Arthur Cayley FRS and the four-colour map problem

2005 ◽  
Vol 59 (3) ◽  
pp. 285-304 ◽  
Author(s):  
Tony Crilly
Keyword(s):  
Detailed Comparison ◽  
London Mathematical Society ◽  
Early History ◽  
Historical Sources ◽  
Short Contribution ◽  
Great Problem ◽  
Geographical Society ◽  
History Of ◽  
The Subject ◽  
Computer Proof

The four-colour map problem (to prove that on any map only four colours are needed to separate countries) is celebrated in mathematics. It resisted the attempts of able mathematicians for over a century and when it was successfully proved in 1976 the ‘computer proof’ was controversial: it did not allow scrutiny in the conventional way. At the height of his influence in 1878, Arthur Cayley had drawn attention to the problem at a meeting of the London Mathematical Society and it was duly ‘announced’ in print. He made a short contribution himself and he encouraged the young A. B. Kempe to publish a paper on the subject. Though ultimately unsuccessful, the work of Cayley and Kempe in the late 1870s brought valuable insights. Using previously unpublished historical sources, of letters and manuscripts, this article attempts to piece together Cayley’s contribution against the backcloth of his other deliberations. Francis Galton is revealed as the ‘go-between’ in suggesting Cayley publish his observations in Proceedings of the Royal Geographical Society . Of particular interest is that Cayley submitted two manuscripts prior to publication. A detailed comparison of these initial and final manuscripts in this article sheds new light on the early history of this great problem.

The atmospheric Cherenkov technique in y-ray astronomy: the early days

1981 ◽  
Vol 301 (1462) ◽  
pp. 611-614 ◽  
Keyword(s):  
High Energy ◽  
Early History ◽  
The Other ◽  
Current Status ◽  
Ultra High Energy ◽  
Energy Bands ◽  
Short Contribution ◽  
Basic Physics ◽  
History Of ◽  
The Subject

At this meeting papers were given by Turver & Weekes and Sreekantan about the current status in the detection of ultra-high-energy y-rays in the energy range 10 11 —10 13 eV, by means of the atmospheric Cherenkov technique. There are two objectives of this short contribution. The first is to describe briefly the early history of the subject, and the second to outline the basic physics involved, which will reveal how the technique is essentially quite different from those used in the other energy bands in the y-ray spectrum.

scholarly journals Art. II.—Chronology of the Medes, from the Reign of Deioces to the Reign of Darius, the son of Hystaspes, or Darius the Mede

1860 ◽  
Vol 17 ◽  
pp. 39-69 ◽  
Author(s):  
I. W. Bosanquet
Keyword(s):  
Early History ◽  
History Of ◽  
The Subject

The origin and duration of the empire of the Medes, which occupied 80 important a position in early Asiatic history, has been the subject of attention to many recent writers. The Lectures of Niebuhr on the Medes and Persians are probably familiar to us all. Dr. Leonard Schmitz, the translator of Niebuhr's works, has recently published his matured views on the same subject. Mr. Johannes Von Gumpach in 1852, Professor Brandis in 1853, and Jacob Kruger in 1856, have also expressed their views upon Median history and chronology; and within the last twelve months, the works of Marcus Von Niebuhr on Assyrian and Babylonian history, and the translation of Herodotus by the Rev. George Rawlinson, have appeared, embracing and commenting upon the early history of the Medes.

Past Belief

2019 ◽  
pp. 13-40
Author(s):  
Anthony Grafton
Keyword(s):  
Early Modern ◽  
Catholic Church ◽  
Saint Augustine ◽  
Fourth Century ◽  
Early History ◽  
Ecclesiastical History ◽  
Royal Road ◽  
History Of ◽  
The Subject ◽  
The Church

This chapter examines the centrality of early modern ecclesiastical history, written by Catholics as well as Protestants, in the refinement of research techniques and practices anticipatory of modern scholarship. To Christians of all varieties, getting the Church's early history right mattered. Eusebius's fourth-century history of the Church opened a royal road into the subject, but he made mistakes, and it was important to be able to ferret them out. Saint Augustine was recognized as a sure-footed guide to the truth about the Church's original and bedrock beliefs, but some of the Saint's writings were spurious, and it was important to be able to separate the wheat from the chaff. To distinguish true belief from false, teams of religious scholars gathered documents; the documents in turn were subjected to skeptical scrutiny and philological critique; and sources were compared and cited. The practices of humanistic scholarship, it turns out, came from within the Catholic Church itself as it examined its own past.

The Early History of the Gyroscope and Gyro Compass

1970 ◽  
Vol 24 (1) ◽  
pp. 86-89
Author(s):  
G. B. Lauf
Keyword(s):  
Current Literature ◽  
Early History ◽  
Historical Account ◽  
Half Century ◽  
History Of ◽  
The Subject ◽  
Gyro Compass

Most of the current literature in the field of gyroscopic theory and in the use of gyroscopic instruments for the determination of azimuth begins the historical account of the subject with the work of Leon Foucault during the period 1850-1852. But little is known of the work in this field by others during the preceding half century. In this paper, the development of the gyroscope and gyro compass is traced back to a date earlier than 1813.

scholarly journals XI.—On the Discovery of the Remains of the Priory of Austin Friars at Ludlow

Archaeologia ◽  
1863 ◽  
Vol 39 (1) ◽  
pp. 173-188
Author(s):  
Beriah Botfield
Keyword(s):  
Early History ◽  
History Of ◽  
The Subject ◽  
The Town ◽  
Graphic Description ◽  
At Will

The early history of Ludlow has been so well detailed by Mr. Eyton in his Antiquities of Shropshire, and has been so elaborately illustrated by Mr. Wright in his volume specially devoted to the subject, that I need not enlarge on its general history in endeavouring to elucidate the recently discovered remains of the Priory of Austin Friars. I cannot, however, refrain from quoting the graphic description of Churchyarde, who, writing in the reign of Queen Elizabeth, thus describes Ludlow:—The Town doth stand most part upon an hill,Built well and fair, with streets both large and wide,The houses such where strangers lodge at will,As long as there the Council liste abide.Both fine and clean the streets are all throughout,With condits cleere and wholesome water springe,And who that list to walk the Town about,Shall find therein some rare and pleasant thinge;But chiefly here the ayre so sweet you have,As in no place you can no better crave.

The Orpheus Metope from Bassai

1981 ◽  
Vol 76 ◽  
pp. 323-328
Author(s):  
Carlos Arturo Picón
Keyword(s):  
Fifth Century ◽  
Early History ◽  
History Of ◽  
The Subject ◽  
New Evidence ◽  
To Receive ◽  
The Temple

A fruitful combination of excavation, fieldwork, and research has in recent years increased our knowledge of the Temple of Apollo Epikourios at Bassai. In particular, the sculptured frieze which encircled the interior of the cella has been the subject of numerous studies, the most recent being the monograph by C. Hofkes-Brukker and A. Mallwitz published in 1975. The investigations made at Bassai by N. Yalouris and F. A. Cooper have produced important new evidence. As a result of the excavations conducted by Yalouris since 1959, the early history of the sanctuary and of the structures preceding the classical (‘Iktinian’) temple are reasonably clear. Furthermore, Cooper has shown that the ‘Iktinian’ building, the fourth in a series of temples to Apollo on the site, was not designed to receive pedimental sculpture, and that some, if not all, of this temple's akroteria were floral. The traditional attributions of pedimental and akroterial statues must be discarded, along with the theory that the ‘Iktinian’ building was started as early as the middle of the fifth century B.C.Yet, despite this progress, and the fact that the temple is one of the best-preserved monuments from antiquity, many issues remain controversial. Scholars postulate several building phases for the Classical temple. The chronology of the sculptures is still debated, as is the order of the twenty-three frieze-slabs within the cella.

Church Historians of the Early Twentieth Century: Adolf von Harnack (1851–1930)

2001 ◽  
Vol 52 (1) ◽  
pp. 83-102 ◽  
Author(s):  
W. H. C. FREND
Keyword(s):  
Historical Development ◽  
Principal Factor ◽  
Early History ◽  
Early Church ◽  
Divine Revelation ◽  
History Of Christianity ◽  
The Past ◽  
History Of ◽  
The Subject ◽  
Great Complexity

As in every other branch of learning, the study of the early history of Christianity has undergone massive changes during the last century. This has been due not only to the vast accumulation of knowledge through new discoveries, but to new approaches to the subject, together with the rise of archaeology as a principal factor in providing fresh information. The study of the early Church has as a result moved steadily from dogma to history, from attempts to interpret divine revelation through the development of doctrinal orthodoxy down the ages, to research into the historical development of an earthly institution of great complexity and of great significance in the history of mankind over the past two thousand years.

Schweigger’s (1812) chelonian types from the extinct eighteenth century Portuguese “Royal cabinet of natural history of Ajuda”: some contributions for their identification and nomenclatural implications

Zootaxa ◽  
2012 ◽  
Vol 3395 (1) ◽  
pp. 18 ◽  
Author(s):  
LUIS M. P. CERÍACO ◽  
ROGER BOUR
Keyword(s):  
Eighteenth Century ◽  
Natural History ◽  
Zoological Nomenclature ◽  
Historical Sources ◽  
History Of ◽  
The Subject ◽  
Intense Debate

The work Prodromus Monographiae Cheloniorum, published by Schweigger in 1812, has recently been the subject ofseveral studies. One result of these studies—the rediscovery of the Testudo gigantea Schweigger, 1812holotype—triggered an intense debate in The Bulletin of Zoological Nomenclature, where, among other issues in dispute,the identity and nature of the specimen indicated as the holotype for the species is put in question. Using historical sources,mostly unpublished, and analysis and comparison of taxidermic characteristics of the specimen with other specimens ofthe same nature, we can clearly trace its origin to the extinct Royal Cabinet of Natural History of Ajuda in Lisbon, fromthe “philosophical journey” of Alexandre Rodrigues Ferreira to the specimens transported to Paris by Geoffroy Saint-Hilaire in 1808, thus helping dispel any doubts regarding the identity and nature of what is being identified as the Testudogigantea holotype, along with other chelonian specimens. This information is of great importance in the current taxonomicdebate as well as in recognizing the historic importance of the Royal Cabinet of Natural History of Ajuda and Geoffroy Saint-Hilaire’s 1808 mission to Lisbon.

Footprints of "Experiment" in Early Arabic Optics

2009 ◽  
Vol 14 (1-3) ◽  
pp. 79-104 ◽  
Author(s):  
Elaheh Kheirandish
Keyword(s):  
Experimental Science ◽  
Historical Sources ◽  
History Of ◽  
The Subject ◽  
Point Of Departure

AbstractThis study traces the early developments of the concept of experiment with a view of extending the subject in both content and approach. It extends the content of the subject slightly backward, prior to the methodological breakthroughs of the Optics of Ibn al-Haytham (Alhazen or Alhacen, d. ca. 1040), which are credited as a "significant landmark in the history of experimental science." And it extends the approach to the subject slightly forward, from the premise that early science was "largely carried out in books," to a close examination of the books through which the footprints of 'experiment' may be traced. The point of departure is the Optics of Ahmad ibn 'Ī;sā, a revealing text for the early developments of concepts such as 'demonstration' and 'experiment', and one through which some modern discussions are examined and extended with reference to this and other historical sources.

The Rutherford Memorial Lecture, 1980 - Magnetic oscillations in metals

1982 ◽  
Vol 379 (1776) ◽  
pp. 1-14 ◽  
Keyword(s):  
Electronic Structure ◽  
Early History ◽  
Memorial Lecture ◽  
Metal Crystal ◽  
History Of ◽  
The Subject ◽  
Magnetic Oscillations

Oscillations in the magnetization of a metal crystal were first observed by de Haas and van Alphen in bismuth 50 years ago, and over the years this effect has developed into a powerful tool in the study of the electronic structure of metals. The lecture describes in simple terms how this has come about, with some emphasis on the early history of the subject in which Rutherford was indirectly involved.

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