild(testTextArea);

deleteText = function(el, start, end, moveSelection) { var val; if (start != end) { val = el.value; el.value = val.slice(0, start) + val.slice(end); }           if (moveSelection) { setSelection(el, start, start); }       };

deleteSelectedText = function(el) { var sel = getSelection(el); deleteText(el, sel.start, sel.end, true); };

extractSelectedText = function(el) { var sel = getSelection(el), val; if (sel.start != sel.end) { val = el.value; el.value = val.slice(0, sel.start) + val.slice(sel.end); }           setSelection(el, sel.start, sel.start); return sel.text; };

insertText = function(el, text, index, moveSelection) { var val = el.value, caretIndex; el.value = val.slice(0, index) + text + val.slice(index); if (moveSelection) { caretIndex = index + text.length; setSelection(el, caretIndex, caretIndex); }       };

replaceSelectedText = function(el, text) { var sel = getSelection(el), val = el.value; el.value = val.slice(0, sel.start) + text + val.slice(sel.end); var caretIndex = sel.start + text.length; setSelection(el, caretIndex, caretIndex); };

surroundSelectedText = function(el, before, after) { var sel = getSelection(el), val = el.value; el.value = val.slice(0, sel.start) + before + sel.text + after + val.slice(sel.end); var startIndex = sel.start + before.length; var endIndex = startIndex + sel.length; setSelection(el, startIndex, endIndex); };

rangyTextInputs = { getSelection: getSelection, setSelection: setSelection, collapseSelection: collapseSelection, deleteSelectedText: deleteSelectedText, deleteText: deleteText, extractSelectedText: extractSelectedText, insertText: insertText, replaceSelectedText: replaceSelectedText, surroundSelectedText: surroundSelectedText };

initialized = true; }

// Wait for document to load before creating API

var docReady = false;

var loadHandler = function(e) { if (!docReady) { docReady = true; if (!initialized) { init; }       }    };

// Test whether we have window and document objects that we will need if (typeof window == UNDEF) { fail("No window found"); return; }   if (typeof document == UNDEF) { fail("No document found"); return; }

if (isHostMethod(document, "addEventListener")) { document.addEventListener("DOMContentLoaded", loadHandler, false); }

// Add a fallback in case the DOMContentLoaded event isn't supported if (isHostMethod(window, "addEventListener")) { window.addEventListener("load", loadHandler, false); } else if (isHostMethod(window, "attachEvent")) { window.attachEvent("onload", loadHandler); } else { fail("Window does not have required addEventListener or attachEvent method"); }

});

title: User:Prosody/textinputs standalone.js


text: Our American Holidays - Christmas/Christmas Bells (Anonymous)


text: Dictionary of National Biography, 1885-1900/Doyle, Richard


text: Our American Holidays - Christmas/The Birth of Christ


text: Our American Holidays - Christmas/The Christmas Carol


text: Our American Holidays - Christmas/Christmas At Fezziwig’s Warehouse


text: Our American Holidays - Christmas/Christmas Bells (Keble)


text:
Mary Wollstonecraft and Fuseli

O but is it not hard, Dear? Mine are the nerves to quake at a mouse: If a spider drops I shrink with fear: I should die outright in a haunted house; While for you—did the danger dared bring help— From a lion's den I could steal his whelp, With a serpent round me, stand stock-still, Go sleep in a churchyard,—so would will Give me the power to dare and do Valiantly—just for you!

Much amiss in the head, Dear, I toil at a language, tax my brain Attempting to draw—the scratches here! I play, play, practise and all in vain: But for you—if my triumph brought you pride, I would grapple with Greek Plays till I died, Paint a portrait of you—who can tell? Work my fingers off for your "Pretty well:" Language and painting and music too, Easily done—for you!

Strong and fierce in the heart, Dear, With—more than a will—what seems a power To pounce on my prey, love outbroke here In flame devouring and to devour. Such love has laboured its best and worst To win me a lover; yet, last as first, I have not quickened his pulse one beat, Fixed a moment's fancy, bitter or sweet: Yet the strong fierce heart's love's labour's due, Utterly lost, was—you!

title: Mary Wollstonecraft and Fuseli


text:
Adam, Lilith, and Eve

One day, it thundered and lightened. Two women, fairly frightened, Sank to their knees, transformed, transfixed, At the feet of the man who sat betwixt; And "Mercy!" cried each—"if I tell the truth Of a passage in my youth!"

Said This: "Do you mind the morning I met your love with scorning? As the worst of the venom left my lips, I thought, 'If, despite this lie, he strips The mask from my soul with a kiss—I crawl His slave,—soul, body, and all!' "

Said That: "We stood to be married; The priest, or someone, tarried; 'If Paradise-door prove locked?' smiled you; I thought, as I nodded, smiling too, 'Did one, that's away, arrive—nor late Nor soon should unlock Hell's gate!' "

It ceased to lighten and thunder. Up started both in wonder, Looked round and saw that the sky was clear, Then laughed "Confess you believed us, Dear!" "I saw through the joke!" the man replied They re-seated themselves beside.

title: Adam, Lilith, and Eve


text:
Never the Time and the Place

Never the time and the place And the loved one all together! This path — how soft to pace! This May — what magic weather! Where is the loved one's face? In a dream that loved one's face meets mine, But the house is narrow, the place is bleak Where, outside, rain and wind combine With a furtive ear, if I strive to speak, With a hostile eye at my flushing cheek, With a malice that marks each word, each sign! O enemy sly and serpentine, Uncoil thee from the waking man! Do I hold the Past Thus firm and fast Yet doubt if the Future hold I can? This path so soft to pace shall lead Thro' the magic of May to herself indeed! Or narrow if needs the house must be, Outside are the storms and strangers: we — Oh, close, safe, warm sleep I and she, — I and she!

title: Never the Time and the Place


text:
Page:A colonial autocracy, New South Wales under Governor Macquarie, 1810-1821.djvu/107

 Bligh admitted that the Governor imposed "duties on trade and on merchants and exports at his own pleasure". But he added "the Governor had the power of levying duties at his own will, and was justified in that power by his orders from home". The trace of misgiving apparent in this answer was not without cause. The assumption of power, though unquestioned until 1815 and exercised by each Governor from 1794, was quite without legal foundation. Yet the Governor's Instructions assumed it, and though not especially mentioned in his Commission it was taken for granted by Secretaries of State and Governors alike. It could not indeed have been conferred without an Act of Parliament, for New South Wales was not a Colony obtained by conquest; and even had it been originally conquered, Parliament had already intervened in its affairs by the Act establishing the Criminal Court in 1787.

But the assumption of power went farther than the raising of revenue. The Governor made laws "of a most important and penal nature," as well as imposing duties and taxes, though "such a power is not founded on any Act of Parliament nor provided for by the Governor's Commission." The Secretary of State said in 1815 "The power of the Governor to issue Government and General Orders in the absence of all other authority, and the necessity of obeying them, rests now on the same foundation on which it has stood since the first formation of the Colony". In that position the matter rested until 1817.

The chief items of revenue were the duties on imports and port dues. Of these Macquarie allocated three-fourths to the Police Fund and one-fourth to the support of the Orphan School. The other sources of revenue were fees and fines and


text:
Page:A colonial autocracy, New South Wales under Governor Macquarie, 1810-1821.djvu/108

 the payments for licences. There is no need to include quit-rents, as none were collected before 1822. In 1811 the Police Fund reached £10,000, and by 1820 it had risen to £25,884.

The objects for which the Fund was established were specified as "gaol and police expenses of every description … together with such other expenses as might necessarily be incurred in ornamenting and improving the town of Sydney and in constructing and repairing the quays, wharfs and bridges, streets and roads within the limits thereof". But there was in fact no charge which could be incurred which was not from time to time defrayed out of the Police Fund. It went, however, but a little way in meeting the needs of the Colony. The burden on the Imperial Treasury before 1817 was nearly £240,000 per annum, and after that year it increased in consequence of the increase in the number of convicts transported. In 1814, a fair average year, the expenditure in round numbers was as follows :—


text: Page:Three Books of Occult Philosophy (De Occulta Philosophia) (1651).djvu/611


text: Index:Poincare Goettingen En.djvu

title: Index:Poincare Goettingen En.djvu


text:
Page:Poincare Goettingen En.djvu/1

N this world, as you know, nothing is final, nothing immutable; the most powerful, the most stable empires are not eternal: this is a theme the preachers abundantly develop.

Scientific theories are like empires, they are not certain of the morrow. If any one of them seemed beyond the effects of time, it was certainly the Newtonian mechanics. It seemed undisputed, it was an imperishable monument; and behold in its turn, I shall not say the monument is thrown down, that would be premature, but anyhow it is greatly shaken. It is subjected to the attacks of powerful destroyers. There is one in Göttingen, Max Abraham, another is the Dutch physicist Lorentz. I wish to say a few words about the ruins of the ancient edifice and about the new structure by which it is sought to replace them.

First of all what is it that characterizes the old mechanics? It is this very simple fact: Consider a body at rest, impart to it an impulse, that is to say make a given force act upon it for a given time; the body moves, acquires a certain velocity; the body being impelled by this velocity, apply to it again the same force for the same time, the velocity will be doubled; if we still continue, the velocity will be tripled when we shall have given a third time the same impulse. So beginning again a sufficient number of times, the body will end by acquiring a very great velocity which can exceed all limit, an infinite velocity.

title: Page:Poincare Goettingen En.djvu/1


text:
Page:Poincare Goettingen En.djvu/2

 In the new mechanics, on the contrary, we assume it to be impossible to communicate to a body starting from rest a velocity beyond that of light. What happens? Consider the same body at rest; give it a first impulse, the same as before, it will take the same velocity; repeat this impulse a second time, the velocity again augments, but it no longer will be doubled; a third impulse will produce an analogous effect, the velocity increases but less and less, the body opposing a resistance which becomes greater and greater. This resistance is inertia, it is what is commonly called mass; all this happens then in this new mechanics as if the mass was not constant, but increased with the velocity.

We can represent the phenomenon graphically: In the old mechanics the body after the first impulse takes a velocity represented by the sect $$\mathrm{O}n_{1}$$; after the second impulse $$\mathrm{O}n_{1}$$ increases by a sect $$n_{1}n_{2}$$ equal to it; at each new

impulse the velocity increases by the same quantity, the sect representing it increasing by a constant length. In the new mechanics, the velocity sect increases by sects $$n'_{1}n'_{2},\ n'_{2}n'_{3},\dots$$ which become smaller and smaller so that we cannot pass beyond a certain limit, the velocity of light.

How have we been led to such conclusions? Have we made direct experiments? The divergences only come out for bodies impelled by great velocities; only then do the indicated differences become perceptible. But what is a very great velocity? Is it that of an automobile making 100 kilometers an hour? We would go wild with excitement over such a speed in the street. But from our

title: Page:Poincare Goettingen En.djvu/2


text:
Page:Poincare Goettingen En.djvu/3

 point of view this velocity is still very small, a snail’s pace. Astronomy does better. Mercury, the fastest of the heavenly bodies, also runs over about 100 kilometers, no longer per hour but per second. However, that still does not suffice; such velocities are too slight to reveal the differences we wish to observe. I do not mention our cannon balls; they are faster than automobiles, but much slower than Mercury.

You know that we have discovered an artillery whose projectiles are much swifter; I mean radium which sends out energy projectiles in every direction. The speed of this shooting is far greater, the initial velocity being about 100,000 kilometers a second, one-third the velocity of light. The caliber of the projectiles and their weight are, it is true much slighter and we cannot count on this artillery to increase the fighting power of our armies.

Can we experiment on these projectiles? Such experiments have been actually undertaken; under the influence of an electric field, of a magnetic field, a deviation occurs which enables us to take account of the inertia and to measure it. Thus we have ascertained that the mass depends upon the velocity and we enunciate this law: The inertia of a body increases with its velocity which remains less than that of light, 300,000 kilometers a second.

I pass now to the second principle, the principle of relativity. Suppose there is an observer moving to the right; everything is as if he were at rest, with the objects about him moving to the left. There is no way of knowing whether the objects really move, whether the observer is at rest or in motion. We teach in all courses on mechanics that the passenger on a boat thinks he sees the river bank moving, while he is gently borne along by the motion of the boat. Examined more closely, this simple idea acquires capital importance; there is no way of settling the question, no experiment can disprove the principle that there is no

title: Page:Poincare Goettingen En.djvu/3


text:
Page:Poincare Goettingen En.djvu/4

 absolute space, all displacements we can observe are relative displacements. I have often had occasion to express these considerations so familiar to philosophers. They have even given me a publicity I would gladly have avoided. All the reactionary French journals have made me prove that the sun turns around the earth. In the famous case between the Inquisition and Galileo, Galileo should be all wrong.

To return to the old mechanics. It admitted the principle of relativity; in place of being founded on experiments, its laws were deduced from this fundamental principle. These considerations sufficed for purely mechanical phenomena, but not for important parts of physics, for example optics. We considered the velocity of light as absolute with reference to the ether. This velocity could be measured. We had theoretically the means of comparing the displacement of a moving body to an absolute displacement, the means of deciding whether or not a body was in absolute motion.

Delicate experiments, apparatus exceedingly precise, which I shall not describe to you, enabled us to attempt the practical realization of such a comparison: the result was null. The principle of relativity admits of no restriction in the new mechanics; it has, if I may so speak, an absolute value.

To understand the role the principle of relativity plays in the new mechanics, we are led first to speak of apparent time, a very ingenious invention of the physicist Lorentz. We suppose two observers, the one A at Paris, the other B at Berlin. A and B have identical chronometers and wish to set them; but they are exceptionally scrupulous observers and require in their setting an extraordinary exactitude not only, for instance, to the second, but to the thousand-millionth of a second. How can they do it? From Paris to Berlin, A sends a telegraphic signal, by wireless,

title: Page:Poincare Goettingen En.djvu/4


text:
Page:Poincare Goettingen En.djvu/5

 if you will, to be wholly modern. B notes the moment of reception and this will be the starting time for both chronometers. But it takes a certain time for the signal to go from Paris to Berlin; it travels only with the speed of light. B's watch would therefore be slow. B is too intelligent not to take this into account, and he proceeds to remedy it. The thing seems very simple. They cross signals, A receiving and B sending; they take the mean of the corrections thus made and so have the exact time.

But is this certain? We are assuming that it takes the signal the same time to go from A to B as from B to A. Now A and B are carried along in the motion of the earth with reference to the ether, the vehicle of the electric waves. When A has sent his signal it flies on before him, B moving away in the same way, and the time employed will be longer than if the two observers were at rest. If, on the other hand, it is B who sends, and A who receives, the time is shorter because A goes to meet the signal. It is absolutely impossible for them to know whether or not their chronometers mark the same time. Whatever the method employed, the troubles remain the same. The observation of an astronomic phenomenon and all optical methods run against the same difficulties. B can never know more than an apparent difference of time, more than a species of local hour. The principle of relativity applies completely.

In the old mechanics, however, we prove with this principle all the fundamental laws. We might be tempted to take up the classic arguments and reason as follows. Suppose again two observers, A and B, to call them what we always call two observers in mathematics. Suppose them in motion, going away from each other. Neither can surpass the velocity of light; for example let B go at the rate of 200,000 kilometers toward the right, A of 200,000 kilometers toward the left. A may think himself at rest, and

title: Page:Poincare Goettingen En.djvu/5


text:
Page:Poincare Goettingen En.djvu/6

 the apparent velocity of B will for him be 400,000 kilometers. If A knows the new mechanics he will say: "B has a velocity he cannot attain, therefore I also am in motion." It seems he could decide about his absolute state. But he must be able to observe the motion of B himself. To make this observation A and B commence by setting their watches, then B sends telegrams to A to indicate to him his successive positions; putting them together A can reckon B's motion and trace the curve of this motion. Now the signals go with the speed of light. The watches which mark the apparent time vary at each instant and everything will happen as if B's watch went too fast. B will think himself going much less rapidly and the apparent velocity he will have relatively to A will not surpass the limit it should not attain. Nothing can reveal to A whether he is in motion or at absolute rest.

It is still necessary to make a third hypothesis, which is much more surprising, much more difficult to admit, and which greatly disturbs our present modes of thought. A body in motion of translation undergoes a deformation in the direction of its displacement; a sphere, for instance, becomes like a species of flattened ellipsoid with the short axis parallel to the translation. If we do not perceive such a transformation every day this is because it is so small as to render it almost imperceptible. The earth, borne along in its revolution through its orbit, is deformed about $1/200 000 000$. To observe such a phenomenon would require measuring instruments of extreme precision, but if their precision were infinite it would not avail, because they also are borne along in the motion and would undergo the same transformation. We should perceive nothing; the meter we could use would shorten like the length to be measured. We could not learn anything except by comparing the length of one of these bodies to the velocity of light.

title: Page:Poincare Goettingen En.djvu/6


text:
Page:Poincare Goettingen En.djvu/7

 These are delicate experiments, carried out by Michelson and I shall not expound their details ; they have given results altogether remarkable. However strange it may seem to us, it is necessary to admit that the third hypothesis is perfectly verified.

Such are the bases of the new mechanics; with the help of these hypotheses we find that it is compatible with the principle of relativity.

But it is necessary to connect it then to a new conception of matter.

For the modern physicist, the atom is no longer the simple element; it has become a veritable universe in which thousands of planets gravitate around tiny suns. Suns and planets are here particles electrified either negatively or positively; the physicist calls them electrons and with them builds the world. Some represent the neutral atom as a positive central mass around which circulate a great number of negatively charged electrons, whose total electric mass equals in magnitude that of the central nucleus.

This conception of matter enables us easily to account for the augmentation of the mass of a body with its velocity, which we have made one of the characteristics of the new mechanics. Since a body is only an assemblage of electrons, it will suffice to show it to be true of them. To this end we note that an isolated electron moving through the ether engenders an electric current, that is to say an electromagnetic field. This field corresponds to a certain quantity of energy localized not in the electron but in the ether. A variation in magnitude or in direction of the electron's velocity modifies the field and expresses itself by a variation of the electromagnetic energy of the ether. While in the Newtonian mechanics the expenditure of energy is due only to the inertia of the moving body, here a part of this expenditure is due to what may be called the

title: Page:Poincare Goettingen En.djvu/7


text:
Page:Poincare Goettingen En.djvu/8

 inertia of the ether relatively to the electromagnetic forces. The inertia of the ether increases with the velocity and its limit becomes infinite when the velocity approaches the velocity of light. The apparent mass of the electron therefore increases with the velocity; Kaufmann’s experiments show that the constant real mass of the electron is negligible in relation to the apparent mass and may be considered as null.

In the new conception, matter’s constant mass has disappeared. Only the ether, and no longer matter, is inert. Only the ether opposes a resistance to motion, so that we might say that there is no matter, but only gaps in the ether. For stationary or quasi-stationary motions, the new mechanics does not differ — within the range of approximation of our measurements — from the Newtonian mechanics, with the sole difference that the mass is no longer independent either of the velocity or of the angle this velocity makes with the direction of the accelerative force. If, per contra, the velocity has a considerable acceleration, in the case, for instance, of very rapid oscillations, Hertzian waves are produced which represent a loss of energy of the electron involving the deadening of its motion. Thus in wireless telegraphy the waves emitted are due to the vibrations of the electrons in the oscillatory discharge.

Analogous vibrations take place in a flame and likewise also in an incandescent solid. Lorentz thinks that in an incandescent body a considerable number of electrons circulate which, not being able to get out of it, fly in every direction and are reflected on its surface. We may compare them to a swarm of gnats enclosed in a jar and striking with their wings against the walls of their prison. The higher the temperature, the more rapid becomes the motion of these electrons and the more numerous the mutual impacts and the reflections on the wall. At each impact

title: Page:Poincare Goettingen En.djvu/8


text:
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 and at each reflection an electromagnetic wave is emitted and it is the perception of these waves which makes the body appear to us incandescent.

The motion of the electrons is almost tangible in a Crookes tube. There a veritable bombardment takes place of electrons issuing from the cathode. These cathode rays violently strike the anticathode and are there in part reflected, thus giving birth to an electromagnetic agitation which many physicists identify with the Röntgen rays.

In closing, it remains for us to examine the relations of the new mechanics to astronomy.

If the notion of constant mass of a body vanishes, what will become of Newton’s law? It will hold good only for bodies at rest. Moreover it will be necessary to take into account the fact that attraction is not instantaneous. It may therefore well be asked whether the new mechanics will not result in complicating astronomy without obtaining an approximation superior to that given by the classic celestial mechanics. Lorentz has taken up the question. Starting from Newton’s law, which he assumes to be true for two electrified bodies at rest, he calculates the electrodynamic action of the currents engendered by these bodies in motion. He thus obtains a new law of attraction containing the velocities of the two bodies as parameters.

Before examining how this law explains astronomic phenomena, we remark again that the acceleration of the heavenly bodies has as consequence an electromagnetic radiation, therefore a dissipation of energy making itself felt in return by a deadening of their velocity. Therefore, in the long run, the planets will end by falling into the sun. But this prospect can hardly frighten us, since the catastrophe can not happen for some millions of milliards of centuries.

Returning now to the law of attraction, we easily see

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 that the difference between the two mechanics will be the greater the greater the velocity of the planets.

If there is an appreciable difference, it will therefore be greatest for Mercury, which has the greatest velocity of all the planets. Now it happens precisely that Mercury presents an anomaly not yet explained. The motion of its perihelion is more rapid than the motion calculated by the classic theory. The acceleration is 38" too great. Leverrier attributed this anomaly to a planet not yet discovered and an amateur astronomer thought he observed its passage across the sun. Since then no one else has seen it and it is unhappily certain that this planet perceived was only a bird.

Now the new mechanics explains perfectly the sense of the error with regard to Mercury, but it still leaves a margin of 32" between it and observation. It therefore does not suffice for bringing concord into the explanation of the velocity of Mercury. If this result is hardly decisive in favor of the new mechanics, still less is it unfavorable to its acceptance since the sense in which it corrects the deviation from the classic theory is the right one. Our explanation of the velocity of the other planets is not sensibly modified in the new theory and the results coincide, to within the approximation of the measurements, with those of the classic theory.

In conclusion, it would be premature, I believe, in spite of the great value of the arguments and of the facts set up against it, to regard the classic mechanics as finally condemned. However it may be in other respects, it will remain the mechanics of very small velocities in relation to that of light, the mechanics therefore of our practical life and of our terrestrial technic. If however, in some years, its rival triumphs, I shall venture to point out a pedagogic danger that a number of teachers, in France at least, will not escape. These teachers will find nothing

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 more important, in teaching elementary mechanics to their scholars, than to inform them that this mechanics has had its day, that a new mechanics where the notions of mass and of time have a wholly different value replaces it; they will look down upon this lapsed mechanics that the programs force them to teach and will make their scholars feel the contempt they have for it. Yet I believe that this disdained classic mechanics will be as necessary as now and that whoever does not know it thoroughly cannot understand the new mechanics.

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The New Mechanics (Göttingen)

La Mécanique nouvelle (Göttingen)

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general principles of Dynamics, which have, since Newton, served as foundation for physical science, and which appeared immovable, are they on the point of being abandoned or at least profoundly modified? This is what many people have been asking themselves for some years. According to them, the discovery of radium has overturned the scientific dogmas we believed the most solid: on the one hand, the impossibility of the transmutation of metals; on the other hand, the fundamental postulates of mechanics.

Perhaps one is too hasty in considering these novelties as finally established, and breaking our idols of yesterday; perhaps it would be proper, before taking sides, to await experiments more numerous and more convincing. None the less is it necessary, from to-day, to know the new doctrines and the arguments, already very weighty, upon which they rest.

In few words let us first recall in what those principles consist:

A. The motion of a material point isolated and apart from all exterior force is straight and uniform; this is the principle of inertia: without force no acceleration;

B. The acceleration of a moving point has the same direction as the resultant of all the forces to which it is subjected; it is equal to the quotient of this resultant by a coefficient called mass of the moving point.

The mass of a moving point, so defined, is a constant; it does


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Rh not depend upon the velocity acquired by this point; it is the same whether the force, being parallel to this velocity, tends only to accelerate or to retard the motion of the point, or whether, on the contrary, being perpendicular to this velocity, it tends to make this motion deviate toward the right, or the left, that is to say to curve the trajectory;

C. All the forces affecting a material point come from the action of other material points; they depend only upon the relative positions and velocities of these different material points.

Combining the two principles B and C, we reach the principle of relative motion, in virtue of which the laws of the motion of a system are the same whether we refer this system to fixed axes, or to moving axes animated by a straight and uniform motion of translation, so that it is impossible to distinguish absolute motion from a relative motion with reference to such moving axes;

D. If a material point A acts upon another material point B, the body B reacts upon A, and these two actions are two equal and directly opposite forces. This is the principle of the equality of action and reaction, or, more briefly, the principle of reaction.

Astronomic observations and the most ordinary physical phenomena seem to have given of these principles a confirmation complete, constant and very precise. This is true, it is now said, but it is because we have never operated with any but very small velocities; Mercury, for example, the fastest of the planets, goes scarcely 100 kilometers a second. Would this planet act the same if it went a thousand times faster? We see there is yet no need to worry; whatever may be the progress of automobilism, it will be long before we must give up applying to our machines the classic principles of dynamics.

How then have we come to make actual speeds a thousand times greater than that of Mercury, equal, for instance, to a tenth or a third of the velocity of light, or approaching still more closely to that velocity? It is by aid of the cathode rays and the rays from radium.

We know that radium emits three kinds of rays, designated by the three Greek letters α, β, γ; in what follows, unless the contrary be expressly stated, it will always be a question of the β rays, which are analogous to the cathode rays.


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 After the discovery of the cathode rays two theories appeared: Crookes attributed the phenomena to a veritable molecular bombardment; Hertz, to special undulations of the ether. This was a renewal of the debate which divided physicists a century ago about light; Crookes took up the emission theory, abandoned for light; Hertz held to the undulatory theory. The facts seem to decide in favor of Crookes.

It has been recognized, in the first place, that the cathode rays carry with them a negative electric charge; they are deviated by a magnetic field and by an electric field; and these deviations are precisely such as these same fields would produce upon projectiles animated by a very high velocity and strongly charged with electricity. These two deviations depend upon two quantities: one the velocity, the other the relation of the electric charge of the projectile to its mass; we cannot know the absolute value of this mass, nor that of the charge, but only their relation; in fact, it is clear that if we double at the same time the charge and the mass, without changing the velocity, we shall double the force which tends to deviate the projectile, but, as its mass is also doubled, the acceleration and deviation observable will not be changed. The observation of the two deviations will give us therefore two equations to determine these two unknowns. We find a velocity of from 10,000 to 30,000 kilometers a second; as to the ratio of the charge to the mass, it is very great. We may compare it to the corresponding ratio in regard to the hydrogen ion in electrolysis; we then find that a cathodic projectile carries about a thousand times more electricity than an equal mass of hydrogen would carry in an electrolyte.

To confirm these views, we need a direct measurement of this velocity to compare with the velocity so calculated. Old experiments of J. J. Thomson had given results more than a hundred times too small; but they were exposed to certain causes of error. The question was taken up again by Wiechert in an arrangement where the Hertzian oscillations were utilized; results were found agreeing with the theory, at least as to order of magnitude; it would be of great interest to repeat these experiments. However that may be, the theory of undulations appears powerless to account for this complex of facts.


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Rh The same calculations made with reference to the β rays of radium have given velocities still greater: 100,000 or 200,000 kilometers or more yet. These velocities greatly surpass all those we know. It is true that light has long been known to go 300,000 kilometers a second; but it is not a carrying of matter, while, if we adopt the emission theory for the cathode rays, there would be material molecules really impelled at the velocities in question, and it is proper to investigate whether the ordinary laws of mechanics are still applicable to them.

We know that electric currents produce the phenomena of induction, in particular self-induction. When a current increases, there develops an electromotive force of self-induction which tends to oppose the current; on the contrary, when the current decreases, the electromotive force of self-induction tends to maintain the current. The self-induction therefore opposes every variation of the intensity of the current, just as in mechanics the inertia of a body opposes every variation of its velocity.

Self-induction is a veritable inertia. Everything happens as if the current could not establish itself without putting in motion the surrounding ether and as if the inertia of this ether tended, in consequence, to keep constant the intensity of this current. It would be requisite to overcome this inertia to establish the current, it would be necessary to overcome it again to make the current cease.

A cathode ray, which is a rain of projectiles charged with negative electricity, may be likened to a current; doubtless this current differs, at first sight at least, from the currents of ordinary conduction, where the matter does not move and where the electricity circulates through the matter. This is a current of convection, where the electricity, attached to a material vehicle, is carried along by the motion of this vehicle. But Rowland has proved that currents of convection produce the same magnetic effects as currents of conduction; they should produce also the same effects of induction. First, if this were not so, the principle of the conservation of energy would be violated; besides,


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 Crémieu and Pender have employed a method putting in evidence directly these effects of induction.

If the velocity of a cathode corpuscle varies, the intensity of the corresponding current will likewise vary; and there will develop effects of self-induction which will tend to oppose this variation. These corpuscles should therefore possess a double inertia: first their own proper inertia, and then the apparent inertia, due to self-induction, which produces the same effects. They will therefore have a total apparent mass, composed of their real mass and of a fictitious mass of electromagnetic origin. Calculation shows that this fictitious mass varies with the velocity, and that the force of inertia of self-induction is not the same when the velocity of the projectile accelerates or slackens, or when it is deviated; therefore so it is with the force of the total apparent inertia.

The total apparent mass is therefore not the same when the real force applied to the corpuscle is parallel to its velocity and tends to accelerate the motion as when it is perpendicular to this velocity and tends to make the direction vary. It is necessary therefore to distinguish the total longitudinal mass from the total transversal mass. These two total masses depend, moreover, upon the velocity. This follows from the theoretical work of Abraham.

In the measurements of which we speak in the preceding section, what is it we determine in measuring the two deviations? It is the velocity on the one hand, and on the other hand the ratio of the charge to the total transversal mass. How, under these conditions, can we make out in this total mass the part of the real mass and that of the fictitious electromagnetic mass? If we had only the cathode rays properly so called, it could not be dreamed of; but happily we have the rays of radium which, as we have seen, are notably swifter. These rays are not all identical and do not behave in the same way under the action of an electric field and a magnetic field. It is found that the electric deviation is a function of the magnetic deviation, and we are able, by receiving on a sensitive plate radium rays which have been subjected to the action of the two fields, to photograph the curve which represents the relation between these two deviations. This is what Kaufmann has done, deducing from it the relation between


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Rh the velocity and the ratio of the charge to the total apparent mass, a ratio we shall call ε.

One might suppose there are several species of rays, each characterized by a fixed velocity, by a fixed charge and by a fixed mass. But this hypothesis is improbable; why, in fact, would all the corpuscles of the same mass take always the same velocity? It is more natural to suppose that the charge as well as the real mass are the same for all the projectiles, and that these differ only by their velocity. If the ratio ε is a function of the velocity, this is not because the real mass varies with this velocity; but, since the fictitious electromagnetic mass depends upon this velocity, the total apparent mass, alone observable, must depend upon it, though the real mass does not depend upon it and may be constant.

The calculations of Abraham let us know the law according to which the fictitious mass varies as a function of the velocity; Kaufmann’s experiment lets us know the law of variation of the total mass.

The comparison of these two laws will enable us therefore to determine the ratio of the real mass to the total mass.

Such is the method Kaufmann used to determine this ratio. The result is highly surprising: the real mass is naught.

This has led to conceptions wholly unexpected. What had only been proved for cathode corpuscles was extended to all bodies. What we call mass would be only semblance; all inertia would be of electromagnetic origin. But then mass would no longer be constant, it would augment with the velocity; sensibly constant for velocities up to 1,000 kilometers a second, it then would increase and would become infinite for the velocity of light. The transversal mass would no longer be equal to the longitudinal: they would only be nearly equal if the velocity is not too great. The principle B of mechanics would no longer be true.

At the point where we now are, this conclusion might seem premature. Can one apply to all matter what has been proved


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 only for such light corpuscles, which are a mere emanation ofmatter and perhaps not true matter? But before entering upon this question, a word must be said of another sort of rays. I refer to the canal rays, the Kanalstrahlen of Goldstein.

The cathode, together with the cathode rays charged with negative electricity, emits canal rays charged with positive electricity. In general, these canal rays not being repelled by the cathode, are confined to the immediate neighborhood of this cathode, where they constitute the ‘chamois cushion,’ not very easy to perceive; but, if the cathode is pierced with holes and if it almost completely blocks up the tube, the canal rays spread back of the cathode, in the direction opposite to that of the cathode rays, and it becomes possible to study them. It is thus that it has been possible to show their positive charge and to show that the magnetic and electric deviations still exist, as for the cathode rays, but are much feebler.

Radium likewise emits rays analogous to the canal rays, and relatively very absorbable, called α rays.

We can, as for the cathode rays, measure the two deviations and thence deduce the velocity and the ratio ε. The results are less constant than for the cathode rays, but the velocity is less, as well as the ratio ε; the positive corpuscles are less charged than the negative; or if, which is more natural, we suppose the charges equal and of opposite sign, the positive corpuscles are much the larger. These corpuscles, charged the ones positively, the others negatively, have been called electrons.

But the electrons do not merely show us their existence in these rays where they are endowed with enormous velocities. We shall see them in very different roles, and it is they that account for the principal phenomena of optics and electricity. The brilliant synthesis about to be noticed is due to Lorentz.

Matter is formed solely of electrons carrying enormous charges, and, if it seems to us neutral, this is because the charges of opposite sign of these electrons compensate each other. We


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 may imagine, for example, a sort of solar system formed of a great positive electron, around which gravitate numerous little planets, the negative electrons, attracted by the electricity of opposite name which charges the central electron. The negative charges of these planets would balance the positive charge of this sun, so that the algebraic sum of all these charges would be naught.

All these electrons swim in the ether. The ether is everywhere identically the same, and perturbations in it are propagated according to the same laws as light or the Hertzian oscillations in vacuo. There is nothing but electrons and ether. When a luminous wave enters a part of the ether where electrons are numerous, these electrons are put in motion under the influence of the perturbation of the ether, and they then react upon the ether. So would be explained refraction, dispersion, double refraction and absorption. Just so, if for any cause an electron be put in motion, it would trouble the ether around it and would give rise to luminous waves, and this would explain the emission of light by incandescent bodies.

In certain bodies, the metals for example, we should have fixed electrons, between which would circulate moving electrons enjoying perfect liberty, save that of going out from the metallic body and breaking the surface which separates it from the exterior void or from the air, or from any other non-metallic body.

These movable electrons behave then, within the metallic body, as do, according to the kinetic theory of gases, the molecules of a gas within the vase where this gas is confined. But, under the influence of a difference of potential, the negative movable electrons would tend to go all to one side, and the positive movable electrons to the other. This is what would produce electric currents, and this is why these bodies would he conductors. On the other hand, the velocities of our electrons would be the greater the higher the temperature, if we accept the assimilation with the kinetic theory of gases. When one of these movable electrons encounters the surface of the metallic body, whose boundary it can not pass, it is reflected like a billiard ball which has hit the cushion, and its velocity undergoes a sudden change of direction. But when an electron changes direction, as we shall see further


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494 on, it becomes the source of a luminous wave, and this is why hot metals are incandescent.

In other bodies, the dielectrics and the transparent bodies, the movable electrons enjoy much less freedom. They remain as if attached to fixed electrons which attract them. The farther they go away from them the greater becomes this attraction and tends to pull them back. They therefore can make only small excursions; they can no longer circulate, but only oscillate about their mean position. This is why these bodies would not be conductors; moreover they would most often be transparent, and they would be refractive, since the luminous vibrations would be communicated to the movable electrons, susceptible of oscillation, and thence a perturbation would result.

I can not here give the details of the calculations; I confine myself to saying that this theory accounts for all the known facts, and has predicted new ones, such as the Zeeman effect.

We now may face two hypotheses :

1° The positive electrons have a real mass, much greater than their fictitious electromagnetic mass; the negative electrons alone lack real mass. We might even suppose that apart from electrons of the two signs, there are neutral atoms which have only their real mass. In this case, mechanics is not affected; there is no need of touching its laws; the real mass is constant; simply, motions are deranged by the effects of self-induction, as has always been known; moreover, these perturbations are almost negligible, except for the negative electrons which, not having real mass, are not true matter;

2° But there is another point of view; we may suppose there are no neutral atoms, and the positive electrons lack real mass just as the negative electrons. But then, real mass vanishing, either the word mass will no longer have any meaning, or else it must designate the fictitious electromagnetic mass; in this case, mass will no longer be constant, the transversal mass will no longer be equal to the longitudinal, the principles of mechanics will be overthrown.


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 First a word of explanation. We have said that, for the same charge, the total mass of a positive electron is much greater than that of a negative. And then it is natural to think that this difference is explained by the positive electron having, besides its fictitious mass, a considerable real mass; which takes us back to the first hypothesis. But we may just as well suppose that the real mass is null for these as for the others, but that the fictitious mass of the positive electron is much the greater since this electron is much the smaller. I say advisedly: much the smaller. And, in fact, in this hypothesis inertia is exclusively electromagnetic in origin; it reduces itself to the inertia of the ether; the electrons are no longer anything by themselves; they are solely holes in the ether and around which the ether moves; the smaller these holes are, the more will there be of ether, the greater, consequently, will be the inertia of the ether.

How shall we decide between these two hypotheses? By operating upon the canal rays as Kaufmann did upon the β rays? This is impossible; the velocity of these rays is much too slight. Should each therefore decide according to his temperament, the conservatives going to one side and the lovers of the new to the other? Perhaps, but, to fully understand the arguments of the innovators, other considerations must come in.


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know in what the phenomenon of aberration, discovered by Bradley, consists. The light issuing from a star takes a certain time to go through a telescope; daring this time, the telescope, carried along by the motion of the earth, is displaced. If therefore the telescope were pointed in the true direction of the star, the image would be formed at the point occupied by the crossing of the threads of the network when the light has reached the objective; and this crossing would no longer be at this same point when the light reached the plane of the network. We would therefore be led to mis-point the telescope to bring the image upon the crossing of the threads. Thence results that the astronomer will not point the telescope in the direction of the absolute velocity of the light, that is to say toward the true position of the star, but just in the direction of the relative velocity of the light with reference to the earth, that is to say toward what is called the apparent position of the star.

The velocity of light is known; we might therefore suppose that we have the means of calculating the absolute velocity of the earth. (I shall soon explain my use here of the word absolute.) Nothing of the sort; we indeed know the apparent position of the star we observe; but we do not know its true position; we know the velocity of the light only in magnitude and not in direction.

If therefore the absolute velocity of the earth were straight and uniform, we should never have suspected the phenomenon of aberration; but it is variable; it is composed of two parts: the velocity of the solar system, which is straight and uniform; the velocity of the earth with reference to the sun, which is variable. If the velocity of the solar system, that is to say if the constant part existed alone, the observed direction would be invariable.


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 This position that one would thus observe is called the mean apparent position of the star.

Taking account now at the same time of the two parts of the velocity of the earth, we shall have the actual apparent position, which describes a little ellipse around the mean apparent position, and it is this ellipse that we observe.

Neglecting very small quantities, we shall see that the dimensions of this ellipse depend only upon the ratio of the velocity of the earth with reference to the sun to the velocity of light, so that the relative velocity of the earth with regard to the sun has alone come in.

But wait! This result is not exact, it is only approximate; let us push the approximation a little farther. The dimensions of the ellipse will depend then upon the absolute velocity of the earth. Let us compare the major axes of the ellipse for the different stars: we shall have, theoretically at least, the means of determining this absolute velocity.

That would be perhaps less shocking than it at first seems; it is a question, in fact, not of the velocity with reference to an absolute void, but of the velocity with regard to the ether, which is taken by definition as being absolutely at rest.

Besides, this method is purely theoretical. In fact, the aberration is very small; the possible variations of the ellipse of aberration are much smaller yet, and, if we consider the aberration as of the first order, they should therefore be regarded as of the second order: about a millionth of a second; they are absolutely inappreciable for our instruments. We shall finally see, further on, why the preceding theory should be rejected, and why we could not determine this absolute velocity even if our instruments were ten thousand times more precise!

One might imagine some other means, and in fact, so one has. The velocity of light is not the same in water as in air; could we not compare the two apparent positions of a star seen through a telescope first full of air, then full of water? The results have been negative; the apparent laws of reflection and refraction are not altered by the motion of the earth. This phenomenon is capable of two explanations :

1° It might be supposed that the ether is not at rest, but that


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498 it is carried along by the body in motion. It would then not be astonishing that the phenomena of refraction are not altered by the motion of the earth, since all, prisms, telescopes and ether, are carried along together in the same translation. As to the aberration itself, it would be explained by a sort of refraction happening at the surface of separation of the ether at rest in the interstellar spaces and the ether carried along by the motion of the earth. It is upon this hypothesis (bodily carrying along of the ether) that is founded the theory of Hertz on the electrodynamics of moving bodies.

2° Fresnel, on the contrary, supposes that the ether is at absolute rest in the void, at rest almost absolute in the air, whatever be the velocity of this air, and that it is partially carried along by refractive media. Lorentz has given to this theory a more satisfactory form. For him, the ether is at rest, only the electrons are in motion; in the void, where it is only a question of the ether, in the air, where this is almost the case, the carrying along is null or almost null; in refractive media, where perturbation is produced at the same time by vibrations of the ether and those of electrons put in swing by the agitation of the ether, the undulations are partially carried along.

To decide between the two hypotheses, we have Fizeau’s experiment, comparing by measurements of the fringes of interference, the velocity of light in air at rest or in motion. These experiments have confirmed Fresnel’s hypothesis of partial carrying along. They have been repeated with the same result by Michelson. The theory of Hertz must therefore be rejected.

But if the ether is not carried along by the motion of the earth, is it possible to show, by means of optical phenomena, the absolute velocity of the earth, or rather its velocity with respect to the unmoving ether? Experiment has answered negatively, and yet the experimental procedures have been varied in all possible ways. Whatever be the means employed there will never be disclosed anything but relative velocities; I mean the


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Rh velocities of certain material bodies with reference to other material bodies. In fact, if the source of light and the apparatus of observation are on the earth and participate in its motion, the experimental results have always been the same, whatever be the orientation of the apparatus with reference to the orbital motion of the earth. If astronomic aberration happens, it is because the source, a star, is in motion with reference to the observer.

The hypotheses so far made perfectly account for this general result, if we neglect very small quantities of the order of the square of the aberration. The explanation rests upon the notion of local time, introduced by Lorentz, which I shall try to make clear. Suppose two observers, placed one at A, the other at B, and wishing to set their watches by means of optical signals. They agree that B shall send a signal to A when his watch marks an hour determined upon, and A is to put his watch to that hour the moment he sees the signal. If this alone were done, there would be a systematic error, because as the light takes a certain time t to go from B to A, A’s watch would be behind B’s the time t. This error is easily corrected. It suffices to cross the signals. A in turn must signal B, and, after this new adjustment, B’s watch will be behind A’s the time t. Then it will be sufficient to take the arithmetic mean of the two adjustments.

But this way of doing supposes that light takes the same time to go from A to B as to return from B to A. That is true if the observers are motionless; it is no longer so if they are carried along in a common translation, since then A, for example, will go to meet the light coming from B, while B will flee before the light coming from A. If therefore the observers are borne along in a common translation and if they do not suspect it, their adjustment will be defective; their watches will not indicate the same time; each will show the local time belonging to the point where it is.

The two observers will have no way of perceiving this, if the unmoving ether can transmit to them only luminous signals all of the same velocity, and if the other signals they might send are transmitted by media carried along with them in their translation. The phenomenon each observes will be too soon or too


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500 late; it would be seen at the same instant only if the translation did not exist; but as it will be observed with a watch that is wrong, this will not be perceived and the appearances will not be altered.

It results from this that the compensation is easy to explain so long as we neglect the square of the aberration, and for a long time the experiments were not sufficiently precise to warrant taking account of it. But the day came when Michelson imagined a much more delicate procedure: he made rays interfere which had traversed different courses, after being reflected by mirrors; each of the paths approximating a meter and the fringes of interference permitting the recognition of a fraction of a thousandth of a millimeter, the square of the aberration could no longer be neglected, and yet the results were still negative. Therefore the theory required to be completed, and it has been by the Lorentz-Fitzgerald hypothesis.

These two physicists suppose that all bodies carried along in a translation undergo a contraction in the sense of this translation, while their dimensions perpendicular to this translation remain unchanged. This contraction is the same for all bodies; moreover, it is very slight, about one two-hundred-millionth for a velocity such as that of the earth. Furthermore our measuring instruments could not disclose it, even if they were much more precise; our measuring rods in fact undergo the same contraction as the objects to be measured. If the meter exactly fits when applied to a body, if we point the body and consequently the meter in the sense of the motion of the earth, it will not cease to exactly fit in another orientation, and that although the body and the meter have changed in length as well as orientation, and precisely because the change is the same for one as for the other. But it is quite different if we measure a length, not now with a meter, but by the time taken by light to pass along it, and this is just what Michelson has done.

A body, spherical when at rest, will take thus the form of a flattened ellipsoid of revolution when in motion; but the observer will always think it spherical, since he himself has undergone an analogous deformation, as also all the objects serving as points of reference. On the contrary, the surfaces of the waves of


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Rh light, remaining rigorously spherical, will seem to him elongated ellipsoids.

What happens then? Suppose an observer and a source of light carried along together in the translation: the wave surfaces emanating from the source will be spheres having as centers the successive positions of the source; the distance from this center to the actual position of the source will be proportional to the time elapsed after the emission, that is to say to the radius of the sphere. All these spheres are therefore homothetic one to the other, with relation to the actual position S of the source. But, for our observer, because of the contraction, all these spheres will seem elongated ellipsoids, and all these ellipsoids will moreover be homothetic, with reference to the point S; the excentricity of all these ellipsoids is the same and depends solely upon the velocity of the earth. We shall so select the law of contraction that the point S may be at the focus of the meridian section of the ellipsoid.

This time the compensation is rigorous, and this it is which explains Michelson’s experiment.

I have said above that, according to the ordinary theories, observations of the astronomic aberration would give us the absolute velocity of the earth, if our instruments were a thousand times more precise. I must modify this statement. Yes, the observed angles would be modified by the effect of this absolute velocity, but the graduated circles we use to measure the angles would be deformed by the translation: they would become ellipses; thence would result an error in regard to the angle measured, and this second error would exactly compensate the first.

This Lorentz-Fitzgerald hypothesis seems at first very extraordinary; all we can say for the moment, in its favor, is that it is only the immediate translation of Michelson’s experimental result, if we define lengths by the time taken by light to run along them.

However that may be, it is impossible to escape the impression that the principle of relativity is a general law of nature, that one will never be able by any imaginable means to show any but relative velocities, and I mean by that not only the


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502 velocities of bodies with reference to the ether, but the velocities of bodies with regard to one another. Too many different experiments have given concordant results for us not to feel tempted to attribute to this principle of relativity a value comparable to that, for example, of the principle of equivalence. In any case, it is proper to see to what consequences this way of looking at things would lead us and then to submit these consequences to the control of experiment.

Let us see what the principle of the equality of action and reaction becomes in the theory of Lorentz. Consider an electron A which for any cause begins to move; it produces a perturbation in the ether; at the end of a certain time, this perturbation reaches another electron B, which will be disturbed from its position of equilibrium. In these conditions there can not be equality between action and reaction, at least if we do not consider the ether, but only the electrons, which alone are observable, since our matter is made of electrons.

In fact it is the electron A which has disturbed the electron B; even in case the electron B should react upon A, this reaction could be equal to the action, but in no case simultaneous, since the electron B can begin to move only after a certain time, necessary for the propagation. Submitting the problem to a more exact calculation, we reach the following result: Suppose a Hertz discharger placed at the focus of a parabolic mirror to which it is mechanically attached; this discharger emits electromagnetic waves, and the mirror reflects all these waves in the same direction; the discharger therefore will radiate energy in a determinate direction. Well, the calculation shows that the discharger recoils like a cannon which has shot out a projectile. In the case of the cannon, the recoil is the natural result of the equality of action and reaction. The cannon recoils because the projectile upon which it has acted reacts upon it. But here it is no longer the same. What has been sent out is no longer a material projectile: it is energy, and energy has no mass: it has


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 no counterpart. And, in place of a discharger, we could have considered just simply a lamp with a reflector concentrating its rays in a single direction.

It is true that, if the energy sent out from the discharger or from the lamp meets a material object, this object receives a mechanical push as if it had been hit by a real projectile, and this push will be equal to the recoil of the discharger and of the lamp, if no energy has been lost on the way and if the object absorbs the whole of the energy. Therefore one is tempted to say that there still is compensation between the action and the reaction. But this compensation, even should it be complete, is always belated. It never happens if the light, after leaving its source, wanders through interstellar spaces without ever meeting a material body; it is incomplete, if the body it strikes is not perfectly absorbent.

Are these mechanical actions too small to be measured, or are they accessible to experiment? These actions are nothing other than those due to the Maxwell-Bartholi pressures; Maxwell had predicted these pressures from calculations relative to electrostatics and magnetism; Bartholi reached the same result by thermodynamic considerations.

This is how the tails of comets are explained. Little particles detach themselves from the nucleus of the comet; they are struck by the light of the sun, which pushes them back as would a rain of projectiles coming from the sun. The mass of these particles is so little that this repulsion sweeps it away against the Newtonian attraction; so in moving away from the sun they form the tails.

The direct experimental verification was not easy to obtain. The first endeavor led to the construction of the radiometer. But this instrument turns backward, in the sense opposite to the theoretic sense, and the explanation of its rotation, since discovered, is wholly different. At last success came, by making the vacuum more complete, on the one hand, and on the other by not blackening one of the faces of the paddles and directing a pencil of luminous rays upon one of the faces. The radiometric effects and the other disturbing causes are eliminated by a series of painstaking precautions, and one obtains a deviation which is very


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504 minute, but which is, it would seem, in conformity with the theory.

The same effects of the Maxwell-Bartholi pressure are forecast likewise by the theory of Hertz of which we have before spoken, and by that of Lorentz. But there is a difference. Suppose that the energy, under the form of light, for example, proceeds from a luminous source to any body through a transparent medium. The Maxwell-Bartholi pressure will act, not alone upon the source at the departure, and on the body lit up at the arrival, but upon the matter of the transparent medium which it traverses. At the moment when the luminous wave reaches a new region of this medium, this pressure will push forward the matter there distributed and will put it back when the wave leaves this region. So that the recoil of the source has for counterpart the forward movement of the transparent matter which is in contact with this source; a little later, the recoil of this same matter has for counterpart the forward movement of the transparent matter which lies a little further on, and so on.

Only, is the compensation perfect? Is the action of the Maxwell-Bartholi pressure upon the matter of the transparent medium equal to its reaction upon the source, and that, whatever be this matter? Or is this action by so much the less as the medium is less refractive and more rarefied, becoming null in the void?

If we admit the theory of Hertz, who regards matter as mechanically bound to the ether, so that the ether may be entirely carried along by matter, it would be necessary to answer yes to the first question and no to the second.

There would then be perfect compensation, as required by the principle of the equality of action and reaction, even in the least refractive media, even in the air, even in the interplanetary void, where it would suffice to suppose a residue of matter, however subtile. If on the contrary we admit the theory of Lorentz, the compensation, always imperfect, is insensible in the air and becomes null in the void.

But we have seen above that Fizeau’s experiment does not permit of our retaining the theory of Hertz; it is necessary therefore


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Rh to adopt the theory of Lorentz, and consequently to renounce the principle of reaction.

We have seen above the reasons which impel us to regard the principle of relativity as a general law of nature. Let us see to what consequences this principle would lead, should it be regarded as finally demonstrated.

First, it obliges us to generalize the hypothesis of Lorentz and Fitzgerald on the contraction of all bodies in the sense of the translation. In particular, we must extend this hypothesis to the electrons themselves. Abraham considered these electrons as spherical and indeformable; it will be necessary for us to admit that these electrons, spherical when in repose, undergo the Lorentz contraction when in motion and take then the form of flattened ellipsoids.

This deformation of the electrons will influence their mechanical properties. In fact I have said that the displacement of these charged electrons is a veritable current of convection and that their apparent inertia is due to the self-induction of this current: exclusively as concerns the negative electrons; exclusively or not, we do not yet know, for the positive electrons. Well, the deformation of the electrons, a deformation which depends upon their velocity, will modify the distribution of the electricity upon their surface, consequently the intensity of the convection current they produce, consequently the laws according to which the self-induction of this current will vary as a function of the velocity.

At this price, the compensation will be perfect and will conform to the requirements of the principle of relativity, but only upon two conditions :

1° That the positive electrons have no real mass, but only a fictitious electromagnetic mass; or at least that their real mass, if it exists, is not constant and varies with the velocity according to the same laws as their fictitious mass;

2° That all forces are of electromagnetic origin, or at least


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506 that they vary with the velocity according to the same laws as the forces of electromagnetic origin.

It still is Lorentz who has made this remarkable synthesis; stop a moment and see what follows therefrom. First, there is no more matter, since the positive electrons no longer have real mass, or at least no constant real mass. The present principles of our mechanics, founded upon the constancy of mass, must therefore be modified. Again, an electromagnetic explanation must be sought of all the known forces, in particular of gravitation, or at least the law of gravitation must be so modified that this force is altered by velocity in the same way as the electromagnetic forces. We shall return to this point.

All that appears, at first sight, a little artificial. In particular, this deformation of electrons seems quite hypothetical. But the thing may be presented otherwise, so as to avoid putting this hypothesis of deformation at the foundation of the reasoning. Consider the electrons as material points and ask how their mass should vary as function of the velocity not to contravene the principle of relativity. Or, still better, ask what should be their acceleration under the influence of an electric or magnetic field, that this principle be not violated and that we come back to the ordinary laws when we suppose the velocity very slight. We shall find that the variations of this mass, or of these accelerations, must be as if the electron underwent the Lorentz deformation.

We have before us, then, two theories: one where the electrons are indeformable, this is that of Abraham; the other where they undergo the Lorentz deformation. In both cases, their mass increases with the velocity, becoming infinite when this velocity becomes equal to that of light; but the law of the variation is not the same. The method employed by Kaufmann to bring to light the law of variation of the mass seems therefore to give us an experimental means of deciding between the two theories.

Unhappily, his first experiments were not sufficiently precise for that; so he decided to repeat them with more precautions, and


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Rh measuring with great care the intensity of the fields. Under their new form they are in favor of the theory of Abraham. Then the principle of relativity would not have the rigorous value we were tempted to attribute to it; there would no longer be reason for believing the positive electrons denuded of real mass like the negative electrons. However, before definitely adopting this conclusion, a little reflection is necessary. The question is of such importance that it is to be wished Kaufmann’s experiment were repeated by another experimenter. Unhappily, this experiment is very delicate and could be carried out successfully only by a physicist of the same ability as Kaufmann. All precautions have been properly taken and we hardly see what objection could be made.

There is one point however to which I wish to draw attention: that is to the measurement of the electrostatic field, a measurement upon which all depends. This field was produced between the two armatures of a condenser; and, between these armatures, there was to be made an extremely perfect vacuum, in order to obtain a complete isolation. Then the difference of potential of the two armatures was measured, and the field obtained by dividing this difference by the distance apart of the armatures. That supposes the field uniform; is this certain? Might there not be an abrupt fall of potential in the neighborhood of one of the armatures, of the negative armature, for example? There may be a difference of potential at the meeting of the metal and the vacuum, and it may be that this difference is not the same on the positive side and on the negative side; what would lead me to think so is the electric valve effects between mercury and vacuum. However slight the probability that it is so, it seems that it should be considered.

In the new dynamics, the principle of inertia is still true, that is to say that an isolated electron will have a straight and uniform motion. At least this is generally assumed; however,


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508 Lindemann has made objections to this view; I do not wish to take part in this discussion, which I can not here expound because of its too difficult character. In any case, slight modifications to the theory would suffice to shelter it from Lindemann’s objections.

We know that a body submerged in a fluid experiences, when in motion, considerable resistance, but this is because our fluids are viscous; in an ideal fluid, perfectly free from viscosity, the body would stir up behind it a liquid hill, a sort of wake; upon departure, a great effort would be necessary to put it in motion, since it would be necessary to move not only the body itself, but the liquid of its wake. But, the motion once acquired, it would perpetuate itself without resistance, since the body, in advancing, would simply carry with it the perturbation of the liquid, without the total vis viva of the liquid augmenting. Everything would happen therefore as if its inertia was augmented. An electron advancing in the ether would behave in the same way: around it, the ether would be stirred up, but this perturbation would accompany the body in its motion; so that, for an observer carried along with the electron, the electric and magnetic fields accompanying this electron would appear invariable, and would change only if the velocity of the electron varied. An effort would therefore be necessary to put the electron in motion, since it would be necessary to create the energy of these fields; on the contrary, once the movement acquired, no effort would be necessary to maintain it, since the created energy would only have to go along behind the electron as a wake. This energy, therefore, could only augment the inertia of the electron, as the agitation of the liquid augments that of the body submerged in a perfect fluid. And anyhow, the negative electrons at least have no other inertia except that.

In the hypothesis of Lorentz, the vis viva, which is only the energy of the ether, is not proportional to v². Doubtless if v is very slight, the vis viva is sensibly proportional to v², the quantity of motion sensibly proportional to v, the two masses sensibly constant and equal to each other. But when the velocity tends toward the velocity of light, the vis viva, the quantity of motion and the two masses increase beyond all limit.


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 In the hypothesis of Abraham, the expressions are a little more complicated; but what we have just said remains true in essentials.

So the mass, the quantity of motion, the vis viva become infinite when the velocity is equal to that of light.

Thence results that no body can attain in any way a velocity beyond that of light. And in fact, in proportion as its velocity increases, its mass increases, so that its inertia opposes to any new increase of velocity a greater and greater obstacle.

A question then suggests itself: let us admit the principle of relativity; an observer in motion would not have any means of perceiving his own motion. If therefore no body in its absolute motion can exceed the velocity of light, but may approach it as nearly as you choose, it should be the same concerning its relative motion with reference to our observer. And then we might be tempted to reason as follows: The observer may attain a velocity of 200,000 kilometers; the body in its relative motion with reference to the observer may attain the same velocity; its absolute velocity will then be 400,000 kilometers, which is impossible, since this is beyond the velocity of light. This is only a seeming, which vanishes when account is taken of how Lorentz evaluates local time.

When an electron is in motion, it produces a perturbation in the ether surrounding it; if its motion is straight and uniform, this perturbation reduces to the wake of which we have spoken in the preceding section. But it is no longer the same, if the motion be curvilinear or varied. The perturbation may then be regarded as the superposition of two others, to which Langevin has given the names wave of velocity and wave of acceleration. The wave of velocity is only the wave which happens in uniform motion.

As to the wave of acceleration, this is a perturbation altogether analogous to light waves, which starts from the electron at the instant when it undergoes an acceleration, and which is then


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 propagated by successive spherical waves with the velocity of light. Whence follows: in a straight and uniform motion, the energy is wholly conserved; but, when there is an acceleration, there is loss of energy, which is dissipated under the form of luminous waves and goes out to infinity across the ether.

However, the effects of this wave of acceleration, in particular the corresponding loss of energy, are in most cases negligible, that is to say not only in ordinary mechanics and in the motions of the heavenly bodies, but even in the radium rays, where the velocity is very great without the acceleration being so. We may then confine ourselves to applying the laws of mechanics, putting the force equal to the product of acceleration by mass, this mass, however, varying with the velocity according to the laws explained above. We then say the motion is quasi-stationary.

It would not be the same in all cases where the acceleration is great, of which the chief are the following:

1° In incandescent gases certain electrons take an oscillatory motion of very high frequency; the displacements are very small, the velocities are finite, and the accelerations very great; energy is then communicated to the ether, and this is why these gases radiate light of the same period as the oscillations of the electron;

2° Inversely, when a gas receives light, these same electrons are put in swing with strong accelerations and they absorb light;

3° In the Hertz discharger, the electrons which circulate in the metallic mass undergo, at the instant of the discharge, an abrupt acceleration and take then an oscillatory motion of high frequency. Thence results that a part of the energy radiates under the form of Hertzian waves;

4° In an incandescent metal, the electrons enclosed in this metal are impelled with great velocity; upon reaching the surface of the metal, which they can not get through, they are reflected and thus undergo a considerable acceleration. This is why the metal emits light. The details of the laws of the emission of light by dark bodies are perfectly explained by this hypothesis;

5° Finally when the cathode rays strike the anticathode, the negative electrons constituting these rays, which are impelled with very great velocity, are abruptly arrested. Because of the


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Rh acceleration they thus undergo, they produce undulations in the ether. This, according to certain physicists, is the origin of the Röntgen rays, which would only be light rays of very short wave-length.


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may be defined in two ways:

1° By the quotient of the force by the acceleration; this is the true definition of the mass, which measures the inertia of the body.

2° By the attraction the body exercises upon an exterior body, in virtue of Newton’s law. We should therefore distinguish the mass coefficient of inertia and the mass coefficient of attraction. According to Newton’s law, there is rigorous proportionality between these two coefficients. But that is demonstrated only for velocities to which the general principles of dynamics are applicable. Now, we have seen that the mass coefficient of inertia increases with the velocity; should we conclude that the mass coefficient of attraction increases likewise with the velocity and remains proportional to the coefficient of inertia, or, on the contrary, that this coefficient of attraction remains constant? This is a question we have no means of deciding.

On the other hand, if the coefficient of attraction depends upon the velocity, since the velocities of two bodies which mutually attract are not in general the same, how will this coefficient depend upon these two velocities?

Upon this subject we can only make hypotheses, but we are naturally led to investigate which of these hypotheses would be compatible with the principle of relativity. There are a great number of them; the only one of which I shall here speak is that of Lorentz, which I shall briefly expound.

Consider first electrons at rest. Two electrons of the same sign repel each other and two electrons of contrary sign attract each other; in the ordinary theory, their mutual actions are proportional to their electric charges; if therefore we have four electrons,


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Rh two positive A and A', and two negative B and B', the charges of these four being the same in absolute value, the repulsion of A for A will be, at the same distance, equal to the repulsion of B for Band equal also to the attraction of A for B', or of A' for B. If therefore A and B are very near each other, as also Aand B', and we examine the action of the system A + B upon the system A+ B', we shall have two repulsions and two attractions which will exactly compensate each other and the resulting action will be null.

Now, material molecules should just be regarded as species of solar systems where circulate the electrons, some positive, some negative, and in such a way that the algebraic sum of all the charges is null. A material molecule is therefore wholly analogous to the system A + B of which we have spoken, so that the total electric action of two molecules one upon the other should be null.

But experiment shows us that these molecules attract each other in consequence of Newtonian gravitation; and then we may make two hypotheses: we may suppose gravitation has no relation to the electrostatic attractions, that it is due to a cause entirely different, and is simply something additional; or else we may suppose the attractions are not proportional to the charges and that the attraction exercised by a charge +1 upon a charge —1 is greater than the mutual repulsion of two +1 charges, or two —1 charges.

In other words, the electric field produced by the positive electrons and that which the negative electrons produce might be superposed and yet remain distinct. The positive electrons would be more sensitive to the field produced by the negative electrons than to the field produced by the positive electrons; the contrary would be the case for the negative electrons. It is clear that this hypothesis somewhat complicates electrostatics, but that it brings back into it gravitation. This was, in sum, Franklin’s hypothesis.

What happens now if the electrons are in motion? The positive electrons will cause a perturbation in the ether and produce there an electric and a magnetic field. The same will be the case for the negative electrons. The electrons, positive as


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514 well as negative, undergo then a mechanical impulsion by the action of these different fields. In the ordinary theory, the electromagnetic field, due to the motion of the positive electrons, exercises, upon two electrons of contrary sign and of the same absolute charge, equal actions with contrary sign. We may then without inconvenience not distinguish the field due to the motion of the positive electrons and the field due to the motion of the negative electrons and consider only the algebraic sum of these two fields, that is to say the resulting field.

In the new theory, on the contrary, the action upon the positive electrons of the electromagnetic field due to the positive electrons follows the ordinary laws; it is the same with the action upon the negative electrons of the field due to the negative electrons. Let us now consider the action of the field due to the positive electrons upon the negative electrons (or inversely); it will still follow the same laws, but with a different coefficient. Each electron is more sensitive to the field created by the electrons of contrary name than to the field created by the electrons of the same name.

Such is the hypothesis of Lorentz, which reduces to Franklin’s hypothesis for slight velocities; it will therefore explain, for these small velocities, Newton’s law. Moreover, as gravitation goes back to forces of electrodynamic origin, the general theory of Lorentz will apply, and consequently the principle of relativity will not be violated.

We see that Newton’s law is no longer applicable to great velocities and that it must be modified, for bodies in motion, precisely in the same way as the laws of electrostatics for electricity in motion.

We know that electromagnetic perturbations spread with the velocity of light. We may therefore be tempted to reject the preceding theory upon remembering that gravitation spreads, according to the calculations of Laplace, at least ten million times more quickly than light, and that consequently it can not be of electromagnetic origin. The result of Laplace is well known, but one is generally ignorant of its signification. Laplace supposed that, if the propagation of gravitation is not instantaneous, its velocity of spread combines with that of the body