bluuebunny/crossref_metadata_2025 huggingface dataset:
The rocking rigid pendulum
Authors: Brearley Maurice N.
Published: January 2007

This device could be a useful teaching aid. It can easily be built by students who like to use their hands; its behaviour can easily be examined quantitatively and compared with theoretical predictions; the mathematics required to analyse its motion is not at all advanced; and it provides a good exercise in mathematical modelling. The problem appears to have been overlooked in books on mechanics, which is surprising in view of the simplicity of the device and of the mathematics associated with it.
Some velocity and position calculations
Authors: Althoen Steven C. , Wyneken Matthew F.
Published: January 2007

Classically, the force of gravity between two masses m and M is given by the Principle of Universal Gravitation or the inverse-square law

where x is the distance between the centres of mass, and G is the universal gravitation constant (approximately 6.67x10–11 m3 kg–1s–2). In elementary calculus, a common application is to assume that the acceleration due to gravity near the Earth’s surface is a constant, and then to do simple velocity and position calculations. If instead we apply the above law of force, then the acceleration due to gravity of an object of mass m is a function of the distance x = x(t) beween its centre of mass and the centre of the Earth at time t. Then, on applying F = ma

so the velocity and position calculations will be different. The purpose of this note is to present these calculations and their interesting consequences in a manner appropriate for a first year calculus course. (See also Temple B., and Tracey, C.A., “From Newton to Einstein”, American Mathematical Monthly, 99, 507–521,1992).
The twenty-seven card trick
Authors: Long Calvin T.
Published: January 2007

Mathematical magic, properly used, can play an important role in the mathematics classroom. Students need to be motivated to study mathematics (or any subject), and unusual and unexpected results, though sometimes frivolous, often provide more effective motivation than the utilitarian ideas of real world applications. Such an idea was discussed by Anderson in his article on the twenty-one card trick.
The generalised Gamow-Stern problem
Authors: De Subhranil , Sen Abhijit
Published: January 2007

This problem refers to an observation made by George Gamow and Marvin Stern [1]. They found that concerning multi-storey buildings whenever one requires the lift on a particular floor, the probability of the lift coming from above or below varies according to the height of the floor concerned. It was observed that on the second floor of a seven-storey building, the probability of the lift coming from below is very small whereas it is much greater when the sixth floor is concerned. This is very similar to the case of finding the probability of a bus coming from a particular direction at a stop on a bus route.
The jealous husbands and The missionaries and cannibals
Authors: Pressman Ian , Singmaster David
Published: January 2007

The classical river crossing problem of the jealous husbands involves three couples who have to cross a river using a boat that holds just two people. The jealousy of the husbands requires that no wife can be in the presence of another man without her husband being present. This can be accomplished in 11 crossings (i.e. one-way trips). Tartaglia gave a sketchy solution for four couples but Bachet pointed out that this was erroneous and that four couples could not get across the river. In 1879, De Fontenay pointed out that four or more couples could cross the river if there was an island in the river and gave a solution for n couples in 8n – 8 crossings. Dudeney improved the solution for n = 4 and Ball noted that this gives 6n – 7 crossings for n couples.
Teaching
Authors: Orton A.
Published: January 2007

In teaching a sixth form class recently it occurred to me that there must be a more gentle, perhaps more intuitive, approach to this result than is normally found in textbooks and that some Advanced level mathematics candidates really need a simpler approach. What follows is an account of one lesson. I make no claim to originality, for I find it hard to believe that others have not previously thought of such a simple introduction. However, other teachers did indicate that they had not seen this approach before.
A geometrical creation myth
Authors: Cable John
Published: January 2007

It has struck me that axiomatic treatments of mathematics resemble the creation myths of primitive religion. In both cases the attempt is being made to provide an ordered account of something that already exists. In the one case the ordering is by deduction; in the other by the temporal sequencing of narrative. By way of illustration I offer a paraphrase of the opening pages of Hubert's Grundlagen in the style of a creation myth.

Of course, I do not use ‘myth’ with any derogatory intention. Nor do I wish to disparage historical attempts from Euclid onwards to present mathematics as a deductive system; indeed I will join the current chorus of regret that this aspect of the subject is now absent from school mathematics. The trouble is to know how best to present axiomatics. It is no longer possible, as it was for Euclid and even for Frege, to suppose that deduction leads back to ‘primitive truths’. One cannot pretend that the mathematics lies wholly in the deduction itself; as Wittgenstein observes, this is like saying that cabinet-making consists in gluing. To say that an axiomatic system is a ‘free creation of the human mind’ does not begin to address the question of purpose and motivation. Perhaps the geometrical deductive systems of Euclid and Hilbert should be seen as conceptual models, designed to make sense of geometrical phenomena, rather as a creation myth is designed to make sense of biophysical phenomena.
Leaper graphs
Authors: Knuth Donald E.
Published: January 2007

An {r, s}-leaper is a generalized knight that can jump from (x, y) to (x ± r, y ± s) or (x ± s, y ± r) on a rectangular grid. The graph of an {r, s}-leaper on an m x n board is the set of mn vertices (x, y) for 0 ≤ x < m and 0 ≤ y < n, with an edge between vertices that are one {r, s} -leaper move apart. We call x the rank and y the file of board position (x,y). George P. Jelliss raised several interesting questions about these graphs, and established some of their fundamental properties. The purpose of this paper is to characterize when the graphs are connected, for arbitrary r and s, and to determine the smallest boards with Hamiltonian circuits when s = r + 1. or r = 1. (A Hamiltonian circuit is a closed path that visits every cell exactly once.)
Averaging sequences
Authors: Sanders Paul
Published: January 2007

Starting with a finite set of numbers {xl, x2, x3, …, xn} we can generate a sequence of numbers {yi} by the rule

so that yi is the average of the previous n terms of the sequence.
Idiot-proof tiles
Authors: Grünbaum Branko , Shephard G. C.
Published: January 2007

MacKinnon introduced the interesting
concept of an idiot-proof tile. This is a
polyomino-shaped tile P
which has the property that wherever two copies
are placed (“by an idiot”) on the square grid,
then—so long as the copies do not overlap or
enclose a region (“even an idiot would not do
that”)—it is possible to adjoin further copies of
P so as to complete a
tiling of the whole plane. MacKinnon proved that
the L-triomino is an idiot-proof tile, and
indicated how one could prove that the W-pentomino
has the same property. The purpose of this note is
to extend MacKinnon’s results, and to formulate
some open problems.
Steiner-Lehmus and the automedian
triangle
Authors: Parry C. F.
Published: January 2007

The celebrated Steiner-Lehmus theorem
states that if two internal bisectors of a
triangle are equal then the triangle is isosceles.
It beautifully illustrates the point that the
converse of a theorem may be far more difficult to
prove than the direct statement. The literature of
the Steiner-Lehmus theorem is considerable with
many contributions in the
Mathematical
Gazette.

An interesting variation on this theme may
be found by examining the triangle formed by the
second intersections of the medians with the
circumcircle. Let the median point of a triangle
ABC be
G and let the medians
meet the opposite sides at
DEF and the
circumcircle again at
LMN.
Cycling digits
Authors: Burn Bob
Published: January 2007

Cyclic pairs

2 x 13 = 31 in base 5.

3 x 15 = 51 in base 7.

2 x 25 = 52 in base 8.

4 x 17 = 71 in base 9.

2 x 37 = 73 in base 11.

5 x 19 = 91 in base 11.

When you transpose the digits of a two
digit number and obtain a multiple of the
original, the original may be called a “cyclic
pair”. I have before me, a computer printout
obtained by Mr F. B. Satterthwaite of 439 East
51st Street, New York 10022, exhibiting all the
cyclic pairs for which the multiple of the
original obtained by transposing the digits is ⩽
16. This computer printout exhibits patterns of
many kinds. The most striking pattern that
Satterthwaite identified was that cyclic pairs do
not exist when the base is one less than a prime
number, but do exist for every other base ⩾ 5. His
claim may be substantiated as follows.
Looking back - and looking forward
Authors: Howson Geoffrey
Published: January 2007

The day I was asked to write this article, I was visited by an old friend. ‘Look at this Geoff’, he cried, showing me a periodical from a sister association in which a university mathematics lecturer told how he had solved a trigonometrical problem which had baffled all his engineering colleagues. ‘It’s the kind of thing we used to do when we were fourteen!’ Actually, this was not strictly true: I did it at fifteen and I was running a year in advance of my age group. It is indeed very easy to throw up one’s hands in despair about the deficiencies of today’s students and teachers. Yet, while there is much to cause concern, it is important that, if we are to take a historical view, as your editor requested, then we should bear many facts in mind other than what was achieved fifty years ago by a restricted number of pupils in a small part of our educational system.
‘Problem-solving’? Or problem solving?
Authors: Gardiner A.
Published: January 2007

David Hilbert (1862–1943) was one of the most outstanding mathematicians of the modern era. At the International Congress of Mathematicians in Paris in 1900 he presented twenty-three major research problems which he felt would be important for the development of mathematics in the twentieth century. These problems all seemed very hard, but in bringing them to the attention of other mathematicians Hilbert felt the need to stress that this should not be used as an excuse to put off trying to solve them.

‘ However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes. This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call: There is the problem. Seek its solution. You can find it by pure reason. In Mathematics there is no ignorabimus.’ [1]
Turtles on skis
Authors: Willson William Wynne
Published: January 2007

Nowadays many children meet the idea of a locus at an early age. This is because of the great (and deserved) success of LOGO as an educational tool to introduce geometrical ideas to young children. The challenge is to devise lists of instructions to make a ‘turtle’ move in a certain way. Originally the turtle would have been an actual mechanical object moving on the floor. It is now more usually an image on a computer screen. The mechanical turtle held a pen which marked out its path; the computer version* whether it looks like a cartoon turtle or an arrowhead (or even remains ‘hidden’) leaves as its trail a series of dots showing where it has been. The end product drawn on the floor or the screen is thus seen as the path of a point moving according to a prescribed set of rules. In this way children are encouraged to think of any geometrical diagram—whether it is a square or a hexagon, a rectangle or a house, a star or a circle—as a locus. Geometry is built up from collections of points.
Who named the radian ?
Authors: Cooper Michael
Published: January 2007

While looking at old copies of the journal Nature I chanced upon correspondence regarding the origin of the word radian. Textbooks today simply state it is an angular measure and have no interest in, nor space for, the history of the word. The Oxford English Dictionary states that the word first appears in print in 1879 in the second edition of the Treatise on natural philosophy by William Thomson (later Lord Kelvin) and Peter Guthrie Tait. In their discussion of angular velocity they wrote: “the usual unit angle is … that which subtends at the centre of a circle an arc whose length is equal to the radius. For brevity we shall call this angle a radian.”
Rigorous thinking and the use of instruments
Authors: Gardiner Tony
Published: January 2007

The title is a section heading from the lovely biography [1] by Florian Cajori of the English mathematician William Oughtred (15647-1660). Though Cajori was writing history he chose his subject and style to give modern readers (of 1916), and especially teachers of mathematics, something to think about.

Oughtred was a fine amateur mathematician and a thoughtful teacher. John Aubrey in his brief lives (quoted in [1p12]) wrote:

He was a little man, had black haire, and black eies (with a great deal of spirit). His head was always working. He would drawe lines and diagrams on the dust… did use to lye a bed till eleaven or twelve a clock… Studyed late at night; went not to bed till 11 a clock;… and on top of his bed-staffe, he had his ink-horne fix't. He slept but little. Sometimes he went not to bed in two or three nights.
The remarkable Ibn al-Haytham
Authors: Smith John D.
Published: January 2007

‘I saw that I can reach the truth only through concepts whose matter are sensible things and whose form is rational.’

The achievements in experimental and theoretical science of the Arab scholar al-Haytham (also known as Alhazen, from his latinized first name al-Hasan) make him as much a figure of the sixteenth and seventeenth centuries as of his own tenth and eleventh centuries.

When his writings become known in the West the importance of his contribution to optics was widely recognized and he was studied by Galileo, Kepler, Fermat, Snell and Descartes. Mathematicians remember al-Haytham chiefly for Alhazen's Problem on the reflection of light from a circular mirror, which he solved by the method of conic sections; Huygens, Gregory, l'Hospital, Barrow (and many others) later took up the problem with the new analytical methods of geometry. Al-Haytham also wrote a commentary on the postulates of Euclid, and his attempted proof of the parallel postulate has similarities to Lambert's quadrilateral and Playfair's axiom in the eighteenth century. His theory of cognition may produce yet further interest in his work.
Why are proofs difficult?
Authors: Barnard Tony
Published: January 2007

For several years, the notion of ‘mathematical proof’ has been at the centre of much discussion, writing and educational research. To a very large extent the discussions have focused on the nature of the acceptability of the reasons for a mathematical conclusion. Admittedly there have been contributions concerning the role of proof in mathematics and also the mechanics of pupils‘ proof behaviour, including works which discuss both affective and pedagogical aspects, but the dominant context has usually been one of validation. That is to say, discussions have largely been in the domain of what ‘counts as a proof’ and for whom. However, I claim that there is another dimension to proof that is of central importance in the intellectual development of students at school and university. This relates to the phenomenon in mathematical thinking in which a section of mathematical structure is mentally compressed into a single unit, small enough to fit into the conscious focus of attention at a given time, and possessing an interiority which is able to both guide manipulation of the unit and also be subsequently expanded without loss of detail. This article discusses the role of this phenomenon in the manipulation of mathematical statements involved in proof. An analysis in these terms of the dynamics of certain types of mathematical proof suggests both an explanation for students’ difficulties and a possible means of help in some cases.
Using House margins to compare casino gambling opportunities
Authors: Croucher John S.
Published: January 2007

One of the more interesting uses of mathematics and statistics is their application to everyday situations in assisting people to make informed choices about their courses of action. Nowhere is this more evident than in the application of basic mathematical principles to the range of gambling opportunities. Indeed, a new university statistics course that I give in Australia on Gambling and Sport has attracted an enrolment of over 400 students in its first year alone. In this subject we discuss the intricacies of games such as Craps, Keno, Roulette, poker machines, horse racing, and a wide variety of lotteries. The sports content of the course relates largely to using mathematics to formulate optimal playing strategies.
Gregory of St Vincent and the rectangular hyperbola
Authors: Burn Bob
Published: January 2007

The Belgian Jesuit, Gregory of St Vincent (1584 - 1667), along with Cavaleri, Fermat and Descartes was amongst those who prepared the way for the calculus of Newton and Leibniz. He was the author of one long book Opus Geometricum (1647) in which he gave a more precise account of progressions and limits than had been previously available and which Leibniz particularly valued. The term ‘exhaustion’, for the limiting process of the Greeks, is due to Gregory of St Vincent. This book contains a section on the hyperbola in which Gregory studied the area between the curve and an asymptote and this section provided the basis for Anthony de Sarasa's claim in 1649 that the area here was like a logarithm.
Snubbing with and without eta
Authors: Cundy H. Martyn
Published: January 2007

In the recent Gazette [1], John Sharp has given us a most entertaining account of the number η (eta) which is the only real root of the equation x3 - x2 - x - 1 = 0 , and its connection with the snub cube. I have been investigating this a bit further, with some results that may be of interest.
The Fermat-Torricelli points of n lines
Authors: Barbara Roy
Published: January 2007

For convenience, if P, P′ are points in the Euclidean plane R2, [PP′] will denote the closed segment . Excluding the endpoints, we get the open segment ] PP′ [. Further, if Px is a half line, ]Px will stand for Px - {P}.
Diophantine boxes
Authors: MacHale Des
Published: January 2007

I have a soft spot for geometric problems which lead to diophantine equations, that is, equations for which only positive integer solutions are sought. I have not seen the following naturally occurring problem discussed anywhere.

Problem A

A closed rectangular box has its volume numerically equal to its total surface area. If the length, breadth and height of the box are all positive integers, find all possible sets of dimensions of the box.

The solution of this pretty problem is completely elementary and can be fully understood by those with a basic knowledge of algebra.

We remark that to solve any three-dimensional problem it is often useful to step down a dimension and to consider the corresponding problem for plane figures.
A conic theorem generalised: directed angles and applications
Authors: Nickalls R. W. D.
Published: January 2007

A new and general proof of theorem [1] is presented, which accommodates directed angles and covers all possible configurations of line and conic. A sign convention for the use of directed angles in this setting is developed, and examples are given showing how this fundamental theorem can be used to establish, much more directly and succinctly, the many tangent/focus properties of conies.
Excavations at Hacılar, second Preliminary Report, 1958
Authors: Mellaart James
Published: January 2007

The second season at Hacılar lasted from the middle of August till the middle of September. The writer was in charge, assisted for part of the time by Mrs. Mellaart, and by the Director in an advisory capacity. Miss Elizabeth Beazley, Mr. David Stronach and Mr. David French dealt most efficiently with the architecture, photography and field supervision and pottery respectively. The Turkish Government was again represented by Bay Osman Aksoy. The expedition is much indebted to the Vali of Burdur, Bay Turhan Kapanlı, especially for his generous loan of a bulldozer to assist in re-levelling the site after excavation; also to the Gendarme Commander of Burdur and the Maarif Müdürü, for facilitating our relations with the peasant owners of the site, and for permission to use the large school at Hacılar as expedition headquarters.
Excavations at Polatli: A New Investigation of Second and Third Millennium Stratigraphy in Anatolia
Authors: Lloyd Seton , Gökçe Nuri
Published: January 2007

In our 1949 budget, the Directing Committee of the Institute put at my disposal a sum of one hundred pounds, for the purpose of an excavation in collaboration with the Turkish Department of Antiquities. On discussing the matter with the Director, Dr. Hamit Koşay, I found that the mound in which he was at the moment most interested was near the small modern town of Polatli, about forty miles from Ankara, on the main railway line to Istanbul. I understood from Dr. Koşay that a large part of this mound had been quarried away by peasants in need of earth for making bricks, and that, as a result, a number of whole pots and metal objects of the Copper Age had found their way to Ankara. I was subsequently shown these objects by Bay Nuri Gökçe, Director of the Hittite Museum, and a few days later visited the site in his company.

The hüyük, which takes its name from Polatli (Plate II), is situated on the outskirts of the modern town, near a spring of water. Its height is impressive, though the area which it covers suggests that the ancient settlement which it represents would have been hardly more than a village.
Harran
Authors: Lloyd Seton , Brice William , Gadd C. J.
Published: January 2007

The great interest and importance attaching to the ruins of Harran, particularly in relation to the city's age-old association with the Mesopotamian moon-cult, has never been in doubt. The remarkable degree to which, during the past generation, they have escaped the attention of archaeologists has been due entirely to their geographical inaccessibility. So many references to Harran, either under its own name or in the classical guise of Carrhae, occur throughout the length of Mesopotamian, Roman and mediaeval Arab literature, that it has acquired a strong historical personality, almost without reference to its material remains.

In fact, the few and brief investigations of the site so far accomplished by archaeological explorers, have failed to throw any light whatsoever on the outstandingly important matter of local topography in relation to the several religious shrines for which the city was famous during nearly three millennia. In the middle of the last century, it was successively visited by members of Chesney's Euphrates Expedition and the English missionary, G. P. Badger.
Le dieu Baal et le dieu Moloch dans la tradition Biblique
Authors: Dhorme Par Edouard
Published: January 2007

A mon vieil ami, le Professeur J. Garstang, en souvenir de nos visites archéologiques aux sites bibliques de jadis.—E. Dhorme.

Si J'associe ces deux dieux dans une même étude, c'est non seulement parce qu'ils représentent l'un et l'autre une conception similaire de la divinité dans les anciennes religions sémitiques, mais aussi parce qu'ils ont subi, l'un et l'autre, un même traitement de faveur, ou plutôt de défaveur, dans la transmission du texte massorétique appuyée par le grec des Septante. En revanche, si la personnalité du Baal n'a fait que s'agrandir en se précisant, grâce surtout aux découvertes de Ras Shamra, l'ancienne Ugarit, celle du Moloch a été l'objet de contestations énergiques depuis une vingtaine d'années, au point qu'une brochure, parue en 1935, annonçait dans son titre “la fin du dieu Moloch”. Nous allons donc examiner les faits qui, selon nous, exigent la présence de Moloch à côté de Baal dans le plus ancien panthéon sémitique attesté par la Bible.
Prehistoric Sites in Northwest Anatolia I. The İznİk Area
Authors: French D. H.
Published: January 2007

The Sea of Marmara straddles one of the greatest of the natural routes between Europe and Asia. Along this route, it might be expected, passed the movements of objects and materials, the trade, the transference of ideas, the migrations of peoples between Anatolia and the Aegean and Balkan worlds. One small part of this region is presented archaeologically in this article. This is not the first publication of the sites and pottery in this area but since the last presentation there have been new discoveries, both in this region and in other areas of Anatolia. At the same time it has become clear that the theories of Kulturtrift and the like can be evaluated only by an investigation of the areas and routes along which Kulturtrift may have moved. After the excavations at Nea Nikomedia in Central Macedonia, the problem of connections between Anatolia and the Aegean in the early pottery phases must be studied anew. In any assessment, Northwest Anatolia must be considered as a possible source or intermediary for ideas or developments that may have passed between these two areas.
Unpublished Inscriptions from Pisidian Antioch
Authors: Levick Barbara
Published: January 2007

It is many years since scholars began systematically to copy and publish the inscriptions of Colonia Caesarea (Pisidian Antioch), but the site of the colony and the houses and streets of the neighbouring town of Yalvaç still have much to yield. The following inscriptions, hitherto unpublished, were collected in 1955. They are arranged here according to language. The Latin inscriptions come first: a group of architectural fragments and dedications to Roman emperors, ranging widely in date but belonging for the most part to the early fourth century, is followed by some dedications to private individuals, probably persons of good standing in the colony. The Greek inscriptions may be divided into three classes: epitaphs, dedications to the gods, and some late, Christian, fragments; official tituli are wanting.

I. In the garden of the Ortokul at Yalvaç, on a broken entablature now measuring 66 cm. in length by 42 cm. in height by 36 cm. in depth (lower surface). The letters range from 7·5 to 5·5 cm. in height. The inscription is complete above, where there is a moulding, and below (on the right at least).
The Sultantepe Tablets (continued)VIII. Shalmaneser In Ararat
Authors: Lambert W. G.
Published: January 2007

Among the Sultantepe tablets one attracts attention by its unexpectedness. It is, to quote O. R. Gurney's description,

an account of the campaign of Shalmaneser III against Urartu [the Biblical Ararat], preceded by a speech in which reference is made to previous campaigns against Bit-Adini, Til-Barsip and the Kings of the Hittites.

The Sultantepe Tablets, I, p. 4, on No. 43.

Accounts of the campaigns undertaken by Assyrian kings did not ordinarily circulate along with epics, hymns, incantations and the other categories of texts which went to make up a library in an Assyrian town. Such historical accounts were incorporated in inscriptions composed to glorify the king concerned, and however busy scribes may have been multiplying copies during the reign of a particular king, the coming to power of his successor resulted in an immediate and total neglect of these inscriptions.
Report of Textiles from Çatal Hüyük
Authors: Ryder M. L.
Published: January 2007

The textiles examined were from building-level VI provisionally dated as c. 6000 B.C. They were black, stiff and brittle, apparently owing to carbonization, and comprised some found in 1962 and others found in 1963. No attempt will be made to describe the structure of the cloth except to say that no weave was evident in the 1962 specimens; one series of yarns lay parallel, with no other yarns woven through them. In places other parallel yarns were fused at an angle across (but not interwoven with) the first ones. It was as if either the warp or weft had decayed, but there were no waves in the remaining yarns to indicate where the decayed yarns had been. This was probably the material described by Helbaek as resembling fishnet without knots. The yarns were less than 0·5 mm. in width, yet despite this fineness most were clearly two-ply. The specimens found in 1963 comprised one that had apparently been like the above but had broken into many short, straight pieces of yarn. There were also two pieces of cloth clearly woven, in apparently plain weave, from even finer yarns that nevertheless appeared to be two-ply. One piece of cloth had a selvedge.
Carchemish: Reflections on the Chronology of the Sculpture.
Authors: Mallowan M. E. L.
Published: January 2007

To Seton Lloyd, who has been my friend for 45 years, and long ago met me in the field at Khorsabad, Ur and Eridu, I dedicate this essay on Carchemish, a subject on which he has written with his customary distinction.

The chronology and sequence dating of the rich series of sculpture discovered at Carchemish remains a problem, even after 60 years of investigation, but it is generally recognised that Leonard Woolley exaggerated the antiquity of some of the orthostats and it is no longer possible to assign any of them to the second millennium B.C. On the contrary, many critics will now support Frankfort's view that none of this particular series of sculptures could have been executed without an awareness of neo-Assyrian art.

Frankfort's view is also shared by Akurgal who has judiciously assigned much of the Carchemish sculpture to a period ranging from the middle of the ninth to the latter half of the eighth century B.C. and has justified his sequence dating by reference to the development of sculpture at Zincirli where we have a sequence of carving which ranges from about 850–830 B.C. (Kilamu) or possibly a generation earlier, through Panammu I c. 790 B.C., Panammu II c. 760 B.C. and Bar-rakib c. 740 B.C.
Urartian Irrigation Works.
Authors: Burney Charles
Published: January 2007

If there is one aspect of life in the ancient Near East which may be taken as a common factor between lands and cities so far removed in space and time as Sumer and Urartu, Eridu and Van, it is irrigation. This is a subject crying out for more research, especially on the ground. Here too is a link between Seton Lloyd's excavations at Eridu and in the Diyala region, his publication of Sennacherib's acqueduct and his later interest in Urartu. The writer can claim first-hand knowledge only of the last. Without Seton Lloyd's encouragement in the Institute at Ankara and likewise during the weeks spent as an assistant during the first season's excavations at Beycesultan, the writer would scarcely have set out on his first archaeological survey in northern Anatolia, followed by that in the Pontic region of Tokat and Amasya (1955). These two surveys were but the prelude to those of 1956 and 1957 in eastern Anatolia. These, undertaken initially in the expectation of discovering mounds of the Bronze Age and earlier periods, became instead largely a revelation of the great number of Urartian sites, including numerous fortresses recognizable as such from their surface remains.
Valerius Valentinianus, Praeses of Isauria.
Authors: Hall A. S.
Published: January 2007

Since it was my good fortune to begin working in Anatolia while Seton Lloyd was Director of the Ankara Institute, and to enjoy his friendly encouragement for several years, I am glad to have the opportunity of dedicating this article to him.

In June, 1958, the following inscription was discovered by the writer in Yazdamıköy, one of a group of villages near the ancient site of Isaura (Zengibar Kalesi), which is situated on a mountain crest some 10 km. east of Bozkır and the valley of the Çarşamba Çayı. Large quantities of material from the site have been recorded within these villages since Hamilton first visited the area in 1837. There can, therefore, be little doubt about the provenance of this particular block of limestone, slightly moulded at the top, broken bottom left and to right; H. 0·34, W. 0·93, Th. unknown (buried behind), letters 2·5 cm.
Two Notes on Lydian Topography
Authors: Lane Eugene N.
Published: January 2007

In my recent publication of the epigraphical evidence for the cult of the god Men, I made a couple of topographical equations on which further comment is necessary. One of these (Kula/Koloe) has been generally abandoned in recent scholarship, but I think that it is defensible, and would like to take this opportunity to defend it. The other (Ayazviran/Koresa), I would like to withdraw, in favour of proposing the possible equation Köres/Koresa.

Following an old tradition, based on the principle of survival of proper names, I stated that the present day town of Kula was called Koloe in antiquity. Koloe was a widespread place-name in Greco-Roman Lydia. The name is apparently of non-Greek origin, and whatever it may have meant, it seems to have been very much suited to place-names. Three places in Lydia are definitely known to have borne the name in antiquity: a lake, a polis, and a katoikia. At some Koloe in Lydia, Attalus I of Pergamum defeated Antiochus Hierax in 229/8 B.C.
A New Duplicate Fragment of the Hittite Instructions to Temple Officials
Authors: Hulin P.
Published: January 2007

This piece was shown in Ankara some years ago to the present writer, whose copy of it is reproduced overleaf. It contains most of what corresponds to lines 2–14 of column III of the best preserved text (Bo. 2019, KUB. XIII, 4, Sturtevant's A) of the instructions to priests and temple officials published, with supplements from six fragmentary duplicate pieces, by E. H. Sturtevant in JAOS. 54 (1934), 363–406 (at pp. 380–1, 402–3), and, with improvements but with omission of some fragmentary passages, by Sturtevant and G. Bechtel in A Hittite Chrestomathy (1935), 127–74 (at pp. 137, 156–7, 172); five more fragments have been published as KUB. XXXI, 92–5; XL, 63.

None of these eleven fragments contains the part of the instructions surviving on the present piece, though what appears to be a similar double vertical ruling at the right of the fragment Bo. 3914 (KUB. XXVI, 31, Sturtevant's F, belonging also to column III and beginning at a point a little after the point at which the text of the present piece ends) permits the suggestion that that fragment may have belonged to the same tablet as the present piece. But the condition in which Bo. 2019 itself has survived in the passage partly covered by the present new fragment leaves little room for completion or improvement of the text; most of the variants now offered, and listed below the following transliteration, are orthographic.
The European Merchants in Angora
Authors: Barnett R. D.
Published: January 2007

Ties linking Britain with Ankara go back many centuries; probably the earliest evidence of them was published by David French in the last number of this Journal, in the form of a letter from Ambassador William Harborne to James Towerson dated to 1583; other evidence can certainly be gleaned from the extensive papers of the long extinct Levant Company. The present writer is able to point to a little more evidence formerly visible in Ankara itself.

Angora, the modern Ankara, now so easily reached by rail and air services, under the ancien régime must have seemed to Europeans almost forbiddingly remote.

The wildest guesses were made about its population and opinions fluctuated as to its attractions and importance. In 1700, a French traveller, Tournefort gave its population as 40,000 Moslems, 5,000 Armenians and 600 Greeks. Pococke (1737) speaks of 10,000 Christians. Poujoulat (1836–7) describes it, apart from Nicomedia, as the poorest Turkish town he had seen. He estimated its population as 20,000 Turks, 3,000 Catholic Armenians, 700 Greeks and 500 Jews. Yet in 1834–7 von Tschihatscheff spoke of it as having 8,000 Catholic Armenians, 500 Armenians of the national church, and 1,500 Greeks.
Prehistoric Sites in Northwest Anatolia: II. The Balıkesir and Akhisar/Manisa Areas
Authors: French D. H.
Published: January 2007

In this article I have presented the second synthesis of information and material gathered from surface survey in Western Anatolia. This article, in fact, completes the publication of the work that I undertook in 1959–60 when I was joint Scholar of the British Institute of Archaeology at Ankara. My aim in 1959–60 was to discover what prehistoric remains could be found, especially in the Akhisar/Manisa region but also in the area around Balıkesir. Both regions were archaeologically almostterra incognita—at least in the publications.

I have, therefore, felt that it is justifiable to publish the information that was recorded ten years ago although, at the same time, it must be admitted that aims and methods in archaeology have radically changed since 1959, and that methods of illustration and publication have changed along with the aims themselves. Much of modern archaeology is turning (? rightly) to the new approaches—the new “models”—but analytical archaeology, however propounded, is at the mercy of the data available for it. Data must still be collected, especially from sources where basic, primary information did not exist before. It is perhaps unfortunate that in Anatolia, until recently, scant attention has been paid to the accurate compilation of basic information.
The Babil Stele of Assurnasirpal
Authors: Hawkins J. D.
Published: January 2007

The three fragments of a much worn Assyrian stele to be seen in Adana Museum were not, as might have been supposed, found locally in Cilicia. Instead they have been identified as pieces found by C. F. Lehmann-Haupt in the spring of 1899, in the course of a journey down the Tigris from Siirt to Mosul. They were discovered at the village of Babil, some 25 km. south-west of the modern town of Cizre, which is situated in south-eastern Turkey on the Tigris, at the point where the present Turkish-Syrian border joins the river. Babil also now lies directly on the Turkish border. Lehmann-Haupt related the site, circumstances and finds on two occasions in his published works. The finds included “eine Anzahl von Steinfragmenten mit assyrischen Inschriften”, six of which he described perfunctorily and with considerable inaccuracy. He correctly identified parts of a stele of Assurnasirpal II, but did not attempt any further reading of the worn and broken text.
Regio Ipsina et Moeteana
Authors: Ballance M. H.
Published: January 2007

This article stems from the writer's discovery in 1955 of an inscribed sarcophagus at Prymnessus, the modern Süğlün, 8 km. south-east of Afyon. It had been intended to follow this up by a reexamination of the stone itself and by an intensive survey, on the ground, of the ancient topography of the valley of the Phrygian Caÿster. But the necessary field-work has been prevented by various considerations, both inside and outside Turkey, and it seems only fair to others interested in this part of Phrygia to publish the inscription and draw at least preliminary conclusions from it.

Süğlün; reused as a horse-trough in a fountain, Güvercinlik Çeşmesi, at the south end of the village. Pink trachyte sarcophagus, moulded above, buried below, with tabula ansata. Height 0·57 m. plus, width 2·07 m., thickness 0·83 m., letters 0·03–0·04 m.
Early Neolithic Skeletons from Çatal Hüyük: Demography and Pathology
Authors: Angel J. Lawrence
Published: January 2007

The opportunity to study the early farming population at Çatal Hüyük came to me through the foresight and kindness of the excavator, Mr. James Mellaart, and the successive Directors of the British Archaeological Institute Mr. Michael Gough and Dr. David French. I am most grateful to them for the opportunity to publish this report. In the autumn of 1967 I worked in collaboration with Dr. Denise Ferembach of the CNRS in Paris, who is reporting on the morphology and geographic relations of the population. We worked in the laboratory of Professor Enver Bostancı, head of the department of Palaeoanthropology at the University of Ankara, who most kindly aided us and allowed us facilities for study. The successive Directors General of Antiquities and Museums, Bay Mehmet Önder and Bay Hikmet Gürçay, also gave us permission to study this material and expressed gracious interest in it.
A Sanctuary of Leto at Oenoanda
Authors: Hall Alan
Published: January 2007

Among the new inscriptions which have come to light during the Oenoanda surveys of 1974 to 1977 is a group of four which are of particular interest in view of their subject matter and place of origin on the site. All were found close together in 1975, among recently overthrown and heavily disturbed ruins of a building or buildings constructed against a cliff face on the lower, north-western slopes of the site. These ruins lie some 300 m. northwards along the hill-side from a set of rock-cut tombs, which were first reported by Rudolf Heberdey and Ernst Kalinka in their monograph of 1897. One inscription from this group had already been published by Maurice Holleaux and Pierre Paris in 1886 and names Κατάγραφος son of Ἀρτέμων as ἱερεύς πρὸ πολέως Λητοῦς διὰ βίου.
Forschungen im Artemision von Ephesos von 1976 bis 1981
Authors: Bammer Von Anton
Published: January 2007

Der letzte größere Bericht zum Artemision von Ephesos beruhte auf den Grabungen bis 1975 mit einem kleinen Nachtrag aus der Grabung 1976. Auch im Katalog zur Ephesosausstellung in Wien 1978 erschien ein Bericht über neue Forschungsergebnisse, insbesondere das Modell des spätklassischen Altares (Pl. XIa). Außerdem wurde anläßlich eines Kongresses der École Française de Rome 1980 über “Architecture et Société” auch zu neueren Ergebnissen am Artemision Stellung genommen. Ansonsten war nur den jährlich erscheinenden Berichten über die Grabungen in Ephesos im Anzeiger der Akademie der Wissenschaften in Wien einiges zu entnehmen.

Eine Überraschung der Grabung im Jahre 1977 war die Freilegung des Fundamentes eines apsidalen Baues, mit seiner Apsis nach Osten. Erhalten ist das Fundament aus kleinen Hausteinen (Pl. XIb). Der südliche Ast des Fundamentes dürfte irgendwann teilweise zerstört worden sein, weil aus seinen Resten eine Verbindung zur schräg laufenden Rinne aus Kalkmergelsteinen hergestellt worden ist. Der Boden des Apsidenbaues ist noch erhalten, er bestand aus einem ockerfarbenen Lehm-Sandgemisch. Auf dem Boden fand sich das Fragment eines polychromen Gefäßes mit einem Gesicht am Gefäßrand (Pl. XIc). Das Fragment stammt offenbar aus jüngerer Zeit als der Apsidenbau.
Ear Studs for Greek Ladies
Authors: Brein Friedrich
Published: January 2007

By the following lines I should like to express my gratitude to Fritz Eichler, the late Director of the Austrian Archaeological Institute, a gentleman whose like may not be found so easily nowadays, who made possible A. Bammer's work at the Ephesus Artemisium, and who directed my interest to East Greek art and artistry as well, since at the moment times are hard for an archaeologist who works on other than Roman Imperial trifles at Efes City.

When Bammer came across bobbin-like objects made of rock crystal, some people thought that he had found parts of Wood's surveying devices or the like, in spite of the fact that they came without any doubt from stratified layers dated between 650 and 550 B.C. Besides, Hogarth had unearthed some 15 pieces of this type already. These “large studs or buttons”, as Hogarth had called them, are hyperboloids of specific shape turned on a lathe, as can be inferred by a faint deepening in the centre of the larger side of some of these hyperboloids. The larger side is always concave, the smaller one plane or slightly convex.
Dalbergia Sissoo Roxburgh
Authors: Maxwell-Hyslop K. R.
Published: January 2007

The identification of Old Persian yakā- with Dalbergia sissoo Roxburgh was suggested by Ilya Gershevitch in a memorable article in 1957 after extensive investigations in the Bashākard mountains of northern Iranian Makran (east of L. 58, c. 100 miles north-east of Jask). The sissoo has been defined as a “large deciduous tree, bark grey, heartwood brown with darker veins, leaflets 3–5, broadly elliptical or ovate”, and K. A. Chowdhury has studied its distribution in northern India, starting from the Indus, spreading east to Assam, sticking to the sub-Himalayan tracts and usually going up to 1,000 m. above sea level. It also extends far into the plains along river banks. In Baluchistan it grows in the Suleiman range between the Indus and the Zhob rivers, having been noted as early as 1890 by J. H. Lace in his study of the vegetation of Baluchistan in the Wam Tangi forest situated in the limestone ranges in the Hurnai district, where it reached a height of 35 feet. Its distribution within Pakistan includes the districts of Dera Ghazi Khan, Dera Ismail Khan, Bannu, Hazara, and it can be seen in Peshawar growing on the University campus and in front of Dean's Hotel (Pl. XXIIIa). A specimen from Nepal was given to Sir Max Mallowan in 1973 and is illustrated here (Fig. 1).
The Gymnasium at Alexandria Troas: Evidence for an Outline Reconstruction
Authors: Smith A. C. G.
Published: January 2007

The principal ruin at the site of the city of Alexandria Troas entered the consciousness of European travellers anonymously, and was referred to simply as a castle or palace; when Thomas Coryate saw it in 1613 he was overcome by its magnificence and concluded, since he thought he was at Troy, that it must have been the main castle or palace of the city, but already in Lithgow's time it was known simply as “The Palace of Priam”. The name was to persist for well over a century, but by 1675 Spon had recognised it as Roman work and Wheler, basing his conclusions (as later did Pococke) on a comparison with the Harbour Gymnasium at Ephesus – at that time commonly regarded as the Temple of Diana – thought it might be a temple. Chandler, in 1764, called it a gymnasium; Lechevalier and Clarke, and after them Choiseul-Gouffier, were confident that it was a bath-building, and although Prokesch-Osten eccentrically disagreed and Texier and Napier pointed out that the two functions were not incompatible, Koldewey in his study called it a bath, and that designation is still with us.
Troy and Anatolian Early Bronze Age Chronology
Authors: Yakar Jak
Published: January 2007

The use of an absolute chronological framework based on tree-ring calibrated C-14 dates has been recently proposed by D. F. Easton in his attempt “… to come to grips with the crucial and difficult dating of Troy” (Easton 1976:146). Easton points out that unlike Tarsus, whose relative dating vis-a-vis Mesopotamia and Egypt is stable, Troy's relative chronology is not agreed upon and this “impinges not only on Anatolia, but on the Aegean and Bulgaria as well”.

In establishing his chronology Easton uses, in addition to “the normal comparative methods”, two sources: (a) radiocarbon dates which, after calibration, especially when using Suess's calibration curve, affect both relative and absolute dating, (b) his reassessed stratigraphy of the Bronze Age levels at Troy (Easton 1976; 1977).

Easton in his new chronological structure has not taken into consideration certain facts and opinions surrounding tree-ring calibrated radiocarbon dating. In view of the persisting controversy regarding this scientific dating method, it is premature, at least as far as Anatolia is concerned, to replace the relative dates derived from historical synchronisms with calibrated “absolute” C-14 dates.