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# Relativity (1931)/Section 26

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New York: Peter Smith, pages 108–110
XXVI
THE SPACE-TIME CONTINUUM OF THE SPECIAL THEORY OF RELATIVITY CONSIDERED AS A EUCLIDEAN CONTINUUM
WE are now in a position to formulate more exactly the idea of Minkowski, which was only vaguely indicated in Section XVII. In accordance with the special theory of relativity, certain co-ordinate systems are given preference for the description of the four-dimensional, space-time continuum. We called these “Galileian co-ordinate systems.” For these systems, the four co-ordinates $x$, $y$, $z$, $t$, which determine an event or—in other words—a point of the four-dimensional continuum, are defined physically in a simple manner, as set forth in detail in the first part of this book. For the transition from one Galileian system to another, which is moving uniformly with reference to the first, the equations of the Lorentz transformation are valid. These last form the basis for the derivation of deductions from the special theory of relativity, and in themselves they are nothing more than the expression of the universal ​validity of the law of transmission of light for all Galileian systems of reference.
Minkowski found that the Lorentz transformations satisfy the following simple conditions. Let us consider two neighbouring events, the relative position of which in the four-dimensional continuum is given with respect to a Galileian reference-body $K$ by the space co-ordinate differences $dx$, $dy$, $dz$ and the time-difference $dt$. With reference to a second Galileian system we shall suppose that the corresponding differences for these two events are $dx'$, $dy'$, $dz'$, $dt'$. Then these magnitudes always fulfil the condition.
$dx^{2}+dy^{2}+dz^{2}-c^{2}dt^{2}=dx'^{2}+dy'^{2}+dz'^{2}-c^{2}dt'^{2}$.
The validity of the Lorentz transformation follows from this condition. We can express this as follows: The magnitude
$ds^{2}=dx^{2}+dy^{2}+dz^{2}-c^{2}dt^{2}$,
which belongs to two adjacent points of the four-dimensional space-time continuum, has the same value for all selected (Galileian) reference-bodies. If we replace $x$, $y$, $z$, ${\sqrt {-1}}ct$, by $x_{1}$, $x_{2}$, $x_{3}$$x_{4}$, we also obtain the result that
$ds^{2}=dx_{1}^{2}+dx_{2}^{2}+dx_{3}^{2}+dx_{4}^{2}$
is independent of the choice of the body of refer​ence. We call the magnitude $ds$ the “distance” apart of the two events or four-dimensional points.
Thus, if we choose as time-variable the imaginary variable ${\sqrt {-1}}ct$ instead of the real quantity $t$, we can regard the space-time continuum—in accordance with the special theory of relativity—as a “Euclidean” four-dimensional continuum, a result which follows from the considerations of the preceding section.
Footnotes
# Relativity (1931)/Section 3

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New York: Peter Smith, pages 9–11
III
SPACE AND TIME IN CLASSICAL MECHANICS
“THE purpose of mechanics is to describe how bodies change their position in space with time.” I should load my conscience with grave sins against the sacred spirit of lucidity were I to formulate the aims of mechanics in this way, without serious reflection and detailed explanations. Let us proceed to disclose these sins.
It is not clear what is to be understood here by “position” and “space.” I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve. I now ask: Do the ‘‘positions” traversed by the stone lie “in reality” on a straight line or on a parabola? Moreover, what is meant here by motion “in space”? From the considerations of the previous section the answer is self-evident. In the first place, we entirely shun the vague word ‘‘space,” ​of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by “motion relative to a practically rigid body of reference.” The positions relative to the body of reference (railway carriage or embankment) have already been defined in detail in the preceding section. If instead of “body of reference” we insert “system of co-ordinates,” which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of co-ordinates rigidly attached to the carriage, but relative to a system of co-ordinates rigidly attached to the ground (embankment) it describes a parabola. With the aid of this example it is clearly seen that there is no such thing as an independently existing trajectory (lit. “path-curve”), but only a trajectory relative to a particular body of reference.
In order to have a complete description of the motion, we must specify how the body alters its position with time; i.e. for every point on the trajectory it must be stated at what time the body is situated there. These data must be supplemented by such a definition of time that, in virtue of this definition, these time-values can be regarded essentially as magnitudes (results of measurements) capable of observation. If we take our stand on the ground of classical me​chanics, we can satisfy this requirement for our illustration in the following manner. We imagine two clocks of identical construction; the man at the railway-carriage window is holding one of them, and the man on the footpath the other. Each of the observers determines the position on his own reference-body occupied by the stone at each tick of the clock he is holding in his hand. In this connection we have not taken account of the inaccuracy involved by the finiteness of the velocity of propagation of light. With this and with a second difficulty prevailing here we shall have to deal in detail later.
Footnotes
# Relativity (1931)/Section 30

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New York: Peter Smith, pages 125–127
XXX
COSMOLOGICAL DIFFICULTIES OF NEWTON’S THEORY
APART from the difficulty discussed in Section XXI, there is a second fundamental difficulty attending classical celestial mechanics, which, to the best of my knowledge, was first discussed in detail by the astronomer Seeliger. If we ponder over the question as to how the universe, considered as a whole, is to be regarded, the first answer that suggests itself to us is surely this: As regards space (and time) the universe is infinite. There are stars everywhere, so that the density of matter, although very variable in detail, is nevertheless on the average everywhere the same. In other words: However far we might travel through space, we should find everywhere an attenuated swarm of fixed stars of approximately the same kind and density.
​This view is not in harmony with the theory of Newton. The latter theory rather requires that the universe should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards from this centre the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of space.
This conception is in itself not very satisfactory. It is still less satisfactory because it leads to the result that the light emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects of nature. Such a finite material universe would be destined to become gradually but systematically impoverished.
​In order to escape this dilemma, Seeliger suggested a modification of Newton’s law, in which he assumes that for great distances the force of attraction between two masses diminishes more rapidly than would result from the inverse square law. In this way it is possible for the mean density of matter to be constant everywhere, even to infinity, without infinitely large gravitational fields being produced. We thus free ourselves from the distasteful conception that the material universe ought to possess something of the nature of a centre. Of course we purchase our emancipation from the fundamental difficulties mentioned, at the cost of a modification and complication of Newton’s law which has neither empirical nor theoretical foundation. We can imagine innumerable laws which would serve the same purpose, without our being able to state a reason why one of them is to be preferred to the others; for any one of these laws would be founded just as little on more general theoretical principles as is the law of Newton.
Footnotes
# Robin Adair (Glasgow)/The Wealth of the Cottage is Love

The wealth of the cottage is love.
# Robin Adair (Glasgow)/John Barleycorn

John Barleycorn.
# Robin Adair (Glasgow)/When the kye comes hame

When The Kye Come Hame.
# Robin Adair (Glasgow)/Robin Adair

SONGS
Robin Adair.
# Robin Adair (Glasgow)/The Boatie Rows

The Boatie Rows.
# Robin Adair (Glasgow)

ROBIN ADAIR;
To which are added;
John Barleycorn,
When the kye come's hame,
The Boatie Rows,
AND
The wealth of the cottage is love.
GLASGOW
PRINTED FOR THE BOOKSELLERS.
* Robin Adair
* John Barleycorn
* When the kye come's hame
* The Boatie Rows
* The wealth of the cottage is love
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
Public domainPublic domainfalsefalse
# Royal Naval Biography/Halliday, John Richard Delap

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JOHN RICHARD DELAP TOLLEMACHE, Esq (late halliday.) Rear-Admiral of the White.
This officer is the eldest son of the late John Delap Halliday, of Castlemains, in the Stewartry of Kircudbright, N.B., and of the Leasowes, in Shropshire, Esq., by Lady Jane Tollemache, daughter of Lionel, third Earl of Dysart, whose ancestors were settled at Bentley, in Suffolk, previous to the Norman Conquest.
​He entered the naval service as a Midshipman, on board the Otter sloop of war, commanded by Captain John Oakes Hardy, in 1787, and continued in that vessel till June 1789, when he joined the Adamant, of 50 guns, bearing the flag of Sir Richard Hughes, from which ship he removed into the Thisbe frigate on the coast of North America.
Mr. Halliday subsequently served in the Juno frigate, with the late Sir Samuel Hood; in the Lion, 64, Captain Finch, on the West India station; and Melampus frigate, Captain (now Sir Isaac) Coffin. From the latter he was appointed in June, 1793, to command a hired cutter employed under the orders of Rear-Admiral Macbride, at the siege of Dunkirk, and in various services on the coast of Flanders. His promotion to the rank of Lieutenant took place in 1795, on which occasion he was commissioned to the Serpent sloop of war; but soon after joined the Culloden, a third-rate, commanded by the late gallant Sir Thomas Troubridge, with whom he served on the Mediterranean station, where he was made a Commander, and appointed to act as Captain of the Nemesis frigate, in which he escorted a large fleet of merchantmen to England. His post commission bears date Sept. 19, 1796.
Captain Halliday subsequently commanded the Doris, of 36 guns, in which frigate he cruised with considerable activity and success. His next appointment was, in 1807, to the Gibraltar, of 80 guns; and from her he appears to have removed into the Repulse, 74, on the Mediterranean station. During the autumn and winter of 1810, he was entrusted with the command of the in-shore squadron off Toulon, and whilst on that service displayed great gallantry in a single-handed affair with a French squadron which had come out of port for the purpose of liberating two store-ships then blocked up at Porquerolle, and by which, but for Captain Halliday’s determined conduct, the Philomel sloop of war would inevitably have been captured.
In the spring of 1811, our officer exchanged into the Montagu, 74, and in that ship returned to England. During the ensuing four years, he commanded the Tigre, of 80 guns; and served successively on the Channel and North Sea stations, at St. Helena, and in the West Indies. His advancement to the rank of Rear-Admiral took place Aug. 12, 1819. He assumed ​the name of Tollemache in conformity to the will of his maternal uncle, the late Earl of Dysart, who died March 9, 1821.
The Rear-Admiral married, Feb. 28, 1797, Lady Elizabeth Stratford, daughter of John, third Earl of Aldborough, and has a numerous family.
Country seat.– Tilstone, Cheshire.
Town Residence.– 148, Piccadilly.
# Royal Naval Biography/Hall, William

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WILLIAM HALL, Esq. [Commander.]
Served as midshipman under Captain (now Sir Richard G.) Keats, in the Boadicea frigate; obtained the rank of lieutenant on the 1st May, 1807; and commanded the Bouncer gun-vessel, under the orders of the same distinguished officer, at the defence of Cadiz; during which arduous service he appears to have been badly wounded. He was promoted from the Bellerophon 74, (bearing the flag of Vice-Admiral Keats, on the Newfoundland station) to the command of the Sabine sloop, July 29th, 1814. He married, in 1816, Ann, youngest daughter of Peter Churchill, of Dawlish, co. Devon, Esq.
# Royal Naval Biography/Hall, William Sumner

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WILLIAM SUMNER HALL, Esq. [Post-Captain of 1817.]
Was made a lieutenant in 1801; commander. May 18, 1806; and Post-Captain, Jan. 1, 1817.
# Royal Naval Biography/Hallowell Carew, William Henry

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WILLIAM HENRY HALLOWELL CAREW, Esq. [Commander.]
A son of the late Admiral Sir Benjamin Hallowell Carew, G.C.B., and brother to Captain Charles H. Carew, R.N. He was made a lieutenant in June 1828; appointed to the Barham 50, Captain (now Sir Hugh) Pigot, Mar. 26th, 1831; and promoted to the rank of commander on the 14th Feb. 1834.
# Royal Naval Biography/Hall, Roger

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ROGER HALL, Esq. [Commander.]
Passed his examination in Jan. 1810; obtained the rank of lieutenant on the 26th Sept. 1811; served as such, under Captain Edward Brace, in the Berwick 74, on the Mediterranean station; and Impregnable 98, bearing the flag of Rear-Admiral (now Sir David) Milne, at the battle of Algiers. He was promoted to the command of the Carnation sloop, at Halifax, Nov. 10th, 1819; and put out of commission, at Plymouth, in the autumn of 1821.
# Royal Naval Biography/Halsted, George

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GEORGE HALSTED, Esq. [Commander.]
Brother to Admiral Sir Lawrence W. Halsted, K.C.B. He was made a lieutenant in 1796, and promoted to the rank of commander in Jan. 1809.
# Royal Naval Biography/Halliday, Francis Alexander

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FRANCIS ALEXANDER HALLIDAY, Esq. [Commander.]
Was made a lieutenant in 1801, and commander Aug. 29th, 1808. He lost the Ferret sloop, near Leith, in 1812; and died at Caen, in Normandy, July 25th, 1830.
# Royal Naval Biography/Halliday, Michael

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MICHAEL HALLIDAY, Esq [Post-Captain of 1799.]
This officer was born in Dec. 1765, at St. Petersburgh; where his father, a native of Dumfriesshire, N.B., practised ​as a Physician, and an inoculator of the small pox, after the introduction of that system into the Russian empire, by Baron Dimsdale. He entered the British naval service in Feb. 1782, as a Midshipman, on board the Africa of 64 guns; which ship formed part of the fleet under Sir Edward Hughes, in his last battle with M. de Suffrein, June 20, 1783; on which occasion Mr. Halliday received a slight wound in the arm. The total loss sustained by the Africa, was 5 killed and 25 wounded.
Mr. Halliday, after serving for a short time in a merchant vessel, completed his time as a Midshipman in the Crown 64, Fairy sloop of war, and Sprightly cutter. He then accepted a Lieutenancy on board the Twelve Apostles, a Russian first rate, and served under several Admirals; one of whom, Povalishin, was killed in a general battle with the Swedes. At the commencement of the war between England and the French republic, he embarked as a Master’s-mate in the Nymphe frigate, commanded by the present Viscount Exmouth; his promotion to the rank of Lieutenant in the British navy took place about Oct. 1793.
Mr. Halliday was first Lieutenant of the Inspector sloop of war, during the West India campaign in 1794; and subsequently served in the Stag frigate, St. George, a second rate, and Phoebe of 44 guns, the latter commanded by Captain (now Sir Robert) Barlow, whom he gallantly seconded in the action with la Nereide, a French frigate, which surrendered after a running fight of some duration, and close action of forty-five minutes.
In July 1798, Lieutenant Halliday was made a Commander, and appointed to the Woolwich 44, armed en flute. On the 29th June in the following year, he obtained post rank in the Leander, a 50-gun ship, which had been re-captured from the French at Corfu, and restored to England by the Russians. During the greater part of the late war, Captain Halliday commanded the Sea Fencibles at Penzance.
Agent.– ___
* ↑ See Vol. I, note at p. 425.
* ↑ See id. note §, at p. 292, et seq.
* ↑ See Vol. II. p. 45, et seq.
* ↑ See Vol. I, p. 397.
# Proclamation 7864

Delivered on 14 January 2005.
By the President of the United States of America A Proclamation
George Washington wrote, "The liberty enjoyed by the people of these States, of worshipping Almighty God agreeably to their consciences, is not only among the choicest of their blessings, but also of their rights." On Religious Freedom Day, Americans commemorate the passage of the Virginia Statute for Religious Freedom in 1786, which helped set the course for freedom of religion to be included in the First Amendment to our Constitution.
Our Founding Fathers knew the importance of freedom of religion to a stable and lasting Union. Our Constitution protects individuals'rights to worship as they choose. Today, we continue to welcome the important contributions of people of faith in our society. We reject religious bigotry in every form, striving for a society that honors the life and faith of every person. As we maintain the vitality of a pluralistic society, we work to ensure equal treatment of faith-based organizations and people of faith.
As the United States advances the cause of liberty, we remember that freedom is not America's gift to the world, but God's gift to each man and woman in this world. This truth drives our efforts to help people everywhere achieve freedom of religion and establish a better, brighter, and more peaceful future for all.
Now, Therefore, I, George W. Bush, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim January 16, 2005, as Religious Freedom Day. I encourage all Americans to reflect on the great blessing of religious freedom, to endeavor to preserve this freedom for future generations, and to commemorate this day through appropriate events and activities in homes, schools, and places of worship.
In Witness Whereof, I have hereunto set my hand this fourteenth day of January, in the year of our Lord two thousand five, and of the Independence of the United States of America the two hundred and twenty-ninth.
George W. Bush
This work is in the public domain in the United States because it is a work of the United States federal government (see 17 U.S.C. 105).
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# Proclamation 7872

Delivered on 2 March 2005.
By the President of the United States of America A Proclamation
During Women's History Month, we celebrate the achievements of our Nation's women. For generations, American women have helped build our great Nation through their leadership as writers, teachers, artists, politicians, doctors, and scientists, and in other professions. As mothers, daughters, and sisters, women have supported and strengthened American families and communities. Women are at the forefront of entrepreneurship in America, creating millions of new jobs and helping to build our Nation's economic prosperity.
We celebrate those who have broken down barriers for women, such as Jacqueline Cochran, who was the founder and director of the Women's Air Force Service Pilots during World War II and the first woman to break the sound barrier. Gerty Theresa Radnitz Cori was the first American woman to receive a Nobel Prize in the sciences, and her research significantly advanced the treatment of diabetes. In 1926, Olympic Gold Medalist Gertrude Ederle became the first woman to swim the English Channel. Marian Anderson, a Presidential Medal of Freedom recipient, opened doors in music as the first African American to perform with the New York Metropolitan Opera. Juliette Gordon Low encouraged community service and the physical, mental, and spiritual development of America's young women as founder of the Girl Scouts of the United States of America. As we work to advance freedom and peace and fight the war on terror, American women in uniform are serving at posts at home and across the world, taking great risks as they make our Nation more secure.
As we commemorate Women's History Month, I encourage all Americans to celebrate the extraordinary contributions and accomplishments of American women and to continue our progress in making our society more prosperous, just, and equal.
Now, Therefore, I, George W. Bush, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim March 2005 as Women's History Month. I call upon the people of the United States to observe this month with appropriate programs, ceremonies, and activities that honor the history, accomplishments, and contributions of American women.
In Witness Whereof, I have hereunto set my hand this second day of March, in the year of our Lord two thousand five, and of the Independence of the United States of America the two hundred and twenty-ninth.
George W. Bush
This work is in the public domain in the United States because it is a work of the United States federal government (see 17 U.S.C. 105).
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