Procedimientos servianos de lectura acerca de los certámenes fúnebres en Eneida V : La naumaquia (vv. 104-285)

La figura de Servio y su comentario a la obra virgiliana constituye la summa opera de la tradición escolar tardoantigua; su importancia reside porque es el resultado de numerosas estratificaciones que recogen diversos abordajes exegéticos. Al tratarse de un comentario ?continuo?, los Commentarii servianos comprenden un conjunto de saberes que examinan la obra literaria desde la perspectiva histórica y de todo aquello que se relacionaba con esta. A partir de esta mirada lectora, la comunicación se centrará en el análisis que Servio realiza sobre la naumaquia del libro V de la Eneida (vv. 104-285), donde el texto base expone una secuencia narrativa caracterizada por epicismos homéricos y pos-homéricos que el gramático desarticula, privilegiando aspectos como el lingüístico, retórico, fabuloso y histórico-arqueológico. Asimismo, se comprobará que el certamen virgiliano constituye un pretexto para instalar un nuevo contexto que garantice la continuidad del sistema burocrático imperial

El término religio, su aparición y su uso en Eneida de Virgilio

El término "religio" en la antigüedad difiere en muchos aspectos del término "religión" en la actualidad, en consecuencia, en nuestro trabajo se intenta conceptualizar el vocablo a partir de su aparición y uso en Eneida. Asimismo, se establece un paralelismo entre el concepto de pietas, término que describe la relación entre la esfera humana y la divina, religio caracterizada como la consecuencia de dicha relación y el rito como la forma pragmática de ésta última. El objetivo del trabajo es determinar las acepciones que utiliza Virgilio y destacar su funcionalidad en la obra teniendo en cuenta las relaciones sistemáticas antes nombradas. Se estudiarán los siguientes pasajes: libro II, VV. 151, 188, 365, 715; libro III, VV. 363, 409; libro VII, VV. 172, 608; libro VIII, VV. 349, 598; libro XII, VV.182

Filón de Alejandría : Obra y pensamiento. Una lectura filológica

Filón de Alejandría (30?a. C.-50? d. C.) es una figura clave para conocer la profunda relación entre Judaísmo y Helenismo en el siglo I d. C. Judío practicante, su profundo dominio de la lengua, la literatura y, de modo especial, la retórica griegas lo convierten en una personalidad extraordinaria de su tiempo, tanto por su exégesis de la Torá (o Pentateuco) como por sus escritos apologéticos, históricos y filosóficos. Su testimonio es de gran valor para todo estudioso de la Antigüedad clásica por los muchos datos que aporta acerca de la filosofía, el pensamiento, la educación y la tradición clásica en el momento histórico que le tocó vivir, precisamente en un centro cultural de excepcional importancia dentro del Imperio romano

"Recados" Sobre Grecia y Roma, en la prosa de Gabriela Mistral

Este artículo examina la recepción de la cultura clásica en la prosa de Gabriela Mistral. Frente a la retórica y la idealización academicistas, Mistral busca la Antigüedad viva en los poetas y los pueblos mediterráneos, y reivindica para América la herencia grecolatina del humanismo cristiano

El Carmen Paschale de Sedulio como poema alegórico : El simbolismo de los números

Sedulio recurre con cierta frecuencia en su Carmen Paschale a las imágenes alegóricas o simbólicas para interpretar determinados sucesos bíblicos. En este trabajo se estudia el uso y función de la alegoría en dicho poema latino y en su versión prosificada, Opus Paschale. Se presta especial atención a determinados pasajes del Carmen Paschale relativos a la simbología del número: los tres regalos de los tres Reyes Magos, los cuatro brazos de la cruz en la que Jesús fue crucificado, los cuatro evangelistas y los Doce Apóstoles

Wedges and plate-bandes: mechanical theories after De la Hire

Plate-bandes are straight masonry arches (they are called, also, flat arches or lintel arches). Ideally they have the surfaces of extrados and intrados plane and horizontal. The stones or bricks have radial joints converging usually in one centre. The voussoirs have the form of wedges and in French they are called "claveaux". A plate-bande is, in fact, a lintel made of several stones and the proportions of lintels and plate-bandes are similar. Proportions of plate-bandes, that is the relationship between the thickness t and the span s (t/s)varies, typically between 1/4–1/3 in thick plate-bandes, and is less than 1/20 in the most slender ones. A ratio of circa 1/8 was usual in the 18th Century and follows a simple geometrical rule: the centre form with the intrados an equilateral triangle and the plate-bande should contain an arc of circle. The joints are usually plane, but in some cases present a «rebated» or «stepped» form. Plate-bandes exert an inclined thrust as any masonry arch. This thrust is usually very high and it requires either massive buttresses, or to be built in the middle of thick walls. Master builders and architects have tried since antiquity to calculate the abutment necessary for any arch. A modern architect or engineer will measure the arch thrust in units of force, kN or tons. Traditionally, the thrust has been measured as the size of the buttresses to resist it safely. Old structural rules, then, addressed the design problem establishing a relationship between the span and the depth of the buttress. These were empirical rules, particular for every type of arch or structure in every epoch. Thus, the typical gothic buttress is 1/4 of the vault span, but a Renaissance or baroque barrel vault will need more than 1/3 of the span. A plate-bande would require more than one half of the span; this is precisely the rule cited by the French engineer Gautier, who tried unsuccessfully to justify it by static reasons. They were used, typically, to form the lintels of windows or doors (1-2 m, typically); in Antiquity they were used, also, though rarely, at the gates of city walls or in niches (ca. 2 m, reaching 5.2 m). Plate-bandes may show particular problems: it is not unusual that some sliding of the voussoirs can be observed, particularly in thick plate-bandes. The stepped joints on Fig. 1, left, were used to avoid this problem. There are other «hidden» methods, like iron cramps or the use of stone wedges, etc. In seismic zones these devices were usual. Another problem relates to the deformation; a slight yielding of the abutments, or even the compression of the mortar joints, may lead to some cracking and the descent of the central keystone. Even a tiny descent will convert the original straight line of the intrados in a broken line with a visible «kink» or angle in the middle. Of course, both problems should be avoided. Finally, the wedge form of the voussoirs lead to acute angles in the stones and this can produce partial fractures; this occurs usually at the inferior border of the springers at the abutments. It follows, that to build a successful plate-bande is not an easy matter. Also, the structural study of plate-bandes is far from simple, and mechanics and geometry are related in a particular way. In the present paper we will concentrate on the structural aspects and their constructive consequences, with a historical approach. We will outline the development of structural analysis of plate-bandes from ca. 1700 until today. This brief history has a more than purely academic interest. Different approaches and theories pointed to particular problem, and though the solution given may have been incorrect, the question posed was often pertinent. The paper ends with the application of modern Limit Analysis of Masonry Structures, developed mainly by professor Heyman in the last fifty years. The work aims, also, to give some clues for the actual architect and engineer involved in the analysis or restoration of masonry buildings.

Modelización del registro y proceso de datos espectrales, referidos a superficies líticas, en un ámbito arqueológico.

La determinación del origen de un material utilizado por el hombre en la prehistoria es de suma importancia en el ámbito de la arqueología. En los últimos años, los estudios de procedencia han utilizado técnicas que suelen ser muy precisas pero con el inconveniente de ser metodologías de carácter destructivo. El fenómeno de la minería a gran escala es una de las características que acompaña al Neolítico, de ahí que la revolución correspondiente a este periodo sea una de las etapas más importantes para la humanidad. El yacimiento arqueológico de Casa Montero es una mina de sílex neolítica ubicada en la Península Ibérica, de gran importancia por su antigüedad y su escala productiva. Este sitio arqueológico corresponde a una cantera de explotación de rocas silícicas desarrollada en el periodo neolítico en la que solamente se han encontrado los desechos de la extracción minera, lo cual incrementa la variabilidad de las muestras analizadas, de las que se desconoce su contexto económico, social y cultural. Es de gran interés arqueológico saber por qué esos grupos neolíticos explotaban de forma tan intensiva determinados tipos de material y cuál era el destino de la cadena productiva del sílex. Además, por ser una excavación de rescate, que ha tenido que procesar varias toneladas de material, en un tiempo relativamente corto, requiere de métodos expeditivos de clasificación y manejo de dicho material. Sin embargo,la implementación de cualquier método de clasificación debe evitar la alteración o modificación de la muestra,ya que,estudios previos sobre caracterización de rocas silícicas tienen el inconveniente de alterar parcialmente el objeto de estudio. Por lo que el objetivo de esta investigación fue la modelización del registro y procesamiento de datos espectrales adquiridos de rocas silícicas del yacimiento arqueológico de Casa Montero. Se implementó la metodología para el registro y procesamiento de datos espectrales de materiales líticos dentro del contexto arqueológico. Lo anterior se ha conseguido con la aplicación de modelos de análisis espectral, algoritmos de suavizado de firmas espectrales, reducción de la dimensionalidad de las características y la aplicación de métodos de clasificación, tanto de carácter vectorial como raster. Para la mayoría de los procedimientos se ha desarrollado una aplicación informática validada tanto por los propios resultados obtenidos como comparativamente con otras aplicaciones. Los ensayos de evaluación de la metodología propuesta han permitido comprobar la eficacia de los métodos. Por lo que se concluye que la metodología propuesta no solo es útil para materiales silícicos, sino que se puede generalizar en aquellos procesos donde la caracterización espectral puede ser relevante para la clasificación de materiales que no deban ser alterados, además, permite aplicarla a gran escala, dado que los costes de ejecución son mínimos si se comparan con los de métodos convencionales. Así mismo, es de destacar que los métodos propuestos, representan la variabilidad del material y permiten relacionarla con el estado del yacimiento, según su contenido respecto de las tipologías de la cadena operativa. ABSTRACT: The determination of the origin of a material used by man in prehistory is very important in the field of archaeology. In recent years the provenance studies have used techniques that tend to be very precise but with the drawback of being destructive methodologies. The phenomenon of mining on a large scale is a feature that accompanies the Neolithic period; the Neolithic revolution is one of the most important periods of humanity. The archaeological site of Casa Montero is a Neolithic flint mine located in the Iberian Peninsula of great importance for its antiquity and its scale. This archaeological site corresponds to a quarry exploitation of silicic rocks developed in the Neolithic period, in which only found debris from mining, which increases the variability of the samples analyzed, including their economic, social and cultural context is unknown. It is of great archaeological interest to know why these Neolithic groups exploited as intensive certain types of material and what the final destination of flint was in the productive chain. In addition, being an excavation of rescue that had to process several tons of material in a relatively short time requires expeditious methods of classification and handling of the material. However, the implementation of any method of classification should avoid the alteration or modification of the sample, since previous studies on characterization of silicic rocks have the disadvantage of destroying or partially modify the object of study. So the objective of this research wasthe modeling of the registration and processing of acquired spectral data of silicic rocks of the archaeological site of Casa Montero. The methodology implemented for modeling the registration and processing of existing spectral data of lithic materials within the archaeological context, was presented as an alternative to the conventional classification methods (methods destructive and expensive) or subjective methods that depend on the experience of the expert. The above has been achieved with the implementation of spectral analysis models, smoothing of spectral signatures and the dimensionality reduction algorithms. Trials of validation of the proposed methodology allowed testing the effectiveness of the methods in what refers to the spectral characterization of siliceous materials of Casa Montero. Is remarkable the algorithmic contribution of the signal filtering, improve of quality and reduction of the dimensionality, as well the proposal of using raster structures for efficient storage and analysis of spectral information. For which it is concluded that the proposed methodology is not only useful for siliceous materials, but it can be generalized in those processes where spectral characterization may be relevant to the classification of materials that must not be altered, also allows to apply it on a large scale, given that the implementation costs are minimal when compared with conventional methods.

The spanish professional soccer foundations. (Las fundaciones clubes de futbol profesionales en España)

Sports foundations aiming at promoting sports activities partly outline the nonprofit area with specific concern. This study attempts to know the functions, general interests of professional soccer foundations in Spain, to describe their main characteristics and to ascertain if there are significant differences among them, according to their descriptive features. A document survey and analysis was carried out, with an assistance of own establishment of documental database. The findings not only indicate a significant difference between the classification of Spanish soccer foundations and their antiquities, but also manifest the tendency of the existence of physical person in members of founders with regard to its antiquity. The results of the present work implied that there were great dissimilarities of the elaboration of regulations depending on different regions in Spain.

La habitación subterránea en la Península Ibérica : investigación geológica

La habitación rupestre en la Península Ibérica conforma un amplio conjunto de manifestaciones cuyos orígenes son difíciles de dilucidar. Existen conjuntos primitivos, posiblemente horadados durante la Antigüedad Clásica y Tardía, y otros que probablemente se originaron y excavaron en la Alta Edad Media, en los que se mezclan grupos de origen religioso y otros de probable uso defensivo. El conjunto peninsular es sin duda el más variado de Europa Occidental, pues recibió influencias árabes y usos de la cristiandad antigua, importados de Oriente Próximo, que por tanto relacionan estas manifestaciones con otras del arco mediterráneo. La supervivencia del uso de las cuevas a lo largo de la Baja Edad Media -una vez afianzada la Reconquista- es una incógnita, pero los usos rupestres volvieron a generalizarse en ciertos sectores de la Península durante la Edad Moderna, toda vez que el hábitat cuevero manifestó una eclosión relacionada con la peripecia de los moriscos, primero desterrados de sus habitaciones en el Sur y Este peninsular y luego expulsados en los albores del siglo XVII. Los que quedaron, nominalmente conversos, debieron habitar de nuevo cuevas en sus lugares de origen. Esos núcleos son los más abundantes, particularmente en la provincia de Granada y aledañas. Este substrato fue seguramente el punto de apoyo para la proliferación de las cuevas de habitación a partir del siglo XIX, en el cual un creciente proletariado agrícola y urbano necesitó de alojamientos baratos y no hizo sino imitar usos preexistentes, que se pueden rastrear en muchos de los núcleos rupestres que sobrevivieron mayoritariamente hasta bien entrado el siglo XX, y que se abandonaron gradualmente a partir de los años 60 de esa centuria. Para entonces, existían barrios de cuevas extensos en muchas provincias, destacando, aparte de las andaluzas, ciertas zonas de la Cuenca del Ebro (aragonesa, navarra y riojana), del arco periurbano de Valencia, del Sur de Madrid, de la Mancha toledana, o de las provincias de Albacete, Guadalajara, Murcia e incluso de Palencia. Los núcleos antiguos se excavaron -en razón de su origen dedicado a defensa y refugio- en lugares poco accesibles, que mayoritariamente se dan en relieves anfractuosos, en las orlas marginales detríticas y carbonatadas de las cuencas terciarias y en terrenos más antiguos de la geológicamente denominada Cuenca Vasco Cantábrica, en las cuales florecieron centros de eremitismo del primitivo condado de Castilla. También son lugares inaccesibles los riscos asomados a cantiles fluviales, cuya regularización morfológica natural ha sido causa de la ruina de múltiples hipogeos que se labraron con las mismas intenciones de refugio, defensa o retiro espiritual. Los núcleos modernos se han excavado ya en terrenos más propicios (los que componen las cuencas terciarias o "España arcillosa", mayoritariamente), y por ello observamos cómo abundan las litologías sedimentarias, que son aquellas en las que se horadaron casi todas las "colmenas" de habitación moderna en la Península. En unos casos y otros, existen rasgos comunes en lo relativo a la litología y comportamiento de los materiales excavados, y también en lo relativo a su evolución, meteorización y conservación. Se han estudiado por ello estas pautas comunes -como un posible avance para el establecimiento futuro de estudios de geoconservación del patrimonio rupestre habitado-, que se traducen en la determinación de los procesos de meteorización más característicos en los antros de la Península Ibérica -sean modernos o antiguos- y en la determinación de las relaciones más habituales entre geomorfología y tipología de las cuevas de habitación. También se exponen algunas conclusiones relativas a la resistencia de los tipos pétreos en relación a la antigüedad de los emplazamientos. Esta relación se explica bien si tenemos en cuenta que las cuevas antiguas trataban de ser lugares apartados en los que dominan rocas más resistentes -como se ha explicado- y que en las modernas se ha buscado la habitación permanente, en los materiales más blandos ocupan las depresiones terciarias del Centro, Este y Sur de la Península, colonizados no ya como refugios sino de modo seguro, y ya en arrabales "extramuros" de las ciudades. Geomorfológicamente, esta razón histórica tiene consecuencias sobre la posición de las cuevas, sobre su organización, y sobre su conservación. La extensión del dominio estudiado obliga prácticamente a bosquejar algunas de estas conclusiones geológicas, pero permite a su vez proporcionar una visión global acerca del patrimonio troglodítico desde una perspectiva geológica, y en ello radica la principal novedad de la investigación. Cave dwelling in the Iberian Peninsula comprises a great deal of examples whose origins are sometimes difficult to elucidate. There are primitive groups of caves, probably belonging to Classical and Late Antiquity, and other settlements that appear to have been created and excavated in the Early Middle Ages. Some of them are due to religious reasons and some others may probably have served for defensive uses. The Peninsular group is very likely the most diverse in Western Europe, for it was not only influenced by Arabs, but it also assimilated uses from the Antique Christendom, imported from the Middle East. In this sense, Iberian cave dwellings connect with those of the Mediterranean area. There is not total certainty about the survival of caves serving for dwelling throughout the Late Middle Ages, once the Reconquista was a fact. However, underground excavations for human habitation were once again dispread in certain zones of the Peninsula during the Early Modern period. This growth of underground habitats appears in connexion with Morisco’s vicissitudes; first of all, their removal from their settlements in South and Eastern Peninsula, and finally their expulsion from Spanish territory at the very beginning of XVII th century. Those of them who rested in Spain –and that were nominally “converts”- seem to have returned to cave dwelling in their places of origin, particularly in the province of Granada and its neighbouring zones. This substrate may have been the toehold for a new spreading of cave dwellings since XIX th century, when the increasing rural and urban proletariat returned to the pre-existent uses of caves in order to solve the necessity of affordable housing. This fact can still be detected in many of the rock settlements that have survived during a great part of the XX th century and which were gradually abandoned from the 60´s onwards. There were important cave dwelling districts in many Spanish territories by that time, and not only in Andalusia. We also find them in certain areas of the Ebro basin (those of Aragon, Navarra and La Rioja), in the peri-urban arc of Valencia, in the South of Madrid province and also in the provinces of Toledo (the so called “Mancha toledana”), Albacete, Guadalajara, Murcia or even Palencia as well. Due to their defensive and refuge uses, primitive underground habitats were dug in hardly accessible places. The majority of them are located in mountainous and rough areas, when not in the marginal borders of Tertiary basins, where coarse detritic and carbonate formations outcrop. Cave dwellings can also be found in more ancient rock masses, such as those of the Basque Cantabrian Mesozoic Basin, which is the area where hermit centres of the primitive County of Castile first flourished. Cliffs surrounding fluvial valleys are as well inaccessible places, but here we find that geological evolution has caused the destruction of many rock sanctuaries and cliff dwellings that were originally dug with the same purposes of defence, refuge and spiritual retreat. Later modern cave settlements were dug in quite more favourable terrains, mainly in the soils that compose the Tertiary basins, generally known as “España arcillosa” or “Clayey Spain”. Therefore, we find abundant sedimentary fine and medium grained lithologies, which are the ones that have hosted the majority of Modern Era warren cave dwellings in the Iberian Peninsula. Actually, both types of cave dwelling share some standards regarding the lithology of the excavated materials, and they share as well certain patterns that affect to their evolution, weathering and preservation. These common patterns have been studied here in order to determine the most characteristic weathering processes that affect the majority of the Iberian caves, both Antique and Modern. And also with a view to establish the most habitual relationships between geomorphology and typology of cave dwellings. The study may as well provide a first basis for future studies on geo-preservation of cave dwellings heritage. We also reach some conclusions about the strength of different rocks concerning the antiquity of the sites. As we have already pointed out, this relation comes from the fact that ancient caves were placed in remote or isolated locations, where harder rocks outcrop, while more modern ones result from people´s search of permanent dwelling. In this sense, the softer rocks of the Tertiary Basins of Middle, East and South Peninsula provided a secure colonization to this second and modern group. And moreover, considering geomorphological features, this historical reason has had an effect not only on the position and location of the caves, but also on their organisation/structure/distribution and preservation. The huge extension of our domain of interest almost forces to sketch out some of these geological conclusions. But at the same time it gives a global panorama of Spanish troglodyte heritage, seen from a geological perspective. And here is the main novelty of this research.

Modelo gráfico para la datación de vías romanas empedradas a partir del estudio de sus estados de frecuentación y del análisis superficial de roderas

La presente tesis doctoral se orienta al estudio y análisis de los caminos empedrados antiguos, desde la época prerromana, tanto desde el punto de vista histórico como desde el técnico. La cuantificación de la romanidad de un camino representa un objetivo importante para la mayoría de los estudiosos de la caminería antigua, así como para los arqueólogos, por los datos que ofrece acerca del uso del territorio, los trazados de caminos en la antigüedad y los tráficos asociados. Cuantificar la romanidad de un camino no es tarea sencilla debido a que intervienen multitud de condicionantes que están vivos y son cambiantes como consecuencia del dinamismo inherente al propio camino. En cuanto al aspecto histórico, se realiza una descripción y análisis de la evolución del camino en la Península Ibérica desde sus orígenes hasta mediados del siglo XX, que permite diferenciar la red itineraria según su momento histórico. Así mismo, se describen y analizan: las ruedas y los carros desde sus orígenes, especialmente en la época romana -incluyendo una toma de medidas de distintos tipos de carro, existentes en instituciones y colecciones particulares-; las técnicas de transporte en la antigüedad y las características de la infraestructura viaria de época romana, detallando aspectos generales de sus técnicas de ingeniería y construcción. Desde el punto de vista técnico, el enfoque metodológico ha sido definir un Índice de Romanidad del Camino (IRC) para la datación de vías romanas empedradas, basado en un análisis multicriterio, a partir de los distintos factores que caracterizan su romanidad. Se ha realizado un exhaustivo estudio de campo, con la correspondiente toma de datos en las vías. Se han realizado una serie de ensayos de laboratorio con un prototipo creado exprofeso para simular el desgaste de la piedra producido por el traqueteo del carro al circular por el camino empedrado y dar una hipótesis de datación del camino. Se ha realizado un tratamiento estadístico con la muestra de datos medidos en campo. Se ha definido además el concepto de elasticidad de rodera usando la noción de derivada elástica. En cuanto a los resultados obtenidos: se ha calculado el Índice de Romanidad del Camino (IRC) en una serie de vías empedradas, para cuantificar su romanidad, obteniéndose un resultado coherente con la hipótesis previa sobre la datación de dichas vías; y se ha formulado un modelo exponencial para el número de frecuentaciones de carga que lo relaciona con la elasticidad de rodera y con su esbeltez y que se ha utilizado para relacionar la elasticidad de la rodera con la geología de la roca. Se ha iniciado una línea de investigación sobre la estimación de tráficos históricos en la caminería antigua, considerando que el volumen de tráfico a lo largo del tiempo en un tramo de vía está relacionado con los valores de elasticidad de rodera de dicho tramo a través de la tipología de la roca. En resumen, la presente tesis doctoral proporciona un método para sistematizar el estudio de los caminos antiguos, así como para datarlos y estimar la evolución de sus tráficos. The present Ph. D. Thesis aims to study and to analyze ancient cobbled ways, since pre-roman times, both from the historical and technical points of view. The quantification of the Roman character of a way represents an important target for most of the researchers of ancient ways, as well as for the archaeologists, due to information that it offers about the use of the territory, the tracings of ways in the antiquity and the associate flows. To quantify the Roman character of a way is not a simple task because it involves multitude of influent factors that are alive and variable as a result of the dynamism inherent to the way. As for the historical aspect, a description and analysis of the evolution of the way in the Iberian Peninsula from its origins until the middle of the twentieth century has been done. This allows us to distinguish between elements of the network according to its historical moment. Likewise, a description and analysis is given about: the wheels and the cars since their origins, especially in the Roman time - including a capture of measurements of different types of car, belonging to institutions and to particular collections-; the transport techniques on the antiquity and the characteristics of the road infrastructure of Roman epoch, detailing general technical engineering and constructive aspects. From the technical point of view, the methodological approach has been to define an Index of the Roman Character of the Way (IRC) for the dating of cobbled Roman routes, based on a multi-criterion analysis, involving different factors typical of Roman ways. An exhaustive field study has been realized, with the corresponding capture of information in the routes. A series of laboratory essays has been realized with an ad hoc prototype created to simulate the wear of the stone produced by cars circulating along the cobbled way, and to give a dating hypothesis of the way. A statistical treatment has been realized with the sample of information measured in field. There has been defined also the concept of elasticity of rolling trace using the notion of elastic derivative. As for the obtained results: there has been calculated the Index of Roman Character of the Way (IRC) in a series of cobbled routes, to quantify its Roman character, obtaining a coherent result with the previous dating hypothesis of the above mentioned routes; and an exponential model has been formulated for the number of frequent attendances of load that relates this number to the elasticity of rolling trace and to its slenderness and that has been used to relate the elasticity of the rolling trace to the geology of the rock. An investigation line has been opened about the estimation of historical flows in ancient ways, considering that the traffic volume over the course of time in a route stretch is related to the values of elasticity of rolling trace of the above mentioned stretch by means of the typology of the rock. In short, the present Ph. D. Thesis provides a method to systematize the study of ancient ways, as well as to date them and to estimate the evolution of their flows.

Extension of Euskalduna Conference Centre and Concert Hall: A Contemporary Application of Irregular Reciprocal Frames

Reciprocal frame structures, formed by a set of self-supported elements in a closed circuit, have long been used since antiquity to cover large spans with small elements. The roof structure of the Euskalduna conference centre and concert hall extension in Bilbao, covering an irregu- lar geometry of 3000 m2 with a maximum span of 45 m, presented an interesting opportunity to revisit the concept and to apply these classical systems. Furthermore, its analysis and develop- ment led to an interesting discussion on reciprocal frames. They showed great sensitivity of these systems to the local modification of a particular element, establishment of irregular load paths, mobilisation of almost the entire sys- tem when locally applying a punctual load and, finally, its large deformability. Besides, reciprocal frames present particular construction complexities and possibilities due to the moderate length of the structural elements, the predominance of shear-only connec- tions and the necessity of the entire system to be completely erected to guarantee its stability. Euskalduna extension, completed in 2012, is one of the largest and a very par- ticular case of irregular reciprocal frame structures built in the world. It shows the formal possibilities and potentiality of reciprocal frames to respond to free and irregular geometries.

Outreach Testing of Ancient Astronomy

This work is an outreach approach to an ubiquitous recent problem in secondary-school education: how to face back the decreasing interest in natural sciences shown by students under ‘pressure’ of convenient resources in digital devices/applications. The approach rests on two features. First, empowering of teen-age students to understand regular natural events around, as very few educated people they meet could do. Secondly, an understanding that rests on personal capability to test and verify experimental results from the oldest science, astronomy, with simple instruments as used from antiquity down to the Renaissance (a capability restricted to just solar and lunar motions). Because lengths in astronomy and daily life are so disparate, astronomy basically involved observing and registering values of angles (along with times), measurements being of two types, of angles on the ground and of angles in space, from the ground. First, the gnomon, a simple vertical stick introduced in Babylonia and Egypt, and then in Greece, is used to understand solar motion. The gnomon shadow turns around during any given day, varying in length and thus angle between solar ray and vertical as it turns, going through a minimum (noon time, at a meridian direction) while sweeping some angular range from sunrise to sunset. Further, the shadow minimum length varies through the year, with times when shortest and sun closest to vertical, at summer solstice, and times when longest, at winter solstice six months later. The extreme directions at sunset and sunrise correspond to the solstices, swept angular range greatest at summer, over 180 degrees, and the opposite at winter, with less daytime hours; in between, spring and fall equinoxes occur, marked by collinear shadow directions at sunrise and sunset. The gnomon allows students to determine, in addition to latitude (about 40.4° North at Madrid, say), the inclination of earth equator to plane of its orbit around the sun (ecliptic), this fundamental quantity being given by half the difference between solar distances to vertical at winter and summer solstices, with value about 23.5°. Day and year periods greatly differing by about 2 ½ orders of magnitude, 1 day against 365 days, helps students to correctly visualize and interpret the experimental measurements. Since the gnomon serves to observe at night the moon shadow too, students can also determine the inclination of the lunar orbital plane, as about 5 degrees away from the ecliptic, thus explaining why eclipses are infrequent. Independently, earth taking longer between spring and fall equinoxes than from fall to spring (the solar anomaly), as again verified by the students, was explained in ancient Greek science, which posited orbits universally as circles or their combination, by introducing the eccentric circle, with earth placed some distance away from the orbital centre when considering the relative motion of the sun, which would be closer to the earth in winter. In a sense, this can be seen as hint and approximation of the elliptic orbit proposed by Kepler many centuries later.