gg av. Es En poi vad es ix & THE - GEOMETRY - AND - OPTICS OF ANCIENT - ARCHITECTURE. THE-GEOMETRY-AND-OPTICS OF ANCIENT - ARCHITECTURE ILLUSTRATED-BY:-EXAMPLES- FROM THEBES-ATHENS- AND: ROME. BY JOHN -PENNETHORNE * Esq. ASSISTED : IN: THE: DRAWING :- AND: COLOURING: OF: THE - PLATES AND:.IN: THE- ARRANGEMENT OF: THE :- TEXT BY JOHN « ROBINSON ARCHITECT. SM aaa LONDON + AND « EDINBURGH: PUBLISHED - BY - WILLIAMS + AND + NORGATE. MDCCOCLXXYVI1II. LANDSCAPE ARCHITECTUKE Lithographed and Printed by C.-F. Rui, at No. 8, Casrir Strep, HorBoRrRN, LoNDON. Farrand Gift PREFACE. A FEW remarks as to the origin and growth of the present work will be sufficient to explain how the first ideas relating to the subject originated, and also to account for the delay which has occurred in the publication of the same. In the year 1830 I left England as a travelling architectural student, and after a winter spent in Rome, and a few months at Naples and in Sicily, 1 embarked for Athens in 1832. 1 was at once impressed with the beauty of the designs of the architectural remains in the Acropolis of Athens, and with the extreme accuracy with which they were executed in the marble, and 1 was convinced also that there was much yet to be observed with regard to the colouring of the Greek works of Architecture, but I was not aware at the time that in those works we possessed some of the earliest and most valuable remains of the ancient (reometry. I therefore carefully studied all that I was able to observe of the coloured Ornaments traced upon the several forms of the Mouldings, also the colouring still to be found on the Ceilings and on the Entablatures of the Parthenon, of the Temple of Theseus, and of the Propylsea, and with the information thus collected I spent the winter of 1833 at Thebes, in Upper Egypt, for the sake of instituting a comparison between the colouring of 141 1i PREFACE. the Egyptian and of the Grecian Temples. This comparison convinced me that the origin of the Ornaments that were employed in Greek Archi- tecture, and that the Grecian ideas of colour were derived from the same Egyptian source, I therefore returned to Athens for the sake of studying the Temples there more carefully, and afterwards arrived in England in the beginning of the year 1835. This long investigation of the Monuments led me to the considera- tion of the refinements of Grecian Architecture, namely, to the study of the Proportions, of the entasis in the shafts of the Columns, of the curved profiles of the Capitals and of the Mouldings, ete.; and I saw no reason to doubt the assertion of Vitruvius, that the horizontal lines were all convex lines. In 1837 1 again visited Athens to make more accurate observations upon all the curved lines and upon the measurements generally: about the same time, and, I believe, quite independently of myself, Herr Shaubert, a German Architect, residing in Athens, had observed a certain amount of convexity in the lines of the Upper Step of the Parthenon. I then determined, with a small level, so far as the state of the ruins permitted, the amount of the convexity in the Steps and in the Entablatures of the different Athenian buildings, and I also measured the entasis of the Columns, and moulded in wax all the smaller curves of the Capitals, of the Cornices, and of the Mouldings, and traced the sections upon paper. Failing health at the time prevented my doing more, and I finally returned to England and laid the foundation of the present work. Study convinced me that the subject required still further investi- cation and more accurate data than 1 possessed at the time. The Parthenon PREFACE. 111 was still encumbered with ruins, so that I could not ascertain the full amount of curvature in the Upper Step on the return sides; the Acropolis had not been cleared down to the original level of the lines of road; the position of the pedestal of the great statue of Minerva had not been ascer- tained, and the Propyleea was surrounded by modern fortifications; thus without the true levels and the true plan of the whole of the Acropolis the requisite calculations could not with certainty be made, as the original given quantities were still unknown. I therefore laid the work aside, not intending to resume the subject, feeling that I did not possess sufficient data to enable me to complete it, nor, at the time, the means of making any further researches, and that it was not an investigation likely to receive the support either of the Knglish Government or of any private Society, so I became engaged for some years in agricultural pursuits. In the year 1860 an illness compelled me to relinquish agriculture, and forced me into great retirement, when looking over Mr. Penrose’s work on Athenian Architecture, published by the Society of Dilettanti, and Mons. Beule’s work, “ 1 Acropole d’Athenes,” I found that nearly all the information I required had been collected between the years 1846 and 1854; I therefore resumed the work, partly for amusement, and partly from a wish not to leave my papers unfinished, and with the fresh data thus acquired I made all the calculations again, and corrected some errors relating to the theory of the horizontal lines and other details, into which I had been led. The object of Mr. Penrose in visiting Athens in 1846 was especially to measure the “ curvature of the horizontal lines and the inclinations of 1v PREFACE. “ the Columns; also, to observe the mathematical knowledge exemplified by “ the Greeks in the forms of the Mouldings, and especially in the hyperbolic “ entasis of the Columns.” For this purpose Mr. Penrose employed instru- ments of a more delicate nature than are generally used for admeasure- ments in Architecture, and nothing can exceed the scientific accuracy of all his observations. With regard to the curvature of the horizontal lines and to the entasis of the Columns, the dimensions taken by Mr. Penrose supersede all those previously obtained, for he has certainly proved by measurement that all the horizontal lines are very correct arcs of circles, and that the entasis of each Column is the true arc of a hyperbola. All his general measure- ments are more to be trusted than any previously made : 1 have, therefore, in the following work adopted them whenever 1 have been able to do so, in preference either to my own or to those in Stuart and Revett’s valuable work, “The Antiquities of’ Athens,” published in 1762. Also, without Mr. Penrose’s general plan of the Acropolis, on which the levels of the original roads and platforms below the Upper Step of the Parthenon are carefully noted, I could not have made my calculations with any degree of certainty. For the profiles of the Capitals, and of the Mouldings and smaller curves, I have used either accurate casts taken in wax, or the forms traced upon paper direct from the marble, in preference to measurements, however carefully made. The work of Mons. Beule, “I’Acropole d’Athenes,” published in 1862, is a valuable addition to our knowledge of the original plan of the Acropolis, particularly with regard to the Propyleea, and to the plan of the marble staircase of approach to the central Portico. PREFACE. Vv In addition to all the observed facts derived from the Monuments, which have been slowly accumulating since 1762, there are certain allusions, in the works of Plato, of Aristotle, and of Vitruvius, to the ancient principles of Greek Architecture and Art, which throw some light upon the subject, and these allusions are made perfectly intelligible by the recovery of the original laws. The observations which have been made on the remains in the Acro- polis of Athens lead to the conclusion that these works were originally laid down and calculated with mathematical accuracy, and this being the case, we can inductively recover the laws by which they were designed, and demonstrate them by recalculating the same works step by step, in the same manner as have been demonstrated the laws in Astronomy, and in all the other exact Sciences; and it is some of the mathematical principles of the Greek Architects and Artists that I have endeavoured, however imperfectly, to recover and lay down in the following work. These principles were evidently the result of many centuries of careful thought and study by the leading scientific minds of the ancient world ; we can discover the germ of them in the best period of egyptian Architecture, at least B.C. 1300; we can trace them through all the works | of the Greeks that remain to us, either in Asia Minor, in Magna Gracia, or in Greece proper, and we find their greatest development in the Greek works of the age of Pericles, B.c. 450, at which period all the mathematical and artistic talent of’ the world was collected in Athens as a centre; and the accumulated knowledge thus brought together was applied by the Greeks to the restoration of their Temples in the Acropolis, which had all been destroyed by the Persians. If the remains of ancient Art are worth measuring and publishing, vi PRBEFACLE. I see no reason why they should not be restored and laid down as they were originally conceived and designed, or why the scientific thought and intellect that was once brought to bear upon them, and which still exists in their ruins, should not be recovered and preserved to us. The Greek ancient mind has influenced us in Geometry, in Litera- ture, and in Philosophy, without retarding our advance in knowledge, and there is no just reason why it should be totally excluded from all influence upon the Architecture and the Arts of Europe, when we know that Art allied with the Geometry was carried by the Greeks to the highest state of pertection. I am fully aware of the many literary imperfections that will be found in the following pages, for I have felt it to be far easier to recover a few simple laws and principles than to embody them in the form of a connected work; but if these principles are in any degree true, as I believe them to be, other minds more trained in classical and scientific acquirements, will ultimately give a fuller development to what I have only imperfectly traced out. JOHN PENNETHORNE. HAMSTEAD, NEAR YARMOUTH, Ist or WicHT, 1878. I cannot close these few remarks without expressing my obligation to Mr. John Robinson (who obtained the Gold Medal from the Royal Academy of Arts in 1851, and who was afterwards awarded the Travelling Studentship for three years) for the time and consideration he has given to the drawing and arrangement of the Plates, to the colouring of the PREFACE. vil Ornaments and Entablatures, and also to the preparation of the diagrams and letter-press for publication. Some errors have been corrected, and the work improved by the study he has bestowed upon it, and without his assistance I should have failed in the recovery of the method of describing the spiral lines forming the volutes of the Ionic capitals. J.-P. CONTENTS. INTRODUCTION PART 1. THE FIRST GIVEN PROPORTIONS. CHAPTER IL —PROPORTION . : : The Proportions of Egyptian Architecture and Sculpture . CHAPTER II..-THE FIRST GIVEN PROPORTIONS The First Given Proportions of the Athenian Porticoes, as derived from observation CHAPTER III..-THE PROJECTIONS . The Given Projections in the several Athenian Porticoes of the Steps and of the Details of the Intablatures, and the First Inclination Inwards of the Masses The Pediments : ; The Return Sides of the Temples Dimension CHAPTER 1V.—POSITION - , : . : The Plan of the Acropolis of Athens, showing the Roads of Approach and the Position of the Principal Works General Remarks PART 11. THE APPARENT PROPORTIONS. CHAPTER I.—INTRODUCTION Observations on the Geometry of three Dimensions, and on the Trigonometrical Calculations applied to Architecture PAGE 15 16 19 21 24 24 27 27 29 32 53 38 45 46 CHAPTER CHAPTER CHAPTER CHAPTER CHAPTER CONTENTS. The Geometry of three Dimensions Plane Trigonometry : ; : To determine the Point of Sight and Position of the Design upon the Horizontal Plane XY, and Vertical Planes Y Z and X Z To determine upon the Given Plane H OZ the True Apparent Perpendicular Magnitudes measured by the Visual Angles, and the True Height of the Ixecuted Design at the Angle nearest to the Given Point of Sight O . To Determine the Apparent Height , : : The Application of the Theory of the Corrections to Selected Fxamples 1I.—THE PARTHENON . : : ] : The North-West Angular Design and the South-East Angular Design, showing the True Heights Trigonometrically determined upon the Plane HO Z . III... THE ERECHTHEIUM The East Portico The South Portico The North Portico IV...THE PROPYLAA The West Portico The North Wing The Temple of Victory V.—-THE TEMPLE OF THESEUS ; The North-East Angular View of the East Portico Corrected VI.—ALGINA AND PRIENE , ; : : The Temple of Jupiter Panhellenius at Afigina, and the Temple of Minerva Polias at Priene Summary PART Ll1l. THE CURVES OF THE HORIZONTAL LINES CHAPTER CHAPTER I.—INTRODUCTION II..-THE OBSERVED FACTS RELATING TO THE HORI- ZONTAL CURVED LINES 47 49 50 52 59 57 60 61 64 65 66 67 68 71 71 72 73 4 75 /¥ | 81 84 CONTENTS. The Observed Curvature of the Horizontal Lines in the Entabla- ture of the Inner Court of the Temple of Medinet Haboo The Observed Difference of Level found to exist in the Four Angles of the Parthenon : : The Measured Horizontal Curvature of the Lines in the Upper Step and in the Architrave of the Parthenon, and of the Temple of Theseus : : ; The Character of the Horizontal Curved Lines CHAPTER III..-THE CALCULATION OF THE HORIZONTAL CURVED LINES : : ; The Calculated Horizontal Curvature of the Lines in the Upper Step of the Parthenon and of the Temple of Theseus . The Calculated Appearance of the Horizontal Lines when Viewed from the Given Point of Sight O The Calculated Concave Appearance of the Horizontal Lines of the Portico of the Parthenon . Conclusion PART 1V. THE COLUMNS. CHAPTER I—THE ORIGIN AND PROPORTION OF THE COLUMNS. The Origin and Proportion of the Egyptian Columns The Proportions of the Greek Columns CHAPTER II.-THE ANCIENT APPLICATION OF THE CONIC SEC- TIONS TO THE DESIGNING OF WORKS OF ART . CHAPTER III.-THE CAPITALS ‘ The Proportions and Curves of the Doric Capitals The Ionic Capitals : : The General Method of Proportioning the Volutes of the Ionic Capitals : : : The Method of Describing the Spiral Lines of the Ionic Volutes . The Volute of the Capital of the Ionic Column in the Vestibule of the Propylea . ; : : The Volute of the Capital of the Ionic Column of the North Portico of the Krechtheium X1 PAGE 84 85 88 93 95 96 100 101 105 111 111 116 119 127 128 132 134 139 141 142 xii CONTENTS. The Return Sides of the Capitals of the Ionic Columns of the Propyleea and of the North Portico of the Erechtheium The Colouring of the Ionic Capitals CHAPTER IV..-THE BASES The Proportions and Curves of the Bases of the Columns CHAPTER V..——THE CURVED OUTLINE OF THE SHAFTS The Egyptian Columns ; : The Entasis of the Greek and of the Roman Columns CHAPTER VITHE FLUTING OF THE SHAFTS The Fluting of the Shafts of the Greek Columns . CHAPTER VII.—_THE INCLINATIONS IN THE AXES . The varying Inclinations in the Axes of the Shafts of the Greek Columns PART Y, THE ORNAMENTS, THE MOULDINGS, AND THE ENTABLATURES. INTRODUCTION CHAPTER I-—-THE ORNAMENTS AND CEILINGS The Egyptian Origin of the Greek Ornaments The Egyptian Origin of the Greek Ceilings CHAPTER II.—THE MOULDINGS The Designing of the Mouldings . Examples of Interior Cornices, Mouldings, and Capitals of Ante traced from the Marble : The Geometrical Outlining of the Mouldings ; The Geometrical Methods of Tracing the Outlines, with the Colouring of the Ornaments, in the several classes of Greek Mouldings The Colouring of the Ornaments The Ornaments Sculptured on the Mouldings and Fascie CHAPTER III..-THE ENTABLATURES ; The Egyptian Origin of the Greek Entablatures . PAGE 143 148 149 149 151 151 153 157 157 160 160 167 169 169 173 175 176 179 180 181 183 185 187 187 CONTENTS, The Designing and the Colouring of the Egyptian Entablatures . The Doric Entablatures . The Designing and the Colouring of the Doric Entablatures The Colouring The Designing of the Ionic Entablatures CHAPTER IV..—THE SCULPTURE, PAINTINGS, AND INSCRIPTIONS . Inscriptions CHAPTER V.——THE SPIRAL ORNAMENTS PART YI. ROMAN ARCHITECTURE. INTRODUCTION CHAPTER I..—The Corinthian Monument of Lysicrates The Position of the Roman Temples The Designing of the Masses of the Roman Porticoes A Comparison between the General Proportions of the Greek and of the Roman Porticoes The Apparent Proportions The Curvature of the Horizontal Lines CHAPTER II..-THE CORINTHIAN COLUMNS The General Proportions of the Masses of the Corinthian Columns The Entasis of the Roman Columns CHAPTER III..-THE DESIGNING OF THE ROMAN CORINTHIAN ENTABLATURES The Designing of the Corinthian Entablatures The Mouldings and Ornaments of the Roman Corinthian Entablatures . Summary of the Comparison of the Greek and Roman Porticoes Internal Architecture The Basilicas of Trajan and Maxentius . Christian Basilicas X111 PAGE 189 191 194 196 201 204 207 208 213 217 219 220 226 227 228 231 232 234 236 237 239 239 242 244 245 INTRODUCTION. XV INTRODUCTION. Tre History of ancient Art and Science shews a concentration at different epochs of the greatest Intellects mn certain schools of Philosophy, which were founded first in Egypt, then in Asia Minor and Magna Grecia, after these in Athens, and, lastly, in Alexandria. The founding in succession of these several schools of Philosophy and Art depended, in a great degree, upon the political changes which occurred in the ancient world; and the state of the Arts at any period may, to a certain extent, be ascertained from an accurate knowledge of the condition of these seats of learning. Aristotle informs us ““ that the Mathematics were born in Egypt, because the Priests “ there enjoyed the privilege of being detached from the affairs of life, and had leisure to “ devote themselves to study ;” and the existing Egyptian Monuments will, upon investigation, quite confirm the early traditions of the Greeks, both as to the origin of the Geometry and of the Arts of Greece. In the Temples still existing at Thebes, B. c. 1300, will, I believe, be found the first ideas of Proportion, applied not only to the making of lines commensurable one with another, but also to the determination of commensurable Visual angles by Trigonometrical calculations. We meet also with curved horizontal lines of considerable extent carefully executed, and in the profiles of the shafts of the Columns, as well as in the curved sections through the Cornices, we have, I believe, the arcs of Hyperbolas, and other Conic Sections, laid down with mathematical care. On the Ceilings we see also the early ideas of Astronomy, and in the construction of the Pyramids, and in the moving and raising of the Obelisks, there is the evidence of considerable mechanical skill; so that, in the earliest authentic periods of the World's History, we meet with the Arts and Sciences already in a 2 INTRODUCTION, very advanced state, and the Geometry, the Trigonometry, the Conic Sections, Astronomy, and Mechanics, appear to have been all subjects of study in the Schools of Egypt, and were probably applied in the designing of the Egyptian Temples by the Architects of Egypt. To Egypt, where Art and Geometry had been cultivated for many centuries, we know that the founders of the later Greek schools of Art and Philosophy resorted to be instructed in Philosophy, in Science, and in Art. Thales, B.c. 640, after studying in Egypt, became the founder at Miletus of the Tonian school of Philosophy, in which was cultivated earlier than in other parts of Greece, the Geometry, the Astronomy, and every branch of the Mathematics, that we now find to have been applied to ancient Architecture. Among the list of names distinguished in Science who studied at Miletus we meet with Pythagoras, the founder of the School of Philosophy in Magna Gracia, B.c. 590, and Anaxagoras, B.c. 480, the friend and mstructor of Pericles, and one of the first Geometricians who settled in Athens, and became the founder of the Athenian school of Art and Science. We thus perceive that from the earliest period of History until the final conquest of Egypt by the Persians under Cambyses, in B. c. 525, that the Arts and Sciences were cultivated with success by the Egyptian Priests, and the Greeks looked to them as their instructors in Geometry and in Architecture; after that for a time the Sciences were cultivated in Tonia, when a second Persian invasion under Xerxes, B.c. 480, caused nearly all the Cities and Temples in Ionia to be destroyed, as well as the Temples in the Acropolis of Athens. Ultimately by the energy of the Athenians, Xerxes was defeated at the battles of Marathon and Salamis, and finally forced back from the shores of Europe; and Athens at once became the leading power among the states of Greece, and the Athenians encouraged the settlement among them of the Philosophers and Artists educated in the schools of Asia and of Magna Gracia, and thus laid the foundation of the Athenian school of Art and Science, B.c. 480. The works of Architecture still remaining in Egypt, in Tonia, in Magna Grecia, and in Athens, bear witness to the close connection that existed between ancient Art and Geometry up to the period of the decline of Athens, B.c. 300; after this time the pure Geometry returned again almost to its Egyptian birthplace, and was successfully cultivated for a few centuries at Alexandria, but no longer allied with Architecture and the Arts, for we shall see in the best period of Roman Architecture that the traces of the Greek Geometry are very slight, and it soon disappears altogether in the darkness that overshadowed the Western World. When we carefully examine the Parthenon, the Propylea, the Erechtheium, and other designs in Athens, and also the Greek Temples in Ionia, and in Magna Grecia, including as well the Egyptian Temples at Thebes, we find all these Architectural remains to be among the earliest works of the ancient Geometry that we possess; and if all these Temples were INTRODUCTION, 3 originally designed and calculated by Mathematicians, it is possible, inductively, from the observed facts, again to recover the laws, and to re-design and to re-calculate these several works, as they were originally conceived and laid down by the Architects of the age of Pericles, or of any earlier or later period. The recovery of these ancient laws of design, and the mathematical proofs of the same by re-designing the several works of Architecture erected in Athens during the administration of Pericles, will be the leading object of the following work. I principally confine the attention to Athens, and the age of Pericles, for in these celebrated works we not only find every known principle of the art of design applied, but the execution is so perfect, that no difference will ever be found to exist between the calculations and any correct measurements that can be taken. Pythias, when designing the Temples at Priene, appears to have applied to the Inscriptions traced upon the faces of the Ante a principle of proportioning the letters that will be found to apply generally in the designing of the masses of all ancient works of magnitude, and it is probably the only example in which it 1s applied to the designing of the letters of an Inscription. See the work upon the Ionian Antiquities, published by the Dilettanti Society, Vol. 1., Page 15. “ That Priene also shared the favour of Alexander, is evinced by the following valuable ““ record happily preserved to us by a stone which belonged to one of the Ante, now lying at ““ the Kast end of the heap, in large characters, most beautifully formed and cut. BASIAETSAAEZANAPOY, ANEOHKETONNAON AOHNAIHIT'OAIAAI KING ALEXANDER DEDICATED THE TEMPLE TO MINERVA C1VICA ““ This stone, which is inscribed also on one side, with many other fragments by it, “ seems to indicate that the fronts and external faces of the Ante were covered with “ Inscriptions, and from the degrees of magnitude in the letters, it may be conjectured a regard ““ was had to Perspective, the greater being higher and more remote, the smaller nearer to the “ eye, so that, at the proper point of view for reading them, all might appear nearly of the ‘“ same proportion.” fod, Tgp, = B A A > & O 0 3 ; bmi O point of sight. 4 INTRODUCTION. These Inscriptions illustrate a principle of proportioning of very general application to ancient Art, thus, in Fig. 1 the letters being all one size are commensurable one with another, but they would appear when read from a point of sight O, Fig. 2, to be of unequal magnitudes, or apparently incommensurable one with another, owing to the lines of the Inscription being seen at varying distances from the point of sight O, therefore, as Plato informs us in the Sophist, ““ that if Artists in large works were to give the true proportions of beautiful things, ““ the upper parts would appear smaller than is fitting, and the lower parts larger, through the “ former being seen by us at a distance, and the latter close at hand ;” consequently, Artists “ bidding farewell to truth, work out not real proportions, but such as will seem to be “ beautiful (namely apparent proportions) in their representations ;” and to effect this, in the case of the Inscriptions, it was requisite that the letters at the top of the Inscription, Fig. 2, should be increased in size, and the letters in the lower parts decreased in size, or as Vitruvius expresses it in Book VI., Chap. 2, “ When, therefore, the kind of symmetry and the magnitudes ““ are settled, it is then the part of the judgement to adapt them to the nature of the place, “and, by diminutions or additions, to qualify the symmetry till it appears rightly adjusted ;” and these ¢ additions and diminutions” were made in the letters of the Inscription, so that they might all appear of one size when read from the point of sight O, that is, the visual angles in Fig. 2 are all made commensurable, and this causes * additions and diminutions” to be made in the several lineal magnitudes, or in the heights of the letters. We thus perceive, from the corrections made in the size of the letters in the above Inscription, that the ancient theory of Proportion may possibly have been divided under three distinct heads : 1st. The given lineal proportions of a portico ; 2nd. The position of the design with regard to the Spectator ; 3rd. The apparent proportions of the design corrected. Then when the position of the extreme points of the Horizontal lines in the steps and entablatures were finally determined in position by calculation, it was perceived that mathematical straight lines of considerable length were not pleasing to the eye, because they appeared, when viewed in certain positions, as Vitruvius informs us, to be ¢ concave lines,” or, as Philo states, that lines which are both parallel and straight, seem not to be parallel ““ or straight, on account of the deception of the eye, as it views them from unequal distances ;” therefore a second correction became requisite, and all the Horizontal straight limes were changed into Convex lines, traced practically as the ares of circles. Thus two corrections were required in the designing of the first masses of every large work of ancient Architecture. 1st. To correct the vertical heights of the given design by additions and “ diminutions,” so as to produce an apparent harmony between all the members of the executed design. Qt INTRODUCTION, - 9nd. To correct the horizontal lines by making them all convex lines, so as to remove the apparent concave appearance of the lines. These two corrections are probably of Egyptian origin, and they will be found to exist in all Greek works of magnitude up to the period when Rome gained the ascendency in Greece, and they are both alluded to by Vitruvius. After these two corrections have been made, then the Columns, with their proportions and curves traced as the arcs of Conic Sections, have to be laid down, the Entablatures require to be perspectively designed and coloured, and all the Mouldings and Ornaments are mathematically traced. The deducing of the laws and principles that anciently guided the Architects of Egypt and Greece, in the designing and calculating of their great works of combined Archi- tecture and Geometry, from a careful observation of the actual remains in Athens and at Thebes, and then applying the recovered laws in the re-designing of each Temple, and thus mathematically demonstrating every principle by restoring in each design the original calculations and working drawings that must have been made by the Greek Architects before their designs were executed, will be the object of the following work, and the subject will naturally divide under several distinct heads, thus— PART 1. THE OBSERVED FACTS RELATING TO THE PROPORTIONS AND THE POSITIONS OF THE SEVERAL DESIGNS. 1st. Thebes. The observed proportions of some of the Chambers in the Tombs of the Kings, and of the Egyptian Columns and Entablatures in the Courts of the Temple of Medinet Haboo. 2nd. Athens. The first given proportions of the several Athenean Porticoes, giving the first Heights, the Projections, and the Inclinations of each Portico. 3rd. Athens. The Plan of the Acropolis, showing the roads of approach and the positions of the several works of Architecture and of Sculpture within the same. PART 11. THE APPARENT CORRECTED PROPORTIONS MEASURED BY THE VISUAL ANGLES. Ist. Observations upon the Geometry of three dimensions, and on the Trigono- metrical forms of calculation applied to Ancient Architecture. 2nd. The determination of the point of Sight O, and the tracing of the Design upon the three rectangular planes XY, XZ, YZ, passing through the given point of sight. INTRODUCTION. 3rd. The law for calculating all the true executed heights of the design at the angle of the Temple nearest to the point of Sight O. 4th. The application of the law to the two designs of the Parthenon, the three designs of the Krechtheium, the two designs of the Propylea, and other examples. PART 111. THE CURVATURE OF THE HORIZONTAL LINES OF ANCIENT ARCHITECTURE. 1st. The observed facts - The observed curvature of the horizontal lines of the Entab- lature in the Inner Court of the Temple of Medinet Haboo. The observed difference of level at the four angles of the Upper Step of the Parthenon, as measured by Mr. Penrose. The observed horizontal curvature in the lines of the Upper Step, and of the Architrave in the Parthenon, and in the Temple of Theseus, as measured by Mr. Penrose in the year 1846. The forms of calculation required for tracing the line of the Upper Step in the Porticoes, and on the return sides, as the Ares of Circles. The calculated concave appearance of the horizontal lines of 2nd. The forms of calculation | a Portico, when viewed from the given point of Sight O, with the application of the same to the horizontal lines of the Parthenon and Temple of Theseus. Observations on the curvature of the lines in the Inner Court of | Medinet Haboo. In Parts I., IL, IT1., we are confined to the arrangement and the calculation of the first masses of the future design, as shown by the boundary lines in Fig. 1, and, within the limits thus marked out, the Columns, the Entablatures with their Ornaments, and all the details of the design, have now to be worked out, each perfect as a separate design, and each found to be a combined and highly-finished work of Art and Geometry. Fig.l. Ts! Tl [1 IL : ] Fntablature ee mm - ———————— — — —————— Co lumns INTRODUCTION. 1 PART 1Y¥. THE THEORY OF THE COLUMNS. This fourth part of the work embraces all that relates to the designing of the Columns, viz.:— 1st. The origin of the Egyptian and Greek Columns, and the given proportions of the first masses of the Columns derived from observation. 2nd. The ancient application of the Conic Sections to the outlining of the curved lines, both in the Columns and in the KEntablatures of Egypt and Greece. 3rd. The ancient methods of designing the Doric and Ionic capitals, applied to the Parthenon and other Doric capitals, also to the Ionic capital of the Propyleea, and the two Ionic capitals of the Frechtheium, also the method of outlining the Bases, and the fluting of the shafts of the Columns. 4th. The outlines of the shafts of the Columns, observed, both in Egypt and mn Greece, to be the arcs of Hyperbolas, with the Greek method of calculating the Entasis of the Column, illustrated by the Columns at Medinet Haboo, as well as the Columns of the Parthenon, the Propylea, and the Erechtheium. 5th. The varying inclinations of the Axes of the Columns. In the combmation of Art and Geometry, which is found in the designs of the Doric and Ionic capitals in Greece, we possess examples of what Plato alludes to, when he remarks on the beautiful Mathematical drawings of the Greek Architects; and in the calculated profiles of the shafts of the Columns, both in Kgypt and in Greece, as the arcs of true Hyperbolas, we have quite the earliest records of the application of the higher branches of the ancient Mathematics to practical science. PART V. THE DESIGNING OF THE ENTABLATURES. Under this head 1s included all that relates to the Ornaments and the Colouring, as well as to the general perspective design of the Entablatures, also the designing of the Mouldings and Cornices, commencing with— 1st. The Egyptian origin of the Greek Ornaments, with the methods of mathe- matically outlining the several classes of Mouldings, and tracing the Geometrical outlines of the Ornaments upon them, with the colouring of the same. 2nd. The designing perspectively of the Egyptian and Greek Entablatures, illus- trated by the redesigning of the Entablature of the outer Court of the Temple of Medinet Haboo, also the Entablatures of the Parthenon, the Propylea, and the North Portico of the Erechtheium. 8 INTRODUCTION, 3rd. The designing of the Mouldings and Cornices of Greek Architecture, illus- trated by eight examples. The proportions and curves of the Entablatures being perspectively and mathematically laid down, then the colouring became requisite to give clearness to the outlines of the Ornaments, and to harmonize the design with the surrounding colours in nature. PART VI. A FEW OBSERVATIONS UPON ROMAN ARCHITECTURE. In this last part are indicated a few of the points of agreement and of difference between the Greek Architecture of the age of Pericles, and the Roman in the time of Augustus, founded upon an investigation of the Porticoes of the Pantheon, the Temple of Jupiter Stator, the Temple of Jupiter Tonans, and the Temple of Antoninus and Faustina. The whole of the above work is devoted entirely to the Outlining and Colouring of the Architectural design; but within the same design were arranged the Inscriptions, the Sculptures, and the Paintings, and, by means of these several works of Art, all forming a part of the general design, was expressed, in the language of Art, all that related to the national Religion and History, both of the Egyptians and the Greeks; and it is this combination of Art with Religion and History, which gave an intellectual interest and beauty to such works as the Parthenon and the Propylea, so that within the limits of the design was combined all that was then known of Art and Science, as well as of the Religion and History of the Athenian people. If the works that were written upon Architecture, during the two centuries that elapsed between the first destruction of Athens by Xerxes and the time when Rome gained the ascendancy, namely, those of Anaxagoras on Perspective, Ictinus on the Parthenon, Pythius on the Temples at Priene, Philo on the symmetry of Temples, and many other authors whose names are known, had all been preserved to us, these works must have treated upon the Proportions, the Curves, the Perspective designs, and the Colouring of the Temples. Problems similar to those in Euclid, as well as the Trigonometry and the Conic Sections, were practically applied in the determination of the dimensions of the finished work, and the calculations could not have been made without them. Thus the written works of Ictinus, and others, must have been combined works of Art and Geometry, different to any we now possess treating upon the subject of Architecture and Art. The remains of all the Greek Temples convince us that the Artists of Greece were able to trace the curved lines and surfaces in marble with all the skill and accuracy of INTRODUCTION, 9 Greometricians ; but, independently of the existing ruins, we possess evidence of a very close connection having existed between ancient Art and Geometry. Thus we find in Plato, see the Republic— “ If one should meet with Geometrical figures drawn remarkably well and elaborately “ by Daedalus, or some other Artist or Painter, a man who was skilled in Geometry on seeing “ them would truly think the workmanship most excellent, yet would esteem it ridiculous to “ consider these things seriously, as if from thence he were to learn the truth as to what were “ in duplicate, or any other proportion,” t.e., let any figure of Euclid, or of the Conic Sections, be ever so well drawn, they would still require a written explanation to understand all the properties. Again, Plato introduces Socrates as saying— ““ But, Hippias, tell me whether as all other Arts are improved, and the workmen of “ former times are contemptible and mean in comparison with ours, shall we say that Pittacus, “ Bias, Thales, with his successors, down to Anaxagoras (i.e., the Geometricians of the Ionian ““ school), were nothing compared to you of the present age.” And in the Memorabilia of Xenophon, Socrates inquires— ‘“ But what employment do you intend to excel in, O, Euthedimus, that you collect so “many books? Is it Architecture ? For this Art to you will find no little knowledge “ necessary.” In the time of Vitruvius, the Greek works upon ancient Architecture were evidently in existence, and some parts of his own work consist possibly of extracts taken from Greek writers ; but the Romans were not intellectual cultivators either of Art or of Geometry, and if it had depended upon them, not only would all the written works upon ancient Art have perished, which is actually the case, but we should also have lost every fragment of the Greek Geometry. The question may be asked, are the principles of Greek Architecture true in themselves, like the elements of the ancient Geometry, or are they principles based upon erroneous views of Art, which, like the Ptolemaic system of Astronomy, may be safely cast aside for something truer and better ? It is, I believe, universally admitted that the subjects the Greeks really excelled in were Geometry and Art; their Geometry is still the basis of the modern mathematics, the beauty of their works we still acknowledge, and have never equalled, and we may feel certain that the Artists who showed such skill in the designing of the works in the Acropolis of Athens, would have known how to apply their principles to the present requirements of European civilization, without copying any of their ancient designs. The laws of Geometry were, by the Egyptians and the Greeks, derived from a careful study of such natural forms as the Sphere, the Cylinder, the Cone, and the Prism, with the sections obtained by cutting through these solids at different angles, and the tendency which is 10 INTRODUCTION, found to exist in all these forms, either Solid or Plane, to exact proportions and true mathe- matical curves described by fixed laws, was very early discovered and applied to Art, and the laws of ancient Art will be found to be simply a practical application of these natural principles, thus— In Proportion, 1t was a principle that everything should combine in aliquot parts, and modern discoveries confirm this as a true law, which is illustrated by many facts in Physical Science. ; | It was also considered necessary that all curvilineal forms should be the arcs of true mathematical curves, such as the Circle, the Ellipse, the Hyperbola, and the Parabola, and there is a tendency in natural forms, when undisturbed, to fall into one or other a these several curves. The outline being thus made mathematically perfect, variety of colour was also considered as an essential part of every design, to give clearness to the ornaments, as well as to harmonize the design with all the surrounding works of nature, in which the greatest varieties of positive colours are found to exist. Besides these general principles, it was requisite, when designing any large work, to convey the idea of the perfect design, as it existed in the mind of the Artist, to the spectator through the medium of the eye, and to prevent any apparent disturbance, either in the Proportions or lines, it was found to be requisite to introduce certain corrections in the Vertical as well as in the Horizontal lines of the first masses ; the position, therefore, of the spectator had to be determined, and confined by artificial means within the limits of certain visual angles, favourable for the contemplation of the general design. The leading principles of Arb appear to have been derived by the Greeks from the Egyptians, and we see in the Greek works of Architecture and of Sculpture, how the Artists of Greece were able to embody the principles of the Egyptians into designs of their own without copying the works of Egypt. In Rome also, we meet with no copies of the Parthenon or Propylea, or of any Greek work. The Roman designs are original, but many of the principles that guided the Artists are ancient. | And there is no reason why the ancient laws of Art, as well as of Geometry, should not be received mm Kurope if they are based upon truth. The principles that guided for centuries the Fgyptians, the Greeks, and the Romans in designing many perfect works which remain to us, are valuable illustrations how true principles of Art were once applied, and, undoubtedly, can be so again. If the ancient laws of the art of design unfolded in the following work are only partially true, many remains of Antiquity will have to be more accurately investigated, and my own Investigation is simply a first and very feeble step upon partly untrodden ground, the results of which I should not venture to publish did I not know that the truths they may contain are neither my own inventions, nor my own discoveries, but that they were INTRODUCTION. Ly worked out at the same time and by the same minds as the ancient Geometry by the leading scientific men of Egypt and of Greece. All that I have attempted is inductively to recover and prove from the actual remains of Antiquity some of the laws and principles that existed im the minds of the Architects when arranging and calculating their several designs. These principles, if correct, will in time be embodied in works of far greater literary and scientific merit, to neither of which can the present work lay any claim; but if I shall have added a little to the mass of truth which is slowly accumulating, I shall have accomplished all that I have aimed at. If I have been led into errors, I have had my reward in the study of much that is beautiful in Art, in Geometry, and in Nature, which has often afforded me real pleasure in many hours of retirement and of study. END OF TBE INTBODUCTION. 13 PABT 1. THE FIRST GIVEN PROPORTIONS. THE PIDRT GIVEN PROPORTIONS. 15 COAPTER 1, PROPORTION. Our first ideas of Proportion appear to be suggested from direct observation of external objects. When we compare the magnitudes of two lines together, we conceive how often the one is contained in the other, and if we perceive the one to be an exact multiple of the other, the idea of the ratio between the two lines is fixed in our minds; thus, in the language of Euclid, Book V.— Def. I. ““ A less magnitude is said to be a part of a greater magnitude when the less is “ contained a certain number of times exactly in the greater.” Def. II. “A greater magnitude is said to be a multiple of a less when the greater “ contains the less a certain number of times exactly.” Def. III. ““ Ratio is a mutual relation of two magnitudes of the same kind to one ‘““ another in respect of quantity.” Def. VI. “ Magnitudes which have the same ratio are called proportionals.” N.B.— When four magnitudes are proportionals it is usually expressed by saying the first is to the second as the third to the fourth. Def. VIII. “Proportion is the similitude of ratios.” Def. IX. “Proportion consists in three terms at least.” Commensurable quantities in Geometry are such as have some common aliquot part, or which may be measured or divided, without having a remainder, by some measure or divisor, called their common measure : the ratio of commensurables is therefore rational. Incommensurable quantities are such as, when compared with each other, have no common measure that will exactly measure both. In general two quantities are said to be incommensurable when no third quantity can be found that is an aliquot part of both. These definitions will apply equally to lines, to angles, or to surfaces. Pappus, Lib. IV., prob. 17, refers to incommensurable angles, and in the Diophantine problems, surfaces, which cannot be measured by a common surface, are said to be mcom- mensurable in power. When the ancient Geometricians began to investigate the Mathematical properties of the natural Geometrical forms, such as the Sphere, the Cylinder, the Cone, the Prism, the Pyramid, et cet., it was soon discovered that there existed certain invariable ratios between 16 THE FIRST GIVEN: PROPORTIONS. these natural bodies, and innumerable ratios and Geometrical properties were found to exist in the plane figures, obtained by cutting sections through these elementary and natural forms. Also we find in Euclid, Book XII., prob. 10, every Cone is the third part of a Cylinder, which has the same base and is of an equal altitude with it. Again, from Archimedes the Sphere is 5 of the circumscribed Cylinder. The ancient Philosophers, finding so much order existing within the limits of their Geometrical observations, conceived that if they could penetrate the mysteries of the creation, that the same order and regularity, and the same principles of proportioning, might be there discovered. Thus Plato, in his Timseus, says, ¢ The composition of the world received ““ one whole of each of these four natures—fire and air, earth and water—for its composing “ artificer constituted it from all fire, water, air, and earth, for he concluded it would thus be “a perfect whole if formed from perfect parts.” This perfect harmony of Proportion which the Mathematicians discovered in the forms they investigated, and which the Philosophers conceived as existing in the composition of the world, the ancient Architects established, as a fundamental principle, in their Architecture ; thus Vitruvius says :— The composition of Temples 1s governed by the laws of symmetry, “ which an Architect ought well to understand : this arises from Proportion.” ¢ Proportion “is the correspondence of the measures of all the parts of a work and of the whole “ configuration, from which correspondence symmetry is produced ; for a building cannot be ““ well composed without the rules of Symmetry and Proportion, nor unless the members, as “in a well-formed human body, have a perfect agreement.” PLATE 1. THE PROPORTIONS OF EGYPTIAN ARCHITECTURE AND SCULPTURE. In the very beautiful work of Mons. Prisse d’Avennes, Histoire de 'Art Egyptien d’apres les Monuments, published by the French Government, in 1859, several examples are given of Kgyptian drawings of Sculpture, laid down according to the Igyptian canon of Proportions, where the Artist has first traced the divisions of squares in red lines, and then outlined the figures in dark ink, guided by certain established Proportions. In Fig. 1, 1s given a copy of one of these outline drawings, taken from the above-mentioned work, and we find that the same ideas of proportioning can be applied to the several chambers of the Tombs of the Kings, at Thebes. In these early works of Kgyptian Architecture, which were most carefully designed and executed, we meet with many illustrations of the first simple ideas of Proportion ; for when we examine the principal chambers in these Tombs, we find that the length, the width, and the height, were generally made commensurable quantities, measured by a common Part] Plate. 1. EB wm Hw THE PROPORTIONS OF EGYPTIAN ARCHITECTURE AND SCULPTURE. a 20 19 18 77 16 75 # 3 12 7 ¥ig 1, From Prisse d’Avennes . Hestotre de 1 Art Lagyptierv = SS SE a a ee me 9 8 7 6 J 4 3 2 7 0g Pr YY NN messemmnt I | i ! ' 1 1 | | | ' ' ! 1 | ' 1 x, = ~ ! ! | 1 1 1 1 EEE Hn NON _ 7 76 75 Fig.2. Tomb of Sethos 1.at Thebes. 381 trches = lengthy of prinapal charrber = w-16 = modulus 2-76 x 18 = 381 = Length 21.76 x #1 = 25% 6 = width 21-76 x 1 = 23276 = herght 216 x 2 = 42-82 = With of pers . 5 2 cy 2-2 NN \ N MAR NN 3687 4 78 72 70 9 8 7 6 4 3 © S ~R ELEVATION . ” 7 snl a i : © Fig 4. | Length of chamber =the width + the height AC-AHR+HR Luclid. book 2. prob. 71. 10 dude the straxght line A B=A C unto two parts N ss WN VN pee — — 1 = Aa me 1 wy smn) Ce LL Fig.3. ” J . HH «8 =.3208 = length of" chamber #7 = 287 = width . ” " v Hx 5 = 205 = hetght ; Ihre Footondon, ded. CF Hl, Leth, Castle Sonor E.C. Part 1. Plate ll. & A Tae PROPORTIONS OF EGYPTIAN ARCHITECTURE. The Temple of Medinet Haboo. B.C. 1220. Fig 2. Outer Comrt 1 1 = 4 4 yo + ; % i L x i die — T as T x AN wn 1 A 1 1 AY 1 1 *’ lm rserireeen Won = srapd yo “spvd 5/¢ Were=comeeouwd pg ~ * 5 1 | | i | | 1 | 1 ' \ X o : re id] Ze ia 1) 1 I UT HE ® f. HET IT 1 CRE alii tT Vemmioning =m gon pp. m= pox pop XT TT : Sar WHTYOD == 309 09-6L == Jl X $862 . KX” smynpouw ge. 7”) R . 8 i x, R 2 Si ~N > oe hi = i = 2 T T N EO He x ~ EN Ax AS ) OS rE aE re EE sR eRe QoL. IS Qt TTT ee Ab si a Jin TT Ee De > oe 4 Ar ® ¥ A ZO A A ~ be aa aid or TTT EE Ny TTT UU] 00 = spend 0¢ EET TTC EE EE TR ERT EE ne Tee aE « spd fp Phe memeee speod g/g peers ate = : i en Sevots spund Zee wee EES gTs Eta eden te Sale “spud pC Fig. 1. Inner Court. gene £8 J FLT RLV 5 NI jle 0 ed V1 Bd | A edi 1] 188 =C X LL: 2C ree eer rE ren ean RT = VUNNO?. = Lt - 08 =U x LL *C TT Terra ~smpnpow LZ os 1 N =~ SS oS = a &~ ~! ~ ~ ~ >} © © + Nn S } * * * He x # * * —¥ * * er P18 - 8% 6 * 393 a b~ ppm mmf sib re i AOATE eee hecght of abacus t 864, LA at of COPIUROL: itive vom mn vii mms FIFE ssn sie enix suimmns height of base. ..___ _ 1 864 VPPCT AU OIPLLE «egooe Hime m2 m5 » lower diameter ...._. == width of base .. 3 ~ x = x x x x S By * 8 Rs» x FF ‘+ CIM - laren Spice Ee >4 : : 5: -3 * Nn @ ot | 3 : ~ + © $s ~ 5% : oy ~1- t : : ~ ~ i ; Nt PL Rad Eg y ~ ~ ; st. LF 2d] | : aang 8 5 2 3 8% ¢ IS 3 ¢ 3 be 2 3 % i= ¢ 4% YT 3% 3 § + ££ FT 3 3 ] 3 DD -3 ¥ ; tT & FE 2 ££ 2 2 ¥ + ¥ ¢ Lb. 1 t a x x x x x X & S x > = .. ¥ Q mr eae WEA OF COPIA «ssf cnn mae an sninnn bon wun. TOAD 79 2. HZ iAoll lth. Laatleost. Tondon Lt. Joh 71 Ieorlanaor ded THE FIRST GIVEN PROPORTIONS. 17 modulus, and these chambers can be laid down by squares, in the same manner that we find the Egyptian Artists traced their works of Sculpture upon the walls, thus— Figs. 2, 8, 4. The Proportions of the Tombs of the Kings at Thebes, 5.0. 1400, B.c. 1200. Fig. 2. The Tomb of Sethos I., discovered by Belzoni. The length of the principal chamber =381 inches . . 381 ——=21"16 inches = modulus. 18 21-16 inches X 18 = 381 inches = length of the principal chamber. 21'116 ,, x11=23276 ,, =width ,, ” 21116 ,, x11=232'76 ,, =height ,, 21.16 ,, XxX 2= 42:32 ,, = width of the piers ,, Fig. 3. The length of the principal chamber = 328 inches. 328 +-8=41 inches = modulus. 41 inches X 8 = 328 inches = length of the chamber. 41 ,, xT7=287 , =width ” 41 ,, X5=205 , =height Fig. 4. This chamber does not divide into aliquot parts, the same as the other examples, but we appear to have a practical application of the 11th problem in Book II. of Euclid, namely to divide a line AB into two parts, so that AB Xx BH= AH” Upon AB describe the square ABDC, bisect AC in E, and join BE, produce CA to F, and make EF = EB, and upon AF describe the square FGHA, then AB is divided mH so that ABXBH=ARN" Let AB . . =the given length of the chamber==2335 ins. AH . . =thewidth “ =207 ,, 335 X 128 = 42880 BH = HK — the height 2. ~/42880=207 ins. = AH to the springing of the arch I give the above dimensions in Fig. 4 as they were taken, for the relation between the lines can hardly have arisen from accident, and it is singular if we should find in Egypt a practical application of one of the problems of Fuclid. PLATE 11. THE PROPORTIONS OF EGYPTIAN ARCHITECTURE. Figs. 1 and 2. The Columns and Entablature of the Inner and Outer Court of Medinet Haboo, at Thebes. ¥ 18 THE PIRST GIVEN. PROPORTIONS, In addition to the designs of internal Architecture above referred to, we meet with the same system of proportioning in aliquot parts applied to the larger works of Egyptian Architecture ; thus, taking the Proportions of the Columns and Entablature in the Inner and Outer Courts of Medinet Haboo, at Thebes, erected about 1220 B.c., we find— INNER COURT. given height 38-741 14 14 .=2'77 X11 = 30471 feet. Entablature =2-77X 3= 831 given height of Cola 3047 = 2°77 feet = modulus. Column . 2) = 6-094 = width 5 4! of abacus. es SS RON rt = sili Go the details of the Columns and of the Projections. Outer Court. given height 38-741 13 13 .=92'983 X 10 = 29-83 feet. Fntablature = 2983 x 3= 8594 given height of Col» 14 2:131 X 3 = 6-393 feet = width of abacus. abacus n 6-393 12 12 details of the Columns and Projections. =2'983 feet =modulus. Column . 33 = 213] feat. = 05327 = modulus for the In these several Egyptian examples the parts are all found to be commensurable one with another, that is to say, they can be measured or divided without having a remainder, by some divisor, called their common measure or modulus ; and we may now proceed to examine to what extent this same idea of Proportion is found to be applicable to the works of Greek Architecture. THE FIRST GIVEN PROPORTIONSR. CHAPTER 11. THE FIRST GIVEN PROPORTIONS. Ir the ancient ideas of Proportion had not extended beyond what has been, in Chapter I, illustrated from the Tombs of the Kings, and from the Temple of Medinet Haboo at Thebes, the subject would never have presented any difficulties ; but Plato and Vitruvius both refer distinctly to two kinds of Proportion, namely, true proportions, such as we have already referred to, measured by linear magnitudes, and apparent proportions, which can only be measured by the visual angles. Thus Plato, in the Sophist,” says: — GUuEsT.—*“ 1 now seem to see two kinds of the imitative Art. I see that one 1s the ‘“ assimilative Art—and this especially takes place when an Artist, according to ““ the proportions of the original in length, breadth, and depth, and, moreover, “ by adding fitting colours, works out the production of an imitation.” (This is the case in the Egyptian Tombs.) Tues. —“ What, then, do not all Artists endeavour to do this?” Guest.—“ Not such as mould or paint any great work. For if they should give the ““ true proportion of beautiful things, you know that the upper parts would ‘““ appear smaller than is fitting, and the lower parts larger, through the former “ being seen by us at a distance, and the latter close at hand.” TaEXE.—* Entirely so.” GuesT.—“ Do not, then, the Artists, bidding farewell to truth, now work out not real “ proportions, but such as seem to be beautiful in their representations?” (namely, apparent proportions.) TaEZ. — Entirely so.” Guesr.—* Is it not then just, as being at least probable, to call one an image ? ” THEE. —* Yes.” Guesr.—*“ And we must call the part of the imitative Art subsequent to this, as we have said ‘“ above, assimilative.” TaEXE. —“ We must so call it.” Guest.—*“ But what shall we call that which appears, indeed, similar to the beautiful, * Plato, translated by G. Burgess, M.A., Vol. IIL, Bohn, London, 1850. 20 THE PIBRT GIVEN PROPORTIOXR, “ through the view taken from a favourable point, but which, when seen by him “ who has the power to look on things sufficiently, is not like that to which it “ professes to be like? Must we not call it an appearance, since it appears to “ be, but is not like?” Taex. —* Undoubtedly.” GuesT.—* Is not this part abundantly to be found mm Painting, and in the whole of the imitative “« Ayt 9” Plato, in the above dialogue, refers to works of Art in general, including Sculpture and Architecture, but Vitruvius bears his testimony to the same fact, of the original designs having been corrected in works of ancient Architecture; thus, in Book VI., Chapter 2, he says— “ When, therefore, the kind of symmetry and the magnitudes are settled, it is then ““ the part of the judgment to adapt them to the nature of the place, the use, or the species, “ and by diminutions or additions, to qualify the symmetry till it appears rightly adjusted, ““ and leaves nothing defective in the appearance.” “ The mode of the symmetry, therefore, being first fixed ” (that is, the first lines of the design being traced commensurable one with another), «the alterations” (namely, the diminu- tions and additions) ‘“ are to be made thereon.” Book ITI., Chapter 2.—¢ Beauty being the province of the eye, which if not satisfied ““ by the due Proportion and augmentation of the members—correcting apparent deficiencies “ with proper additions—the aspect will appear coarse and displeasing.” Thus we find both Plato and Vitruvius agree in stating, that when large works of Art, either of Painting, of Sculpture, or of Architecture, were designed to be “viewed from favourable ““ points of view,” the first given Proportions of the design were changed by ‘ additions and “ diminutions ” being made, so that in the finished work, instead of the original design, with all the parts commensurable, we have, as it were, a new design, in which the parts are only apparently commensurable. But we need not trust to the correct interpretation of these passages either in Plato or Vitruvius, for if such ‘additions and diminutions” were really made upon the original designs by the Athenian Architects of the age of Pericles when designing their works of Architecture, we must expect, upon a careful examination of such large works as the Parthenon, the Propylea, the Erechtheium, the Theseium, in fact, of all architectural works of magnitude, executed either in Greece or in Asia Minor during the best period of Greek Art, and probably also of some early Egyptian works, to be able to discover the actual amount of the variations that were made in the heights of the several members of each design when they were subjected Column 1. The measured heights of’ the Steps. the Columns, Column 2. The heights of the Steps, the Columns, and | Column 3. The ‘amount of he’ and the Futablatures in the Porticoes of the the Entabiabaien mn the several measured -ation between the heighis | | Parthenon. the Temple of Theseus. the Propyleea,, Porticoes, cleared of’ irrational quantities when made commensuyy), and the Erechtheium . when compared with the length of the upper with the upper step, and ie | : 5 :. i yo - step,and the nearest commensurable magnitudes heights as actually exec A Comparison of’ the Doric and lonic Porticoes with the irrational quantities eliminated. as shewn in Column 2. The Par thenon fl mr i oe cast portico . substituted. 5 HEXASTYLE YETRASTYLE Le ) i i Hoe ¥ OCTASTY LE —— et 8 OCTASTYLE OR 8 COLUMNS | : 1 ali ia mn mo i ipod tr OS ed Sntaint | Z rrr | HINA wii Eh ily mlablatare 2 parts. oo 21 43 + II Ne 1 i Sod pd td ; ye lich Regt... + 1 =i rf ht v | i | oh ef 11 e Propyleea = | a : rae a ] : iy le. DORIC ORDER k 5 2 5 pls {3 steps. + - 0056" = gegtil 54 : The: Parthenon The Temple of’ Theseus Jno example l. ee HS > = 7 gas pes 4 : colimps.. oo. * JIS’ w= I 24 i § The Temple of’ Apollo al Basse / |] ; 3 aguiablature —_— 1036 == 7-94 j ’ : 101-336 feet == length of the upper step ch a 1 tect ci ” 7, ind i 7 | ; da ? 2% Ta ” Z | | 24 } i ! no 14 Seta ae ne 7 het : : : - ; g uy 6 5 4 3 2 2 od) He Gal me an fp Aoprine oo x po on pox nl a : 70 9 8 7 ‘ 5 7 3 z 7 0 17 i= / semen anne MOT 336 = length of upper step. A os 07-336 == Ze gle of upper step Come or es - i =! : 228741 —= i a i side . : : or { 10 | ue | esd at ts The Temple of Theseus no lm cast por tice o & : I i Wien | : ERNevviE 9a © cOuU¥AS : hei “The Erechthieum 4. JONIC ORDER i Th oni ii i Beds as TT EET ” 0 at fer: The FErechtheium The Erechthieu i : 3 ah oR ’ Lote Lr dieo Ea. 0 . Hn nl i ay z : = 1 iq ; ; | - he : | ma Sr i ] whole hoght ........ — - 5651'= 4.15 1200 | nit ng oF 0 per 55454 10. = length of the upper step. | | : ¥ par 2 Va | I . 4 ps... — 7957 = 9.4 } : es > a 7% : re a : i 2 2 * 2 columge 6 parts 2 wlumns..... ..... — -o18 = gust z 3 2 oi £0 7% t | | La i edablatore....... + -25° = 34 i | ; : 2% G7 wi on | ia Su et 7 ¢ z 7 3 3 7 0 oneenee. 45 OW = longllh of upper gp... 45-01 — longth of upper step... : : : EL ro : 104-29 : length smiley side. : hy lel the length or the upper step of the Parthenon = #w Pa 7s =AL=1{. and let 7 = par ls : Ip) = arithmetical progression he... ae SAE ithe line A =1 + (i —r) + (l —3) a scale a ) The Propylaca il i 0 Il i im I yl por pie 3 \ es rE my IT . Wl tleenl slr) =u | LL LT re a eps nt a Ets Shorten of Le DAR iii Lie : 1% + entablatare 2 parts ~~ it HD, Tin Binion's Benen SINUS OF Le PEPER GOVT SE : ar Tiin > ’ ; i ’ , ; » ; . , 0 : i Fa Fin oT | rest | ee oe : ii } | i {a gps ............... —-458 = 7.4 | | | : ¥ i : iy column 6 parts I: wlwmns. + 3g = dei 41D — 2 parts. Iv the Dorie Porticoes let the whole height - g parts = AL | 2» PD 2 a : : : ; 3 ; vom | ge] | FY enlablature + -%2 = 4:8 In the londe Porticoes let the whole hewght = 6 parts ZL. | | 2 *7 ee Fm i A pm l il (ONT | ¥ 69°32 — length of upper step errno. 60-32 = length of upper Step. ............. 3 | ig 1. tos Fits Basis Portion oF toe Lovwehilhoctinn. Jn the North lone Portico of” the Erechthcewm. | In the Doric Forticoes. 47 Ldalh IL = 12 parts | : 4 Lt thas whale height EL ee cinins = TD PALS lel the whole hei Pee , Wie whale botght AE ...................= I Parls | ik - 7 The Erechtheium Min cast portico ' | 3 2 Ze vids Jug let ho height of the steps... 1 Ly Ye Sieps.. =] - i nil all | I Wn Wm be a rely aE msrp | lb the haght of the Steps .........e..™= 1, lel the height o hg ! ; Lolita SE, or ee a LL nr 5 1:2 of ntablature » parts | a Wo : y Clwmns... ......—39 , a i Pid ’ ’ man en nn coins : Entaliedare HE | a * =H * x5 foot inches | = : ; FEntablature ro 2 2 7 / : he oh | “+ whole hewght + - 78 == 3. 3 | / J Lntablature...... = ’ 2 ! i 2s = ’ : Ex *7 £ ] : : 7% lps — 2 = 0 | 3 : : : : olan 2 party ¥ Glimns + 1 = 152 Sg TB ¥ Ld I’ tablature + 139° = 1-6 hr Piri i i ; : LY rl ber of equal parts as 9 or 712, Stylobate is ol i : Ue ls Bug J ose bi dovided mito a certain nunbe equal p Ly io i In these examples of the Doric and of the lone Orders, the whole height in each case bang da : Ate serine te Bu Hash thn Gites whi Jl J J Boat detail shia bg : ; : 2 parts, an 2 oe < i 27 | ep TE days made oqual to of these parts, the Enlablature to the Corona is abways made equal to 2 of these parts, 8 7 6 5 4 3 2 7 ¢ : rr NT ha Re ses in the Dorie is equal to 6 parts, and in the lonic equal to 9 parts, or 83 parts : : : hy that : : 97 £ the heights will require the corrections to be made Tea TETRASTYLE OR 4 COLUMNS : did Fir ven. all the other first dimensions will follow, but “ng iy sh I gary The length of the upper step tn any Fortwo bang gover, ail the . | 3 *} tablature 2 parts are observed in Fart [I of thes work. ig od iy 5 i . | ; whole haght ~~ — 0.388" = 4 ¥ ¥ ” : bo | 7 7 Steps... +0230 = 2-5 The Pediments. 3 3 3 3 Ex / column 8% parts $2 / / 2.12 5 1 3 5 2 ; ops min Bt : a Lik of cormedce nearest rato gwen hetght iin a’ varvation: : p of 32 enlablature ¢ 29 Ragin re when, made com between, the Pol Fe 3 4 mex: (358 = 4: able with made cominensurable : | \ i lo COTO tn with the length 7 cornice. oq gs Bh a ACTolertia ......... + 0-158 = 18% oo i fa "i noe Ry - 5 wl 2.9295 : steps 7 part - : as 77 . 46 705 0856 = 7 8 ’ 43 | = 3 736 Hl nae 68’ 2 ! Th 5 7 3 2 7 ’ The Parthenon. E iar) roannt Lgl mm fo ennnnenn 9015 = length. of wppprer step... , Koon 35154 = length of upper step... if The Temple oF Theseus ................ 5-823 47 - 387 a 7 | . phon =. Bl i en — 07 = The Proppllt......n rev itennnsensc: 8 626 : : i i | THE FIRST GIVEN PrororrioNs OF THE Arig PORTICOES DERIVED FROM OBSERVATION. Part 1. Plate. lll EF Kol! lik Cale S Imam. F.C. Ay Lo ondons ad. 3 THE PIRST GIVEN PROPORTIONS, 21 to those corrections which were essential to produce an apparent harmony between all the parts of the finished executed design. The information derived from any ancient sources, except from the actual remains of Greek Art, is but slight, but the works of Greek Architecture of the age of Pericles were executed with such extreme precision, and remain to the present time so perfect, that we are able from them inductively to recover the original laws and principles that appear to have guided the Athenian Architects in the designing of their most perfect works. We shall, therefore, pass on at once to the consideration of the first given Proportions of the several Athenian Porticoes. PLATE 11%, THE FIRST GIVEN PROPORTIONS OF THE ATHENIAN PORTICOES AS DERIVED FROM OBSERVATION. Trusting to direct observation, we shall proceed First. To clear the several Athenian remains of Greek Architecture of the irrational quantities that by measurement may be found to exist, and to substitute instead the nearest magnitudes which shall be found to be commensurable one with another. Secondly. To express the ratios between the commensurable magnitudes in the simplest numerical forms, instead of the actual dimensions, and then, by com- paring together the several selected examples of the Doric and Ionic orders, to ascertain, when thus cleared and reduced, whether any general and constant Proportions can be discovered that may serve as a basis for the calculations that may be requisite to determine the corrections, that Plato and Vitruvius allude to, when they refer to the second kind of Proportion, namely, the apparent Proportion. | The measured heights of the Steps, the Columns, the Entablatures, and the Pediments, in the following Porticoes, viz., the Parthenon, the Theseium, the Column I. {| West Portico of the Propylea, the last Portico of the Krechtheium, and the West Portico of the Erechtheium, also the true length of the Upper Step in | each example. The heights of the Steps, the Columns, the Entablatures, and the Pediments, in the several measured Porticoes, cleared of all irrational or incommensurable Copa quantities, when compared with the length of the Upper Step, and the nearest commensurable magnitudes substituted. 22 THE FIRST GIVEN PBOPORTIOXS. The tabulated amount of the variations that is found to exist between the several executed heights, and the nearest commensurable quantities, ¢.e., between Column IIT. | the several dimensions given in Column I., obtained by measurements, and those given in Column II., derived from Proportion. These additions and diminutions are found generally to be very slight, seldom exceeding a few inches in any one dimension, and by adding or substracting these quantities to or from the dimensions given in Column II., the true executed dimensions will naturally result. Note.—These are the additions and diminutions referred to by Plato and Vitruvius. These variations, observed in Column ITI., will appear again in Part II. of this work, derived in each example from the given dimensions in Column II. by a trigonometrical calculation, and it will be the agreement of the calculations with what is deduced from direct observation that will afford the required proof of what is here simply stated. Having in Column II. reduced each selected Athenian Portico, both in the Doric and Tonic orders, into parts commensurable with the length of the Upper Step, it is next proposed to substitute a comparison between the first given lines of the several Porticoes, in order to ascertain whether any general scales of Architectural Proportion can be laid down that may be made the basis of the future calculations, and the germ out of which each Greek Portico will be gradually developed. This comparison of the Doric and Tonie Athenian Porticoes, when the irrational quantities have been eliminated, shows that the relation between the length of the Upper Step of the several octastyle, hexastyle, and tetrastyle Porticoes, can be expressed by a series in arithmetical progression, as follows :— Let the length of the Upper Step of the Parthenon = AL =10 =, let r = 2 parts. Then the line AD= [| 4- (I —r) + (I— 2 r) = a scale of arithmetical progression. AD=10+4-(10—2)+4 (10 —4) = 1” 1 y AD=10 + 8 +4 6 =a scaleof Proportion of the Upper Step of each series of Portico. 8 6 4 = a scale of Proportion of the numbers of Columns of each species of Portico. THE PIBST GIVEN PROPORTIONS, 23 5 CCTASTYLOS. HEXASTYLOS. TETRASTYLOS. entablature. ~~ The Propylea. 1 DORIC PORTICOES The Parthenon. j X The Thesetwm. column. 25 td 4 L404 Bans ens be $Y 000) 200 NSomuoadep ad AREA NONE rr T I a ny 1 ThekErechtheuun, 1 IONIC PORTICOES Vie Lrectibieinm, Notts Dortice 3 column. RK? ___stylobate. Tae HricHTS. AD = 24 parts. In the Doric Porticoes let the whole height = 5 parts = AE. In the Ionic Porticoes let the whole height = 6 parts = AK. In the Doric Porticoes the whole height AE In the Ionic Porticoes the whole height AK is found to be divided into 9 aliquot parts. 1s found to be divided into 12 aliquot parts. The height of the Steps . . .=1 part. The height of the Steps . . .= 1 part. ’ Colm . .=6 > Colman . .= 9 ,, “ Entablature . = 2 ,, “ Entablature . = 2 ,, AR=90 AK -12 , There is no example in Athens of a Greek Corinthian Portico ; but examining the small Monument of Lysicrates, the height of the Steps, of the Columns, and of the Entablature, can be nearly expressed by the following numbers :— The height of the Steps ; . = 1 part. 5 Columns . : : = " Entablature . : fmm In these several examples in Athens of the Dorie, of the Ionic, and of the Corinthian orders, the whole height, when cleared of all irrational quantities, is found to be divided into a given number of aliquot parts, as 9, 12, or 11, according to the Order, then the height of the Steps is always made equal to one part, and the height of the Kntablature equal to two parts, and the variation occurs in the height of the Columns, which is made equal to 6 parts in the Doric order, 9 parts in the Ionic order, and 8 parts in the Corinthian order. If the several Porticoes be drawn to a large scale, the original Proportions can all be found by measurement with compasses, the variations being always small between the first given design and the executed Portico. 24 THE FIRST GIVEN PROPORTIONS. CHAPTER 111, THE PROJEOTIONNS. In the Second Chapter we have obtained from direct observation the first general Pro- portions of all the Athenian Porticoes ; but in each Portico, before we can proceed with any calculations, the Projections of the Steps, and of the various members of the Entablatures, as well as the inclinations inwards of the masses of the Columns and of the Entablatures, must be determined. Also, in Temples like the Parthenon and the Theseium, the length of the Upper Step on the return side must be accurately laid down, and the heights of the Pediments must be ascertained. The laying down of these several details, with a few general remarks upon the facts that have been derived from direct observation, will form the subjects of this Third Chapter. PLATE 1Y. THE GIVEN PROJECTIONS IN THE SEVERAL ATHENIAN PORTICOES OF THE STEPS, AND OF THE DETAILS OF THE ENTABLATURES, AND THE FIRST INCLINATION INWARDS OF THE MASSES. In all the vertical dimensions it has been found that certain corrections are required before we can arrive at the true executed magnitudes of any Portico; but we find from observation that all the horizontal dimensions are executed exactly as they are first laid down : Still before the plan of any given design can be traced and prepared for the required calcula- tions, all the Projections, namely, the width of the Steps, the Projections of the several parts of the Entablature measured from the face of the frieze, and the first inclination of the masses, must be arranged. The Greeks in all their works never lost sight of the principle of dividing everything into aliquot parts, so that all their designs can be laid down in Proportion, even to the minutest details in the Columns and Entablatures without any reference to dimension, and this we find to be the case with regard to the Projections of the several Porticoes. en a Part]. Pate IV THE GIVEN PROJECTIONS OF THE SEVERAL ATHENIAN PORTICOES. NAMELY THE STEPS tHE DETAILS OF THE LENTABLATURES AND THE FIRST INCLINATION INWARDS OF THE MASSES. < Modulus of vertical heights in the Doric — & of the whole height. ~ Z 7 Q W ; 5 ae . : 2 : ) { These figures are| ether my awn or Stuarts YS ; ; 5 3 2 : 3 8 : ; measurements, but the moarble vs warre cond Fg. 7 Summary of the : 3 g 3 MR : E : 0 : 3 : 5 3 § g : S J 3 av parts disturbed en arrangements oF L.4... -58.629 — gwen] Aelght pf’ Stylobale| | |. 8 I 3 NE EE ---- $970 foe eel ee eee L---1-- Q ) S N IN & 3 3 Bf « ~N - : a S : 8% 3 NY BN 3 oR ] A eid bem Loo tmp] the Projections ip < Z < Q . 2 = 3 3 8 3 2 ] NR | Bresson 4°. vc Wo L.¢.08 1 -}._ _ . 3 3 31 TH i + hp 7 ap - ) @ : E =F 3 Aa | WM 1s Te WW 181 6 3 4 ¢ 37410 arcludrave § E } : 266. _).125 of the sever nA | architrave facia KL 3765432 1 Soe 5 : : £ AL ALIS See 2 i - - y N " upper Step 1 ~ 3 7 ! . 4 by | Fo ¥ : 5 i *5 i “ yo : 8 v LR ap lower step 5 A | / ; by : 8 Mutudes ’ second Step ed 6 lower point of’ Corona facia) F : 171 lowest small step | ! 1 oe! 10 7 loronaw i } z Corona Modding. | : ¥ : ; retin: of | re i : Zi cymutivany § 51 upper facta of coronov ' 8 3 o Lact above Corona 72 ; heer / 0 cyrmodiurmn | > = ne % bole 3.1267 — first: gvery height of Stylobote.... |. | | 7 3 9 middle Step : Ee Crmatiam t : thi bl fo & inl Lb enable iY 0% | = wrd Step x : 1¢ 75 middle Step fbb i ete MT reer Sai EE N. -+ J i > Pe % 16 tr abacus 7 >s Pl ky & i S * | cS o % 77 Pi upper step :! 2 : “\ White i ole: © 18 $10 F 12% se wiatle | ' : * + 3 18. 1. Parthenon. | > ~ Fig. 4. Erectheinm. 1 + S 13 ! >. y l * 78 ™) : 3 * ; . = : ( East Portico ) % 20 + By | \ I -4 1 > i! M4 fourth Step 27 re ~ 144 \ Co ~~ ; * BOY) aN x 22 ; ¥ 75.4 | Q *15 *% 23 middle step + corona moulding ; S ; 3 : 1 R o 3 24 lower Step : 3 : 76 lower Step | x Theseus. Retin, S 4 I : x 8 ‘AP (modulus 0625) + : Fig. 2. Propyleca. + i $ y , 3 I = . West Portico. : i | 3 / There 2 no lower marble step Iu ‘ eocle m WAE _ / the Theseus. 1 | Sl a 3 [25 |. 4 | na| owrv measurements LL / I | ~ . 3 | = 2 2) | _ Ire all these excanples| ~~ J 1 | esi bdrm ss peed os 3.008 ferain sabe nis Lb Fore qrrucendity wieidhy 5 > § ean 2.9295 _ given. |height of Stepd ——-___ at a6 [|_| | I requlates the @ V 1 v > : % L___7.803 _ finst piven height of Stylobate |__| projections is 3 of i ; : obi the gwerv hetghts § Prajectrons of Cornel pH g : os 2 HH HHH Oo 16 415 “ 13 7” 17 0 9 8 7 G 5 & 2 R 74 the scane wu 5 § Ww 88 7006 5 2 2 3H 7 |o : + tft feted Sas ; Doric cd, Tore 3 1 oaachitrowve corrace Orders. R 8 di — Ta The projections R Zens 7g BY 20 I 71947 10 1B 13 12 HoH 9 87 C5 5 z 3 i : upper step of the several X rr Her Here ee Hei Mem pie i a ; or chiitroive {7 members of the © x... } $7 abacus +7 Fntablature and * 9 3 raat ave Cores is of the steps are $ in RB a all comamensurable 6 ___ second) step : : : S : $7 : with thas first given ; treme 1 *& 7 corona rod ding quardity, the details 5 ee 3 | 2 | i 1 x6 s : 8 facia above corona slightly veaying un > : & ! 4 or, pepe Na... : 2 each Portico. 2 Vr , Si S | & | 17 4 Lonard, Propylzea. im These projections | OT 5 : ; e 4 i | © i | le Yo Tridieidis 32) ; 10 third step undergo no correc | 1 3 | tons. ! i “+ *2 F710 471 | i | | 10 u cymadticum 1. ; : x71 +73 I | | I | | | | i $2 +74 | %/3 i5 ! | x74 i. I I | | 2 | | | ! : 7 nuddle Step | ] ! 16 2.389 first given height|Stylobdte._. . I I © $77 Rie oi 3.780 b= % of poight]....}...... tt | ed il ! : : : HBRAUWIDBITIBHBEHBRY WIS TE SiR iii y | 4 y ! 5 fe eae go rt : 1 7. [IAA 7K | : | kg. 2 Minerva Polias 2 4 a lly 1 lower: edge of archatreve i | I | : $20 2 abacus i | : $27 ¢ 2 oachitreve corrace y : y is | | ™ }: FTTH IT rE = = % 25 upper step i 24 lower Step 1s y 8 corona. : lo (537). 1, Lio ; 1 177 cvimnadiuare 213 [213 | : S72 Fig. 3. Propyleea. { / Tu I - ye . 5 : : | a ( North Wing.) besrns Fe B8uarndftott doe 1 00 ranres . 3 9 3 Erecthemm. “ aetdldlie op A 44 | Le olsat. ee : AO T v 3 : « { modidus 1326) 177 | g z 3 § L li i 3 g = 2 : § 5 E ? I 4-19 % JAAR ¥° | * . 3 §3 3 9 120 Q “Th: | 3 g 3 Ht 33 38 7 SQ k.215 %.213 ! > 4 ~ 5 8% Bl : . 272 S base of antce 7 J 15 Q ~ ee 3 g ] : abacus 3 eo US gli “ - : heals i AAT Burt y 24 lower: step : > a 7 z x CC — MN a SOE 2 0 / 7 rote Hote \ upper step { YTo7 7 3 2 5 CP FE 2 2 PH 2 [femntects 1.5638 me ET Reig OF NS pele - S ae ae Rg < ¥ > 2 : ee ere RE a SS Geis 130299 _ 3 of white height] | : mm | 2.925 — first given) height of Stylobate. 3 . vt eae 3.905 — % of given hdight | __ : 3 K L Y Y ¥4 = / 128214 ss z 20 5 20 15 70 4.4 brphs ; ! <2 SI Ae Nd Sh NL NE le NE SLC SC NE SL SH She Se Ske RN 2 pte ms . “ : 2 lower point of corona faciow 5 P. keh ANNAN ere . XC lower line of architrave . -062= inclination of Lrtabloture Ymruwo sn wl HERP 8 Tb 54 0b 1 i oy second, step and, corona O : $2 i ee 1 i tr ¥ i facia above corona ~ +3 , architrave cornice 2 > V tne of abacus p ~ a 2 +3 i Ss aaa L56.565 entre of at: Portico Fo “062 — inclination of the mass of 18 Ne 2 to « great; Lortice.............] oupper Step = 45.011 rrr +# *9 | 3 ¥7 L 5 or i | *5 6 upper step *70 Se & 2%9 17 ~N x71 =~ > I +8 tard, step ” - % S fe 12 CVI “2, 3¥13 fe \ ; Tw, * +71 I 3 : ¥ 72 Ca \ ? *¥ +73 | SL. : . » 4%17 . 3 : 174 The Black marble Step is not connected with the Design. of AN Fig. |6. Theseus. } Minerva Polias. § tis , . / . GY modulus 1627 176 the Wing, but serves to unite the two Designs together. mo. Bit sptetion. of Mttedes / id Lour white marble Steps composing the Stylobate of the centre | ho, % i? 7 « z . 7 7 . y > ™ = -e Lortico, and three white marble Steps composing the Stylobate i SN 1 B v Q Es i 7 . « of 2, Cor ) , CE T of the Weng. Q Yn edye of the lower Step 6}25 edge of the ce Fi 2 + Q 2 I 122 . “oy * ; 123 3% 7120 Gvrnodauany age lower step 1 J = < Modules of ver hts tne ore — 12 of whole he : 3 Modbus of vertical heights in. the A of whole height I eS ! ? dr > : 77 A Cf EF Soll, Leth, Castle SE Jondlon IE tres Tootly reson, det) THE FIRST GIVEN PROPORTIONS, 25 The whole amount of the Projection, from the face of the frieze to the edge of the Lower Step, is always regulated by the modulus that governs the heights, and the whole amount of the Projection is then divided into a given number of aliquot parts; one of these parts is made a fresh modulus, and all the Projections become multiples of this given quantity. In the Doric Porticoes, the modulus regulating the vertical heights is 5 of the whole height, and, in every example of the Doric order, we find all the Projections to be regulated by some lesser multiple of this given modulus. Tn the Tonic Porticoes of the Erechtheium, the modulus regulating the vertical heights is 15 of the whole height, and the Projection of the Steps is equal to this modulus; but the whole amount of the Projection, from the face of the frieze to the edge of the Lower Step, is made equal to § of the whole height, the same as in the Doric, thus— Modulus Given Total Projection regula- height in taken from the frieze ting the feet. to the Lower Step. Eaileo Fic. 1. The Parthendis rE — 562081. ZR g51 f. 43-227 4-803 i Fig. 2. The Propylea, centre Portico Fe 4-803 ft. nT '32 HE : found to Fig. 3. The Propylea, north wing ; i >» Re 3-199 ft. 220 213 3 ony Projec- Fig. 4. The Erechtheium, east Portico . 2 2 = 3186 ft. i = "132 sak selected Fig. 5. The Erechtheium, north Portico na z= 3-905 ft. 2 1627 he amples. Fig. 6. The Temple of Theseus Ee 3-125 ft. BE — 0625 / Fig. 7. A Summary of the arrangements of the Projections of the several Porticoes. Why the whole given Projection in the Parthenon should be divided into 17 parts, in the Propyleea into 15 parts, and in the Erechtheium into 24 parts, we can at present assign no special reason, and simply give the numbers as observed facts, but the modulus being given for any example, then all the minor Projections of the Architrave, Cornice, et cetera, are regulated by the given modulus. THE FIRST INCLINATION INWARDS OF THE MASSES OF THE COLUMNS AND ENTABLATURES. In all the works of Egyptian Architecture we find the walls have a considerable incli- nation inwards, the Columns and Obelisks likewise diminish gradually from the lower to the 26 THE a I 7 $ : / of architrave and’ s 2, friew aboutd in 80 | Vi 7 7 77, 7 _ ” be. inclination irwards iss. Tk $2) %; i of the face of the ee : =. = abacus within Ue ee | fr & upper step abou \ | 7 in 450. 1 I | hl x 1 + 3 = § Si o! ! wil Sf iy 2 3 Ly 2 oi i PIRST GIVEN PROPORTIONS. upper diameters, the gateways also incline inwards; and when we examine the works of Athenian Architecture, more parti- cularly in the Doric order, we observe the same facts, the walls inclining inwards, the Columns diminishing and inclining inwards, and the Entablatures the same; we observe also many adjustments and great refinements in the arrangement of the inclinations in the details of the Cornices and Capitals, so as finally in the finished work to priate a pleasing and harmonious effect upon the eye. Some of these inclinations will be best explained when we consider in detail the Columns and the Entablatures, and, for the present, we will confine our attention simply to the inclination of the first masses of the Columns and of the Entablatures. In Figs. 1, 2, 3, 4, 5, 6, the inclinations required in laying down the first masses of the design can be observed, and they are, in every example, made some multiple of the modulus that regulates the other Projections, thus— Parthenon . Temple of Theseus . Propylza, centre Portico Propyleea, north wing Given distances or the trieza to odulus for the Abacus within the Inclination inwards of ie a Ln of 4 Motus fr ih edge of the Upper the Architrave and Upper Step. Step. frieze. "662 B62 . a 0785 |. . 078. | '073X2="147 374 BY. N=. 062. .]. . 0 fl 209 aay, Jf, 532 . 2 ws |. om. [. om These mclinations appear to be all given quantities, determined by the Greeks from careful observation, and must be given before any future calculations can be made. The remains in Athens are so much disturbed, particularly in the Entablatures, that it would require careful research to be able in some cases to fix with mathematical accuracy the original amount of these inclinations; but there can be but little doubt that they were arranged along with the other Projections, and were some multiple of the given modulus in each case. With regard to the Parthenon, we can depend upon the measurements of Mr. Penrose, but other buildings have not been so carefully examined. THE FIRST GIVEN PROPORTIONS. 27 THE PEDIMENTS. The amount of the Projections being determined, the whole length of the Cornice, in any example, is given ; and when we compare the measured height of the Pediment, with the length of the Cornice, in the Parthenon, the Temple of Theseus, and the Propylea, we meet with the same character of variation as in the other vertical heights, that is, by adding or diminishing a few inches in the height, as the case may be, and substituting the nearest ratios, we find that in all the existing Pediments the height is to the length of the Cornice, as 1 : 8, and that the slight variations, which are found to occur in the executed work, must result from the same law that influences the other vertical corrections, thus— Parthenon . . . Asl1246 #1. : 1050868. :: 1: i) 13-136 ft. 0-68 ft. Temple of Theseus. ,, 5823 : 47-387 1: 1:812:1:8 5923 0-10 Propylosn. . . . ,, 8626 : 758 xx 1: 9) 9-2 0-576 THE RETURN SIDES OF THE TEMPLES. Among the preliminary given quantities that must be settled before any calculations can be made, are the true dimensions of the Upper Step on the return sides of each Temple. The number of Columns in the front, and.on the return side, is regulated by the species of the Portico, thus, in the Parthenon, which is an octastyle Portico, we have 8 Columns in the Portico, and 17 Columns on the return side; in the Theseium, a hexastyle Portico, we have 6 Columns in the Portico, and 13 Columns on the return side. If the intercolumniations were exactly the same in the Porticoes and on the return sides, the length of the Upper Step on the return side would be at once settled; but the dimensions thus given are generally incommensurable quantities, and this, to the Greek mind, destroyed the symmetry of the Temple; it was therefore preferred to substitute the nearest rational quantities, so as to make the length of the steps commensurable, and to throw the variations into the intercolumniations. The Parthenon. | Porteco 8 columns . o ® & & é © 00 101 -341=lenqgtlv of upper step _. 229 -534=1% gverv length of the upper step . .. 226-017 = corrected length of the upper step return swe 77 coluarnres . ©00000 é % & $ & o Ra Q. i o o Upper Step, Upper Step, Portico. return side. Thus, As 101-841 ft. : 229-534 ft. : : 1 : 2:26, or 4 : 9:04, nearest ratio 4 : 9. As 4 r 9 c+ 101-341 ft. : 228017 = corrected length of the return Upper Step. 28 THE PFIRST GIVEN PROPORTIONS, If the distance from the Upper Step of Measured dimensions of the upper step of the St A ii Trees the outer Portico to the Upper Step of the mner ag Portico had been the same at the East and West Fer ali ol ends of the Parthenon, the ratio of 4 : 9 would iL da ~~ have been exact, as it is, there is a difference of SE rea it! ee 0-124 feet = 15 inches between the calculated and measured length of the Step on the return side ; this was probably some adjustment made after the work was first designed. At the West end, the Parthenon is built on old foundations. The Theseium. Portico 6 columns. & & & @ o Chin 47-387 — length of lower marble step... ) return side 13 columns. Ts T0696 = 13L. given length of lower marble STE. ...........coceaeereovmcesmssrmnosvms secenst Konno dit che as amet i AOC 68 = correciediengife of Lower ODE STE. ....... oc cvsoicosrmsmeieconssune sion In the Temple of Theseus, the given quantity appears to have been the marble Step corresponding with the Projection of the Cornice, and, therefore, the limit within which the whole design is contained is made commensurable, thus— Lower Lower marble Step marble Step in Portico. return side. As 47°387 : 106-96 : : 1 : 2-256, or 4 : 9024, nearest ratio 4 : 9. As 4 9 :: 47-387 :106°62 = the corrected length of the Lower marble Step. South Portico. The Erechthemum. The first lines that regulate the Plan. edge of stylobate onwhicl the carvatides rest. 78-08 x 72-05 raiic 2 - 3. south wall architrave. Fast Portico. face of’ architrave: edge of cornice of’ stylobate. north. wall archatrave. Q OU North Portico. wterior architrave 28-4 x418-92 rafio 2.52. With regard to the Erechtheium, as there are no Columns on the return side, the THE FIRST GIVEN PROPORTIONS, 29 Proportion 1s at once given, being simply a double square contained within the face of the Architrave at the Kast end, and the North and South walls. The North and South Porticoes are two distinct designs— In the South Portico the ratio of the Stylobate is as : In the North Portico the ratio of the interior Architrave is as . DIMENSION. The first lines of the several Doric and Ionic Porticoes are now given in proportion, but not in dimension, and before we can proceed with the calculation of any design some dimension must always be given to the length of the Upper Step, and all the other dimensions will follow according to the same scale: thus, in the Parthenon the length of the Upper Step 1s exactly 100 Greek feet, and any change made in this first given dimension would alter every line and every moulding in the whole design, so completely connected together are all the parts by the laws of Proportion. In the words of Vitruvius, ¢“ dimension regulates the general scale of the work, so that ‘“ all the parts may tell and be effective.” The perpendicular magnitudes, as we have seen, are altered by some law before we arrive at the true height of the Steps, the Columns, the Entablatures, the Pediments, et cet., but the transition from these first given quantities to those actually executed is the result of very simple calculations, to be explained in Part 11. The first masses being given, it remains for the geometry and the trigonometry to transform each design into a scientific work of Art. In these preliminary Chapters we have the Proportions of Greek Architecture reduced to their utmost simplicity ; the design is here considered free from all those complex forms into which each part will ultimately sub-divide, free from all the corrections which have to be made, free of anything which constitutes what Vitruvius mentions as ‘‘ those abstruse questions ““ wherein the different Proportions of some parts to others are involved,” and which he says are “solved by the united aid of arithmetic and the laws of geometry.” We find, when the design is reduced to these elementary Proportions, that the lesser magnitudes are all contained a certain number of times exactly in the greater, (i.e.), the ~ heights, the widths, and the projections, are all commensurate one with another. These Propor- tions must, in the first instance, have been derived from observation, and it was probably centuries before they were established as constant and invariable given quantities, yet very superficial observation upon the existing remains in Athens, is sufficient to convince us that 30 THE PIRST GIVEN PBOPORTIONR,. each Architect, in commencing the design, did not alter the fundamental Proportions of a Doric or of an Ionic Portico. Those ratios once discovered that produced the required harmony were made constant quantities, and they will be found to be the same in all the works that were executed from the time that the Athenians commenced the rebuilding of their city, after the Persian invasion, B.C. 478, till certainly after the second Peloponnesian war, this period includes within it the names of all the most distinguished Architects of Greece. To attempt to give any satisfactory explanation why the scales of Greek Architecture that can be traced in the remaining works in Athens, should produce that agreeable impression on the eye, which by universal ancient consent they were acknowledged to do, is, I feel impos- sible, but our inability to give the reasons of innumerable natural laws that we are able to discover, neither invalidates the observed laws themselves, nor yet the science that may be founded on them. Aristotle remarks, Topics, Chapter I., “It is not requisite in scientific principles “to investigate the why, but each of the principles ought to be credible itself through itself.” Again, Posterior Analytics, Chapter I11., Neither is all science demonstrative, but the ““ science of things immediate is indemonstrable.” Chapter X., “I call, however, principles ““ in each genus those things which are indemonstrable, but with respect to principles, indeed ““ it is necessary to assume that they are.” In Music we distinguish a certain number of sounds forming the natural gamut, these sounds are separated from each other by intervals that can be determined by observation, but we can give no explanation why these harmonies and scales should produce an agreeable impression on the ear, or why many other intervals that might be selected would be discordant. Lami, Cours de Physique, page 61, “ La serie des sons de l’echelle musicale, ou celle ““ des sept notes qui forment une periode, parait avoir son origine dans la nature de notre “ organisation.” Page 65, “Dans l'état actuel de la Science il est sans doute difficile de “ donner une explication completement satisfaisante, tant de 'espece de dechirement produit ““ gur Poreille par la succession rapide de deux sons discordans, que de la sensation agréable “ occasionnée par les accords.” Vitruvius also refers to the Greek Sculptors as having traced certain established Proportions between the several parts of the human body, which served them as a guide in the commencement of their works, and he proceeds mm Book III., Chapter 1, to lay down some of these Proportions, and then dwells particularly on the necessity of observing similar laws of Proportion in Architecture, for he says, ““ If Nature, therefore, has made the human body so that the different members of it are measures of the whole, so the ancients have with great THE FIRST GIVEN PROPORTIONS, 31 “ propriety determined that, in all perfect works, each part should be some aliquot part of “ the whole ; and since they direct that this be observed in all works, it must be more strictly “ attended to in Temples of the gods, wherein the faults as well as the beauties remain to the end “ of time.” Also in Book VI., Chapter 2, “It therefore becomes necessary in the first place “ to stitute laws of Proportion, upon which all our calculations must be founded ; according “to these the ground plan exhibiting the length and breadth of the whole work and the “ several parts of it must be found.” We therefore perceive how much the Greeks dwelt upon the necessity of observing some fixed laws of Proportion in Sculpture and in Architecture, as they also did in Music, and how perfectly the words of Vitruvius agree with what can yet be traced in the Athenian remains ; and when we extend our observations into nature generally, determinate and fixed laws of Proportion are ever impressing themselves on our minds, and whether it be in the movement of the planets, in the combination of substances, in the relation of lines traced in any geometrical figure, or in the impressions made upon the ear or upon the eye, still Proportion presents itself as an important element in every perfect work. It is therefore absolutely necessary, in restoring the principles of ancient Architecture, to commence the calculations with the same given quantities that the Greeks had discovered before they were really able to execute a perfect work ; they were probably slowly ascertained, and appear to have remained unchanged through the best period of Greek Art in the Athenian school, but that period was of short duration, and after the founding of the school of Philosophy at Alexandria, B.c. 300, we no longer meet with the names of any distinguished geometricians in Athens, and this absence of the geometry, and a disregard to the established Proportions, is clearly conspicuous in all the later works of Athenian Architecture—they are no longer stamped with precision, the intellect impressed upon them is no longer that which was cultivated in the philosophic schools of Greece, and there is a striking difference between these later works and those of the age of Pericles ; those earlier monuments of Athenian greatness are marked with the highest order of Greek intellect, and are intimately connected and blended with the studies that were pursued in the schools of Thales and Pythagoras; they are works which will ever remain as standards of perfection, and the more highly cultivated the mind that studies them, the more intimately connected will they appear to be with the ancient geometry, and with the most cultivated of the Athenian intellects. In the more refined periods of Art, the Architect The idea of arranging the design in aliquot parts, endeavoured by these “additions and diminutions,” made so that the heights and the widths may all be commen- surable, will probably be found to exist in all works of Architecture up to quite recent times. In the designs of Egypt and of India, in the plan of Solomon’s Temple, in the works of Greece and Rome, and possibly in the cathedrals of the Middle Ages. upon the original design, so to impress the eye of the spectator that the perspective design should appear in all its parts to be commensurable when seen from a favourable point of view. 32 THE PIRST GIVEN PROPORTIONS, CHAPTER 1V. POSITION. Tue Greek idea of enclosing sacred edifices with walls and Propylea, and of marking the roads of approach to them by works of Sculpture, sanctuaries, altars, tombs, et cet., appears to have been derived from Egypt; thus some of the Pyramids were surrounded by square enclosures and gigantic gateways, others by rows of massive tombs; also to each Pyramid the principal road of approach was distinctly marked either by Sphinxes or by tombs. Again, in the ruins of Rermk and of Luxor at Thebes, the roads of approach are marked by long lines of Sphinxes leading up to magnificent Propylea, with their statues, flags, and obelisks, marking the entrance to the Temple or the Palace ; and it was the same in every Egyptian work; the spectator was led to approach the design from certain pre- determined Positions. Fig.1. Egyptian Temple. In the Egyptian examples, Fig. 1, the Propylea and gocaopoooooon i popoooOOoDoOODOOo paintings. The design is arranged more for internal than external effect ; within all 1s roads of approach are placed centrally, and the spectator enters at once into the inner courts and halls of the Temple, which are enriched with columns, statues, and enriched, but externally the appearance is that of massive towers and walls, with their appropriate Sculpture. The Grecian Temples, Fig. 2, were generally surrounded by ex- ternal colonnades, supporting an “= entablature enriched with Sculp- | ai : | | tures both in the frieze and in the * Nee . x | LH ow a cee 20000000000 0aa \ > . . WF Fon ip . pediments; and the external ap Zz XN Lhe, Taos. % . / 3% Te er | pearance of the design was care- Fig. 2, Grecian Temple, A fullystudied, as well as the position with two angular views Aand B. 7), \ : 1t was intended to occupy. Sey Part] Plate V. A N = NMR AN NIRA NS EE | Emm aa LR S — S T r = TT . - or . = WN aman \ NR = Fa RE RRR 3 S\N i i = — : SU rs 0 SI, re : EN SEES NR mink ARR 2 2 = AN PD RRR WA FA msinsint Vr A, rr, Cy S NN NEN NNN \\ NAN AR WW AR NN RW na = me Soe - \ OWN NP \ HNN 3 sy ‘ Ahi === : ETA pe NAN | eS . : ih, PLAN OF THE 3 \ RRR a RN pr RE RR A 3 == $f - = fit g 2 m= ER I, ry, irr : Na MRE = : RN NAM aa nS S S ERR = 2 SIV : Aufl el Eton, ===, Ti “wr, iy it, X NN NN NTH HS == NY AN AN NN NN Wg pa: \ = J \ : Ton Z Z > S35 oy ) ; 4 2 { Zs : Eg = 7 Wi, J 1 110s. S LOAN EE AEE ER | wu nh Pl ACROPOLAS or ATEOEXY \ Lg EN . 3 En ts : NAN Rk \ Wind NN wy bi 20 == = ign ain ' SHOWING THE ROADS OF APPROACH AND NR TT_R WN oe : aa. 7 ZR NY i Sa AN LALA = N as 8 CAN Sn ig, POSITION OF THE PRINCIPAL WORKS. TTT RA C= RNP bis. 2 [>= pre 7 MRS = a Msedityy i) : : : ARN & TE i SS ) <7 fil, media : Hk » 4 “ln i mm / oy Niunbers within |) dencte the level of the spot indicated NN : = 7 a — midi an mon ol “gi mn , below the N.W. angle of the upper step of the Pardienon nN 2 S 2% ~ a rere — GS 3 < = am mn tri I Si) 700 a : FE J es LM mt” Bint oF SigRE~, I = Re ges il 4 Yims nest - NkRatie z 5S \ a = =A 3 Pr Tony 2 a ) \ 7 a he db A, re, SCALE OF FEET. Ninna NN WIINIIIIIIIEZE vv = : 72 sr \ 3 * Wifi [2 ey Is SN 7 my Wit, ess NK = NN min = 2,7 uw Lor \ “0 i ) Mii aa ADE ees : I I NN 2 \ it a nr 4 Ee 7 - , 12s ON YW 0) ANN mn : lh ly T Needle in 1847 x N+ == 9 } : / 7 F Lo. ve} * i 2) os 22 § Tn NA TRV: T= i; 1 7 if Nee wm ¢ Ni EEE = > 3 i gg, 7% : : > Gm . | — > > : x Hy aaa eg aN a Chie x 4 / | ~ \ a = ¥ . 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A : SS ARAN fit J 7 i. 3 : 5 mJ {= 0 - ar arr, The tamile of Vural Vo §@ ® @ > oe BH we . 7) 7 nl, Comparison of the ortentadion RN < : NS the priestess Tvsimochn wy i are V4 (18.6) gdh > ~~ li I l 2 sani), iy wm, “ih of Bon fron dy ge - wd rl = gros brazen nade of Erechtheus ard Cr lh a Dy 1U “i, Gana Propylaa 2 or N 3 Tio weet a upon. the base are nar of m ar 5 I % Wi iy, on, ee TTT Partlieion ean ‘N. ! were are some ancient Rerve, -Zllme > THE Tr TTR Tr o KA 9%, i 2 i also yen En rid 5, ny a | i y Po a of SLL, © Ty, 7 7, Lrecy, ther, Theseus finding the slippers aud sword SH . ; ~ 2 fe Ti I i, Ram 0° 8, Xa : of Lgews and Theseus ectng te (retan ; Lo A, I) i There is likewise a Statue rR bull from Marathon +o be sacrificed te } Ea hi, Ti, 77 2 TH bearings are magnetic or Pericles and another | rns Minerva.” (Poarsanias) Z (Q N Eo me res ln WI 7 nese bearings 4 ip brazen Minerva which vs | i 2 (21.0) ~ ein Ee EE ek 7 7 the finest work of Phidios. : = sat fis > or “iiss, Ay = ey EE ho vi 7 7 7 71) Po ra “gp > ; \ 2 2 im, 7 i No << mn Y= 7 a 2 75 Jr Zz 7 Z 2445 Ke hi 7 ir - Ra SR oak li kK 7 7 / 7! i) i % Se So 4 r, Es iin £ ~ ai 7 J 7 7 BH oy, Sw FREE he ~ ty i 7% 7 / ww SI, 1 LO, by - 1 aT Ne Ke 7 7 ww HI, 4: [hon 3 Ta 8 = EW hr) NW Win, ; i AA 0, 3 2) ign NN 7 ating 7 my / I Iu, : vt. ZA, gpa : ie 270 I mW / 7 “ty te ses . nme ” I II 7 7 7 ny Wy ww Mr SSL i RL p11 _"y witha E: EEL 3 nm; in 71 / my Wr, i, b © & o RA. 2 gy a : ¢ = dg ny, i 7 ny on FU vi, Sa cay : === a Y, ir ; : rE 7) ny wm, , “y ira7750 ii ri a my Mi is Ninian Dis z ed ry EE “ “iy 7 i am nn ty Yl 2 , 2 dll, A En lly mh, hy " ty. Pn yy, = ~. 7 I ; =n, ni arn ve i; g 5; yy, ny ba srs — or mi, 7 my bc, i) Sm I Poin of sight for the es ~ Ce 5 Ne My, : - = 7 wm 7 "7 Cg, ny, emg ot Lartherton.” “veo a >r—~ % ? LL am La i 7 wl (35.0) === ‘ \ i sc ee Bian : & i iy, 7; 3g, oi me em UI Sm wr me aE aE am 7 I, 7 = - 7 < wi, 7 I Z ] Rock cat to a perpendicalor foe or : ” — i > frre is o %, ee le 7% Zo 3 “ry TS ne (I Sy “i eZ : SN 77, XY nn r : Tj; Zo sn 8 . N R i \ Gy I v 7) ps 7, Co A (24.0) X . : 7 2 a vo % dir, 7 22 Ns Fg ry Xx 2 eT 2% i “ on oo : J ¥ ; § 4] > = — £ ; Between the temple of Diana ard the \ 3 Ty “%% 7 "yy 0 wn , TZ ’ Tes Shi z = , Pp Ee 2% ; E SER Portleroog were the Tiojan horse, the \ x \ ¢ Ge ii ’ ZZ a : 5 /: o> 2 Sel 22 = = eat A # x gE = Epicharmirs. the Aiiobugs, the Hermolycws, STEER \ - Su ¢ it Y / 5 bs : i, i, ; Z, = z / TA) Bs RE a %Z Ni this p. of the Acropolis was 0 the Phormio\ Minerva slaying Marsvas, 4 ~ = fm ™~ ny, a So} ! : i mt, rm a uy i Won % 2 my; — l the Sanctuary of Venus Lecenov which & Theses overcgmirng ‘the Whiriotaar, E oe Highest part of the rock | Z li “0 %) /, “, ig “mm “yy; i gh 7) 3 il be. “Sa Soi the brazen lioness and Zz ok 5 = = Phricus sacrificing the earn. Hercules 3 2 : about (2.0) / ; 5 win, RB iy, il 10 Wi, a Ty: . ii i 7 Ee , the Statue of Veraas between the Gel R ED ~~ slaying the serpents, Mirvervo. 1istng 7 I ~N em 3 2 / : sa H 7, lr : 7 “My ; hy i * Srncineay col Toatiof Din. Br rTy 27 ~~ io dhe head of Fupnter, wn the Bull | > r 5.8) : a Ted A Ih X Brauroma stood the Dadrephes, EEE : dedicated by the\Areiop agus” (Leake) [ : / i : A E 8), Ni: 5 9) in J the~two Hygrieioe, the Aspergilliter/= - Oo a he EA, 0h 5 E- : : 5) &) it 7 7 Who. “in by Lyetas, and the Perseas / f - es = os lea Wy iid, "slaying Medusa.” : Eo ! el en] = SIT / 7 i slaying Medusa” (Leake) : Nt for fi ts Loin of 7 \ == = 2 on, . ~ z nl -~ 4 . ! . - i 10% Sy = 7 2 . \ Sop ot tar fromu the lemple of the | { A ine / = : oe rm Sar” 2 y Yrs 5 x i 2 Geraus of Prous Men stood. the Warrror with silver nails bir J Clecetas and Ecrth proying — | for rain, then the Timothews, = | _ the Conon, the Procne, the [contest . of Neptune and Minerva, the = — 0 : Ha 0 Tp Le 7 yy i y , 7 , uw 7; about (6.0) \ Ji Hi N07 7 / 3 ; HH 338 \ Jupiter by Leochares and. the ! 237) 7 : s bn 1 = a ; cen my ~ a 4 NR x Jupiter Polieus.” (Leake): El EEE I Pircearn Stone Pavement i Th, 3 we, 2 —, en 2 Z 2) 7 wivill N ig Z > J 2 3 \=\ hr pis hn ANRC = 2 2) i lm : mw / SI WS p= 2 ® PT v/ My, am ili I ; / l A MIE i nn im : [= rl Hai iid f | 4 : fi tat RRR y Al = T -7 1 an Win fl / wl hi AEN i mn i i \ : oe IPA hii o sl) iil JiR IRR CL 7 ® PARTHENON J XIN Y / E er Dr 7 X 757 {= pn a 0 7 Ds “i tae 7 ) Z) i Ui hi ini wil ih i 7 Er = , 5) % YC il z 3 7) w i ie ; Qn il! a X77 Zs Wd iy i ) = : 2 <4 ’ a) pit Jy i i jl 1 4) 7 z | “7% 2 A i ys ~ ra mh th gp aig 7 > \ . B® To 1, \ i ti ir Wy nn SE : § Over against the, temple is a broxen dpollo 1 NY) / Hi ET 7 XY ’ ; ” A ag 7 ip Z on ; Y “hy 7 7 \ by Phidias. °s ; \ i, 7 / 4 “ , DP, 7 7 7 ot ., Here also ts ar image of Obymprodorus, : SNA : 7 7 _ N\ near which is a brazen statue of Diana, | 7 also an ancient sitting statue of’ Minerva,” Sh (Poausondas) WN N WW \ \ : AW \N \ ai 1 mn J mn / 0 ~ 7 hy / u My Op 7 £; 7 N / B . ji 7 A A | Op 5 77 4 / ) N : . of 4 : Re ; a 0 0 ) 0) : .. (15.0) 3 ef / 304 or 1% 2 2 7 7 : eeantl N, : ° % / 4 Bama oo mn aetin if NL : as — hm 0) Nfl ON fineness ap 2, oo 7 . pS mn) My a i ly af of the Parthenon. asi af 0 rm = Mh ™ : 5 oo ; Ee 7 7) 7 In / nm iy 3 < (oa; — hn / < : =m / 7 i Mt eT a) HR & 4 0, __ . = Re. Zt, Pian ce a IS a ab ma = Ro enn, { a Zz 0) yo / E 2 ETE ZH, I i a 4 i ; E : my Hore the wall vs 65 7. « : 7 | / i ji : 41 wl ; i My : “0, 0 , y) : 7 ; ge Hi ; a. 1 i |] the wall called Not : : = Ni _ LU Wii SN “pp > 5 a mm, EE EE—— zy, Lnanons, the battle of Ryn nl, TTI the Wad of fy on hh Mig wn ye : = or me ee Zt Ln ud the destracuon op JLT the battle of N92, 00 ” ” 000 / sl] " Taiz ee oh, 2. ; Sa —- oe ; bh : : ao E—-— Ea a yy, AABN of the Gord tn, Myre oC. OF the Athenians with & N el hk wl Do 2) i 5) 7 ; = hi ! ] i : | — 2a caidr of these 15 mee tact, nate Bimsenias TB NN %, 1, at Z fii pe zy 7 gpa 2 Wh, hel nn | m . A | | I i Ny i, i hi i i i ll mh! 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R Thm aL CT TH ee a : A bt Fe | p11 Ge HT i CORRE ONT Cg ily ml 7 iY ni im, “yy “, wy ) 7 Mi rn, adil ive my, i If i I i! ab gr Ri La pn { (HEE NY Cul, : Ki A J i: A mn fam i OWE ze il, II In, I vr. ; BE om er i Tm oo i = oe gm RL RR os mime. ith] Wi; Ji rm a, : Ee “on DA i iil TE ima NEE oe ON 4 meme et tii lo PARTHENON SECTION OF THE ACROPOLIS FROM WEST TO EAST SHOWING THE PROPYLAA THE STATUE OF MINERVA AND THE PARTHENON. STATUE OF MINERVA Llighest pound of’ the Acropolis iE upper step a EL ae ae ae ee a tse i i Eh, ee SSR Bt die Ay fran ee —_= ( ents — 3 . level of m— TE 1 ce REET ee gE I. - aig | Ng 5 | PROPYL AA 4 / « oy | | —] y 0 9 n" 4 C 7 N N 30". 2 9 38’, SECTION FROM NORTH SOUTH SHOWING THE ERECHTHEWIM AND THE PARTHENON, level of ii min en - ce—- (= X i w CASA Lith Castle S77 London LC. Sot Soli naorn ded. THE FIRST GIVEN PROPORTIONS, 33 This change in the arrangement of the designs between Egypt and Greece from internal to external colonnades, led to a corresponding change in the position of the Propyleea and roads of approach to the several Temples, which, instead of being central, as we have seen in Egypt, are in Greece planned so as to offer an angular view of the Temple to the eye of the spectator, whenever it is possible to do so, thus— Col. Leake, in the ““ Topography of Athens,” page 516, when speaking of the Olympium at Athens, says, ¢“ The approach to it, as in the instance of the Parthenon, was from the west. ““ The gate of Hadrian formed an entrance to the peribolus at the north-western angle, and ““ presented to the spectator the same kind of view that he obtained of the Parthenon on “ emerging from the Propylea. In both instances his eye, by comprehending at once a view ““ of one of the fronts and one of the sides of the building, enjoyed a more imposing prospect of “ those magnificent edifices than could have been presented to him by an approach immediately “in front. There was a similar approach at the Temples of Minerva at Sunium and Priene, ‘““ and at the Panhellenium of Afgina.” PLATE VY. PLAN OF THE ACROPOLIS OF ATHENS, SHOWING THE ROADS OF APPROACH AND THE POSITION OF THE PRINCIPAL WORKS. Now that the Acropolis of Athens has been partly excavated, and we are again able to trace the original lines of road, and to follow the exact route taken by Pausanias in his ascent to the Propylea, and in his inspection of the several works of Art in the interior of the Acropolis, we shall perceive that all the roads and artificial platforms were so arranged by Art that, at every point where a complete view could be obtained of each design, the work was presented to the eye of the spectator so as to be seen only from an angular point of view ; and to suit these angular points of view, Plato informs us that “ Artists worked out not real Proportions, but such as seem “ to be beautiful in their representations when seen through the view taken from a favourable “ pot.” It is well known that the eye can only see, without moving, a limited extent of view, which may be defined by a visual angle embracing 45°, and in the plan of the Acropolis we shall see that sufficient space was left, when required, to allow of the eye taking in the whole extent of each design within the given visual angle ; we thus obtain two angular views of the Parthenon, viz., a north-west and a south-east angular view ; and two angular views of the Erechtheium, namely, the east portico, and the north portico. i — 0.poind of sight Tt appears, also, that Pausanias, in the route he followed when walking round the interior of the Acropolis, was led to pass through the several given points of view, for which each design 34 THE PIBST GIVEN PROPORTIONS. was calculated and corrected; but Pausanias dwells far more in his descriptions, upon the Sculpture and the Paintings, than upon the Architecture within the enclosure ; still, in describing the plan of the Acropolis, we shall follow him in the route he took, commencing with the Propylea.* DESCRIPTION OF ATHENS BY PAUSANIAS.—THE PROPYLZA. ““ There is but one entrance into the Acropolis, the hill being on every other side pre- “ cipitous and surrounded with a strong wall.” ““ The roof of the Propyleea is of white marble, and excels all other works in ornament ““ and in the magnitude of the stones.” ““ On the right hand of the Propylea is the Temple of Victory, without wings.” “On the left of the Propylea is a building containing pictures.” In regard to the position of the principal entrance to the Acropolis, great uncertainty at present exists, but it is probable that the carriage road must always have been on the south side, where the rock is less steep, than on the north and west sides; but there also appears to have been an entrance on the north side for pedestrians only, by means of steps cut in the rock. The carriage road passes into the enclosure of the Acropolis by a gateway near the Temple of Victory, without wings, and opens upon a level platform, from which ascends a marble staircase to the west portico of the Propylea with a central inclined plane. From the level platform the eye exactly embraces within the angle of 45° the central Doric portico which forms the true entrance to the Acropolis, and in the vestibule are the six Ionic columns, supporting the roof of white marble, referred to by Pausanias. This central portico is a design complete in itself, and the only example we possess in Athens of a design made to suit a central point of view, which, from its position, was essential. Pausanias then mentions as two separate works, the Temple of Victory on the right of the Propylea, and on the left of the Propylea a building containing pictures; this is the north wing of the Propylea, which is in itself a very perfect design, arranged to be seen from an angular point of view, as shown on the Plan. We thus have in the Propylea three separate designs connected together into one group, and forming one of the most original and finest works of Greek Architecture. Passing through the vestibule of the Propylwea, we at once enter the interior of the Acropolis, which was so filled with monuments, altars, statues, bassi relievi, paintings, offerings of all kinds, inscriptions of public interest, et cet., that it was considered by the ancients as * The road taken by Pausanias is marked by a dotted line, thus —..—.. en THE PIBRBT GIVEN PROPORTIOXS. 35 one complete monument of the Arts and Sciences, and of the Religion and History of the Athenian people ; but although containing such a variety of works, there was order and design visible in every detail—one superior mind appearing to have planned and arranged the whole. Tae STATUE OF MINERVA AND THE BRAZEN CHARIOT. Besides innumerable statues and paintings, Pausanias describes, as near to the Propylezea, two dedications from the tenth of military spoils. He says— “One of these is in honour of the victory gained over the Medes at Marathon. It is ““ a brazen image of Minerva, by Phidias.” “This statue is so placed that the crest of the ““ helmet and the point of the spear are seen in sailing from Sunium towards Athens. ““ The other offering from the tenth of military spoils is a brazen chariot, dedicated “ after the victory of the Athenians over the Beeotians and Chalcidenses of Eubcea.” The pedestal of the brazen statue of Minerva has been discovered, and is found to be placed in a line with the centre of the east portico of the Propylea, and about 120 feet in front of it. The pedestal is 183 feet square, and presents an angular view to the spectator. The statue, including the pedestal, must have been 70 feet in height, both from the representations of it on coins and from the description of it by Pausanias, the whole height would have been perfectly seen from the east portico of the Propylea. When further explorations are made, we may hope to find some traces of the site of the brazen chariot (with the four horses) a little to the north of the statue of Minerva. These two works were the first of real importance seen imme- diately upon entering within the enclosure of the Acropolis, and they were so placed by Phidias as clearly to indicate the line of road to be taken either to the Parthenon or to the Erechtheium—they formed, as it were, the inner gateways to the artificial enclosures of these two Temples. THE PARTHENON. The road first taken by Pausanias was the one leading direct to the east portico of the Parthenon ; it is slightly worked out of the rock, and on the right hand near the Propylaea are the remains of votive altars and other works of Art; and he informs us that there were several sanctuaries and important statues on the south side of this road. Arrived at the base of the colossal statue of Minerva, we enter within the limits of the Parthenon enclosure, and the first uninterrupted angular view of the Parthenon is presented 36 THE PIRST GIVEN PROPORTIONS, to the eye of the spectator, containing the west portico and the north side, combined in one perspective view, seen exactly within the angle of 45° ; some steps cut in the rock serve to give additional apparent height to the design; Pausanias however takes little notice of Athenian Architecture, and passes on to the east portico, describing the works of Sculpture in the pediment, and the statue of ivory and gold within the Temple. In front of the east portico is an extensive platform, nearly level, formed partly out of the natural rock, and partly by being filled in with the ruins of the earlier Temple and with the fragments of the present one that were laid aside while it was being built, and then paved over where required with Piraic stone. This platform is bounded on all sides; on the north the rock is cut to a perpen- dicular face ; on the east are still some traces of a Piraic stone wall ; and on the south is the fortification wall, which Pausanias describes as the “wall called Notium,” towards which he went, for he says, ¢“ On the wall, called Notium, are represented the war of the giants, the ““ battle of the Athenians with the Amazons, the battle of Marathon, and the destruction of the “ Gauls in Mysia; each of these are three feet in height.” These works of Art were clustered near the second angular view of the Parthenon, containing the picture of the east portico and the south return side, seen also within the visual angle of 45°, for which sufficient space is allowed on the platform. Thus it was arranged that two perspective angular views of the Parthenon should be obtained—one at the north-west angle, designed from near the base of the statue of Minerva ; the other at the south-east angle, designed for a point of view near to the works of Art on the wall called Notium. At the other two angles, the north-east and the south-west, the spectator is brought close up to the building. (See Plan.) | Ter ErRECHTHEIUM. Pausanias passes direct from the south wall of the Parthenon enclosure to the platform in front of the east portico of the KErechtheium, possibly along the road, marked by the rock being cut to a perpendicular face, which unites the level road bounded by the north fortifi- cation wall, with the Parthenon platform. Pausanias merely says, ©“ There is a building called Erechtheium, before the entrance ““ of which is an altar to Jupiter Hypatus.” But a large platform was formed in front of the east portico of the Erechtheium, partly enclosed by the north fortification wall, and the roads and the fortification walls are so arranged as to allow an angular view of the portico to be obtained within the invariable visual angle of 45°, THE FIRST GIVEN PROPORTIONS, 37 and we know that works of Sculpture and altars were grouped on this platform the same as at the Parthenon. Descending about six feet, by means of the marble staircase (a), we arrive upon the completely enclosed area of the north Temple, where Pausanias again refers to many statues and works of Art, and space is left for an angular perspective view of the portico as a distinct design to be seen within the visual angle of 45°. The road then passes on to the Propylea, between the colossal statue of Minerva and the brazen chariot already referred to, the line of road being marked to the portico of the Propylea by successive works of statuary. Although Pausanias notices so briefly the Architecture in the Acropolis, probably because the writings of Ictinus and of other authors referred especially to the subject, still we shall see that he was naturally led through all the selected points of view of the several designs by an artificial arrangement of the platforms, roads, Sculpture, et cet., by a contraction of the fortifi- ‘cation walls at some points, by ample space being given at other points, and by the natural rock being levelled and cut to a perpendicular face; these simple means enabled the spectator to contemplate the several works of Architecture from favourable positions, which were more particularly indicated by the works of Sculpture. The necessity for confining the spectator within narrow limits is evident, for, if we are to substitute apparent for true symmetry, the calculations must be made to suit some predetermined points of view. Pausanias refers to innumerable works of Sculpture et cet. in the Acropolis that were placed along the lines of road; or grouped on the separate platforms; the positions of some of these are indicated on the Plan, but they are fully described both by Col. Leake and Mons. Beullé. My object has been simply to mark the lines of road, the arrangement and levels of the several platforms, and the true positions of the assumed points of view for the Architectural designs, from which points the calculations will be made for determining the true heights, and these calculations must afford the proof that the points of view, as well as all other given quantities, have been correctly assumed. Figs. 1 AND 2.—THE SECTIONS OF THE ACROPOLIS. In the Plan of the Acropolis the supposed position of the several points of view for each design has been indicated, but it is important also that the levels should be accurately laid down, as the true position of the point of sight, either above or below the upper step, in each design must be correctly assumed, and before any calculations can be made each design must be fixed in its true position, and the points of sight accurately given. The point of view was among the first given quantities, the same as the first Proportions 38 THE. EI1BST GIVEN PROPORTIONS, and first Projections, the Plan, et cet. These first elements being correctly given, the calcula- tions become very simple. In Figs. 1 and 2, complete Sections are given through the Acropolis, showing all the general levels, and the true level of each of the given points of sight. Fig. 1 is a general Section from west to east, showing the Propylea, the statue of Minerva, and the Parthenon. Fig. 2 is a general Section from north to south, showing the Parthenon and the Erechtheium. The points of view are numbered upon the Sections, as well as upon the Plan. For the levels that are given we are indebted to Mr. Penrose, who has laid down both the Plan and the levels with his usual accuracy, and without this data it would be impossible with any certainty to make the required calculations. GENERAL REMARKS. From direct observation we become sensible that objects in nature often assume an apparent form, different from their true geometrical form: thus the apparent magnitudes of lines, surfaces, and solids, vary from the true magnitudes, and consequently the eye presents objects to the mind different in form and in magnitude from what they really are, but we are enabled in many instances, from the picture that the eye presents of the object, mentally to restore the geometrical forms. From our physical organization, the eye has not the power of presenting a picture to the mind otherwise than in perspective. The stars, as we see them traced on the imaginary celestial sphere, are a perspective representation of the firmament, every landscape is a perspective view, and also each work of Architecture when executed can only be viewed in perspective. The mind of the observer is supposed to judge of the design by the pictures that are presented to it through the medium of the eye, and the Architect must not expect the ‘beholder, when contemplating the executed work, to correct and make perfect that which presents itself as apparently imperfect. If we intend the design to appear perfect in Proportion, the parts must be so arranged that, when the work is executed, it should appear to all who contemplate it, exactly proportioned in all its parts ; if the lines are intended to appear, either mathematically straight or curved, they must be adjusted so as apparently to produce that effect. The idea, as it exists in our own minds as a perfect work of Art, must be preserved when it is no longer a mere conception, but becomes visible to the eye, and is contemplated from some fixed point of view, towards which the observer is led by the arrangement of the roads, the Sculpture, and the entrances. Therefore, commencing with the given Proportions and forms, we have firstly to conceive the whole design, and, secondly, to translate it into an external visible work that shall agree THE FIRST GIVEN PROPORTIONS. 39 with our own conceptions. The converting of the design from a mental idea to an external work, introduces two other elements that must be considered : the first, the eye supposed to be fixed in position with regard to the design, and, the second, the position of the visible design fixed on its artificial platform. Something similar is done in Astronomy when we fix upon some one point that shall be the same for all observers, so that observations made at any point on the earth’s surface may be corrected to suit this point, in which the eye of the observer is always supposed to be placed. This point in Astronomy is the centre of the earth, and for this point the tables are calculated and the corrections are made. Supposing no corrections to be essential, there is little doubt but that in each Greek design all the magnitudes would be found to be commensurable one with another, and the lines, if intended to be straight, would be traced with all the precision required in geometry—indeed, instances occur where this is actually the case both in the Proportion and in the lines, therefore all the observed irregularities in the works of the Greek Architects will, I believe, become a. succession of proofs, and most conclusive evidence of the truth that general laws guided them in the designing of their works of Art, and, if the laws that I propose to trace be correct, they must in every instance give the same results as are found in the observed works, for such is the accuracy with which the Greeks executed all their designs, that it may be relied on to within the tenth part of an inch in a dimension of any length, consequently the theory and the observa- tions must always be found to agree when the given quantities are correctly stated. If it were necessary to show that the two elements—the first, the position of the design, and, the second, the point of sight for which it is to be adjusted—have never been altogether disregarded, although the observance of them has been reduced to little more than an acknow- ledgment of the truth of the vague words in which they are expressed by Vitruvius, I might quote from the writings of Wren, Palladio, Vignola, Milizia, and others, who have all acknowledged the necessity of adjusting the design to suit certain fixed points of view. But the words of Vitruvius, which were influenced by the Greek writings, and which have influenced all subsequent Architects, will be sufficient, and will fully express all that has since been felt upon the subject. He says— Book VI., Chapter 2.—¢ After having determined upon such Proportions as the necessity ““ for the commensuration of the parts with the entire building seems to require, the greatest “ judgment must be exercised in ““ Adapting them to the nature of the spot "—position ; ““ The use to which the edifices are designed "—dimension ; ““ The appearance they ought to assume "—the corrections. These corrections are adjusted ‘by making such additions or diminutions that, although “ the Proportions are not strictly what they ought to be, the eye may not be conscious wherein “ they fail.” ““ The same objects appear differently under dissimilar circumstances, if near the ground ““ or at a considerable elevation—if in a confined space, or an exposed situation. Under every 40 THE FIRST GIVEN PROPORTIONS. “ peculiar circumstance great judgment is necessary in calculating the effect that will be “ ultimately produced.” ““ The impression made upon the sense of seeing is not always a correct image of the ““ object.” ““ Since, therefore, objects sometimes assume an appearance of being otherwise than they ““ really are, it will not be denied that additions and diminutions may be made, as the nature of ““ the situation or the exigencies of particular occasions require, in such a manner that the ““ deviation from the general laws of Proportion will not be perceptible.” “ Tt therefore becomes necessary, in the first place, to institute laws of Proportion, upon ““ which all our calculations must be founded. According to these the Ground Plan, exhibiting ““ the length and breadth of the whole work, and the several parts of it, must be formed.” ““ When the magnitude of these is once determined, the parts must be arranged so as ““ to produce that external beauty which suffers no doubt to arise in the minds of those who ‘““ examine it as to the want of Proportion in any part.” Throughout the writings of Vitruvius, the eye is referred to as a perceptive power for which the parts of the design must be adjusted, but it would be useless to multiply extracts, as he nowhere gives any geometrical laws for the mathematical adjustment of the visible design. Aristotle defines the beautiful to consist in magnitude and order. Magnitude being a relative term is made to comprise the whole “ extent of that scale which the eye 1s able to “ embrace at one view.” Even in the minute details of the inscriptions engraved on the Ante, the principle appears not to have been neglected, for in the “Antiquities of Ionia,” Vol. I., p. 13, already mentioned in the Introduction, we find that the fronts and external faces of the Ants belonging to the Temple at Priene were covered with inscriptions, ““ and from the degrees of magnitude “ in the letters, it may be conjectured a regard was had to perspective, the greater being higher “ and more remote, the smaller nearer to the eye, so that at the proper point of view for J “ reading, all might appear nearly of the same Proportion.” But I shall confine my attention to the Greek remains in Athens. In these works every principle of Art is fully developed, and they are executed with such extreme precision, that all the general laws of Art can be restored from them with as much certainty as we can trace and prove, by observation and by calculation, the fundamental laws of Astronomy and of Mechanics. Taking it, therefore, as a natural law that the eye can only present objects to the mind perspectively outlined, and that this outline varies for every position of the eye with regard to the object, it will at once appear as essential in the first opening of the work to agree upon some fixed point in which all observers are supposed to be placed, and all within the optical angle subtending the greatest extent of the design must be made to appear in perfect harmony THE FIRST GIVEN PROPORTIONS. 41 and Proportion according to the definitions of perfect Proportion previously agreed upon—that is, all the apparent magnitudes must be made to appear commensurable one with another, and any apparent defects in the appearance of the horizontal lines (that is, if they should have a concave appearance as mentioned by Vitruvius) must be rectified. It is of the utmost consequence in each design to determine with accuracy this point, as it is impossible to re-calculate any work of Greek Architecture and to arrive at the same dimensions until it is fixed with precision. But as we have seen, there is sufficient data remaining in the Acropolis of Athens to enable us, in every case, accurately to assume the original position of the eye with regard to each design, and it must then be proved by the calculated dimensions agreeing in mathematical accuracy with those that are executed. The results obtained by theory must in every example agree with those derived from observation, not approximately, but positively. It being evidently intended that the several designs should be seen from angular points of view, we may in every example— 1st. Assume the greatest diagonal line in the plan of the design as the base of a triangle whose angle at the vertex shall always be equal to 45°, which may be considered as the visual angle of distinct vision. The vertex of this angle determined on the horizontal plane will be found to be the fixed designing point. 9nd. The distance of the Upper Step of the design above or below the eye of the spectator (i.e, above or below the horizontal plane) must also be made a given quantity. 3rd. The centre of the given road of approach is generally the point selected for the position of the observer. We have now derived from observation all the given quantities that are required to be ascertained before we proceed to the second part of the theory of Proportion, namely, the determination of the apparent magnitudes. These given quantities are the first Proportions of these several Porticoes; the true projections of the Steps, Cornices, and other members of the KEntablatures; the length of the return sides; the inclination inwards of the masses of the Columns and Kntablatures; the given length in feet of the Upper Step, which regulates all the other dimensions ; the position of each design upon its artificial platform ; the true height of the Upper Step in each design, either above or below the level of the eye; and the true position of the eye with regard to the whole design, which design has now simply to be corrected by trigonometrical calculations to determine, firstly, the true executed heights of the Steps, the Columns, and the Entablature, with its subdivisions into Architrave, Frieze, and Cornice, and the several members of the Cornice, and lastly, the height of the Pediment. 42 THE PIRRT GIVEN PROPORTIONS. The design must now be considered complete as an idea—the plan, the dimensions, the position, the order of Architecture, the arrangement of the Sculpture and of the inscriptions, only requiring the few corrections named, so that the impression on the eye of the beholder shall be made to convey the true idea of that perfect conception of the work which has been formed in the mind of the Architect. It will be the expression of this idea in some given material (marble or stone), by making those corrections which become essential when the point of view is no longer in our mind but is transferred to a fixed point common to all, so that the visible work shall appear to every one to be similar to the perfect mental idea, that will lead to the application of the several branches of the ancient geometry, and will prove how closely the Greeks united Art with Science. THE END OF THE FIRST PART. PART Ill. THE APPARENT PROPORTIONS. 43 THE APPARENT PROPORTIONS, 45 CHAPTER 1. INTRODUCTION. It 1s only by continued researches that we arrive at any knowledge of the general laws of nature; the laws that have been discovered either in Chemistry or in Astronomy have been obtained by deducing general principles from a few well observed facts. The eye alone could never convey any idea of the definite proportions that exist between the elements composing any given substance, nor could the eye discover in the movement of the Planets, the proportions that exist in each orbit between the areas described and the time of describing them; when by investigation we obtain a knowledge of these laws, and are able mentally to perceive the harmony and the exact proportions in which the several parts of the Universe are linked together, we feel an intellectual pleasure, arising perhaps from an original impression on our own minds of what appear to be the essential attributes of a perfect work: certain it is, that we feel a pleasure in the discovering of exact proportions and perfect mathematical forms in any portion of nature, and, such being the constitution of our minds, it is natural to us, in the conception of any work of Art possessing the three dimensions of length, breadth, and depth, to conceive the design perfect both in proportion and in form. To be perfect in proportion, the several parts composing the design should all apparently combine in definite and exact proportions according to some general principles of arrangement. To be perfect in form, every line, both straight and curved, in the design should be conceived to be traced with mathematical accuracy. But a work of Art is not merely a mental conception ; it must be executed: and the Art is to convey our own impression with mathematical precision to the minds of all who contemplate it through the medium of the executed work, the eye being the channel through which the idea of the Architect must pass from the executed work to the minds of others. Now a principle in Euclid’s “ Theory of Apparent Magnitudes” (see his work upon Optics) is that we judge of the magnitude of an object altogether by the magnitude of the optical angle. This principle is true when limited to the several magnitudes composing a work of Architecture, viewed, as the work must be, from some fixed point, and at a sufficient distance for the eye to embrace the whole extent of the design. From this fixed point the magnitudes of the several members of the work are measured by the visual angles, and if these apparent magnitudes, measured in degrees and mutes upon 46 THE APPARENT PROPORTIONS, the arcs of great circles, of which the eye is the centre, are incommensurable one with another, the whole design would appear inharmonious, and the ratios between the several apparent magnitudes would all be irrational quantities; consequently, the perfect idea of proportion that had existed in the mind of the Architect would be apparently lost in the executed work, and as a work of Art it would entirely fail. This primary idea, that the executed design should reflect the original idea of the Architect, with all the perfection of form and proportion with which it Was first conceived in his mind, gave rise to the several corrections we meet with in ancient Architecture, and led to the study and cultivation of the several branches of the ancient mathematics. To produce this effect of an apparent harmony between the several portions of the work upon the minds of those who viewed the executed design, it was requisite that certain corrections should be made upon the several visual angles, so that all the apparent magnitudes should be commensurable one with another; this change in the visual angles produced a corresponding change in the dimensions of the primary figure, and it is the altering of the positions of the points and lines of the design as originally conceived, and the determining of the true dimensions at the angle of the design nearest to the point of sight, which will constitute the second part of the Theory of Proportion. The subject may be considered under four distinct heads— First. A few observations on the ancient method of laying down the design upon three given horizontal and vertical planes XY, XZ, YZ, passing through the point of sight O, so as to fix each point and line of the design correctly in space, and the few simple trigonometrical forms of calculation that are required for the determination of the sides and angles of the visual angles. Second. To determine by calculation the point of sight O, and the position of the design upon the horizontal plane XY and vertical planes XZ, YZ. Third. The law for determining upon the given plane HOZ the true apparent perpendicular magnitudes measured by the visual angles, and the true heights of the executed design at the angle nearest to the given point of sight O. Fourth. The application of the theory explained in Part II. to the designing of the Parthenon, the Frechtheium, the Propylea, and other Athenian Works, showing the perfect mathematical agreement between the dimensions obtained from observation, and those arrived at by the trigonometrical calculation. PI1IBgT, OBSERVATIONS ON THE GEOMETRY OF THREE DIMENSIONS, AND ON THE TRIGONOMETRICAL CALCULATIONS APPLIED TO ARCHITECTURE. Ix the most simple questions that occur in the Geometry, it is seldom that we can by any direct means measure any line or surface ; if we imagine ourselves at a distance from the body THE APPARENT PROPORTIONS. 47 it becomes impossible. This has given rise to the series of geometrical considerations, which, in the modern System of the Mathematics are embodied in the general forms of the Analytical Geometry. Now, although the Greeks did not possess any analytical forms, we must not conceive that they were limited to the mere measuring by scale of their lines and angles. The evidence is in favour of their having been able to calculate with great precision (and we find in the ancient Astronomy many elaborate calculations are preserved), and their works of Architecture, when examined with the proper degree of knowledge, also prove beyond a doubt that it was requisite for them in their designs to fix points, lines, and surfaces in space by the projection of visual rays (imaginary lines) often three and four hundred feet in length ; yet with all our modern improvements in the Trigonometry and in the Analytical Geometry, we can discover no error in their calculations. They arrived, by their ancient methods of calculating, at exactly the same results as we now do with the aid of our modern Logarithmic Tables, improved Formulze, and simple Arithmetic. The calculations to them were more laborious, but the results obtained, either by the ancient or by the modern methods, are exactly the same. If any evidence were required, beyond the existing works in the Acropolis, to prove the close connection that subsisted between the ancient Architecture and the ancient Geometry, we have, mentioned by Vitruvius, and copied most likely from some ancient Greek writer, an account of those subjects in which an Architect was to be instructed ; he says, “an Architect “should be versed in Geometry, Optics, Arithmetic, Astronomy, Music, a skilful Draughtsman, “&ec.” That the several branches of the Geometry were early cultivated by the Greeks we have convincing evidence, both in their Astronomy and in their Architecture; but, although we find their calculations made with remarkable accuracy, and with reference only to their Architecture with all the precision that a modern geometrician would require in making similar calculations, yet we shall rest satisfied by arriving at the same results without following the intricate processes to which the Greeks were forced to have recourse. 1 shall, therefore, in all calculations use the modern Arithmetic in preference to the ancient, the modern trigonometrical forms and tables of sines and tangents instead of the ancient Trigonometry with its tables of chords and arcs, and similarly with the Geometry. A previous acquaintance with the first elements of the plane Trigonometry and of the descriptive Geometry will be supposed; but for the sake of reference there will be tabulated, at the commencement of each subject, the few simple equations that it may be found requisite to employ. THE GEOMETRY OF THREE DIMENSIONS. Vitruvius, referring to those things on which Architecture depends, in Book I., Chapter II., says, Arrangement is the ‘disposition in their just and proper places of all the Nore.—All that relates to the Mathematical and Arith- sufficient to refer to their works for a detailed account of metical forms that were employed by the Greeks in making the ancient methods of making their Trigonometrical and their Astronomical calculations (and consequently in their Arithmetical calculations, and also for the ancient theory Architecture), has been so ably condensed by Mons. of the Conic Sections and of Optics, which will be noticed Delambre, “Histoire de I’Astronomie Ancienne,”” and also later in this work. by Montucla, * Histoire des Mathématiques,” that it is 48 THE APPARENT PROPORTIONS. “ parts of a building, and the pleasing effect of the same, keeping in view its appropriate “ character. It is divisible into three heads, which, considered together, constitute design; ‘“ they are called Ichnography, Orthography, and Scenography. ““ The first is the representation on a plane (XY, Fig. 1) of the ground plan of the work. “ The second is the elevation of the front and the return side (on the planes ZY, ZX). Cn The third is the front and a receding side, the lines being drawn to their proper “ vanishing points (namely, a perspective view showing the shadows and colours) ; these three ‘“ are the result of thought and invention. Thought is an effort of the mind ever incited by the “ pleasure attendant on success in compassing an object. Invention is the effect of this effort, ‘ which throws a new light on things the most recondite, and produces them to answer the ‘““ intended purpose.” Book I., Chapter I.—¢ Arithmetic, assisted by the laws of Geometry, ““ determines those abstruse questions wherein the different proportions of some parts to others ““ are volved.” The three heads into which Vitruvius divides this part of the Theory of Design may be defined as follows :— 1st. Ichnography—the projection of the Fig.l. 4 planupon the given horizontal plane XY, Fig. 1, Perpendicular Perpendicular plane X7.. and the calculating and the drawing of all the planeY.Z. . 2 ss imaginary lines and angles that will be required ORTHORGRAPHY FEE om to be traced on this plane XY during the pro- . gress of the calculations for clearing the given design of all apparent irregularities. 2nd. Orthography—-the fixing of all the points, as they are gradually determined by calculation, upon the two given perpendicular - planes YZ and XZ, Fig. 1, so that when a sufficient number of points composing the = = figure in relief have been calculated, and the projection of each point fixed upon the planes XY, YZ, XZ, each point in space will be determined by the intersection of two horizontal co-ordinates at right angles to each of the planes YZ and XZ ; for example, the point M, the vertex of the Upper Step, is determined in position by the intersection of the ordinates MM" and MM?® and P by the intersection of the ordinates PP' and PP”. Let XY always denote the horizontal plane passing through the point of sight O. Let XZ and YZ be two planes parallel to the front and to the return sides of the design, visible from the point of sight O. These two planes will be each of them perpendicular to the horizontal plane XY, and will each of them pass through the point of sight O; By means of these three THE APPARENT PROPORTIONS, 49 co-ordinate planes XY, YZ, XZ, we shall be able to fix in position, “in their just and proper places,” with mathematical accuracy, all the parts of a building, whatever may be the varieties of curved lines and surfaces of which the whole design may be composed. On these planes was traced the idea of the Architect, the whole arranged with mathematical accuracy, so that the true position of every point and line in the entire design, though not actually exhibited, could be found. For our present system of the Descriptive Geometry we are indebted to Monge ; but the Greeks also possessed a complete system of the Descriptive Geometry of three dimensions, neither were they confined to the mere mechanical measuring of lines and angles; on the contrary, they fixed their points and lines in space by calculation, and, although their methods might have been inferior to ours, their final results were as accurate, within the limit that was required in their works of Art, as every executed design will testify when the mathematical spirit that lies concealed in them is unfolded ; and if the works in Athens were insufficient, we have also the words of Plato to prove to us that the Greek artists were Geometricians (see the ¢“ Republic”). “If one should meet with “ geometrical figures drawn remarkably well and elaborately by Daedalus, or some other artist “or painter, a man who was skilled in Geometry on seeing them would truly think the ““ workmanship most excellent, yet would esteem it ridiculous to consider these things seriously, “as if from thence he were to learn the truth as to what were in equal, in duplicate, or any “ other proportion.” This could only be known by the artist possessing a knowledge of the general principles of Geometry. PLANE TRIGONOMETRY. The only trigonometrical forms at present required for making the calculations will be— Firstly. To find the angles of a right angled triangle when the two sides are given, and Secondly. To find two of the sides of a right angled triangle when the three angles and a side are given. The following forms are therefore all that is required :— 3 Form 1.___ Log.tang. A=log. r + log. a — log. b. a » 2___...Log a=Ilog. b+ log. tang. A — 10. » 8... .Log. b=1og.a+ log.sine B— log. sine A. C A This 8rd form applies to oblique angled triangles when two angles, A and B, and one side a are given, and two sides, b and ¢, and one angle, C, are required. Besides these three Trigonometrical forms, it is often requisite to determine the hypothenuse BA = C, when the two sides, a and b are given. Form 4. _ _ C= Ja*+ 1’. Euclid, Book 1, Prob. 47. 50 THE APPARENT PROPORTIONS. The given quantities being all settled, and the first design fixed in position by being referred to the rectangular planes XY, YZ, XZ, we may proceed with the calculations tor the determination of the true heights of the executed design at the angle of the building nearest to the point of sight O, that is to determine by calculation “the additions and diminutions ” that are always made upon the first given design, and which have been observed in Part I., Chapter IL, Plate II. SECOND. TO DETERMINE THE POINT OF SIGHT, AND THE POSITION OF THE DESIGN UPON THE HORIZONTAL PLANE XY, AND VERTICAL PLANES YZ AND XZ. Tt has been already stated in Part I, Chapter IV., Plate IV., that the Greeks selected, as the most favourable position for the contemplation of any work of Architecture, the vertex of a visual angle of 45° formed by the visual rays embracing the line AB, Fig. 1, of greatest extent in the design. | This line is generally the diagonal of the parallelogram containing the lower step of the building which Aristotle defines ‘as the whole extent of that scale which the eye is able to embrace at one view.” Let the given line AB Fig. 1, the longest diagonal line in the plan of the design, be traced upon the horizontal plane XY, and let this line be made the base of a triangle whose angle, BOA, shall equal 45°, the point will then be the point of sight and the vertex of the given angle. Fig. 1. The design traced upon the three rectangular planes XY, YZ, XZ, all passing through the point of sight O. Fig. 1, KEuchd, Book II1., Prob. 20. The angle at the centre of a circle is double of the ~ angle at the circumference upon the same base, that is upon the same part of the circumference. Therefore, upon the given diagonal line AB describe the right angled triangle AFB, THE APPABENT PROPORTIONS, 51 making the angle I — 90°, then from the centre F, with radius = FA — FB, describe the circle AO', O', OB, the angle AFB at the centre is double of the angle AOB at the circumference, the angle AFB = 90°, consequently the angle AOB = 45° as required. Prob. 20. The angles in the same segment of a circle are equal to one another; therefore, let AO’, O', OB, be the circle, then the angles AO', B, and AOB, are equal to one another, consequently there is an infinity of triangles that would equally solve the problem, but the vertex of each of the triangles is situated in the circumference of the given circle; therefore, the base line AB being given, and also the circumference of the circle AO', OB, the position of the point of sight O, situated in this circumference, must be fixed to suit each separate example, and to depend upon the position of the roads of approach. The angle ABO must always be one of the given quantities, as well as the angle BOA = 45°, and the sides BO, AO, must then be trigonometrically calculated ; also the angle DBO being given, as well as the side BO, the two other sides, OD, DB, are found, by calculation, from the form log. b = log. a -- log. sin. B — log. sin. A, and the distance OC is calculated from the form OC = +/ OD? +- DB?, and in the same manner OH is determined. Fig. 2. Plan of the projections traced upon the horizontal plane XY at the angle of the design nearest to the point of sight O. 7 | a / 7 77 7 7 2 ob yw oH | 7 7 7 © upper step lk _— ; > = ~~ 7g X_ Be 1. 7; Ne = x, ls r 0 De | ~ - ~ | / ~~ : “ ’ Se IN ~i Ts N 7 - ™N | i ~{ > “N | i ~ \ 175 Ne ; fie TA ~ + 76 % : | / = - . ; | lower step | 77 : $l rier i J CO ~, fx i ™~.. re . “© ~~ 7’ 2 v Fig. 2. HK = HO — CO will be divided into the same number of aliquot parts as HL, and all the projections will be regulated by the division into aliquot parts on the line HK, the 52 : THE APPARENT PROPORTIONS. same as HL, then let a vertical plane, HOZ, be given, passing through the angle of the frieze H, and the point of sight O; on this plane HOZ, the true heights of the building will all be trigonometrically calculated, and the design will be fixed in position by being laid down upon the three rectangular planes XY, YZ, XZ. Fig. 1. | The practical examples hereafter given of the Parthenon, and of other designs, will render clear the above description. THIRD, TO DETERMINE UPON THE GIVEN PLANE HOZ, THE TRUE APPARENT PERPENDICULAR MAGNITUDES MEASURED BY THE VISUAL ANGLES, AND THE TRUE HEIGHTS OF THE EXECUTED DESIGN AT THE ANGLE NEAREST TO THE GIVEN POINT OF SIGHT O. In the Introduction to the present work (page 3), I have referred to an inscription, at Priene, upon the external faces of the Ante of the Temple, published in the ‘ Antiquities of Tonia,” Vol. I., Page 13, in which it 1s remarked that “from the degrees of magnitude in ““ the letter, it may be conjectured, a regard was had to perspective, the greater being higher, ‘““ and more remote, the smaller nearer to the eye ; so that at the proper point of view for ““ reading, all might appear nearly of the same proportion.” This agrees with what Plato affirms in the “ Sophist:” that « Artists bidding farewell “ to truth, work out not real proportions, but such as will seem to be beautiful in their ‘“ representations.” Vitruvius also says: “ When, therefore, the kind of symmetry and the magnitudes are “ gettled, it is then the part of the judgment to adapt them to the nature of the place, and to “ the use of the species, and, by diminutions and additions, to qualify the symmetry till it “ appears rightly adjusted, and leaves nothing defective in the appearance.” From observation, we have also found in Part I., Chapter II., Plate III, that certain additions and diminutions exist in the executed dimensions of all works of Greek Architecture, so that the first given design differs in the dimensions of the perpendicular magnitudes from the executed heights, but that these variations are always small quantities, never amounting to more than three or four inches of increase or of diminution, and it is the method employed in the determination of these small plus and minus quantities that 1 shall now proceed to explain— 1st. As applied to a perpendicular line divided into a given number of aliquot parts. 2nd. As applied to the Greek Architectural Designs. THE APPARENT PROPORTIONS. 53 In Euclid’s “Optics,” we meet with the following theorems :— “ 1st. That objects appear larger when the visual angle within which they are seen is larger. ““ Liess when the visual angle is less, ““ Kqual when the visual angles are equal.” “ 9nd. That in equal parts of a given straight line the more distant parts are seen within a ‘““ smaller visual angle, and will, therefore, appear less.” “ 3rd. Magnitudes of equal size, when seen at unequal distances, will appear unequal.” Figs. 1, 2. Applying these theorems of Kuclid to a perpendicular line CB 50 feet in height, and divided into five equal parts, to be viewed from the point of sight O, at a distance of 150 feet, we shall at once perceive what corrections would be required in the division of the line, so as to give the appearance, from the point of sight O, of the line being divided into equal parts, and what the actual differences would be between a line correctly divided into equal parts, as in Fig. 1, and a line apparently divided into equal parts, as in Fig. 2. Given Hricurs. Thus, Fig. 1, let the perpendicular line CB = 50 feet be divided into five equal parts of 10 feet each. And let the distance from C to the point of sight O = 150 feet, then by calculation, we can determine the several visual angles VY. VV. V2 V5, VV from the Form 1, log. tan. A = log. r + log. a — log. b. : § RX ug 53 : B oo iH & Fig 1 i XN is 8-1 |S ND 5 ¥ fo ao : / 5° A $ YS. os. i / Tw © A @ = / 3° =. Ne ~ 1] (Ln TR 2 S| ’ 5H NY $ S / 4 in ~ 0 Ps ® | / g. %2 # TX T—- 2 ! > ™ a bs 1 / > 92 / SY ey NN Hf LY *. ., ; / ee > Qo igs Se ae 81 . 2% . 54 > he > 5 / . Xo Tr i NG ew . ~~ ; ar iti > > x pe 1 / re Bi — US, tT. for re ToS S 3 4 ” { I oT ~—— . fe "9 > he 18) #48 J i Tee NS fd ! | Bam —— : C . ” T= eee an GOO po... DOT OT Sig And we find these several angles V, V', &e., to vary between 3° 48 51" and 3° 30" 10" CorrECcTED HEIGHTS. Thus, Fig. 2, divide the arc CD = 18° 26' 5" into five equal parts, and then, by calculation, the angles being given, to determine the five perpendicular magnitudes. 18°26'5' =8°41'18' = V, V\, V%, V3, V¢ 5 Form 2, log. a =1log. b+ log. tan. A — 10. : 8 338 « Yi3 oo 3 g oA $§ 3° 3 J Is y al Lo> pil 40 kg ; 2 . Ld ~ $ “ x. J Ce} / : ' t Pre f 4 : 2. ™ ! ! ~ 7 ™ 4 3 / Sn > > ; / 0 a £ MN rs (Lr Ay Y= gh. > / ™ 5 J *~ / < 3 ye A sf BAG = / ATR gis Te TS / ois Bac.” Ss J eh. i ; / 7.73 fr 5% oy Xo 5 Sa fo NN A f ee —~—— ~ 8 To bs oS wl/ oe, = Tea ha iD SW PHhy J TE. hoe 5 ] ~— ~~ ~ seb rennin | i Th. a ~. > glo Trt i an MGT, : 3.99.73 | Tr ee. Ta wy La > Bim Ee : re — ~N , » ; L ¢ a soles POY of sight 0) The visual angles being equal, the line CB is divided into five apparently equal 54 | THE APPARENT PROPORTIONS. The line CB is divided into five equal parts, but the dimensions vary between 9-66 parts, but the visual angles being incommen- feet and 10-52 feet. surable, the line will appear from the point of ger corrected Amount of variation sight to be unequally divided; it will be ™°%% “CF | tetwoen thegiven and R the corrected, line CB. apparently incommensurable. Let the visual angles be made commensurable, that is, divide the are CD = 18° 26’ 5 into five equal parts, and then, by calculation, deter- re. ns. ooo] 2 mine the apparent magnitudes (see Fig. 2). 08 = 7.1 Note. these additions correspord vv character arud nearly vv armour with those observed lart l (hap. 2. giver line CB. corrected Lire C.B. | o feet ae I at ay | ~ poll hn foe Ty od ®) By this simple correction in the vertical heights of the line CB, we perceive that it is now actually divided by calculation into really unequal parts, but into apparently equal parts when measured by the visual angles, and that the variations in the lineal magnitudes are = 6 ins., + 1-9ins., — 1-1 ins., — 41 ins. These small additions and diminutions correspond in character with those observed in the several Porticoes, as laid down in Part I., Chapter II., Plate III., and with those noticed by Vitruvius. In the first instance the line CB has a common modulus or multiple = 10. In the second case the arc CB has a common modulus or multiple = 3° 41/ 13. And the line CB will appear from the point of sight O to be equally divided into five aliquot parts, because the visual angles are equal (Fuclid’s Optics”). Exactly the same principle will apply to the vertical heights of the several given Porticoes at the angle of each design nearest to the point of sight O. Firstly. By the trigonometrical form No. 1, log. tan. A = log. r + log. a — log. b, to determine the several angular magnitudes from the given heights of the Portico in Fig. 1. Secondly. To find the nearest angular modulus, that will be an exact multiple of the whole apparent height, and of each of its component apparent parts, namely, the Steps, the Columns, and the Entablature, and then, by the trigonometrical form No. 2, log. a = log. b + log. tan. A — 10, to calculate the true vertical heights, Fig. 2; and the small variations between the given design, Fig. 1, and the executed work, Fig. 2, will be the plus and minus quantities already noticed—thus : THE APPARENT PROPORTIONS. 53 Ist. The given heights of the Porticoes traced upon the plane HOZ, Fig. 1. In Fig. 1.—The apparent heights, measured by the visual angles, of the = Steps == 8, the Colmiis = C. andthe —1 +1. Entablature = E, are calculated by the boo | Fig 1. Ist giver, heights | Form 1, Log. tan. A = log. + log. a 3 + log. 0, then comparing the calculated ot : | pt bl Point of stghit for the North corona os 7 ™ Ey Pod West angular designe 19.3 > id Ppt OQ below the Lpper step 7 4 : / O | A 2 / : vad * / oo] ! | Fo . / * O | ; | 5 5 ; upper step / i 1 | ’ | \ 7 % \ 2, J \ A - z Z 2 bn] a Pe / abacus b vy ad 1 : ge o* / archilraic ol i Lt ” ie” we . ; ; 22 ee : ere orl IP 4. 2-7 2 oY ZL UL Yv | Y The side BO of the oblique trvangle ABO a * feo * freee L | : ND Q > . Aa a ¥ 2] ; or can be delermuned from the Form > " : B ; = en i HOM ts HOM = YW = pes’ } gd 3 log.b = log. a + log. stn. B— log. suv. 4 2 : . this quantity regulates the whole apparent leecqht Be : — = — 1 y - ; HE : i vol | | = be = B < Lo ro EE ee | } ; 3 27 i ; | “0 on Gs A To : : Si 4 . 3 . . - . bles mt. 271 + OD E re me Fig. 4 The given heights of the Portico traced upon the plane HO Z the Fig. 5. The corrected perpendicular magnitudes upon the plane a > A eR] ? S S» © © 6 © SH. a he : 3 erpendicular lineal madnitudes are all commensurable. the HO 7Z the visual andles are all made commensurable, and 5 i = li Atay , % . P P O 2 eS 8&8 8 © 8 & 8 5 rl tered iy on: angular magnitudes determined by the the true executed heights are determined by calculation Adar | ( oo 15 5 Form. log. tan. A= log.r + log. a— log. b. are incommensurable. from the Form. log. a = log. b + log. tan. A-10 > : L : 8 hn Lb Ls : % 5 fF. oop OF iy : . = : he 2 i el os fi 2 3 | Be & ©! heb 1 | 3 | a 5 fii! j $3 : SY : E ) / on | > oN : No S 5 Ee ! Neate : Yes i gf Tee tig : Ey ; : oor 9 facia above corona ee RE _ gE 3 | EE! / : TH jar en et pode 7. = 0 5 ii } 2 ut : > ~ 3 Se : Os / * : E Ss { 7 = i 1 ~S 8 = ~ Pry | % 3 A ry 2 - : : 2 S S x i 3 Fi h re >: 7 ee. X ; ; ES / cag 33 Pray 3 Y S _ >, gs I 4 E j -T 18 > $ Gh uy TL eben re / & 5 S = , 7 eo niet : 7 7 5 Q : = : v le he & / oe. PE / | : z rr A Ph ; En pod P= fs. : | = S. 3 ; \ = | ii 5 fic projection of abacus 7 > a . | | | on, Sl / 3 § - : \ / = = i “hae >. / oy i | | y Fre J a S : . y i o : *6 : as : X § ! ! 2 N EN) i ills el x nd 1 Ld ; | / = 15 / iO Fo HE 3 To, : r - +5 L : J ¥en 2 ! i yo 3 / J TORR. ; | bs Sd 1! | Ny / Seer = op | ! ® / 5 = 5 3 $ 3 i § 9 : = 3 3 ooo § $ $ : ’ = = No ® BN # i : \ N x 7 > = i y y & ~ $ ; ! al X a Hi $ S i 2 8 4 : S f / . > = : vs < : ! s J / : | : | N & 8 ; i Loe 8 = uniw — upper i 3 y hb § 3 : : a § S 9 I | i . i \ & ==] i *o i ; i : | | ¥ \ 206 c 9s 1 no ¢F 7 2 or ve ty 7 \ : iB ls Ao i] i § = Jil HE 2 = ¢ / : as 4 Hi | S ! of HE ri aX \ oo mre Ce ££ 8 8, e $8 £ * i \ : ay | 2 . 3 3 \ 4x : 4 I 2 Fl lh 3 \ / / } 7 ; : g S ; on uppler step 3 > 3 \ ; : : ttl | upper step , J ! Ea . te < \ | ” 4 1 4 ii _ Se » : lo & _ / eb \ it pen hE IE = tril 5 wma oe bnd \ } ; Lx : PS 3 ; NY Ss 2 | « He ie = a ~~ ! D 2 \ | 3 ta wal, 7 : 2 2 rere Ld i 7 az 3g level plane | 2 3 N\ ~ ~~ vy 1 JL 7 Y, a N 3 NA NN \ Ane A) \ Be $ N\A Forse Bt onc aa: Fete \ ] | "a 2 RMLMLIMMIMUYBEOOROVINK rg iveniier,s : tran tetra) \ | | | a Lo A N DM pag J eri A rrr PTT IIIT : | . : | of A We 4] v, / i 5 or i / 7 7 So NL x S$ > / / . 7: a : 1 ik 7 ld z i ge ns ols / / w ; TL — 7 7 7 77 egal ime i \ / # 7 i & v LAAs i Ree / er vor 73 : 7 5 VR, I ddr r A /, 2, 5 rr Fd 7 i 7 Sy TTT / F777 TT rari ~ \ $ f i BR Ld A ih ef rs 0 rr, bie A Ad I I EI, I A ] : “, A 7 J Ll o di 7 z , / / y f / 7 oz “v7 / Y Lf 2 7 4 7 7 i a y 7 L/ ’S oS fA 7 ror 7 fo of / £7 / ofS £4 / IA s S z rr : vy or ol 7 as sy #3 7 i GEAR A oy LALA TATA A LS IRAE Sr Ia 2 2 \ i % ~ : 15 di ; ? f | : Ee 149.899 to lal plane.................. \ i & 3 ; bce crmssnensrons. $61. 439" 40 LoWOSt BL orenrson-mmnsseness ; es gms Td {to facia: above corond...............; \ : bl ein YE5 02 facta HONE (pir women emmrnn = ==l yp, Dovel of Sight | o ss aos to upper step... 158. 515 to Abacus \ to Point of Sight 0. \ ¥ eect oen.. 158, 405 tO upper Peete 152,515 10 Ahas a ; itn U58 23 fo Priee.......s- 159. 110 to Arclatrave .... \ Ho . |! ess nenninny: HE 53 Frieze... 769.710 to Architroe......... ¢ De Aaa 155. SF itor Bodie oo oven soe aa \ *To | A \ z y y = . rr y Pra \ 0 ] whee heh I Corrections tw the West 2orhie. o Lx i528" 62930" == corrected apparent Height \ 2 | ho 1573257 014. 2.5278 incommensurable Biko 4 tal i ons yond Sons resulting 62930" == 6992" = Modulus of’ apparent Hecht \ : | col hele Feekaied RA 10......... nearest ratio a by proporticrv calculations from the corrections 9 92" ot ; Renee, whale heigh By ; 409 1%. = 5.8 is. SIHIDDOLE ooeinssisesronsnnsn = 69 Xx 7 ==1¢699 | fr THE TH gg mee | RG LGR S| \ fo | Lye colvimn Zloty Te rl C298 nr Gi IE... t OST] , = E6.E, Columns from upper 992" x 6= 41952" \ bs | i S AS M392". i 4907" i. A... 2.876 incomumensurable Whole height... 50. 668... 1509.0 on. 4 0.887 . ue y Sap toddrehiitrmien. = 0990" x g= 91932 \ 0 Font a’ Sight 107° the south east 4. : ee Brin nna TUOOTOSL ratio Fediment mio mm i /3 ’ 136 rir 72.485 ipa 0. 657 o” Ze 2 : ’ v " \ angular design 9.2 below the Entablature................== 68392" Xx 2= 13984" + 237" projection of, \ upper Step. iF Abacus. \ Pavement HM. 2 below the upper Step Ge Tole : 6992" x = 62928" +251" = the whole - : apparent haght. Bodirert oe id im A308” 4 207" w= BIN" £. 0.77 4 Wik, Clastle ILA ordon ZC RY 3 Aor 5 nla ore dol ' ' : | Tar ParnrtnENoN N° 3- Tor SouTH Fig. 1. The Plan of the Parthenon with the elevation of the Portico and the return side traced upon the three rectangular planes XY, YZ. XZ, passing through the pomt of sight O Yast . Sluis i og Ee 6 gl 2 ; 8 { N 1 \ i \ | i & 3 SS Lv on foe 1 Hl le e de | | 1 1 | | Lind S S / | | I | 1 1 I I do S ae I 1 iL 3 fils ‘© i 3 2 | B : 0 te te ! | S 8 / i | . 4 1 | — : 5 = ' i S & te J | | 1 I I | I I 1 8 8 | | i | ) : ! : : ! | | doo ol S L N / Ll ev | 33 ! \ NS S 8 Xo, ORL... =i Tw lle of / i ' > : 1 triers im. nN LL ; : ; ; : : Laan aan . ae iY SO 8 [= tee ] ' fe in > rare Serre TH ; Ee io a I [ i te : © i : J h ! | Tse : ™ 1 / : i bo =~] or / x — ! > © ; ; ! ! : I~. 2 A Weel LS Hl iii a) s HO THD re nna iets ] ' he ! ie Siti \ ”” | f : i ! Ji 3 5 > { Md me] Di: fr 5 Jen i ! * 2 ~. | eo! oe : | ; ! : 7 : : poly ; Q i iE FS . 1 | . Lf 5 |. I 0A Q 1 1 ! ~ | | bo] ad J No ) Jl : : 2 : a | ’ ~ | y ¢ | : y ! | ! z ' ! ! ! / ’ 5 : ” i i ~ | 1 | : z SL x y 1 A 0 point of sight for the south east | i angular designs 9-2 below fo Fa upper step. FE pavement #2 below the upper step iy : i A Jl ; ! | \ Lay Laney 1 1 ! | 1 od { bi oa ll % oh fo BEd : . iv) Fi The side BO of the cbligue triangle A B 0 ; boy jo can be determined from the Form | w 2g 7 0 i 7 5.9 pio log.b = log a + log. stn. B — log.sin. 4. : ; ] ihe 9 9 iY | or oy \ L3 \ i X 14 x % 35 le See coi a 7 - =. 1 +8 =~ a TT i — ee Fig. 2. Plan of the projections traced upon the Horizontal plane WE oF ThA pEDE PR WINER X.Y. at the South Fast angle nearest to the point of sight 0. 2 = 444% 7 C57 72 (5% Z * * XR F< 1X) architrave abacus apper step corona tac above corona aymadaam muddle step lower step lowest step the perpendicular lineal magnitudes are all commensurable, the log. tan. A = log. r + log. a log. b. are ncommensurable. ithe Form. log . a TE I~ : 0 pt | ~ y By : de or ee 7 fl no 9 ti 5 nl To ” facta above corona i [Ay aia aoove corona = T 0 ' Sa = £0 NNW 1: 7 1 i.” Ta | ; il i | Q | < ! 7 ~ 9 i 3 } & | : “3? 3 § i 9 *8 : > a $ ‘ > 4, | Toe. - 9 . i eg 3 ey X 0 / | Be.” ® ~v 8 8 = Ta / be Ea ] ~ cS Foy Eg Ian 8 2 << Mk Z abacus 7 / ! : { = a / : / ¥.. 2 La Bunn. / x / : / df i te 2 = 9 m- $ i tee. © og de Sty iy i 2 § Pe Teens , S$ tot & ! Tse J a S {oe Bam J w i : ! i : 2. Ss N SN i | on] nlf Bo vd 3 i ne Pr i re hod 8 Ben el by 8 3 i TF. © yh $f Tr il ie $ j fl Tra ~ 4 ii t Y bo Ten § FJ fh, Is 3 | oi s £0 A 4 3 / J AY ; 9 3 / & i ay 3 3 , / ; $s = | 3 3 / * / | 1 a ! 18} 1 : : 5 3 3 1 , ! EJ REN Doe 2 i |! : Ife 33 a i : I I pes FR ® ' : y th I . 3 3 $ § i | : i! y S ND < / Q *3 5 : : | Ny : &N “gy ; S y I 0 i 3 N x $ 1s f= 3 Jo 4 fo > 3 pol . : boa Hi 3 $ fit) 3 / od qe 3 = Fh * | : iS : | ! |! ! 2 ; = : a 3 : yo i : = ] i § ! I : y : NN) : ! Poa i | [ ! ! i ! gl 7 upper step : : pr NA per stp Medan ; By ret nidaeid £ g fo 0 line |g i ow % 2 14 < N < 8 33. dy ia 3% fre ra 3 LF FF Bs a © % ~ eg Sl S gt : 25 preeat. RR ns _ lL or : ® : : A LL i SL > HORIZON __ | ines Ti vr frogs oo Simin err an oo mete are Natt i 8 et hk ee en A ae. 0 15877 rien. lowest fo T5913 Pon over: Sle. E | i ommee In “from Year step enti a ee b-- To ry 91 fom facia above cororva 163° 06 from peduanent eet nit of ait O fore ceeeaeee 182 I from facia above. COTO .....cdomaecv mnninn oo | | 165-437 from upper step... 165-537 fiom abacus ..... PIL £1) Pl Rees 163 06 fiom pediment : : to point of sight 0 166-117 rom architrave Esa | fo incesnceindugasess 165 + 437 from upper step 165.5 537 Bion aban ee f= 60 Geass be ABC TT Pot HRI OHE oneness eons : A 54" irae : : 3 X 44564" = 61956" sorrect o height 3 Z __ nearest ratio : 7, ‘tons and substractons ” y . f i bi ml ms po Fr 5 6 os GC = $884" — modulus of apparent leeraht ds 40765" c1654" 7 I 512 Clamiv........... 38 T188........... 34 2400.......... + 0-462 fi. = 5:5ins. 2 # YA st Ent loloi esi + D596 oon» 1560... —0:703 , = 12, Stvlobate i == GB84" Xx 1 = 6884’ 4s 14068" 40765" / 2-89 Stylobate ........ 5 + 6298 Z -érse. +0048 , = 06, Columns from upper 1 = 6881" x 6 = 41304" 7 - train . elemssetuecgpettton . i step to the architrave Rees Whole haght 50" 668 81 074 0 406, =43-8, Entablature = 6884" x 2 = 13768’ whole ” . ; y 5736. ..... 12 - 454 . — 0 682 = g2 we 884" xX 9 = 61956" + 772" = apparent As 14109 14068" 7: © 999 Podiment ......... 7 ’ Bono a =m omee, Tt hid nearest ratio, sf x 7 or 2 97 ; , > . = PH Gf L.A Al? LH, latte Sr Sowden. lol. 7 A HTS OTC dole angular magnitudes determined by the Form Fig. 4. The given heights of’ the Portico traced upon the plane H O Z Fig. 3. The apparent length and breadth of the Middle step of the ANGULAR DESIGN SHEWING TH RUE HEIGHTS TRIGONOMETRICALLY DETERMINED UPON South East angular design at the given height =9-2 above the horizon. Fig. 5 The corrected perpendicular magnitudes upon the plane HO Z, ihe visual angles are all made commensurable and the {rue executed heights are determined by calculation from MOM + MOM = M = THE PLANE = log. b + log. tan A —10. Part] Plate]ll HOZ. 144564" us quantity regulates the whole apparent height THE APPARENT PROPORTIONS. 61 PLATES I. AND IX. THE PARTHENON.—No. 1, THE NORTH-WEST ANGULAR DESIGN, AND No. 2, THE SOUTH-EAST ANGULAR DESIGN, SHOWING THE TRUE HEIGHTS TRIGONOMETRICALLY DETERMINED UPON THE PLANE HO Z. The plan of the Parthenon, the first given elevations of the Porticoes, and the positions of the points of sight with regard to the Upper Step, have been already assumed as given quantities. Plate I., Fig. 1.—Shows the plan of the Parthenon, with the given elevations of the Porticoes and of the return sides traced upon the rectangular planes XY, YZ, XZ, passing through the two given points of sight O, No. 1, and O, No. 2. It is at once seen that there are two distinct designs to be arranged, namely: No. 1, the north-west angular design, and No. 2, the south-east angular design. The diagonal line AB, No. 1 = 262:72 ft., and the point of sight O is given below the Upper Step 19°3 ft. The diagonal line AB, No. 2 = 277-906 ft., and the point of sight O is given below the Upper Step 9-2 ft. A difference of 10 feet exists between the levels of the points of sight of the two designs, and, to compensate for this difference, the spectator, by means of a longer diagonal line, AB, is thrown to a greater distance from the angle of the design of the Kast Portico than of the West, and {he effect of this arrangement is found to be, that the corrections made in the height of the Columns and of the Entablature, are practically the same for both designs, the difference in the levels being compensated for by the greater distance. Plate I., Fig. 2.—The plan of the projections, traced upon the horizontal plane XY, at the north-west angle nearest to the point of sight O, No. 1; Plate II., Fig. 2—The plan of the projections, traced upon the horizontal plane XY, at the south-east angle nearest to the point of sight O, No. 2. Let H be the angle of the frieze projected on the horizontal plane XY, and let the vertical plane HOZ be conceived passing through H and the point of sight O, then on this plane HOZ the true heights of the Porticoes are trigonometrically calculated. Calculating the distances OC and OH from the point of sight O, the difference between 62 THE APPABENT PROPORTIONS, them OH — OC = HK, gives the whole dimension of the projections = HK on the plane HOZ, then dividing this into the required number of aliquot parts, we at once obtain the distances from the point of sight O, to the several projections traced upon the plane XY, without fresh calculations. Plates I. and II., Fig. 3.—In the case of the Parthenon, as an uninterrupted view is obtained of the fronts and of the return sides, the whole apparent height, = H, must be made commensurable with the apparent length and breadth of the Middle Step at the given height #z above the horizontal plane XY ; therefore, by calculation, the angles MOM + MOM’ = M have to be determined for both designs. No. 1 Design.—MOM' + MOM’ = M = 157325. No. 2 Design.—MOM" + MOM’ = M = 144564. No. 1 AxD No. 2 DEsiaNs. Figs. 4 and 5.—These two sections are traced upon the vertical plane HOZ, passing through the angle of the design nearest to the point of sight O, and the same description will serve for both designs. Fig. 4—The perpendicular lineal magnitudes are all commensurable, as well as the projections divided upon the line HK ; these quantities are derived from Figs. 1and 2. The visual angles trigonometrically calculated from the point of sight O, are found to be incommensurable. Fig. 5.—The visual angles are all made commensurable with each other, and with the whole apparent height, and the true executed heights of the Porticoes are determined by a trigonometrical calculation. The result of the calculations is shown on the Plate under Figs. 4 and 5, and a comparison with Plate II., Part I., shows how closely the corrections, required to be ascertained by calculation, agree with those derived from direct observation. THE AMOUNT OF THE CORRECTIONS ASCERTAINED BY CALCULATION. Column. Entablature. Pediment. Steps. No.1lDesion . .+ 56mg, . .— 18s. . .— 78s. . . + 66 ins No.2 Design . . + 55mg, . .— 121mg. . .— 835s . . + 06ins Corrections derived : 4+ 3BBins. . .— 125mg. . .—B1lns. . . + OBins from observation THE APPARENT PROPORTIONS. 63 By these forms of calculation the amounts of the corrections are determined trigono- metrically for No. 1 and No. 2 Designs, and a comparison with Plate ITI., Part I., shows how closely the corrections ascertained by calculation agree with those derived from observation. THE AMOUNT OF THE CORRECTIONS ASCERTAINED BY CALCULATION. Column. Entablature. Pediment. Steps. Whole Height. No. 1 Design . . . +58. . —PBin... . ~78in. . . +660. ... + W5in No. 2 Design . . ; . BF, =1D3.., . —89 .. 406, Corrections derived from observation ) ’ fe SBS xl =1208 0. 81, 4 O06, {soe Plate TIT, Partl) . .) Comparing together the two designs of the Parthenon, it will be seen that the amounts of the corrections, namely, the small plus and minus quantities, are the same for both designs, although the visual angles and the points of view are found to vary in the two examples. In the south-east angular view, No. 2, the arrangement of the design of the Stylobate differs from the north-west angular view, No. 1, thus— No. 2 Design. No. 1 Design. The length of the diagonal line . : ae : 2277006 11... . 20279 §. The distance from the Architrave to the point of sicht O . 166-117 ,, . < 115011 ,, The point of sight, O, below the Upper Step , : 9:2... hy 1392 The result of these changes in the first given quantities 1s that the calculated variations become the same for the two designs, and that all the executed dimensions are similar. It was, therefore, sufficient in the Parthenon to calculate and correct one design only, and then, by adjusting the point of sight and the length of the diagonal line, the calculated vertical dimen- sions in the two designs became the same. We might at once proceed to the consideration of the horizontal curves of the Parthenon, but, as each step in the ancient theory of design requires to be established by ample proofs, I have preferred to lay down in the same way the first lines of the two designs of the lirechtheium, and of the two designs of the Propylwa, to show how the same principles were applied equally to all designs, large and small. It is only in designs of magnitude, like the Parthenon, the Propylea, and the Erechtheium, and when the points of view were clearly defined, that these corrections were made ; but in designs, such as these were, the Greek principle of designing perspectively, and of making all the visual angles commensurable, was, I believe, correct in theory. 64 THE APPARENT PROPORTIONS. CHAPTER 111. THE BRBCOATHEREIUM. So far as relates to the external Architecture of the Erechtheium we gain but little information from Pausanias; he says— “There 1s a building called Erechtheium, before the entrance of which is an altar of Jupiter Hypatus.” | “The Temple of Pandrosus is contiguous to that,of Minerva.” ““ Not far from the Temple of Minerva Polias is the statue of the priestess Liysimachus.” For the complete discussion of the internal arrarigements of the Erechtheium, and for the correct interpretation of the words of Pausanias, I must refer to the works of Col. Leake and of Mons. Beulé, but an inspection of the actual remains proves to us that, under the general name of the KErechtheium, we have three distinct designs grouped together, yet so arranged as not to interfere the one with the other. SOUTH PORTICO (| H SSSI EAST PORTICO West Last . 1H l North ow ® ® @F | i ® NORTH PORTICO | | [ [1 [11 A NN Nn NAN N \ N 5 # . AL \ N A TH HH HH i Hi Hii i llilAhhhill lin ZInm iinninnae First. The Fast Portico of the Erechtheium, designed to suit the angular point of view O, No. 1, and situated in the lower road, which appears to have been the one taken by Pausanias in walking round the Acropolis; it is also the road leading to the North Portico, on the lower enclosed platform. Sa Pact 1. Plate NL : Oo I T- THE ERECHTHEIUM. N? 1. THE NORTH FAST Wgmar VIEW OF THE EAST PORTICO CORRECTED. Ne J ~ . “. . 2 | ; 3 * e . h 4 . . + . » : Fig . 1. The plan of the Erechtheium with the elevation of the Fig. 4. The angle of the Portico nearest to the point of’ sight O traced upon Fig. 5. The corrected design traced upon the Vertical plane HO Z ‘« ] . 3 4) > » - . » . X 3: 3 st 3 02 s . . | Fast Portico traced upon the three 1 ectangular | the Vertical plane HO Z| In this I® design the lineal magnitudes are : In this design the Visual angles are all made commensurable planes XY. YZ .XZ pas sig through the pont of all commensurable and the angular magnitudes calculated by the and the true executed heights are determined by the form sight 0. : | form log. tan A= 0 log.s.— log. b are slightly mcommensurable lo g. a = log. h + log. tan. A—10. Fig. 2. Plan of the projections traced upon | . TE, ie the Horizontal plane XY at the angle | 4% pa R ; » bas, : : . 7 Pod 5 i. of the Portico nearest to the point of oe ji oy I dale ani Pos, | J . 3 iT f ~ 1% uv 5 sight O 18] J i oe 3 ; | L$ / a x Beg % Z> > Day % ER | Fudd he A a re ; / S . : ! 7 | 37; d Big, ] = 2 x 4 Tene / i 7 go} G0 Ry gh a “ae | +8 o o i ts : | Fe } 3 3 £7 7 / 8 I 3 (SO : ’ : / 13 i i | y _ 2 ; < J © 7 7 ; 3 4 % = modulus pou of sight S ss z 8 : E : | : [ : ; : : % ® ; 7 = Z oy 4 7 N°710 Horivorn ! AS : $s | | 3 5 x 8 2 3 3 “oe ~. : | I 3 S | > % © = 2 a > $ : : x4 | 3 5 > 3 : | 3 2 si ri. 1 ihe OI oro ty 28m * Ea x3 go ae 3 Se 5 oi & I : ie Te Nee ii by *2 = : --- : 1 ! _ : > , ' : 4 i t : Fhe mnie a ! Genoa y ' pmo = Xo 2 2% lower stew iii fdr ss il oo cutest) or : rt er : Pn Ny : \ : x a i SS Ser 23 | ~ 2 & : a 1 dea 7 2 2 |B . . 7 ¥ 22 | NT fey tc be ___ nen _ _ be 7 7 Ls Rn - J _ _ 20 ! <= 2 Si : : en ; I ! > Tel bol Eon 49.603 to lower step Ea a ae oat bt shrine toma and D605 0 LOWE SUD ccorrennssrisnerinmmmrmnmnnssnss sins : I > ea 50.000 tnemmptied sles nn ars ca SE ER ee | L le eg Se 52.402 to cornice ; Se ia Ee eed 37 i Level pladtorm i front of the Erechtheium ' ai SL.T47 to COPE ots ee a Pl ea 52.747 to upper step i x77 eo >= : le 55.801 to frieze © 53.62 tv andiitrave ..........:.. 75¢ given, quantities true dimensions additions fmm mmm amen amnnn GB. BC] to FORE e..neaaneeeneenen. 88.62 Ww Arohitrave * 76 4, : : L. obtained, derived, from and 15 veiddle Hay = Ads 81284 . 126458 By 7 ; 1.556 by proportion. calculations. subtractions. P4588" HS = nodaliis of correction M4 i Foe ho B23. newest vote. BF 04 Gling vi 80] Tenn + 752 34 itis > dv *73 I 7 =~ a ds 87284° : weary 1 v 4.889 NT 172 3 3 . } 2. 98 99 808 penrest vedic. 33. 30 Zotonblotome .... 4-778 .....=d 4.937... + 161 SUPE oan = BTID" XB == HUET’ ell \ J1 cyinatiin y | 0 | | As 18066" : 1H0973” bet ey : 7.611 nearest ratio 7 = € SOBRE eo 2 BE... 3.008 + .009 OLY «oo + «ns 2 = 3719" X 22 == 81518 . \ 2X2 * 10 a Ae EL line ot 5 or J 5 2C Entablatare........ == 370. X &§ = 18595 % ory 5 +9 | minicar UB OH] wp Tower slop HE ou >is ds mz: 1 18008 vr 5g on Whole heii ..... 26.668 ........| 28.899.....; + 322 Pediment ..........== 3719" XxX 4 = 14876" pr 3 8 corona a ERIE at oy Lr ? 4.86 nearest ratio fa Bolen «il BEE d. 55 we gor 3719" XxX 34 =—126458" — apparent whole hig 7 3 wn mm mm mmeaae . j 6 upper: step } 5 | F | : 4 en orm | N® 2. Tar PROPORTIONS OF THE SOUTH PORTICO. ADACUS = ! i 1 awchitirare | 5 Rimmer nl Speck SoS I" = fitexe } $ - * y ¥ 3.8 wm mE ATE BA Ks 16 5a i Fig. 1. The Flevation and Plan of the South Portico. i on = TS or 1 234. 0 = corona a rit rpesg ie pen pan Ny DUSTL ebb naloie. Hel LT ..... == vo 3 Es... Ey = gt FF FEE... % i 2 jms 3 % A = < 9 boxy rf 1.000% 1.1. : 3 3 for 3 > sala $ ore Beefy i Tr _ ~ : — ol bw, | Fig. 2. The plan of the Projections. / ] gars | : § 7 ill I 2 ( \ ; | 40s ‘ ' / x 4m EF I. 24 lower step 3 3 is } 2% im i Fas 123 ; li i221 e ¢ ~ { 3 3 3 : \ E24 ud fo ; 1 : £72 ; I %20 % ; ! bo 19 < 3 / fee i oC 1 » — ook gee Jo 3 Sc 3 18 3 ; I 1 jee a t = 3 i ob re 3.3 17 RS $ Jit 3, ; 476 g & - 3 po 3 : © 15 muddle stop S 2 fF 42 5 = = ® i 3 lwglin yo = Ai Bo : | 2s pris be - iis 3 o . | | : Fk | : x72 = ya ; O al ble cern eesnnapn bef ee * 4 Nx i Y/ - = ni Po 225. 0 == length of upper step ¥ | w ¥ G. . 8 10 o “Syd /! oc @| R | T pepe] * oe | 3 3 Ce | % ne 5 \. 28° pn “.o A WARE he bedi] & - 6 ® 3 IR 9 corona a Be \ ol : x 3 | | i bho 279. 0 = length of lower: step i 12% abd LO ain e > 11 & 2 = will | ET jag ny I 19. 3. Iw the example of the Fast Portico 3 : f 5 @ Wo J ins. 5 i i urn le 2 the Erect 3 ded. % 5 © x! 1 1 length of upper step _ 2 Ce l.b w= medi " dil n Ce a ps wpperglons of rechtheun fig. 3. 1s omitted : ke bed ad 150 7 regulatingthe 1, | £6 j= Ho jolt ard hecahts and i id i Ly the « dk rin Foam [or] 1 the return side is broken by the o LL if ob whee . z jo 0 i fil ia North Portico, therefore the whole of bl lowér step tres 1 ! f*Carvatid, : : x ; Pl £4 pe ee 1 abacus of Carvalides height of the East Portico becomes ro Fa hy oa 23 22 A 20 19 18 11 16 5 Z i 2 pups gos $ £58 ! 0 air ame a givens quantdy requirutg mo ; o 5 | correction . % X ST : . BP BLr ci Oe 33 fe 1 ween 86 fone. 3 El] : | S J ; : ; ! oi oo Hal = he _.——7 Level platform of the North Portico 6 1tbelow the East Portico platform. $3 ETI | 7 Fr | & 2 % 2 | | : | x x : E it" 73.0 pond of ‘sight for the North Portico. x 19 bet t 7 Shy 10 : - jy CA : Z TTT —————e . GF. Koll. lith., Caalle ct ?. 2 ondon. fil : Fotom eo binaon ool. THE APPARENT PROPORTIONS. 65 Second. There is the South Portico of the Erechtheium on the same level as the East Portico : this small design, only 18:75 feet square, appears to have been designed simply in aliquot parts, and to have had no corrections made in the first given heights to suit any selected point of sight. Third. Descending 6 feet by a flight of steps we find ourselves upon the enclosed platform, on which is situated the North Portico of the Erechtheium, designed to suit the angular point of sight O, No. 2, and from this point the Portico is seen as a distinct design, so adjusted as entirely to conceal the other designs. These three designs must be separately laid down and explained in the same manner as the two designs of the Parthenon. PLATE 111, THE EAST PORTICO OF THE ERECHTHEIUM. The two Plates of the Erechtheium fully explain themselves, and the successive steps followed in the laying down of the first lines of each design are exactly similar to those which have been already described in Plates I. and II. of the Parthenon, thus— Fig. 1. The plan of the east Portico of the Krechtheium, with the elevation of the Portico traced upon the two rectangular planes XY, XZ, passing through the point of sight O; in the plan the given mass of the central building is exactly a double square, thus the given length of the frieze of the Kast Portico = 86-64 ft., and the distance from this to the frieze of the West Portico = 36:64 X 2 = 73-28 ft. Fig. 2. The plan of the projections to an enlarged scale, at the angle of the design nearest to the point of sight O; the whole amount of the projections measured on the line HK = 4-198, 412° = 1749 ft. = the modulus of the projections traced upon the plane HOZ. Fig. 3. In this example the apparent length and breadth of the Middle Step are not required to be calculated, as there is no uninterrupted view of the return side to be con- | sidered, and the whole height of the Portico, including the Pediment, becomes the given quantity, by means of which the apparent heights of the Steps, the Columns, the Entablature, and the Pediment, are determined. Fig. 4. The perpendicular lineal magnitudes traced upon the vertical plane HOZ are all com- mensurable, as well as the projections divided upon the lime HK, but the visual angles, trigonometrically calculated from the point of sight O, are found to be incommensurable when compared with the whole apparent given height of the Portico. 66 THE APPARENT PROPORTIONS. Fig. 5. The visual angles are all made commensurable one with another, and the true executed heights are determined by calculation upon the plane HOZ. Tae VERTICAL. CORRECTIONS OBTAINED BY CALCULATION. Column. Entablature. Steps. Pediment. No. 1 Design . . + 153 . . + 161 . + +009 . . — 325. THE SOUTH PORTICO OF THE ERECHTHEIUM. This Portico possesses a separate interest from being a totally distinct design ; the proportions are different, the Entablature is supported by Caryatides instead of Columns, and in the Entablature the frieze is omitted, and is simply composed of two members, the Architrave and Cornice. It is also an example of a design in which the corrections are omitted, and the proportions are regulated by dividing the Upper Step into a given number of aliquot parts, then, taking one of these parts for a modulus, all the heights and the projections become some multiple of this given modulus. The South Portico is so small a design that it was probably considered not requisite to apply the corrections that we meet with in the larger works. Tar PRroPORTIONS. The whole length of the Upper Step of the Erechtheium on the return side is 75:005 ft., then The length of the Upper Step of the South Portico is made equal to “7 = 1875 ft. The whole height of the design equals the length of the Upper Step . . .=1875ft.=2251m. 225 in. — 150 = 1'5 in. = the modulus regulating all the heights and projections. Given Heieats, Fie. 1. The height of the Steps ; , =m X19= 2895 in. 's ” Plinth: . ; . =1Bin X48 = 675 in, 2 ’ Caryatides = 1'5in. X 62 = 930 in. " 2 Entablature . , =15n XM = 36:0. Parts 150 = 2250 1n. GivEN ProsectioNs, Fig. 2. ~ From Architrave to Stylobate . ,, Stylobate to Upper Step ,, Upper Step to Corona . ,, Corona to Middle Step . ,, Middle Step to Lower Step =15in. X3 = 45 1n. =15in. X38 = 4.5 in. = 1.50in. X3 = 4b in. =1b5in. X6 = 90m. = 1.5in. X9 = 13.5 in. Parts 24 = 386.0 m. Part 11. Plate IV THE ERECHTHEIUM No III. THE NORTH PorrICO TRIGONOMETRICALLY CORRECTED. | 8 Sob FRolonson, del) : Ig .1. The plan of the North Portico traced upon the Horizontal plane X Y and the position of the 2. The plah of the Projections at the « Ft dortic + : : gz Cl t the angle of t ‘tic : of Xd lL A , fy : pb P : Pp r Fig. pk J ¢ gle of the Portico nearest to Fig. 3. The apparent length and breadth of the Middle step pomt of sight O determined and the lst. given proportions of the Portico traced upon the plane the point of sight O, traced upon the Horizontal - r f YA : \ 2% 5 ; ; g prop P y | } 8 ’ Pp tal plane XY. MOM +-MOM=M =150393 #ys quantity requlales the apparent XZ passing through the point of sight 0. | : height fiom the lower step to the corona. Y : 7 | Ra bieatibo. oo SL0058 Lod Seen ha | ] * i ee 2 0 22, tis ® : 20 Il Jp Z : Sb 996... ot 12.829 = gin height of steps... _.. M | 7 ZT J 63s olen mmulismyio wy ph \ | Sn eee Ee LTO ” “archidrave. : a WE On sz TET AT A } ; ; 5a ry | abacus td N x »n x * or x ny mfr wie x y x2 7 . ! 2 7 ¢ 3 pong. geet RE f i 1 ; | architrave cornice / | 35.542 = length of corona | ¥17 2 | 3 : \ 32.202 — length of frieze | {2 i yo ns v z : : 59 : | 7 bot | er : 2 | 7 | } y 2 Qo ‘ i . an T ie} [omer * ! 88.757 Tergythe of vpper Sp, 2.908 == moduliis of heights, | by ft. gen A | : 72 > : oe y *9 | X 8 3 : | ~ I 3 > ) gr 2 ay ; : PY | vd | i & ary : 7 > Eu Stephin mm DOOR A ime 2.90 y | je 3 play g Lo | / | bX “3 ee ; ; : 2 5 ; : Pd y % 724 : \ Colveman. A Sh So 2 . 229 X 8 + 5 = 25 O84 | ZL : x7 Q 5 | 3 J | 3 BY . \ 4 5 . \ 0 7 y 7 | Pe ¥ > t y \ Frtablatire. == 2.929 X 7% = 5.858 J i : +6 3 ? meddle step pot 2 : M OM x X / | . ~N ol fag mmm mm 88. 085 == middie Stop oon emmannen as Secs drone iB I AY iennins ; ‘ / J > Ts > 3 = i Acroteria a dn — 2.929 Gy SE No — 5 976 | % x5 2 => 17% De 5 | X oh of ) \ 3 | / > i 184 bie " Sar : I 3 / | 3 9 " Eg 2° = X13 Lge? i / 7 ; y Crs 0" iN ) 2.920 X12 —35.148 — whole height. 'E | ri 20) =~. \ PK if | | : 2 A , \0 > i 1 | La} + % : IN gs : i} 80] ~~ WN ENS \ 35.642 length of corona __ 4 4427 height of pediment. 1 ! 1 | | 2x i 9 £ ’ i % \ / : : = ®fe o \ 8 i i : oi =e a8 Nh , y | 2 lower step 2% x. A ed 3 \ x J | ba 3 Zo Sag vl I i | S. / QP . 5 \ } ge fi s AN 3 mmm en * eo) 7 J x \ dete L 3 : “ey \ \ ! 5 ar 2 iy ! x go A 3 . oh a” . Se. | Fmt ¥. i pe i I. \ \ : 6 5 7 3 % 1 0 re de J y | 1 a \ A : i I | . Ts \ : 2 - nv : foo Tny A | HK 8.328. _ (0.2274 = modidus orn the line HK. : De 2 | 2% 24 : . or \ | > Sn 1 | Ss LE Note. In this excanple the first giverv height of the : | Pe WY * 0.227 x 2 we O.9437 088 mo tale old) i) : ! ; = 0.0887 = modulus or the details of the NY Colum is slightly altered from the original Y 5 SDI, 2 HK F : | | ertablature ore the line J xX Point of sight O proportions and made—to 8+3 parts instead 5 of 9 parts, thus: | Entablature = 2, Steps = 71, Column = 83 parts. = f i ) tvs oC > - ’ . . i 5 i . : To : ns ] . . San 5 en | \ | Fig. 4. The angle of the Portico nearest to the point of sight O fixed mn position Fig. 5. The corrected design traced upon the Vertical plane HO Z, m this the | \! | ry : hn \ | and traced upon the plane HO Z. in this Ist. design the lineal magmtudes visual angles are all made commensurable, and the true executed | | es P 2 . . 3 ; Y a n ~ . y ; \ are all commensurable, and the angular magnitudes calculated by the heights determined by the form log. a =1og. b+ log. tan. A — 10 will be \ \ - j \ , A | , ‘a : : ‘ 2 ra ; So | \ | form log. tan. A=log. r + log a —log. b are shghtly mcommensurable. found to vary from the Ist. given proportions by shght additions and 3 | - 222 | . . % \ | pediment dimmutions. \ 50 j iinet N : vs ; bo \ 3 i Ey a | £3 \ . + : 12 acroteria _ : > | acroteria™. 1 ! 976 y 3S J ’ i > \ b x x J corona 1.75% : | corona ¥. se | | Hh > Fr =. 3 \ ! yl 5 5: ! Lo] Dsth = aS \ $ 3 ¥ ¥ a NS | $ 8 St . g N : x vy SG =. [ ~ ! ny 3 MN Ss rs 2 | | . ei 4 \ g i —+ y or Ss | : b \ gE] dw To En \3 | / | i (6==1 Rng 33 projection >. . : : ! ! £2 - LM. of abacus re 2 Ps ® te | | Te re 57s \% Foe : fi Fa : \ | ’ y ! J ne 7 NE & He 7 } 5! : Tie. 1 VF S ! 5 \ EE | wm, LE | 5 % % Ey 1 ntl By a CAE fo AE ieinet dat a gn ZY. G2 wx LOWEH SUPe ov mmm mmm mmm mpmnm nmr me nm Seid mm mm coz wie dks pi mm mt nm em ed > fo! : | : Yay 3 3 Ber te As No ~~ 5 5 x1 : Pi | it | fy 8 de ST ~~ ’ 3 Q ! : ¥ ! 1 5 Ts x . > i i a No Th 7 3 ™ | XN y > i | i RN i Pon, $ : IS. SN j fe Ss hw : 3 5 } : § of / = ne o os i” i = N NN Te \ C \ | 4 , ! i o nn ee. “3 } A HY I~ ! CS N \ Q : ! % 6 ! : ¥ 7 J 7 Me >a = | =. 7 Nox >= : > \ In} R | | ! BN J / ; Sry, 08 Sey te / 8 Ny Ne : | \ \ IY 2 2 ! RA) / ; 2 Stn g HE 3 Sie. oF Sin Be MN 3 N i 3 / 4 J a ~~. hy / XS = : iY > 3 n : Rien \ SN = 5 ! ' $ J 2 £ s 5 a £3! > 2 i 3 Se ~ | =, \ I Q ~& > 1 ) 5 ’ Ne = ~ so 7 * \ NN ! >* | k : | Q } ' / oe xy “@ J i$ . as . ~~ 1 ao \ { 3 i ' : : a s / } ee = Q rE i Sere . : EY \ 2 a) Q : “ Se 7d Ne . = | | F 2 3 3 “ey > ! : > ~ | 8 \ FP] if 8 3 : i ww i 2 3 gr 1 2 & 9 8 So r: on 0) or | x = \ | | i | | Q J © . © 3 BO : Fl | S04 5 3 : Bl 1) NB } | : 13 > | i | | v 3 > on x \ ’ ! | ! } ! | z th } i Sy: — : x 3 ey H Fy ‘ i 4 ~ | Il it [| 1a ff i ¢ N ; a \ ! x2 ! : | i j i § . tN 3 Ey i= 3 Jae | HoRiZON oo La ie JORIZON - . Na Fo hr TEE gibson bt seth cmos emf Lh’ EB coms mem or _-—Tn 4 BH aA \ Per : bpm rare pr fe 3 B 5 = yore SN hh 0 x a \ I ics J - pre A oh os see Sl eee] rm : 1a i = Ei x / \ PL] : i a “ » He 3 h Co gyrnz rr . : > > ’ = \ | “ 3 \ a g °e ebm TE = Hl x Fo ; No Py 3 yr 3 = errr = ¥ ) 2 Se ’; \ \ | s ~ \ J Emm : i / NN A \ pl gent 2 id | i be. NN : | _ / TN % \ | jo Na hk 0 oh a 3 cnnnnnnssB8 05 lower step | = WN omnis 38. 05 Lower step ¥ rene. 774 corOnIY : Ba 3 7 : eral to point of’ N rnmnmiennen FS OS upper step / nt of sight O Jd “rn vl : Ue upper facut at 13.106 abacus 0 pound of styh . xX 2 _ ed O Foie of a z % ? Se ot ous san aig Corrections the Portico. =) ber anhsimms rss 43 . 282 arclitrave < architrave a 1 oh Dy LO OT ee een mene enh. 3T. Hee \ Yomamann senso nte ar 3 ¢ 37 frieze corrected additions & . > column. apparent given height. dimensions. subtractions. 150393 — cd — corrected. apparent height — middle step M., . : l 4 ‘ haz ‘ 356776 ; i a 384 1.2 924 1..—0 260 arr - _ Tracy 2 167665 7 =1.85679 cle Colin : : 150393 __ 1423 — modulus of apparent hetghts. _ 7 | bth Fomine te i ’ ‘ 25 : 33.929 nearest ratio 25: Ertl Cec ann teen BD. + BOE. I. 5 800.0. —0. 358 34 | As 150393 ’ 51 665 ’ : / 7. 005 nearest radio 7: Steps La 929 1...3 159. .1..+0 . 230 Steps... cesnnina nal 23 ’ X 4 w= 17682 ? . " " . 7; 3 ; 3 on ” 3.1. —0 . i: S 5 n.. f-2.5 25a / 1 15 5 _ _ | tilature, root Whole height. ...... |. 771...4-- 33 183 8 COVUTIL: «ows ines #423 X 2W= 110575 : : ; | ds 23082" ; 111804" :: J : 4.8 nearest ratio 1: Podiinetil..cscevenet---#. . +427. --F ¢ Resid 0 . 2%27 Entablature...... 4423 X 5 — 22115’ % I Hell, Seth: Castle London E. C. THE APPARENT PROPORTIONS. 67 In this example the mass of the Portico is enclosed within an exact square, the Upper Step being equal to the whole height, the same as in the first given quantities of a tetrastyle Ionic Portico; also the whole height of the Entablature is within a fraction of } of the height of the Portico, the same as in other examples of the Ionic order. All the details of this small Portico are beautifully designed and executed, but I do not possess sufficient materials of my own collecting to enable me mathematically to lay down the curves and ornaments. PLATE 1YV, THE XORTH PORTICO COBRECTED. This 1s a very perfect design, laid down and corrected to suit the given point of sight with the same care as the Parthenon, but the Plate requires no explanation beyond what it contains, as it is only a repetition of previous examples. Fig. 1. The plan of the North Portico with the elevation of the same and of the return side traced upon the three rectangular planes XY, XZ, YZ, passing through the point of sight O. In this example there 1s found to be a slight variation from the given general proportions of the Ionic order. The whole height being divided into 12 parts, then the height of the Steps = 1 part, the Entablature = 2 parts, and the Column = 8; parts instead of 9 parts. Fig. 2. The detailed plan of the projections. Fig. 3. The apparent length and breadth of the Middle Step. Fig. 4. The angle of the Portico nearest to the point of sight O, fixed in position upon the vertical plane HOZ. Fig. 5. The corrected design trigonometrically caleulated.upon the plane HOZ. Tae VERTICAL CORRECTIONS OBTAINED BY CALCULATION. Column. Entablature. Steps. Pediment. No.3Desicn. . .—026. . .—0838. . . +008. . .— O02 68 THE APPARENT PROPORTIONS. CHAPTER 1V. THE PROPYLAA. Tae Propylea is the most important work of civil Architecture remaining in the Acropolis of Athens, equalling the Parthenon in execution and beauty of design, and surpassing it in originality and variety of composition; it was commenced in the year B.c. 437, and was finished in five years by Mnesicles, the Architect. Y] py hy BY, oth tpg 7 7 do in a i, ii) Ai Minit il” Mui Wh), ih, Ih ids i If pid 2 THE APPARENT PROPORTIONS. | 69 With regard to the plan of the approaches to the Propyleea, the fortifications at the west end of the Acropolis have been so altered at different periods first by the Romans, and afterwards by the Venetians and by the Turks—that there must be, until further explorations and measurements have been made, a degree of uncertainty as to the original Greek plan ; still we are not without some data to guide us in forming an opinion upon the subject. Ist. There 1s a medal in the Library of Paris on which is given a view of the north side of the Acropolis, with the Parthenon and the colossal statue of Minerva Promachus; on it, also, the grotto of Apollo and Pan is represented as being a little to the left of the Steps, which (as it appears from this medal, as well as from the existing vestiges of the Steps themselves, cut in the rock) formed an ascent for foot passengers from the City to the north side of the Propylea.—(See Col. Leake, page 63). 9nd. The formation of the rock of the Acropolis, which is very steep on the north side, and much more gradual on the south side, renders it essential that the carriage road of approach should always have been on the south side ; probably following nearly in the direction of the present line of road, as shown upon the modern plans of the Acropolis, and entering the enclosure by a gateway near the base of the raised platform on which stands the Temple of Victory without wings, and where some ancient Greek masonry still exists; this opinion is confirmed also by the position of the platform on which the Temple of Victory is built, being placed so as to harmonize with the turning of the road leading up to the Vestibule of the Propylea. The level of the landing H (see Plan), at the top of the flight of steps for pedestrians, on the north side of the Propylea, and the level at the gateway K, on the south side, are both suitable as approaches to a level platform, of which the landing between the present upper and lower flights of stairs might possibly have formed a part ; this idea of an artificially- made platform agrees with what exists at the east end of the Parthenon, and suits also the design of the Propylaea. 3rd. The Doric Portico of the Propylea, with its central approach, appears to be designed to suit a central point of view, and the position of this point, in order to embrace the Portico within the usual angle of 45°, must be 91-32 ft. distant from the Upper Step, upon a platform about 40 ft. in width ; this level space was required in the time of the Greeks both for the ascent of the Panathenaic and other processions, and for a general carriage road into the Acropolis. The ascent from the platform into the Vestibule of the Propylsea must always have been steep, but horses and chariots, as shown upon . the frieze of the Parthenon, could easily have ascended ; and heavy blocks of marble were probably moved by mechanical means up the inclined plane. The early Greek arrangement of the approaches to the Propylea appears to have been changed in the time of the Romans, or even at a later date, when the west end of the Acropolis 70 THE APPARENT PROPORTIONS, was more completely fortified, and was occupied by a guard of soldiers; then it is probable that the Towers in the west fortification wall were built, and that the lower flight of marble stairs were executed, as M. Beule discovered them in 1854, when, after clearing away the modern fortifications, he found in the marble wall in front of the Propylea, exactly in the axis of the central doorway of the West Portico, a Doric doorway for pedestrians only, opening immediately upon a marble staircase 66 ft. in width, and ascending 54 ft. in height, and 100 ft. in length, to the Upper Step of the Portico by means of two distinct flights of stairs, divided by a central landing 17 ft. in width. The approach to the Acropolis by this staircase was one of great grandeur, but it must partly have destroyed the carriage road which originally existed, and when Mr. Cates was in Athens, in 1874, he at once observed that the execution of the lower flight of marble stairs, and of the Doric doorway, showed clearly that they were later works, and that the earlier Greek plan had been superseded, and this I believe he found also to be the opinion of M. Bournouf, the Director of the French Academy in Athens, who, I hope, will be able to recover the true ancient Plan of the approach ; at present, with such data as we possess, we cannot venture further than to suggest what might have been the original Greek arrangement. When Pausanias ascended to the Acropolis, and described the Propylaea, he evidently looked at the general appearance of it from a central point of view ; when he describes the group of buildings of which it is composed, he notices first the ceiling of the Vestibule, which was clearly visible from the point of sight, and he says— 1st. (The Doric Portico.) “The roof of the Propylea is of white marble, and excels all other works in ornament and in the magnitude of the stones.” 2nd. (The Temple of Victory.) “On the right hand of the Propyleea is the Temple of Victory, without wings. From thence is a prospect of the sea.” 3rd. (The North Wing.) “On the left of the Propylea is a building containing pictures.” This description corresponds exactly with the view that presents itself from a central point of sight on the platform 91-32 ft. distant from, and 258 ft. below, the Upper Step ; in front is seen the Doric Portico and the interior of the Vestibule of the Propylea ; on the right is the Temple of Victory, without wings; and on the left is the north wing of the Propylea. We thus see that what is included under the general name of the Propyleea is, in fact, three distinct designs, which must be separately considered, and I will commence first with the central Doric Portico, which is the real entrance into the Acropolis. Tne Prnorvyiza Nol Fig. 1. The plan of the central Portico of the Propylaea with the elevation of the same traced upon the three rectangular planes XY, XZ, YZ passing through the point of sight 0. oe “ : 2 8 7 6 (5 Fy 3 9 =i 2 or em erm meme ee 73.8 = length of eymatizm I x 78 | LY 1 17 de | 37 | © NN 9) ® 8 ai SEN JES e P] [ ey ! ie / fod : 4 3 : fos renner 0 pn Legh OF OPER SUR error enero Ei 8 7 K 15 i = 2 : Jd 0 | 0x i = T 1 en TEES Fee X orion 5 i : 7 | Opowntof sight = 3 : | gm Nirthelmpte 8 3 : 7 | of Vieory gd \ x 7 i Se : Hi x =x ’ Hi N 3 \ : re f J : > . ey \ 3 = i ! Enclosed, plsform of : — © 2 - \ / \ / \ / N 7 ) \ ; Level Plaxforin \ ’ A / \ / x 7 Ni ; v0. Point of view for Taner WesT PORTICO Fig. 2. Plan of the projections traced upon the Horizont plane XY. femora. 4.808 =| GOVERN hight of sylobate. ||. ALR EL 8 5 bb g.2 3 x T T Ed K 32 3= modulus abacus - upper step x4 Sk # #7 | 6 second step 7 corona moulding | | 8 | 4 i | L® 8 fucia above corona | i ig: | TE Eo 9 cymadizumn ; 10 third step {if CRRECTED TO PlateV Part 11 SUIT A CENTRAL POINT Ov View. Fig4. The design with the Ist. given proportions fixed in position, the lineal magnitudes are all commensurable and the angular magnitudes calculated by the form log. tan. A= log rt+log.a—log.b are found to be shghtly incommensurable' endablatiure Column ATOLL GER Ee sg Lg nearest rotio... 1... 3 Ce or... 3 9 79650" 127 "modulus of heights « 27-235 TP loner slap a i ) F908 TOY III see ieee hoes eee ee on ene Sa : ; ¢ to pont of sight O k 97-325 Tron vpn SU)... 97 400 TO OOS. oo ee iii a i ae aE et Bie Sh Ee 97:87 from arehitraye. .... .......... Be LE UF sh S72. £3 $$ 11 S73 fi] 12 fourth step + 33 30 R : ks EEE ERE | RED es 2] : EE 5 g : { 1 i : 10.052 Q fe | 3 —. D | ! % y | 5 : i Q y ! i | ? ; ; L : : 1 | 5 x S ® : & 5 ig I 2 g 3 ft % 3 ; » ! Po BNE : : ee 2 Fig : 3 . An this ecample Fig. 3. is omitted, as no correction ts required tv the first given, height of the portico as there is no réwurn side, the whole height vs made, a gen quantity Thonn Terlonison dd. ry E 0 ' 1 4 : ay i © ! ~ i = # : 1 i RE ET. mer ma dw tp reas Fig.5. The corrected design; inthis the visual angles are allmade commensurable and the true executed heights are determined by calculation from the form log a=log btlog tan. A—10. Whole herght 2000 6127'= modus of apparent heights > ” >. ~ Calum EET XO == 55143" N < < 5 oo Na Zs ’ . NE... S Eraabloture.. ..........== 6127 X 3 == 18381 En < A & a or : : a %. & : Pedimnent........... = g127 X 2 = 1225¢’ ——————— dH : / > Z 0 +. e \ 0 . 5 T A a Ho NE wT : SOLODOLE. eens o.. = grey’% 7 = erm” RE nln” 22 2 ~e : fai ™~ 1 NY 2 th ga F | 3 yo 7” 7 yl p Li / 2 F E Foy 8. Z NJ pe | iid ni 1 >’ . JK Ha jo 3 & 5 i 2 3 § Corrections tn the Portico 5 ; i ef ‘ . ha @ of * hs A> . . Ist given quantities Trae dimensions Additions ard i 1 or J Sugg eit > obtained, by derived from Subtractions aa J 8 / Fe 2s > proportion calerd ations oe > S J ; od QO V4 / oo ¢ = 57 ; - Colom... DRIRIT Leip innins EH rere ign + 0-325 ss F ’ » ’ N 1 2 ; g- f Zrwablainre.............. | Sen 9-606 | 10 - 052 + 0-446 ¥ / / Q % $ 1 3 2 ¥ de Stylobate G808 oo. ret 4-026 —0-777 2 2 oy RE & Fo 3 ££ no Eo 3 / / / : at So ee Whole height ............}.......... 43: 227 wt PEER. fee J 7 / 7 Se 5 8 % Poditneng...............0x...........9 oa 8-49... — 0-71 7 > 7 70000000 7 070 77 7 7 Z 07 7 HH, 77 z T0000, 7 | | i | __..87 185 tolower step ____ Es eae 3 | | 2 BY 0 YOON... oo es oninsimmos risa ianims dite wantin | EL rdenesteempiees 39 WE TOFU OUONCCOTOTUL oon vis sa vninin vo ae rm sa mmmtamtn sen avis ssuns : | Ee 0.7 TIOPOBTIIAINY oon Tania ton an aseenestrencstst persper irs a ist ismemy memset) | EE a sa EE Ee a Sn Rh LS | Cit iat Lomeend ADORE eis | Shean 9088 Weir eB loardieoNe , i... no | : yr C.F Hell tith Castle St London EC - Part 11. Plate V1. THE PROPYL ZA NY ll. THE NorTH WING DESIGNED TO SUIT AN ANGULAR POINT OF VIEW. Fig. 1 The Plan of the North Wing of the Propyleea with the elevation of the same Fig . 2 Plan of’ the Projections of the angle of the traced upon the three rectangular planes XY. XZ.Y Z. passing through the Portico nearest to the point of sight 0. point of sight 0. of ferries traced upon the plane XY. 3 b Tb - i] ; " i Nn i : N. a | no : 13 sas 1 Cn Rss Tope SEE stor id er : send ster SERRE gz i 0 TE I.E ai shia a a N third step 9 facia above corona i . : : ; 5 ~ . : : : iy Ge 4 Fig. 3 "the given heights of the Portico traced upon = Fig. 4 The corrected perpendicular magnitudes ; i 3 bos J i RNY bem on ; yah : : . : ! \ bus ; ; . Fon 3 2) the plane HOZ the perpendicular lineal magmni- } 5 upon the plane HOZ, the visual angles are all hs 8 x ! | lie ! 2 \ - | Q Na | NN : : Ee 3 ~._ tudes are all commensurable and the angular fo” \ +. made commensurable, and the true executed ; | magmiudes determmed bv the form log. tan. A ; x | =heights are determined {from the Form log. a= 3 | I a : 3 : NN EN oR : s i 24 SE =log. r+loga log.b are found to be Incommen- % idl On # »log.b * log. tan. A 10. = : i ks : : : ns © = . \ . Y ON S : : ~ surable. , 3 , 3 a he 83813 2890" dulus of T | Sx Ber CA colar whole hecght $ : : $y nn, Whole height R= 2890 "= modulus o 3 : SA Sen’ est tA 1 NE SE oe BL pret fale 3 2 3 4 ~ 3 A $s 8 N : 3 : SL i Vi = 3 g ¥* Hl S$ & 0 20.00 I ~ | | oN Stylobade goog 2890" Xx 2 = 5780 “ 34 * i nearest rate... 20... © .29 3 La Ny Og een ane 2890" x 20 = 57800" $3 i NN | | 2 n © s S / B en . 2 | Pad ra & i ba ’d A Entablatare...... 2890 Xx 7 = 20230 2 Eo 4 i i | ol 7 Si O NN | $ £ 3 | © $ . NI 8 § . £5 : v 5 A ; | 6 oP TE Fa 2 | $ % +7 2 NN ; Fae. we we Ihe ee SR / 1h “~ y/ od v Na > So - : : 3 : y a BN 3 : : 8 ta ! scl | ¥ %. SE / x z ; 5 de : / = ; ; 3 2 ~ y \ 1 < ; R 3 : : bo i % Tesi | fre an Sin : 3 1. 46.685 lower step a ee i 16. 685 lower step ecg : | pe 48.7184 facta ro . : : 2 | fenrtansas 48.184 facia above OIUY eel oeoope tt copes : . : A - __.._ 80.283 upper ep ih 30.353 = to point of” sight 0. | fests diochtene 50.28% wppor step... -- 50-353 abacus port of sight 0. fo-oe enemas 50.953 ardiilrae —...——— ovine HORIZON a bese OA veered] © wotmon a ie ms mm 1 a btm + SnD Ne Ne Sean ba in en is wl, mn’ —— in 4 iwi. = i Sr me an eit’ 4 A lt 4 st me | LH . i I I I | . I | | LE sa of sight . > I 2 RE Mg \ \\NN \ es BS pan all ee 00, po _ _ wy NN) CANA! Lith, Catto S Lindon LA, ‘ Sohn W olnson ad. 2 THE APPARENT PROPORTIONS. 71 "PLATE VY. THE WEST PORTICO OF THE PROPYLZAA. This is the only example in the Acropolis of Athens of a design made to suit a central point of sight, which in this case was essential, and it is also the only instance in which the Doric and Ionic orders are combined together to be seen from the same point of view. The arrangement of the design is the same as in the other examples already explained, but the calculations are simplified by the corrections being made to suit a central point of sight. Fig. 1. The Plan of the West Portico traced upon the horizontal plane XY passing through the point of sight O, No. 1, with the first masses of the elevation of the Portico traced upon the vertical plane XZ. Fig. 2. Plan of the given projections, to an enlarged scale, traced upon the plane XY. Fig. 38. In this example Fig. 3 is omitted, as no correction is required in the first given height of the Portico = 43-227 ft. ; as there is no return side, the whole height is made a given quantity. Fig. 4. The given heights of the Portico, traced upon the planes HOZ; the lineal magnitudes are all commensurable, and the apparent magnitudes are found by calculation to be incommensurable, when they are compared with the apparent whole height. Fig. 5. The corrected design in which all the visual angles are commensurable with each other and with the whole apparent height. The result of this first calculation gives the following additions and subtractions in the design of the Portico— Column. Entablature. Steps. Pediment. +0372. .. +0640. . . .=07H5. . . .-0064 PLATE V1. THE NORTH WING OF THE PROPYLAA. This is a design in Antis, with three columns between the Ante, and with the Pediment omitted ; it, therefore, differs from other Greek examples. Another peculiarity is, that it was first designed as a separate work, to be seen from the angular point of sight O, No. 2, and then annexed to the Propylea, by building the wall A, Fig. 1, upon the line of the Lower 72 THE: APPARENT PROPORTIONS, Step, and by omitting in execution the wall B, upon the line of the Upper Step; this simple adjustment closes the Acropolis, and connects the North Wing with the West Portico. | This design is beautifully executed in every detail, and the diagrams on the Plate will explain themselves, being the same as in the other examples already described. PAOBYE/AA Figs. 1, 2. Are the plan, the elevation, and the pro- é& & jections traced upon their respective planes XY, > g ia — -— a YZ, XY ; Fig. 8. Is omitted in this example, the whole height 1 poral being the given quantity. @ Figs 4, 5. The determining of the true height of the corrected design upon the vertical plane HOZ. THE TEMPLE OF VICTORY. Of this design I have simply given the Plan, and what appears to have been the position of the angular point of sight O, No. 3, but I have no original observations or measurements of my own relating to the Temple, neither was it examined by Mr. Penrose ; therefore I leave it for future observers, as we require no further illustration of the method of making the ““ Additions and Diminutions ” referred to by Vitruvius. THE APPARENT PROPORTIONS. 73 x Ee = I Fam { { TT a i Te ely ] T {HL Ti T= hain RA Ee - 7 { La Tu A) : oR CHAPTER YY. THE TEMPLE OF THESEUS. Tae Temple of Theseus, B.c. 470, although of an earlier date than the Parthenon, is not less harmonious in the first general proportions, or in the optical refinements and corrections existing in the design. We find the same calculated “additions and diminutions” in the heights of the Columns and of the Entablature, Steps, etc., the same delicate convex curvature in the horizontal lines, the same slight increase in the diameter of the angle Columns, the same beauty in the designing of the mouldings, in the tracing and colouring of the ornaments, and in the general execution of the design, as in the Parthenon and in the Propylzea. Like the Parthenon, the Temple of Theseus is built upon the highest point of a rocky summit, and the level platform for the marble steps is formed partly by the natural rock, and partly by Piraic stone foundations; but in the case of the Parthenon the original roads, levels, 74 THLE APPARENT PROPORTIONS. platforms, and enclosures remain, as well as the design of the Stylobate below the three marble steps; but in the case of the Temple of Theseus all this must, in a measure, be left to con- jecture, as the gateways and enclosures of the Temple have all disappeared, although, possibly, traces of the original Plan might be found if excavations were properly made ; still we cannot doubt that the design of the Temple, with the gateways and roads of approach, were arranged to suit an angular point of view, the same as at Afgina, at Priene, at the Temple of Jupiter Olympius in Athens, and in the several designs in the Acropolis. The North-Kast angular view of the Temple of Theseus is very similar to the South- East angular view of the Parthenon, reduced to nearly half the size, i.c.— The height of the Columns of the Temple of Theseus is 18:73 ft., and of the Parthenon 84-240 ft. The height of the Entablature 3 is G6OH., oi 11-156 ft. Therefore the description of the Plate of the Temple of Theseus, showing the North-East angular view, 1s almost identical with the description of the South-East angular design of the Parthenon. PLATH VII, THE NORTH-EAST ANGULAR VIEW OF THE EAST PORTICO CORRECTED. Fig. 1. The Plan of the Temple of Theseus, showing the North-East angular point of sight, traced upon the horizontal plane XY ; in this case no attempt is made to show the Plan of the Enclosure, as the present data are insufficient. Fig. 2. The apparent length and breadth of the Middle Step at the given height = 5:54 feet above the horizon. Fig. 8. The Plan of the Projections at the angle of the design nearest to the point of sight O. Fig. 4. The Design with the first given proportions traced upon the vertical plane HOZ, etc., ete., ete., Fig. 5. The Corrected perpendicular Magnitudes upon the plane HOZ, etc., ete., ete. ’ =~ 7 Ss : length of’ Piraze stone Basement length. of Upper step 708 - 42 104- - 24 = Tae Temerirr of THESEUS. Fig. 1. The Plan of’ the Temple of Theseus traced upon the horizontal plane XY and the point of Sight O for the east Portico determined . X THE NORTH EAST ANGULAR VIEW OF THE EAST PORTICO CORRECTED. Part 11. Plate VIL Fig. 2. The apparent Length and Breadth of the middle Step at the north east angle at the given height = 5-54 above the horizon. Z : % \ yy « A : ~ 5 5 . a S \ 3 \ ~ e—— 0 pout of sight MOM + HOM = M = 158530" this quantity requlates the whole apparent haght Fig. 3. Plan of the Projections traced upon the horizontal plane XY at the north east angle nearest to the Point of Sight 0. £0 (oA }--- 3TRT = first given Co Z 26x r hexght: of” Sty labate de oid \ A , : \ : WW eo gi ae i / a AN A. LE Lo Pod of \ | ' . \ a : wr \ pod \ a pk \ = ot Sst Rey ALN \ SE / as , | \ fred tug ----8-49-187 ru Lomsiedlin = Npihins ae BESTE Josie smn sitar SR rte wink in bmn a ai AGED LN needa 3] TS 8 ! | y 7 i : ENG ot i |e \ Be I oe \ af > \ A ¥ = \ J > 3 < d Sa al > A ] oD 0 = a or < = % = a) | I Pr 2 i$ ©’ 0 pV wl dN \ 7 < ~ 4 = \ ) 5 0 pou of sight Fig. 4. The given heights of the Portico traced upon the Plane HOZ, the perpendicular lineal ma guitudes are all commmensurable and the angular ma guitudes, determined by the form log. tan. A = log. v + log. a —log. b. are mcommensurable. > ~ ne i 7-30 (226_5 = modulus 7 2 3 4 5 6 7 & 9 70 71 72 g * * * * x ¥ X archilrave abacus / appaer Step 2% 7 x 4 madade Ss lower step & corona 6 facia above corona ovinadiuan 7 Ek puaic stone basement 9 7% 71% 72% ig. 5. The corrected perpendicular magnitudes upon the Plane HOZ , the visual angles are all made commensurable and the true executed heights are determined by calculation from the form. log. a= log. b+ log. tan. A—10. : ats oe G0. RS Ry I 29 2 a ®® 3 = : | Ts Cory, 727 | Loot ©. Nitin be 74 O ete ind inal | td | terre reg | __ or - ) ee : ks x rd Homa) ea | ¥ ! 3 - bias mcomisn aire mt os se 75 de sm ea ob fs ee i wm 1 me 1 mm pe ee i Fin me nm NOR LZ ON, i i Fo fa i | fie & *8 | PQ iT Lt Z oo ES = 7 Ser. 312 ! projection of abacus Es | i sa ' | freA i & ES I ' 1 y "Sm. ? * 0 < : i 6 hs y bd Kk. ! ! * See / > y 1 = Tra N » 7 DT Q ! v Peso x5 NN X nel 5 g ; £2 3 3 : = x4 ' & t SX | a S a = x Foo N ' o z oe |» ren. PF Bow i Se aa La 5 : 3 3 : 4 “ = = visa. CL Ta [ ©» : & weft nnn meen, = ene ) ty 1 = / ; pet > HORIZON — a ono — a; S— i — — io oe ad dm 0 iis esti sti 4c. et] en 4 reat: eS set oe se 4 i Se cet 5 ee en fe 5 sme : } ruins _ 68.9256 omy lower step --. of x heres 70.008 1Pom facta above corona to pond of’ sight 0. whole height As 77623" gery column 3 As 50993" ie 71.94 (rom abacis : 72.3 from archidrave ima a a i / = apparent ( length & breadth 158530’ 7 2-04 2 | nwarest rato First gwen guarndilies 30" obtarned by 58530 == 79007 proportion 2 312 = projectiony of abacus 79576 == corrected height Colum .78.754....... Entablativre.. ..... 6.2567 corrected heights 79575" 7 1-6604 Stvicbhate ....-..-- 3.725... ITD fe . 16 24-996 Whole haght ..... 28.725 -........ 16 25 nearest ralio Podimenty .......0.... 5+ 223 71.86 fhonv upper step 68,925 from ptraie stone platform... : | to pou of” sight 0. eenvo 70.008 from facdaw above corona _ == wrmnnn-a- 71.880 from upper step . . .- arr) ~ %- n= 72.300 from arclilrawe ............... Summary. True dimensions derwed from Cal adatoms Additions and Sub stractions L019 Whole height aap” = 37183 = modulus of apparent heights Height of Stylobate 2783" » 3 9549" a | , Column = 3/183" x 16 = 50928’ 6.69 44 | , Enlablatare == 3183" Xx 6 == 19098" 8.428 303 3183" x 25 == J9578" == corrected 28.8563 728 apparent hewght et 5.823 J Sohn « Folynson del. CS Kell eth baatle St. Sondon J.C Part II. Plate VIII. THE TEMPLE Plan of the Temple at Zgina. B.C. 6 wert! ah a i 4 il Tm Nil fi li] Hil Lill, Tr ox SRN ER fi ll Ji Ti in i HT nl a eh NW Ni i hil | I iim ibe FE pin lt fii iil 1,7 J Hi OL ff Jy W Wit 2 al il in 7 A 7 oo NN hi fi i I J i ill 111) ii 0 Be He al il wh 0 tn A Sa I il 5 i . i bi i wi Bn i mn i ; i i, oo J | \ hl mm i; _ Or ne 0 Nl Ln hil Cl bs er 12 z i z Ran \ ll hi (0 ip i f fin lh Aut i bi nN na ul ANN hi . OTL ENESH AA SA em i an SS A A SRE eb 7 im, it J EES inl) ul LE hl i = & NaS ii I il di ol ltUi ay HLL i SL il fii ile WH cs / = NaS ) 7% i pe fats ce bet ET i a vedas ss saan ROD Hoth. Lone dbiine tonite amin scab TTI T= TTT TT in [1 i Ti A THY > hi AN] oe ras STS me iT a SR an HH] 2 i pT yi i IN ot “lm i Ti | ere - She i 8 hh ") I he: = il i l= % ‘ y : fr. hy, on hl Ts Kd VD a on uy ’s : 4 217 7 77 Jt ' is /, i, Sr i AI vvrct? Mi ry i 7 =. yr ih il Ui i ms WT mn oo : 5 ‘ ls TG yi TR = = 2 i Kl it) "y = : ag ta > Torr ace pean, 7 Hg) Ty ey hd rl ZZ =: i Til If Ty eH ATV (TT 7727 aa ST 0] Tr 2 KZ mm ii ii I, Ta rn / = Lo gen NS! ii AMI = et / = el ak A ras = a Weg ed ~ ry "i 2 Se ts 4 ert tt Ca, ty Yili i = y Leet ii — Terra goo = — length of upperstep = 340.9 ing. = 47 487 tus. = modulus. 67-487 X 5= 337 435 tns.= whole hetght. 337-435 = 42-179 = modulus of heights. 8 first given heights. corrected hetg his, additions and diminutions. : Projections. Stylobaie......... == 42 ATE RR 1 = 45979... .......- PERE cin ninmmmpin nas + 2:97 42-779 = 44-059 3 Coliermm, ..-.oeae BEAT 4T0 XS = 20808... BOGE es inins 0S — 4-095 44-059 x 2 = 28718 ins. = projection. of steps. Entabloture... m= 42170 % 8 "2 84388 eee iaaii OBE ee oie t 12H 28-118 ins. = 3-124 — modulus of projections. > 9 Whole height... == 42-719 x 8 = 337-435... 337488 en siaton msn vas Fig. 2. Plan of the Temple of Minerva Polias at Priene. OF JUPITER PANHELLENIUS AT AA GINA AND TEMPLE OF MINERVA AT PRIENE. 00. B. Temple. length of upper step = 770-62 ins. = 96-327 = modulus. 8 96-327 tns. X 6 = 577- 96 ins. = whole height. 577-96 — 48 16 — modulus of heights. 72 additions and first giver heights. corrected height diminutions. Stylobate =A KX J EEE A S23. + 4-4 Colm... m=a8 70 X80 == 428 Ad... i. na... Ertabliiure =4876 * 2 = 96-32 _______. DEE + 0-3 Propyleeurre. lengthof upper step —299-32 ins. = 49-88 = modulus. 6 49-88 ins. X 6 = 299-32 ins. = whole height. i i [ C. 320. si PROPYLAZUM. 299-32 = 24-94 = modulus of heights. i Cy a a 42 in i vi Hi HS dd i additions arc Ha Te i i i fi iil bi 17 hin Ur rm i tn pmol | confetti "I I Ls i in Sag ih ng I i, Stylobate_...= 24-94 x 1 = 24-94 aE hd + 4-2 ’ ht thi oi ee Vt ote A ) hy hu Ji re Se Ha in I mi = a J Column... — 24-94 X9 — 224-46. __._____ oe = 096 “i EHS, 1s é JAN Wm wm nn hi iY hi Mi i Jill Entablalure== 14-94 X2 = 49° 88uneeecltfoeornen.. - 5-38 “atl Ziti Wi no i i i ait 11 il ; Fig. 4. Fig. 3. The first given Proportions. 8 . — 5 | ! ae % ' 2 ! 7 7 k S i or 4 : i § 7 i of ; ] i |, 3 Sk 2 J 2 ty AEGINA 7 1S 2 Ry 3 ; : / | | & = Dorie Portico / 2 3% N 3 / “t | | : / NY | nine length of upper step BF DUE eae am ! 7 J / § 42179 | { 2 ; . LC Sk I lc | 2 T= 5 : 7 x7 Xo X% 5 #5 6 i 4 *3 Te a z 0 3 : oe : 1% = \ is : i $ \ : ~ ~ 2 3 T | x 7 2 x 4 : \ id | © * \ : ' : > : : i : % 2 > 7% | % ; 5 3 \ 5g w. 3 PRIENE \ PRIENE 3 i i 64 \ : ; Bo ; 3 Tonic Portico, Temple. Tonic Portico Propylea. 3% i 1 3 x Ly Pod | 8 ' i aA MN EL jo] 5% “ | oe 0 % | 3 | nme tl length of upper step 770-62 tns. Jongthat wppeiore 299-32 ins... 1 > = - | 4876 Bie. TL, 94 6 | 12 sm, ig DT Wi Wit mr Wit ati) ih ih i pi iif i 17 Il / hs i wi Hp WIN i ON J Jin I 1) ; The Temple of Jupiter at Adina. tea of the proportions at the angle of the porto. 680 1t to point of sight 0. 0-233 ft. This is probably the oldest existing example of the curvature of the horizontal lines of Greek Architecture, B.c. 800, or four centuries later than the Temple of Medinet Haboo. But it is in the designs of the Greek Architects of the age of Pericles, that we meet with the principal development of these curved lines, and, fortunately, of all the horizontal curves now remaining, the best preserved and the most carefully executed will be found to be in the Upper Steps of the Parthenon, in both the East and West Porticoes, and on the north and south return sides. These are the curves Mr. Penrose has most accurately observed, and his own measurements are given by perpendicular ordinates measured from the horizontal line. For the sake of comparing one segment of a circle with another, namely the curves of the Upper Steps in the Hast and in the West Porticoes, or on the north and on the south return sides, or for comparing together the curvatures of the Upper Step and of the Architrave, it will be more convenient to measure the per- -pendicular ordinates from the chord line BB), bib LL passing through the extreme points of the arc | BB. This method I have adopted, for the reason | stated, but the measurements are all founded Fr amg ——+———— upon Mr. Penrose’s original observations. Part ll, Plate 111 THE MEASURED HORIZONTAL CURVATURE OF THE LINES IN THE UPPER STEP AND ARCHITRAVE OF THE PARTHENON AND TEMPLE OF THESEUS. observed by MY Penrose. Fig. 1. The Parthenon. The given dimensions shewing the Levels and Curvature of’ the upper Step on the four sides ‘3297 18835 Tr fe te ma ln Gns. % atte es es 8 TE ee eee Se Tr SEA IT meee smrs a et =r = . 208-101 == Joti OF VOIOCH SOI = woaeoniiie ios os oonassensaannt mest sonss oan il NORTH EASY meee. 4 ry rete — = Ran ma rei oa hs lagi rer ip SOUTH or mn 2 pe 2 0 tt re ie mere mn Ee ar the architrave curve. ~ restored position of’ SS mm et ee maim minim Sa mim em is i ie fi mf ee ma Ce et TE ie ier om em em li 2 mn er i Um Fa nt hn et we Te en Sh ne fe Em i i I eA TE SE Er rer aE height of’ SW column = 34-255 oi . The carve of the Architirave at the Fast and West ends has fallen inwards about 0-712 feet, and now inclines to the Horixon at an angle : a of 54° This disturbance of the curve was caused by the cxploston which destroyed the centre portions of the Ertablature and caused } tN : a = ; it 2 the twe porticoes to fall inwards 72. The cryginal vertical height of the curve of the cendre was the bine B’a =-22, the same as the HORN Ei - 27 : HAE SR curvature of’ the Upper step. Fig. 3. The Temple of Theseus. The given dimensions shewing the Levels and Curvature of the upper Step on the four sides. EE a Dr ee oa He ei iD i eh Se ee 103-87 — length of fiiere of 27 == or wn mi hv i al we nm i i en eh wa i a a Se re st ts fe ——— We — eee TR ed 102+ 38 == Vorifrthe OF OPPIr Shell ores xen sone eine resrarenend NORTH SOUTH 405 wm Ye a ———- - ei feminism anh Sim anise ims in sn nine TOS BF == UWI OF BUOHE coo oeannis oni om some tmnimnr sn ame smns snow msn wea] Note. In the case of the Temple of Theseus both the levels and the horvzondal curvature of the lines have been slightly disturbed by Earthquakes, one of which occurred while I was in Athens tn 1834. ? . THE CURVES OF THE HORIZONTAL LIXES, 89 Fig. 1.—TaE UrPER STEP OF THE PARTHENON. In the Kast Portico of the Parthenon, the chord passing through the extreme points BB’ of the Upper Step may be considered as a level line; in the West Portico, and on the north and on the south return sides, the chords passing through the extreme points of the Upper Step all incline, as we have seen, very slightly at different angles to the horizontal plane. [ Lone splat Baie. | Ld - © 3 3 hy : B 02 3 = 6 2 10 = 7 ever or 7 2 3 ! 4 Measured ordinates from the chord he i this Zonggthe of Poorol JIB ves bosororerinnnte vas . 9) BB of the curvature of the upper 4 3 Upper step West Portico : step ue the East and West FPortccoes . we ope at fons a an © D a m 3 : Thus the measured ordinates to the two arcs forming the Upper Steps of the Kast and of the West Porticoes so nearly coincide, that the two curves may safely be considered as having been originally identical. Upper step South retire side . (B i < 3 : " are of our, A -16 N ND N 3 8 0 re eel ! God \ 0158 : £ 3 Va TT Tr oie yt, 6 7 8 cenirenn LUGE OF CROP LEH] oeeooeoaeene..o ee eas 3 ) Upper step North returr side . the upper step or the return side. Measured ordinates from the chord, BB1 of the curvature of ~ Mr. Penrose observes that the ‘difference of curvature between the (Upper Step) “north and south flanks is so exceedingly small, that the increment of curvature was intended “to be the same in both flanks ;” and this was evidently the case. Thus we perceive that the Upper Steps of the Parthenon were composed simply of two distinct ares of curves, the arcs of the Upper Steps of the Kast Portico and of the south return side corresponding in every particular with the arcs of the Upper Steps of the West Portico and of the north return side. Fig. 2.—TaE CurvED LINES oF THE ENTABLATURES. Mr. Penrose, referring to the curved lines in the Kntablature of the Parthenon, in 90 TRAE CURVES OF THE HOBIZONTAL LINES. Chapter III., Sec. 1, makes the following important observations :— These curves as they “ stand, at least in the fronts of the Parthenon, have certainly a curvature in a horizontal as “ well asin a vertical plane. The Architrave of the east front is bowed inwards about ‘1 foot, ““ and the line of the under side of the corona of the cornice about twice that quantity, and “In a comparatively regular manner, more resembling, however, a plane curve inclined to ““ the horizon at about an angle of 45° than a line of double curvature. “ During my examination of the Temple I met with many proofs that the curve, so “ far as its horizontal direction (i.e. the curvature on plan) is concerned, has resulted from “ accident, and formed no part of the original design. Of these proofs the following are “ the most satisfactory :—The great stones forming the cornice at the angles of the Temple, “ which are upwards of eight feet long on each face, are rectangular on the plan, whereas “if a horizontal curve in the cornice had been designed, there would have been a sensible “ difference from the right angle in so considerable a length. Again, the openings and “ cracks in the Architrave of the east front (leaving out of the question the ragged cracks “ which occur upon and close to the abaci of the angle columns, and which are sufficiently “ explained by the twisted position of the southern capital, and the sliding of the broken “ portion of the Architrave upon the north abacus) are on the whole considerably greater “mm amount on the mternal than they are on the external face of the Architrave, thus showing “ that the curve has resulted from accidental movements. The nature of these movements “may be thus explained: The various concussions which the building has undergone, ““ having loosened the joints of the Architraves and Entablatures on the flanks, caused them “to spread outwards, moving the capitals of the angle columns a little towards the east, “ while the centre of the front was comparatively little disturbed. Similar indications ““ occur 1n the west front, and in the Portico of the Posticum (inner door), where the angle “ Columns have been also slightly pushed forward by the spreading of the upper part of ‘“ the cella wall.” When observing the curves of the Architrave in 1837, I was led into an error with regard to the curvature in a horizontal direction of these lines, for the curve inwards is so regular, both in the Kast and in the West Porticoes, and also in the Inner Porticoes, that, at the time, I considered it as a part of the original design, and that all the lines forming the Kntablature were curved m two directions, namely, in the horizontal and in the vertical planes. But Mr. Penrose clearly proves the curvature in the horizontal plane to be the result of the various concussions which have so seriously shaken the Parthenon, and which have destroyed the central part of the Temple, and which have caused the Kast and the West Porticoes, as well as the inner Porticoes, to fall slightly inwards, and the original vertical curve of the Architrave to incline to the horizon at an angle of nearly 54°. THE CURVES OF THR HORIZONTAL LINER. 91 The original rise of the curve will thus be the present diagonal line ac — 22 ft. in the Architrave of the Parthenon, instead of the present vertical rise of bc —=-17 ft., and this restored, position -—— of the architrove ve 2 So a so nearly corresponds with the rise of the : curve of the Upper Step, both in the East and in the West Porticoes, that I believe we may safely consider the statement of Vitruvius to be correct, and that the line of the “ Architrave was made to deviate from the straight line “ drawn through the extreme points in proportion to the addition given in the centre of the ““ Stylobate.” | CT rT Thus in the Architrave the ordinates, mea- arc of cwmwe en sured from the chord BB to the arc of the ER engin or sir oosze 5 curve, will correspond with the ordinates of Ubper step East, Birt the Upper Step, measured also from the chord Tl a BB/, and the columns will all be exactly of the re a same height,—which we find to be the case. In the West Portico exactly the same result works out, see Fig. 2; the curved line of the Architrave agrees with the curved line of the Upper Step. On the north and on the south return sides the lines have been more disturbed by concussions, but in the portions of the Entablature remaining, which adjoin the Iast Portico, the curved lines of the Upper Step and of the Architrave so nearly coincide, that we may consider them to have been originally identical. It follows that no additional calculations will be required to determine the curves in the Entablatures, and in the sloping lines of the Pediments, but simply to trace the curve of the Architrave the same as that of the Upper Step; this again determines the curve of the line of the Cornice, and the Cornice will regulate the lines of the Pediment, as shown in Plate 1V., Fig. 4, so that having once determined the curve of the Upper Step, in the front and on the return sides, no further calculations are needed for the tracing of all the horizontal curved lines of the design. The stones forming the Entablatures of the several Temples have been more disturbed from different causes than the stones forming the Upper Steps; in the one case the Columns are the only supports to the Entablatures, in the other the Upper Steps rest either upon a solid built-up platform or on the primitive rock ; therefore there has been, from several causes, a tendency in the horizontal curved lines of the Entablatures slightly to flatten and move out of their original positions ; the only surprise is, that they should have remained as perfect as we actually find them after a period of between two and three thousand years. 92 THE CURBYER OF THE HORIZONTAL LINES, Fic. 8.—THE CURVATURE oF THE UPPER STEP AND OF THE ARCHITRAVE IN THE TEMPLE OF THESEUS. In this example 1 have taken no notice of any variations in the levels of the Upper Step, if such originally existed, for they are quite independent of the curvature of the lines, measured from the chord passing through the extreme points. The measurements given are deduced from Mr. Penrose’s observations, and the amount of curvature is measured in the centre of each line, thus—— Upper Step.—The amount of curvature in the centre | pro ee Pron pilin of the line measured from the chord BB. . . . | Frieze.—The amount of curvature in the centre of the | 054 8. . 04048. i. . line measured from the chord BB’ . b Wa 074i We observe the same tendency in the lines of the Entablature slightly to subside, as in the Parthenon, but there has been so much displacement of the stones in this Temple that it is only what we might expect. Supposing the length of the Upper Step of the Temple of Theseus to have been the "same length as that of the Parthenon, then the amount of curvature would have been— East. West. South. North. Theseiam .— Upper Step. -. 1878 .. . 178 . . 2878 . . sf Parthenon. Upper Step. . 228. . . BK, .. ..B664% . .. 3554. From this it 1s apparent that there is a larger amount of curvature in the lines of the Parthenon than of the Temple of Theseus. The curvature of the lines in the Temple of Theseus agrees with that of the earlier Parthenon, destroyed by the Persians, and the Architects ventured to increase the amount of curvature in the lines of the Parthenon, when it was rebuilt. The amounts of curvature in the Upper Steps of the Kast and of the West Porticoes of the Temple of Theseus appear to agree, also the curvatures on the north and on the south return sides. The Architrave, as it exists, 1s flatter than the Upper Step in each Portico, and nearly agrees in curvature on the north and on the south return sides, the variations not being greater than we might expect considering how much this Temple has been shaken. We may, therefore, safely consider that the curves of the Temple of Theseus agree in character with those of the Parthenon. THE CURVES OF THE RORIZONTAL LINES, 93 THE CHARACTER OF THE HORIZONTAL CURVED LINES. Mr. Penrose has not only measured with scientific accuracy the horizontal curves of the Parthenon and of the Temple of Theseus, but he has also, I believe, deduced from his observations the true character of the curved lines in the case of the Parthenon, for when speaking of the curve of the Upper Step at the east end, he says, “ A circle drawn so as to “ pass as near as possible to all the measured points, taking them in their actual positions, “ would be subject to an error of ‘0065 foot. If the curve be corrected as suggested in the “ note, and as shown by the dotted line, the error would be diminished to ‘004 foot, which ““ 18 less than the height of the short letters of the type used in the notes of .this work, for ‘““ the ordinates measured at the centre of the Columns become— “033. .N9, .-181. 2+, Ns. 184. . AF. . 063) “while . ‘080. .°116. . "184. 218. . NS, .184. . 116. . 030 ““ are those of the circle of nearest approximation, in which the difference amounts to ‘004. Had “ we only considered the northern half, where the foundation is the most solid, the same circle “ might have been drawn so as to have its ordinates 220 . . “186 . . "118 ws 953 .. “ which only differs from the measurements by ‘002. From this correspondence we may feel “ satisfied of the extreme regularity of the curvature of the eastern Stylobate.” en vOTEO OF portico tpg wr 22 ¥ - half the chord 60 668 — r 3 Again, when referring to the Upper Step of the north return side of the Parthenon, Mr Penrose says, “A circle in the actual building may be drawn so as to coincide with all ““ the measured parts of this curve subject to a maximum error of ‘006 foot, excepting in -“ the cases of the 6th and 7th Columns from the north-east angle, where the Steps have “ evidently been somewhat injured by the falling of the masses of the superstructure upon ““ them in the time of the explosion. Even admitting these points without correction, the ““ error would only amount to "01 in a length of 998-14 feet.” “ The difference in curvature between the south side and that of the north side is so “ exceedingly small, that we may readily believe that the increment which here is “366, was “ intended to be the same quantity in both flanks. The existing differences are quite ““ accounted for by the greater lability of the south side to disturbances, owing to the height “ of its Stylobate above the rock.” 94 THE CURVES OF THE HORIZONTAL LINES We therefore derive from direct observation, the fact of these curved horizontal lines being simply the arcs of circles, and that one segment of a circle will fit all the horizontal curved lines in the East and in the West Porticoes of the Parthenon, and one segment of a circle also fits all the horizontal curved lines on the north and on the south return sides of the Temple. This reduces the calculation of the horizontal curved lines of the Parthenon to the determination of the arcs of two circles, one to suit the Porticoes and the other the return sides, and the same with regard to the Temple of Theseus. We can also derive from observation the fact that the amount of curvature given to the lines on the return sides depends altogether upon the curvature of the lines of the Upper Steps in the Porticoes, for these curved lines of the Upper Steps of the Porticoes being laid down, then tracing the level lines, Bch, Fig. 1; B%B’ Fig. 2, Plate 1V., they will give the required third point B* in the curvature of the Upper Step on the return side, through which the arc of the circle must be made to pass, so the only quantity that remains to be determined is the rise of the curve Bl in the centre of the Upper Step of the Portico, either in the Parthenon or in the Temple of Theseus, and the method of ascertaining this quantity Bh, in both examples, will be considered in the following Chapter, as well as the forms of calculation that were required for determining the arcs of the circles passing through the three given points B, B?, B, # THE CURVES. OF THE HORIZONTAL LINES, 95 CRAPTER 111. THE CALCULATION OF THE HORIZONTAL CURVED LINES. So long as we were under the impression that the horizontal curved lines in the Entablatures of the Parthenon and of the Temple of Theseus varied from the curved lines of the Upper Steps, we had every reason to suppose that the horizontal curved lines were separately corrected, according to some Greek Optical Theory, and such for a long time was my own impression, but now that we can deduce from Mr. Penrose’s measurements the facts, that the observed variations in the lines of the Entablatures are due to concussions which have shaken the stones, and thus flattened the curves, as well as caused the Entablatures to bend inwards, that when the lines are restored, originally there was no difference in the curvature of the lines of any given Portico, whether they were seen at 10 feet or at 50 feet above the level of the eye, and that the curvature of the Upper Step in the Portico regulated the curvature of the Upper Step on the return sides as well as all the lines in the Entablatures, we at once perceive that the Greeks never attempted to correct these lines according to any optical law, so as to make them all appear as perfectly straight lines when viewed from the point of sight, which it would have been impossible to do without a great disturbance in the general dimensions, but that the Greek Architects laid aside the straight lines, in their larger works of Architecture, as apparently imperfect lines, when the design was viewed upon the angle of the building from a point of sight below the Upper Step, as in the case of the Parthenon and of the Temple of Theseus, owing to the lines appearing to the eye, as stated by Vitruvius, to be concave lines, and that they substituted instead convex lines, tracing their horizontal lines as the arcs of true circles, and giving as much convexity to them as they could venture upon without disturbing the symmetry of the design. The actual amount of curvature to be given to the horizontal lines in any Portico had to be decided by the judgment of each Architect, who may have been guided to a certain extent by works previously executed, and possibly also, as we shall see, within certain limits, by the calculated concave appearance of the lines of the Portico when viewed from the given 96 THE CURVES OF THE HORIZONTAL LINES. point of sight, according to the theory of apparent magnitudes referred to in Euclid’s “Optics ; ” but in every example the amount of curvature, B’h, in the centre of the Upper Step of the Portico being once determined upon, either arbitrarily or by theory, then this given quantity, Bh, is found to regulate all the curved horizontal lines in the design, both in the Kast and in the West Porticoes, as well as on the north and on the south return sides, in the designs of the Parthenon and of the Temple of Theseus. Firstly.—In the calculations, I shall adopt the measured rise of the curve in the centre of the Upper Step of the Parthenon B’h = 0-22 ft., and in the Temple of Theseus Bh — 0-07 ft., as given quantities derived from observation, and shall proceed to make the necessary calculations for determining the curvature of all the horizontal lines in these examples. Secondly.—1I shall make a few general observations upon the concave appearance of the horizontal lines that was observed by the Greek Architects, and shall suggest for con- sideration a form of calculation, derived, as I have stated, from Euclid’s Theory of ““ Optics,” that might have influenced them in determining, within certain limits, the amount of curvature, B’A, to be given in any example to the centre of the Upper Step of the Portico. First.—To determine by calculation the curve of the Upper Step in the Portico, when the rise of the curve, Bh, in the centre of the Step is taken as a given quantity. PLATE 1VY. THE CALCULATED HORIZONTAL CURVATURE OF THE LINES IN THE UPPER STEP OF THE PARTHENON AND OF THE TEMPLE OF THESEUS. Let the rise of the curve Bh, Fig. 1, in the centre of the Upper Step of the Portico, measured above the chord line BB', be assumed as a given quantity derived from observation. In the Parthenon, let Bh = 0-22 feet, and in the Temple of Theseus let B*h = 0-07 feet. The arc BB’B' may be considered in every example as the segment of a circle, then it is simply required to determine from these given quantities the radius, OB, of the circle, Fig. 1, and as many points in the arc as may be required for tracing accurately the segment BB*B'. The arithmetical calculations involve no greater difficulties than have been already met with in the solution of the sides and angles for determining the ‘additions and diminutions” required in the apparent proportions ; and we shall find that the Greeks made all their calculations with such precision that in the executed curves, after so many centuries of exposure, the measure- ments scarcely differ from the calculations. Part Ul Flats IV THE CALCULATED HORIZONTAL CURVATURE OF THE lL.INFS IN THE UPPER STEP OF THE PARTHENON AND TEMPLE oF THESEUS. rise of curve 103 ( \C.\ rise of carve 103 half length of upper step return side G25 = rise of cave 07 Bz $2. rise of curve 07 rise of canve 148 rise of curve 1/83 curve +07 | 5 Koon mena 45-001 = length, of upper step i idtnbicci dy Fig. 2. Plan of the Temple of Theseus. mmm ee) fag. 1. Plan of the Parthenon. Fig.3. The Curve of the Upper step of the Parthenon on the South side and Fast portico centre of south return side tn fs = ze. chord of’ arcle 3 : 22 rise at curve a La —iv line. : is Beet a emo ellen Ia BR — | | 4 P05, ; : Sh ered Ey bo 3 | ae Wass.) of Ee Sri Sinaia Lela Saath op LE Foo teas E08 B07 consi tintnnes y BR 'S ER 714-07 == half’ the length of upper step tom mn sma lte ain ee mms ene Bhima) ok 50-668 = half the length of upper step _______ r= { | 228 14] == whole length of upper: step : i 2 oA ie tide curved Une i su * , ee Ee ima re gE tv ner i | 4 \ $ fT tes Sa hen BE Ra res mn ee ee a dae inne whole length of facia above Corona = 705-086 ___._____. 3 | 3 { 8 = - ~ : curved line dei pee REET rene, odie iewrve Goins ans aie h sn ee Shem inns sme Ean Smee me mad Sneak seve = WATE Levitt of archilrave, = 00:326.. .._ rise of curve 703 i ok : : Tm : >% hu : | ie Senay 4 rr sess tmnntote urns sore) ¢ 22H a, 5 be wore n mann od enn sin prin i ge 115 enh on Sgt gen nd weed ma het aan ma gh shins *tttmensoned- eu | half’ length of” upper step : L | ba | : | > ~ ol uly i Ty [ 32 S 1g 3 : feribhiuncessntoanes 22 j= emsnnsaate since masa) S : manana HBS Ls $s 3 : : 8 £ | etn Loodanpon dod. C.F Kel, leith. Castle St London LC. THE CURVES OF THE HORIZONTAL LINES, > 1st. Determine the angle B', contained by the chords B’B' and BB, from the form, log. tan. A = log. r+ log. a — log. b. ; given a = B?h, and b=h B'. 2nd. Bisect the chord B’B' in f, and trace the line Jg0 at right angles to B’B', and determine the hypothenuse ¢B' of the triangle fB'g, from the form, log. ¢ = 10 + log. b — log. cos. A; given fB' = b, the angle fB'g = A, required ¢ = gB'; hg = hB' — ¢gB!, the angle hOg = angle B*BA. 3rd. Determine the side hO, from the form, log. a — log. b + log. tan. A — 10; given b = hg, angle A = angle hgO = angle fyB'; required 10 — a. 4th. The radius of the Upper Step = OB' = #OL* + hB,* =r, and the equation to the circle when referred to the centre O, 1s © = #9*—y* The vertical rise of the curve of the Upper Step for any given point above the chord BB' = x — Oh. Example.——The Upper Step of the Parthenon. Given B*h = 0-220 feet | angle B=001711 . hB' =50668,, | gB' — 21-809 hg = 28859 Angle gO — 89° 42 49') angle 20g = 0° 17' 11", HO = 57792 feet. Radius of Upper Step = OB' = #'5779-2* + 50-668 = 5779-422 feet = r. x — Oh = 5779422 ft.—57792 ft.= 0-22 ft. = rise of Upper Step in centre. Ete. Ete. Ete. Fic. 4.—THE CurvEp LINES IN THE ENTABLATURE AND PEDIMENT. When the curve of the Architrave of the Parthenon is rectified, we find that it agrees in all respects with the rise of the curve of the Upper Step, and that what Vitruvius has stated is correct, namely, “that the Architrave will deviate from the straight Ime drawn from the “ extreme points, in proportion to the addition given to the centre of the Stylobate ;” therefore the columns are all executed of the same height, and the curve of the Architrave is identical with the curve of the Upper Step, and the line of the Cornice naturally follows the curved line of the Architrave. The curved line of the Cornice being traced, this is found to regulate the lines in the Cornice of the Pediment, for making in Fig. 4 the vertical lines a'b’'— ab, cd = cd, ef’ = ¢f, 98 | THE CUBVES OF THE HORIZONTAL LINES, ete., ete., the raking line in the Cornice of the Pediment is set out as a curved line ; and this Mr. Penrose found to be the case, by measurement, in the Pediment of the Temple of Theseus. Figs. 1, 2, 3, AND 5.—To DETERMINE BY CArcurLATION THE CURVATURE OF THE UPPER STEP oN THE RETURN SIDES, THE CURVATURE OF THE UPPER STEP IN THE PORTICO BEING GIVEN. From direct observation, both of the Parthenon and also of the Temple of Theseus, we find that the amount of curvature given to the line of the Upper Step on the return sides of the Temples, is made to depend altogether upon the amount of curvature which is given to the line of the Upper Step of the Portico, and that the Greeks appear not to have objected to the horizontal lines on the return sides of the building appearing slightly convex. Their aim seems to have been, not so much to make the lines appear mathematically straight, as to remove every trace of an apparent concave appearance in them. On the return side it is simply required to determine a third point, B®, in the curve of the Upper Step, and this appears to have been set out in the following manner— The curve of the Upper Step of any given Portico being accurately determined by calculation, then set out upon the pavement, perfectly level, the diagonal line beB® of the square BD, see Figs. 1 and 2, the Plans of the Parthenon and of the Temple of Theseus ; then ¢ will be the point of the Upper Step at the angle of the Inner Portico, and B® will be the required third point in the curve of the Upper Step on the return side. deine : F lay | : : a pe “Fig.l Parthenon. ~ Fig. 2 Theserum. bre ow @ ¥ \&, vA ¥: ve V % 2 pt BY 1d A ef . / 02000000 0.0 0 0 B = Bz ~ 7 Bi Thus the amount of curvature in the segment of the circle forming the Upper Step on the return side, is made to depend altogether upon the amount of curvature that is given to the Upper Step of the Portico, and the rise of the curve Cm, Fig. 8, in the centre of the Step, measured above the chord BB', is determined on the return side by calculation, the given THE CURVES OF TRAE DORIZONTAL LINER. 99 quantity being B*%. The calculations required for the determination of the radius of the circle, are in all respects similar to the forms that have been adopted in the case of the Upper Step of the Portico, the only difference being, that the third required point, B?, is not the centre of the segment of the circle. Ist. Determine the angle B, contained by the chords 3rd. 4th. The radius of the Upper Step = OB = B’B and B'B, from the form, log. tan. A = log. r+ log.a—log. b; a= Bh; b=1IB. 2nd. Bisect the chord B’B in f, and trace the line J90 at right angles to B’B, and determine the hypothenuse gB of the triangle 7 Bg, from the form, log. ¢ = 10 + log. b — log. cos. A; given JB = b, the angle fBg = A, required ¢ = ¢B; mg = mB — ¢B, the angle mOg = angle BBA. Determine mO from the form, log. a = log. b + log. tan. A — 10; given b = my, the angle A = angle mgO = angle f¢B : required mO = a. vOm* + mB® = r, and the equation to the circle referred to the centre O, is @ = #r* — y*; the vertical rise of the curve of the Upper Variable. Constant. Step for any given point above the chord BB' = x — mO. EXAMPLE. Upper Step of the Parthenon, south return side, Fig. 3. Given Feet. Bh = 0-164 [age B= 0° 19 29/ mb = 114-07 gB = 14-476 Angle mgO = 89° 40/ 31"; mOg = 0° 19' 297; m0 = 175728. Radius of Upper Step = OB; OB = 71757287 + 11407" = 1757317 = r; x — m0 = 1757317 — 17572'8 = 6:37; 0-37 = rise of Upper Step in the centre, &e. ExAMPLE. Fig. 5. Upper Step of Temple of Theseus, return side. Given Feet. D2 =007 (Angle B= 0°10 41 mb = 52-115 gB = 11-254 IB = 22-505 mg — 40-861 Angle mgO = 89° 49'19'; mOg — 0° 10/41; m0 = 13169-0 ft. Radius of Upper Step = OB; OB =+13169-0° + 52-115* = 13169-103 =r; x —m0 =13169-103 —13169-0 = 0-103 ft. ; 0-103 = rise of Upper Step in the centre, &e. We thus see that when the rise B%%, in the centre of the Upper Step of the Portico, is once given, there is no difficulty in the laying down of all the horizontal curved lines in the design ; and we may now proceed, in the second place, to consider whether it 1s possible for the Greeks to have had any forms of calculation relating to the curvature of the lines, that might, within certain limits, have guided them in the selection of the amount of curvature, BZ; to be given in the centre of the Upper Step of the Portico. 100 THE CURVES OF THE HOBIZONTAL LINES. THE CALCULATED APPEARANCE OF THE HORIZONTAL LINES WHEN VIEWED FROM THE GIVEN POINT OF SIGHT O. In the first part of this Chapter the curved horizontal lines have been calculated, supposing the rise of the curve B®, in the centre of the Upper Step of the Portico, to be taken as a given quantity, selected according to the judgment of the Architect. In this second part we propose to consider whether it is possible to suggest any probable reason why the Greeks, in the case of the Upper Step in the Portico of the Parthenon, should have made the rise of the curve B°% equal to 0-22 feet, and in the Theseium 0°07 feet; and why, In other examples, the Upper Step is executed as a perfectly straight line. It has frequently been observed in long horizontal straight lines, when viewed in certain positions, that they become to the eye apparently concave lines, and the Greeks appear to have observed the same fact when viewing the long horizontal lines of their Temples from the given points of view, and they endeavoured practically, as far as they were able, to rectify this apparent optical deception ; still there is nothing either in Euclid’s “Optics,” or in the “Optics” of Ptolemy, that refers very directly to the subject of the curvature of the horizontal lines in Architecture. There is a passage in Philo, an author who dates about B.c. 200 (see Schneider's “ Vitruvius,” Tome II., page 427, quoted by Mr. Penrose), which throws some light upon the subject of the correction of these horizontal lines ; it is as follows— “ For some things, although with reference to themselves they are both parallel and “ straight, seem not to be parallel or straight, on account of the deception of the eye respecting ““ such things, as it views them from unequal distances. Therefore, by the method of trial, “by adding to the substance and reducing it, and by experiments in every possible way, they ““ (the ancients) made them regular to the eye and to appearance of good symmetry.” In this passage Philo clearly states that parallel and straight lines, such as the hori- zontal Imes of a Portico are supposed to be when viewed from the point of sight, appear neither parallel nor straight, on account of the deception of the eye as it views them from unequal distances ; and Vitruvius explains what Philo means by saying that the lines do not appear straight on account of the deception of the eye, for he says— “If the line of the Stylobate were perfectly horizontal (or straight) it would appear “like the bed of a channel ;” that is, the line would have a concave appearance. ) Part 1. Plate V. THE CALCULATED CONCAVE APPEARANCE OF THE JjosoNTAL LINES OF THE PORTICO OF THE PARTHENON. mes horizontal cS / Fig. 2. The calculated concave appearance of th / lines of the Portico on the plane of the Picture PDRS. © Dd Ni © N = A ! ¥ FSIS Rizin 213 e Sl gin : : : ¥ 3 Ss. 81S Ri° Fe wo 8 vou X © CES Te eR TN ws £ 9» Bs tp is Nm Wg 5 4 4.0 5 4 ¥ 4 4 3 NN Q ~ Q Qv ~N i » 2 x 8 : 2 } 1% S$ § 3 = } 3 WB ? & I 311i} S 3 Q 2557 32 23 Q Q Q S = = R g 3 F S 2 ¥ fF 3 : 3 3 3 2 $ $ $ § | | ! rt | $ 2g Q 3 2 8 S A o = 3 3 XS KX S NER Q 5 DS Q ~ SS 5 Q 2 = 1 frgoorenasttatsing ony pape Armee sas enne anne ree LOE pg Emme nm an mee fem PEG TTT 0 | ja | Bo h po i" i / J 0 I y he 1 | yet yy | a hl [ i i : ae I | La 1] ve a | a IT auoyds 0 quabuvy| | iS I 9 rd | Ny & I Fo i | y bof J vd Fol bo Hy } yi | ue 5 | ! ; “699 "9t | pao Ps=ss ses smsatfe crated on aver Ite ee 7 Spleens Sinn iD caine I SI Sd auayds 0) po bum gas The calculated concave lines of the Portico reversed Q : = 2 & Q Ea E Dw] ¥ SS Nix Q Q Q S SI Ti % Fl 1% B.S <3 5 ia 4 < Sr a $18 = 3 + ¥ {4% oN |X R|- S SS 3B 3% = | 2 : 28} oS -% u you %d N 2 E214 ~ No. aN NW Q 5 XS 3 3 Dp NX Te BoB now S TI 3 DOA WB TL WD SR Re R 2 94% Ae Hy + HoH + YU = 5 Q 3 3 Ro 3 : Ne x pout bz br! b Corrected tangent Corrected, tangent Vero m Horizon to Chord lune Corrected tangent 35.8718 Zz From Horizon to Chord bre Reversing the concave lines of tg 2 these lines become convex lines on the plane of the peture PDRS. visual rays from the point of sight 0 through to the Lastly make the Vertical tangent lures br bl’ bE &e plane of the Portico lig. 1 thus Architrave..... 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RNS QS | I a | IA DSA \ ; 1 = I SR Ho TINO 4 J, ie — > NN eB er NS Heese SEES Ens ese str nr sear TERETE RFR ANC TEE Samat n nanny GL flyer nese tna a sms ga nn genet sme Teen ene % olor redore. Led oltre ¢ THE CURYES OF THE HORIZONTAL LINES, 101 In Chapter II., Vitruvius likewise, under the head of Seenography, clearly refers to the perspective representations of the design, where he says, after referring to the plan and eleva- tions drawn upon the three rectangular planes X,Y, and Z, Scenography exhibits the front, “and a receding side properly shadowed, the lines being drawn to their proper vanishing “points.” And Philo evidently refers to the perspective appearance of the Portico when seen from the given point of sight, and when traced upon the plane of the picture, the lines on which, are not parallel as they converge to the vanishing point; and he says that in appear- ance they are not straight, that 1s, they appear sometimes to be either concave or convex. Vitruvius, as we have seen, also refers to the design drawn perspectively upon the plane of the picture, which plane must have been a tangent to a given sphere, with the point of sight for the centre. Founded on these slight references to the horizontal lines that we meet with in Philo and in Vitruvius, we may proceed to consider in detail the calculated perspective design of the Portico of the Parthenon, as seen upon the tangent plane of the picture, from the given point of sight. PLATE V. THE CALCULATED CONCAVE APPEARANCE OF THE HORIZONTAL LINES OF THE PORTICO OF THE PARTHENON. Me. 1. 1st.—1In the plane of the Portico of the Parthenon, PDRR/, the vertical heights PR, DR/, &e., &e., are measured from the horizontal plane to the Cornice, to the Architrave, to the centre line of the Portico, and to the Upper Step, and the horizontal Imes RR, R'RY, R’RY, &e., are first considered as straight lines. 2nd.—On the horizontal plane POD, the point of sight O is given, also the radius OP = 165-43 is given, and the angles POD = 23° 5 34/, and POb = 13° 27’ 26", are calcu- lated ; then at right angles to OP draw the line PD'tangent to the sphere in the point P, and this line is the intersection of the plane of the picture PD'RS, Fig. 2, with the horizontal plane. Yic. 2. Calculating by proportion the apparent magnitudes of the vertical lines of the Portico from the points P, d, b), ¢, D!, Fig. 1, to the Upper Step, to the Architrave, to the Cornice, &e., with the constant radius to the sphere OP = 16543, we obtain the apparent magnitudes. 102 THE CURVES OF THE HORIZONTAL LINES. For the line of Cornice PR — 55-4 . bs — 46494 . D'S — 39-84 For the line of the | : PR = 442 ,08d=37"12 . D8 =81"8] ; Architrave . . . , sphere with radius For the centre line of OP = 165-43. PRE=27:7 . Us? =20247 . DSF == 10024 the Portico. Ete. Ete. Kite. And these several tangent lines are traced upon the plane of the picture PRD'S, and Tangent lines to the are measured from the points P, a, 8), ¢/, D' in the horizontal plane, Fig. 2, then through the extreme points R and S, R' and S', R* and §? ete., draw the chord lines RS, R'S', R*S?, and calculate the vertical heights br, b', 8% ete., in the centre of the Portico, from the horizontal plane to the several chord lines. Thus for the Cornice— CORNICE. As 7058 : A555. 22.81: + 682 br = 6:829 + 39:84 = 46°669 es : — tan. Us = 46494 Concave of Cornice = 0-175 lormice —li ~—15 / J V 2 = 2, IS) > 554 Lo 3) fp eae Mmpre Line or Portico. As 7088 : 7796 :: BL : 5415 Vr? = 8415 + 19924 = 23-339 : | — tan. U's? = 28-247 Concave of middle line of Portico = 0:092 therefore, tracing the lines of the Portico through the given points RsS, R's'S', R*s*S? ete., Fig. 2, the result is a series of concave lines traced upon the plane of the picture PD'RS. 46 - 669 ee 3984 mmm hy SN Be S > | an 46-994 Fic. 3. Consists in simply reversing these concave lines, and thus making them convex lines, it by adding to each line what is apparently h lost ; thus— ; : 5 3 For the Cornice— | ® 3 : Bt —Br +rs —46:669 + 175 = 46-844 bot hs mn For the centre line of the Portico— bt? = bh? + 178° = 23'339 + 092 = 23-431 Kite. Kite. Kite. Lastly, making these corrected tangent lines 0't, o't', 't* etc., ete., again tangents to the sphere in the points 1, 2, 3, 4, Fig. 3, and projecting the visual rays from the point of THE ‘CURVES ‘OF THE HORIZONTAL LINES. 103 sight O, through the given points ¢, t!, #, etc., to the plane of the Portico, Fig. 1; the result 18, a series of convex lines, RzR/, R'2'R", R*’R”, ete., amounting, in the centre of the Portico, to 418 in the Cornice, *33 in the Architrave, and ‘22 = B% (Fig. 4), in the centre line of the Portico. Thus, as we see, it was not possible to correct each horizontal line separately, and in the case of the Parthenon Portico, the calculated convexity of the centre horizontal line of the Portico = 22 = B°h, appears to have been adopted as the given amount of curvature, and that all the lines in the Portico were then calculated as the arcs of similar circles, as shown in Fig. 4. In the Temple of Theseus the calculated convexity of the line of the Upper Step of the Portico, B*h, amounts to ‘065, and this appears to have been the amount of curvature adopted for all the horizontal lines of the Portico. In the case of the Theseium the curved Lines are flatter than in the Parthenon. It would have been impossible, separately, to correct these several horizontal lines without causing too great a disturbance in the given dimensions of the Parthenon, or of the Theseium, but by adding to some of the lines and by reducing others, as Philo states, the Greeks, so far as they were able, “made them regular to the eye, and, to appearance, of good symmetry.” In the case of the Krechtheium, the two designs, of the Fast Portico and of the North Portico, are both seen upon the angle, but the line of the horizon is above the Upper Step ; therefore, in these Porticoes, the tendency would be to reverse the calculated appearance of the lines of the Upper Step, as they would appear convex instead of concave to the eye; but in both examples the Greeks have, I believe, met the case by executing the lines of the Upper Step as perfectly straight lines. The West Central Portico of the Propyleea is seen from a central point of view, with the horizon below the Upper Step; and in this example also the correction of the horizontal lines will not apply, and the Greeks have executed the Upper Step of the Portico as a straight line. From these several varying examples, it appears that it was only when the pomt of sight was favourably situated, that the Greeks attempted to substitute the convex Ime for the straight line in their Architectural Designs. The subject of the horizontal curved lines is one requiring additional and accurate observation of the existing Greek and Egyptian remains; but it appears probable that Philo refers to the appearance of the horizontal lines on the plane of the picture, as seen from the 104 THE CUBVES OF THE HORIZONTAL LINES. given point of sight, and that the Greeks first calculated the concave appearance of these lines, to suit the given point of sight, and then selected from the calculated quantities the amount of curvature that could be safely given to the Upper Step; and this regulated all the other dimensions. It is remarkable how carefully the Greeks calculated the perspective effect of their designs, and corrected every apparent defect, both in the general proportions and in the hori- zontal ines. The principle of calculating the perspective effect is no doubt correct, and in such a work as the Parthenon, all the refinements that we meet with were essential to its beauty and perfection as a work of Art. THE CURVES OF THE HORIZONTAL LINES, 105 CONCLUSION. Lede Lirtablaty,, Columns Stvlobare A Tar boundary lines of the future design are now given in dimension and in position, and the curvature of the horizontal lines has also been determined by calculation, and we find in this first part of the “Theory of Design,” sufficient evidence of the truth of what Plato has stated, namely, “ That artists, bidding farewell to truth, worked out not real proportions, but such as “will seem to be beautiful in their representations,” when designing such works of magnitude as the Parthenon, the Propylea, the Frechtheium, and all works of Art that were designed to be seen “from favourable points of view;” and probably, if at the present time the ancient artists existed, and had the same important works to design and execute in the Acropolis at Athens, they would equally now, as they did formerly, make all the visual angles commen- surable, and they would also change the straight horizontal lines into slightly convex lines. The ancient calculations in Astronomy were many of them based upon erroneous principles, and are now altogether laid aside; but this I believe will not be found to be the case with the Greek mathematical calculations applied to works of Art. In Rome we do not meet with these corrections in the visual angles and in the hori- zontal lines applied to the first masses of the design, but in Rome there are no examples existing in which it was possible to confine the spectator within certain fixed limits, as in the Acropolis of Athens : therefore the first part of ancient Architecture, although noticed by Vitruvius as a part of the ancient theory of design, is not found to be practically applied in any of the existing Roman buildings in Italy. This first part of the theory of design only settles the true heights of the masses, and the convex horizontal lines of the future structure; within which, all the details have now 106 THE CURVES OF THE HORIZONTAL LINES, to be worked out; and for this purpose, we must consider separately the designing of the Columns and of the Entablatures; both very elaborate works of Art. The calculations have hitherto been confined simply to the determination of a few lines and angles by plane trigonometry, and to the calculation of the arc of a circle passing through three given points, but in addition we shall now require, in the consideration of the details of the design, the power of calculating and of describing the arcs of the several conic sections, from certain given elements in each case, as these curves, the ellipse, the hyperbola, and the parabola, are all freely used in Greece, and probably were so in Egypt, in the designing of the Columns and of the Entablatures. Tae COLUMNS. The only given quantity with which to commence the design of the Columns is the whole height AB, and this regulates the width of the abacus, and from the abacus we can derive the upper and the lower diameter, and the heights of the capital and of the base; all as carefully proportioned as the first given heights and widths in the several Porticoes. When the dimensions of the masses of the Columns have been determined by proportion, then the forms of the capitals, of the ornaments, and of the other details, are all designed by combinations of the several conic sections, and made clear and distinct to the eye by variety of lights and shadows, and by the introduction of colour when required. The shaft of the Column, with the fluting terminating at the upper and lower diameters in the arc of one or other of the conic sections, and the outline of the shaft, a carefully calculated hyperbola, are by themselves mathematical studies. The Doric and the Ionic Columns remaining in the Acropolis of Athens are not only beautiful works of Art, but are also valuable existing fragments of the ancient Art geometry. The same remarks will, I believe, apply to the Egyptian Columns at Thebes. In these we find that 1t 1s the width of the abacus which regulates the other horizontal dimensions, and the outline of the shafts of the Columns appears to be the arc of a true hyperbola. THE ENTABLATURES. The given quantities for commencing the design of the Entablatures are— 1st. The horizontal projections measured from the face of the frieze (see Part 11.) 2nd. The corrected lineal height of the Entablature BC, and the apparent height measured in seconds upon the arc of a circle. This apparent height 1s always divided into some given number of aliquot parts, which THE CURVES OF THE HORIZONTAL LINES, 107 regulates all the details, and then the true lineal heights of the Architrave, of the Frieze, and of the Cornice, with the subdivisions of each member, are determined by simple trigonometrical calculations. The forms of the mouldings and of the ornaments, the same as in the Columns, are combinations of the several conic sections. The Entablature 1s a perspective design, carefully calculated in all its details; the mouldings and the ornaments are mathematically traced, and the lights and the shadows, as well as the colours, are all perspectively studied in the finished design. Thus both the Columns and the Entablatures are combined works of Art and of Geometry, and the smallest detail bears the impression of the mathematical accuracy which was bestowed alike upon every part of the design; or, to use the words of Plutarch, “every Architect ““ strived to surpass the magnificence of the design by the elegance of the execution.” The same principles will, I believe, be found to apply to the Egyptian, as well as to the Greek Entablatures; but in Egypt the parts were few, simple, and elementary. The facts above stated will be made clear and evident as we consider in detail in— Part IV. The designing of the Columns, with their capitals, bases, ornaments, colouring, ete. Part V. The perspective designing of the Entablatures, with the mouldings, ornaments, colouring, ete. THE END OF THE THIRD PART. 109 PART 1Y. THE COLUMNS. Port IV. Plate 1 3 Tae OrieiNn AND PROPORTIONS oF TRE FEoyrrian COLUMNS. 1g. 3. Proto Ionic Columns from Bas Relief at Fig. 1. Egyptian Drawings of Columns m the Chambers Khorsabad (B.C #00.) of the rock Tombs of Beni Hassan. (B.C. 2000.) Fig. 2. Proto Doric Capital at Karnak. (B.C. 1600.) (B.C. 1220.) Columns at Medinet Haboo. ¥ig. 4. OUTER COURT INNER COURT ol. OE. Sen Sy CG. BIC niin See pk Se +73 ' a i : 2 oO oO ennnns nts Xm mmm m= === x77 bn] SD N Q mmm PD *2 ) ele 0 eo i mn me Fr / x10 8 *7 see densiatene aes snnnmenn nee enppmng go guloy Ball 1h OL ¥ 3 *7 * H2 i mm ee ee TRON mf 20h OOD oi oons RS *7 . Da “fe--- greatest LONE fpeenen sine oe ofsnns Ler. - - dione - Z - lower diameter aOaCUB... . pp er fehnenninns | | | Q k Pel pie endo k ete lower dia Z greatest dieanoter- .......- wid? of base.......... - CONC een snnrzoees upper dian ~ TT...) Km m mmm es height: of capital 6.094 — width of abacus modulus of column 7 4 5 € 30.477 0.6094 094 hetght of abacus. ke-2. 437.. 70 height od, hase...... giver height é IO GPG oe oeienaeaiia -.... 2.757 7 A 5 2.737 X 8 == 6 .393 —= width of abacus 5327 — modulus of coluia kos R9. 8441 4 = 0 . 393 72 Width, of cap. ...peeneemerssnnnseess gwen height height of abacus... height of base... ._. 6. Part IV. Plate IL 0) S. COLUMN THE LEGYPTIAN ™ tl Ol s Offering m the Tomb of Rameses 11. (B.C 134 Ihe 3. Papyru ORIGIN AND PROPORTIONS will TY < Tuy us growing naturally. he P apyt T Fig. 1. S 3 ™N 3 ~ in = Ti oN . S I == Pe, ee —— nnn. | ~e X < | R l 3 - = Tae - | { x ™ 3 Wo SH [QD 2 EAE AS LD SUSHI E103 | DRUID Ro A Nx [f=jos Ng] | | S&S 3 | : : RE \ 3 oy Sl i Sl i = Q g | === EE federated et ee es 0 Xe : > re = —_— sR K ———— en 3 3 3 S > section of the stem. B.A 1220. or ECE \ A . 1 : 18. BD. Egyptian Columns. - Mermoniurn. iE 1 Memnoreiunm Thebes. B.C. 1300. 3 &d ~~ : $s £3: rE 3 ot 8 h 8 { ee 2 I THI Tis EEE EIR & = x DJ Smsamce: H 2 Bas Ney f 3 4 by C— or rns LD Tr El ~ ~ A > LL nd ves I~ Tong os =. A] N S S$ > Q ea ® § oo ~~ Q X > > iT 2} I ~~. Do SF 2% } 3 No No NN Fig. Papyrus Offering. wn the Tomb of Rameses 27% B.C. 1340. section of ‘the stem Fg. 4 Rock Tomb at Beni Hassan. % FToll Sits, Cotte Sonclon EC. Sot, Foot 72.4 on, ded THE COLUMNS, 111 CHAPTER 1. THE ORIGIN AND PROPORTION OF THE COLUMNS. PLATE 1. axp PLATE Il, THE ORIGIN AND PROPORTIONS OF THE EGYPTIAN COLUMNS. Tar earliest existing Egyptian Columns are probably those in the sepulchral grottoes of Beni-Hassan, executed during the 12th Dynasty, and dating about 2000 B.c. These Columns are simple cylindrical shafts cut out of the rock, and formed into 16 faces, with a square abacus (see Plate II., Fig. 4). We meet with the same design at Thebes, with hieroglyphical inscriptions traced on four of the faces, and the shafts of these early Columns bear the closest resemblance, of any we meet with in Egypt, to the idea of the fluted Grecian Dorie. In the chambers of these early tombs at Beni-Hassan, are some very remarkable architectural drawings of Temples that were erected in Lower Egypt by the governors of the province, who are entombed in these grottoes, and we find at this early period representations of exactly the same designs of Columns, that we meet with in the Temples of Thebes executed seven centuries later. (See copy of parts of the architectural drawings, Plate I., Fig. 1.) The designs of these several Egyptian Columns were, therefore, employed in the Temples erected in Lower Egypt about B.c. 2000, and how many centuries it must have taken for Architecture to have attained to the point of excellence that we meet with m the execution of the Pyramids, and in the conceptions of these several varieties of Egyptian Columns, we are unable to determine, but the Arts in Egypt appear to have been in quite as advanced a state when the Pyramids were erected, and when these grottoes were excavated, as at any later period of Hgyptian history. Although we are unable to assign any dates to mark the commencement of Kgyptian 112 THE COLUMNS. Art, yet we feel certain that 2000 years B.c. Egyptian Architecture had attained to a high state of perfection, and, if no dates can be given previously to the building of the Pyramids and to the excavation of the rock tombs at Beni-Hassan, we can see that the first ideas of many of the Egyptian Columns were evidently derived from the natural productions growing on the banks of the Nile, namely, the papyrus and the palm, and that the Columns appear to be simply copies in stone of the offerings that were presented to the several Egyptian deities. Thus comparing an offering of papyrus, copied from the tomb of Rameses I1., Plate 11., Fig. 2, with one of the Columns in the Hall of Assembly at the Memnonium, or in the Outer Court at Medinet Haboo, we see that the capital corresponds in form with the flower of the papyrus, and that it was ornamented with the name of the king, combined with the papyrus plant. The shaft of the Column is made to retain the idea of the triangular stem of the papyrus, by three raised lines, which divide the circumference into three equal portions, and the arrangement of the leaves at the base of the shaft is the same both in the offering and in the Column. Take another offering selected from the same tomb, Plate II., Fig. 3, and compare it with a Column in the Portico of the Temple at Old Koorneh, and we see a cluster of stems bound together, the capital representing the bud of the papyrus, instead of the open flower ; each stem in the shaft of the Column is made triangular, and the leaves at the base of the shaft correspond with those in Fig. 2. Instead of a cluster of stems, the shaft of the Column is frequently a single stem, and the form of the capital an imitation of the bud of the papyrus, as in the Inner Court of the Temple at Medinet Haboo. Therefore, of the three forms of Kgyptian Columns, Plate II., Fig. 5, that we most frequently meet with in the Temples at Thebes, the ideas of two of them appear to be derived from the different forms of the offerings, and the idea of the third from the rock excavations. But, when we compare the natural growth of the papyrus, Plate IL., Fig. 1, with the representations of the same plant in the offerings, we at once perceive a certain degree of Art in the arrangement of these offerings. The Artists did not attempt to copy nature as they saw it, but each offering was symmetrically combined and arranged. So with the Egyptian Columns we can see that the first ideas were derived from these artistically arranged offerings, but the Egyptian Architects were guided in the design of them by the laws of proportion, and by a knowledge of geometry, and between the designs of the Egyptian and of the Greek Columns we shall meet with many points of very close resemblance, quite sufficient to prove that the first ideas of the Doric Columns and the first principles of Greek Art were both derived from Egypt. But in Greece we lose all trace of nature in the designs, and the Columns, as well as the ornaments, are purely intellectual works of geometry, dependent for their beauty upon accurate proportions, upon true mathematical curves, upon a THE COLUMNS, 113 careful study of light and shadow, as well as colour, and, lastly, upon great precision in the execution of every detail. Tae OriGIN oF THE GREEK COLUMNS. The origin of what are known as the three orders of Greek Architecture is, like the origin of the different languages, involved in some obscurity, but there can be no doubt that the first ideas of these orders were borrowed by the Greeks from earlier nations. Thus, we have already seen that the cylindrical shafts of some Egyptian Columns bear a close resemblance to the Doric order. There are also Egyptian capitals that approach equally close to the Doric capital ; taking for example a capital from the southern Temple at Karnak, built in the age of Thothmes III., B.c. 1600, or 1000 years earlier than any known Grecian example, there are found all the members of the Doric order— | | the abacus, the echinus, and the beaded necking: only wanting the elegance which the Greeks added to them. (Fergusson.) TE (see rate 1, wig 2) In the memoir by Mr. Falkener (“Museum of Classical Antiquities,” Vol. I., page 87) there are enumerated 27 proto- Doric Columns as still existing in eight different buildings, ranging from the third cataract to Lower Egypt. Therefore, without being able to identify exactly a purely Capital tn Temple at Karnal: . B.C. 1600. Doric Column in Egypt, we possess all the elements of the order in the different Egyptian examples, and there is no difficulty in tracing the growth of the Doric Porticoes from these Egyptian elements, modified by such changes as the difference of climate and of race between Kgypt and Greece would suggest. In the Ionic order we are not able to establish any relation between Egyptian Archi- tecture and the Ionic Columns, and the first distinct ideas of this order are found in Asia, where the spiral line is frequently employed in the different forms of Asiatic capitals. Thus, in Layard’s ““ Nineveh,” he says (see Plate I., Fig. 3)— ““ The first indication of the use of Columns in buildings 1s to prrsmsresarennnaseresers, De found in the sculptures of Khorsabad. In a bas-relief from that “yuin a Temple is seen standing on the margin of a river. The “facade is embellished by two Columns, the capitals of which so ““ closely resemble the Tonic that we can scarcely hesitate to recognise “in them the prototype of that order. “Tn a bas-relief at Kouyunjik the entrance to a castle was “ flanked by two similar Columns. ‘““ We have, therefore, the Ionic Column on monuments of the “ eighth or seventh century B.c.” 114 THE COLUMNN,. Although the idea is Asiatic, the Ionic order probably did not assume the form in which we recognise it, until after the founding of the School of Geometry by Thales, at Miletus, B.C. 680, after which period the capital became in design a work of the descriptive geometry, with the parts carefully proportioned, the spiral lines mathematically traced, and the other forms and profiles geometrically outlined. The Corinthian order flows naturally from the Tonic, and differs simply in the capital by an addition of foliage to the Tonic spiral lines, and the shafts and bases of the Columns in the two orders are nearly identical. However gradual may have been the growth of the Doric, the Ionic, and the Corinthian orders of Architecture, there can be no doubt but that in the age of Pericles, B.c. 450, they all attained to a very high standard of perfection, and that a practical knowledge of geometry was then required of all who were engaged in the designing of works of Art, and more particularly in the designing of the details of Architecture, and this will be proved as we consider in succession the designing of all the details of the Columns, namely— 1st. The given proportions of the masses of the Egyptian and of the Greek Columns. 2nd. The proportioning of the details of the | capitals, and the tracing of the various mathematical curves in the Doric and in the Ionic capitals. 3rd. The proportions and the curves of the bases of the Columns. 4th. The entasis, or outline, of the shafts of the Egyptian and of the Greek Columns traced as the arcs of hyperbolas. 5th. The fluting of the shafts of the Greek Columns. Tar First GIvEN ProroRTIONS OF THE MASSES OF THE KGYPTIAN AND OF THE GREEK COLUMNS. In the first general proportions of the Porticoes we have observed how careful the ancient Architects were that the heights, the widths, and the projections, should in the first instance be all multiples of a common modulus; and the same method of direct observation that has guided us in the solution of the first part of the theory of design, will assist us in the details of the Columns. From observation of the Columns, both in Egypt and in Greece, we find that the width of the abacus is always made some multiple of the whole given height of the Column. The abacus, again, always divides into some given number of aliquot parts, and one of these parts being taken as a modulus, then, in each example, the upper and the lower diameters of the Columns, and the proportions of the capitals and of the bases, are all regulated by this given modulus. THE COLUMNS, 115 The relation between the height of the Column and the width of the abacus will vary in different examples, and the division of the abacus into a given number of aliquot parts will also vary in the several Columns of the same order, according to the situation and to the judgment of the Architect. Thus interior Columns are generally made lighter than exterior ones ; this 1s found to be the case in Egypt. Also, the Columns in the inner Portico of the Parthenon are lighter than those in the exterior Portico. Again, in the case of the Vestibule of the Propyleea, where the Doric and the Ionic Columns are seen together, the Doric is made lighter ; but in every case each Column can be reduced into its original aliquot parts, and can be laid down more accurately by giving the proportions according to the ancient method of designing the Columns, .and can be made more convenient for reference, than when the parts are figured in feet, and in decimal parts of a foot. These remarks are equally applicable to the Columns of Egypt and of Greece, and I shall commence first with the proportions of the Egyptian Columns. THE PROPORTIONS OF THE MASSES OF THE KEGYpPrTiAN COLUMNS. The two examples, Plate 1., Fig. 4, selected, are from the Inner and the Outer Courts of the Temple at Medinet Haboo, as I have observed these Columns more accurately than other examples ; but at present I can do little more with regard to the proportions in Egypt than direct attention to the subject, for it is requisite to measure very extensively the several works of Egyptian Architecture, before we can entirely unfold the mathematical principles that appear to have guided the Architects when making their designs. CorLumns AT THE TEMPLE oF MEDINET HAaBoO, B.C. 1220. Outer COURT. Height of Column 29-841 ft. 14 - = 2131 ft. 2-131 xX 3 = 6393 ft. = width of abacus. Ga = 05327 ft. = modulus regulating the parts of the Column. Abacus .=05827TX12 = 6393 Upper diameter . = 05327 x 12 6:393 Lower diameter . = 0-5327 Xx 12 = 6-393 Width of base . = 05327 x 16:5 = 88-7895 Height of capital. = 05327 x 135 = 71914 Height of abacus = 0-5327 x 85 = Height of base . = 05327 x 3:5 = 1:864 Width of capital . = 05327 x 19 = 10-1213 1864 INNER COURT. Height of oh 80471 _ 004 width of abacus. oy — 06094 = modulus regulating the parts of the Column. Abacus .=06094 x10 =60941t. Upper diameter = 0°6094 Xx 10 = 6-094 Lower diameter = 06094 x 10 = 6-094 Width of base .= 06094 x15 =9-141 Height of capital = 0:6094 xX 125 = 76175 Height of abacus = 06094 x3 = 2-437 Height of base . =6:0094 x3 =2437 116 THE COLUMNS, Why the Egyptian Architects should have selected these numbers as multiples, in preference to any other proportions, for the details of the Columns no reason can be assigned. We can only observe and record the facts as we find them, either in Egypt orin Greece, but the same Fgyptian principle of making the width of the abacus some multiple of the whole height of the Column, and then of dividing the abacus into a given number of aliquot parts, and of making one of these parts a modulus for regulating the upper and the lower diameters of the Columns, and for the proportioning of the capitals and of the bases, will be found to apply to all the Greek Columns. | PLATE 11). ax» PLATE 1Y. THE PROPORTIONS OF THE GREEK COLUMNS. The proportions of the early Doric Columns at Agina and at Corinth, and of the first Parthenon, will be found to vary from those that were designed by the Athenian Architects after the Persian invasion of Greece, and we find in the time of Pericles, that the Architects had adopted certain general proportions for the first masses of the Columns, from which they did not depart, except for some special reason. Thus— In the Doric order the width of the abacus . == pal #4 Colonia This 1s the case in the Parthenon, in the Theseium, and in the north wing of the Propylea. height of Column In the Ionic order the width of the abacus . , = 3 This 1s the case in the three examples of the Erechtheium, and in the Ionic Temples of the Ilissus, and at Priene. In the Corinthian order the width of the lower diam™ — "=5™ oF Cli The only example in Athens of this order is the monument of Liysicrates. And in any example in which the proportions of the first mass of the Columns are found to vary from these first given quantities, some special reason can always be assigned for the variation. Proportions or THE Doric Corumxs. (Plate III.) 1st. The height of the Column being given to determine the width of the abacus. : : ‘Width of abacus. Thelauthenm . . . oSmoiciumiinowe M2 = 030 The Temple of Theseus . , ([ofstCdom _ 1998 _ 37474 The Propylea, North Wing. ~~. —ostobCoumn — IP _ 3-835. The Temple of Apollo, Phigalia . ~~ |ofre coms - VE aeeR iss . height of Column 29-164; . Yori The Propylea, Centre Portico 51 = “eam = AB0f, given pro- . rel umn : in | The Parthenon, Inner Portico . foigb el Sa ot S208 5.752 ft. 53 575 [7 worl Ye DF MOPUST GARG PII PIP A Parthenon coleman Theses DORIC : Lropviea (north wing ) Propyleea S (centre , portico) Frechtheaun |, [north portico) IONIC Parthenon : C808 Li vn 2 = | i a | : i bois ) | el eee i ’ : ! : | i ! I | | | | | I Br a iat od Vo maa hl = | i 1 I ! I : I ! | . ' 1 I = Proportions the Tonle (OIE. | aed arta eine a nanan ashes sass bes mn mtr me Ginn mame yas oh Temple of’ Theseus SIS mE a a. n i = 7 I 3 3 ] 1 | i 1 I | I I be pe i re nr mm ee Sr ee = mh ap oe ; first fetal or capital : eee eset ae ee ibe 2.322 = 29.045 27; reed | ) lene meee meee wie | JEN J ; fi 33.7788 | 34.4 HU — 58 ma w= 2.05 | | 3 | || 3 | > | ih | | fe & a - 11111 18.754 | 18.735 BIE — 5.747 BIT — 7.000 | | ; | 3 | | x | X | 19.175 19.175 gross Yann i dl hig or) : : fot z : : > > 2.9% : go orl 5 Lo es sl i a be i fm | — % 5.47 | Bid ini : emf] TTI) eel] SLT Ne Cee emia fle CH — 9565 = modulus LHL — 377 = modulus 3890 — 153 = modulus SE —-366 — modulus : The Shaft of the angle columns is 4s more thaw the intermediate columns The abacus setter Sin is st given height = 33. 5778 —¢. 775 Inthe west front the angle abacus = 6.755 and the ndermediaie abact fr less — 6.615 the capitals project less The Shatt of the angle column vs ’as more than the wntermediate columns . The abacus of the angle coltvman ts bs larger than the termediate colvirmns 3.17 + S22 = 5,854 — angle abacus . "SNKRNIO) NAAYY) FHL 430 sNOLLYMO40vNd JH] HW a1vd Aled Part IV. Plate IV. gr pond go yyboy womb ay = +197 — GEG LE a fen on wi i Ee frm se te ze he rt Si te8 me £m re eee re me i Se tv en fa reer we Gn em fmm —X- . Weteil sf rtioeareampise ches abuert tsi pipe sn nner sie games nna ne ARE wunnay Jo ASOYS 65868 2 semen) k----- 2.827 —————) the Ionic Colvemns. THE PROPORTIONS OF THE GREEK COLUMNS. LFroportions of fin {eo eh 18 LL sl 4.4 Freer NE ee ETT nm EE < ' x = reas a Eee LE Ree ga ri ints ted thar de asta aah i 3 3 F ys? Ith 1%: EEE a wuengoy Jo AY LEE OC ' ~ x4 © + pond) po bY — 00°C = [gr 548 | CERNE agli 4 4 She ee Ee Nel el LE ae I Se 3 Aree ee Si i sen me mr REE Tae EE : ; Gh at : )4 st . vi y cl 23 3 3 1. = A : ci — < 0 io 5 25 ois ~ = i Ta 3 F- - ~N 4 > ! = RT giehre g 3 ; abacus height of base ___L. ’ of capital. 2G por Bary ele eeeen. 2H CSR, lth. Castle St London. Lo C. Jeers r=r=w 3.347 4.369 16 fmm mm upper diam” ic. 2,827 -inn-- width of base |... _.__. lower diam’. | -3 » 224 =— modulus 3.7356 VZa steps an melee eo re Portico of the Lrechtheium are vn every respect similar to this except the hetght of" the capital which is 10 parts instead The proportions oP thn Columns of the east oa 9. lower diam™ width of base london dod. > £4 Ahn PrororTioNns oF THE Ionic CoLuMNS. THE COLUMNS, 117 (Plate IV.) 1st. The height of the Column being given to determine the width of the abacus. The Erechtheium, East Portico The Erechtheium, North Portico . The Erechtheium, West Portico . The Temple on the Ilissus . The Temple of Minerva at Priene Variation. The Vestibule of the Propylea height of Column 8 height of Column 8 height of Column 8 hath of Cop 8 height of Column 8 height of Column 83 Width of abacus. 21:608 — Bagg - 22 _ 3136 18:42 gi = 9'3 fi. - WE ies - BE _ ogg 33-989 = TF 4-12 ft. The first masses of the Columns being arranged, then the width of the abacus is always divided into some given number of aliquot parts, as 15, or 14, or 16, &e., and one of these parts being taken as a modulus, then the upper and the lower diameters, and in the Ionic order the heights and widths of the capitals and of the bases, are all made multiples of this modulus. Tar Proportions or THE Doric CoLUMNS. (Plate IIL.) 9nd. The width of the abacus being given to determine the proportions of the parts of the Columns. The Parthenon,— ) East Portico, angular Col- umn : Given width of the abacus, - 6-848. \ The Propylea,— Centre Portico : Given width of the abacus, 5-469. The Temple of Theseus,— | Angular Column: | = Given width of the i Te 3747. The Propyleea,— North Wing: J Given width of the ans 3-835. 0 k F abacus 1.2 9 4 8 6 7 &. 5 10 1 12 34.05 ep ——— Lower dicumeter upper dvoameter } 1 Fa 5 8 7 8 9 10 lower diameter upper diameter 5 20 25 . 4 1 L 4 L 4 pt tower, diameter — upper dimer ght of copital, | of capital 2% — 04565 = modulus of Column. T0366 — modulus of Column. win = 0'3747 = modulus of Column. Ts = 0153 = modulus of Column. 118 THE COLUMNS, Tae Proportions or THE Ionic Corumns. (Plate IV.) 2nd. The width of the abacus being given to determine the proportions of the parts of the Columns. abacus 0. 2 83 4 5 6 7.8 9 10 1 12 ig 14 1 l 1 } } J l l l ; - The Erechiholam, Bosh and] = or cvser 21 lower dicuneter 3-135 North Porticoes: given width| wr Far 11 = 0224 = modulus of Column. ; height of capitol, | ; of the abacus, 3-135. igi hn kwidth of base 18 moduli abacus 01 ra ssETs INN RENE. lower FY | | | The Propylaea, Vestibule: given OR 1 Nhe <= 0257 = modulus of Column. width of the abacus, 4°12. | dem J height of base width of base J Why the special numbers 15, 10, 25, in the Doric examples, and 14, 16, et cet., in the Tonic, were selected for dividing the abacus into aliquot parts, no reason can at present be offered ; it appears to have depended upon the judgment of the Architect; but all the details of the design of the Columns were invariably proportioned in aliquot parts, and this method of proportion will be found to simplify the calculations required for the curves, by the absence of all fractional quantities. CoLUMNS AT THE ANGLES. Vitruvius observes, Book I11., Chapter IL, “ Columns at the angles, on account of the ““ unobstructed play of air round them, should be 5 part of a diameter thicker than the rest. “ The deception which the eye undergoes should be allowed for in execution.” This is found to be the case in the Doric Columns of the Parthenon and of the Temple of Theseus. In both cases the shafts of the angular Columns are 3; larger than the intermediate Columns. In the Columns of the Erechtheium the shafts are all alike ; there is no increase in the diameters of the angular Columns. Each given Column is now reduced into the first masses of the capital, the shaft, and the base, and to complete the design it now remains— 1st. To design the Doric and the Ionic capitals, with their varying proportions and curves. 2nd. To design the Doric and the Ionic bases, with their varying proportions and curves. 3rd. To design the shafts of the Columns, with the entasis and the fluting. And the present elementary masses of the Columns will then be found to be converted into works of descriptive geometry executed in marble. THE COLUMNS, 119 CHAPTER 11, THE ANCIENT APPLICATION OF THE CONIC SECTIONS TO THE DESIGNING OF WORKS OF ART. It can hardly be supposed, after the mathematical accuracy with which the masses of the design have all been arranged, that the curved outlines found in the Columns and in the Entablatures should have been executed with less attention to the laws of proportion and of geometry than these general masses. Neither is it the case, for in the capitals and in the other details, both of the Columns and of the Entablatures, we meet with many interesting examples of the descriptive geometry. The proof of this assertion need not rest upon the consideration of what is essential to render the design in every way perfect, for no geometrician can investigate the forms of the capitals, the outlines of the mouldings, and the ornaments traced upon their surfaces, the soffits of the cornices, and, I believe, also the outlines of many of the ancient vases, without being convinced that the whole of them were originally mathematically traced, and this is capable of direct proof; for if these curves are all mathematical arcs, then, knowing the extreme precision with which the Greeks always executed their lines in the marble, we shall be able from the given properties of the several curves, first, to define the species of each existing curve, and, secondly, by retracing the elements of the same, to fix each given arc in its true position in the curve to which it belongs. Nicholson, in his “ Dictionary of Art and Science,” published in 1819, says, Grecian “ mouldings are formed of some conic section as a portion of the ellipse or hyperbola ;” and Mr. Gwilt observed the same fact with regard to the Doric capital, for he says, “The contour ““ of the Doric capital will be found composed of the segments of curves formed by the section “of a cone.” Mr. Penrose also states that the various sections through the Doric capitals, the curved soffits of the cornices, and the forms of the mouldings, were in the Athenian buildings invariably composed of the different arcs of the conic sections, and he observes also that “the ““ capitals of the Temple at Corinth (which were much earlier) seem also to be hyperbolic.” If the Egyptian Architects applied the curves of the conic sections to the designing of 120 THE COLUMNS, the shafts and of the capitals of their Columns, as we have every reason to believe was the case, then of course we may expect to find them employed in the very earliest of the Grecian Temples, for they were simply taken by the Greeks, like other ideas and principles of Art, ~ from an early Egyptian source. Still it may be true that some of the properties of these curves were discovered, as 1s stated, by the geometricians of the School of Plato. When in Athens, in 1837, I obtained the true arc of every Athenian curve, either from casts in wax, and from sections cut through the wax, and then by tracing the curve on paper, or in many instances, as in the soffits of the cornices and in the profiles of the mouldings, by tracing the curve on paper direct from the marble, and the outlines of the ornaments and of the volutes were traced by means of thin paper laid upon the marble. From the given data it 1s easy, as we shall see, from the properties of parallel chords, to determine geometrically the elements of each curve, viz., the directions and the dimensions of the axes, the centre, the vertex, and the foci. Having thus obtained inductively the elements of each curve, we are in a position to determine the values of the original given quantities in each example, and the methods employed by the Greeks in the tracing of the several curved lines and surfaces; and before commencing to retrace the Athenian curves, it may be useful to give a few of the simple properties belonging to the different conic sections, that will enable us not only to recover the elements of any given curve, but also from the elements, again to re-construct the curve in any given example. For a complete description of these lines IT must refer to the ancient works still existing upon the conic sections, and to the many valuable modern treatises upon the same subject. I shall simply give in succession the few elementary properties in the ellipse, the hyperbola, and the parabola that will be absolutely required in the tracing of the various details. THE PROPERTIES OF PARALLEL CHORDS. The arc of any conic section being given, the species of the curve must in the first place be determined, which is done as follows: Draw a straight line, bisecting any two parallel chords, and also a second lime bisecting two other parallel chords, then, according as the point of intersection of these lines—in other words, the centre—is on the concave or on the convex side of the given arc, that arc belongs to the ellipse or to the hyperbola; when the straight lines are parallel, the arc is a portion of the parabola : thus— > N he ; gi The Ellipse oD Lhe typerbola The Parabola ~~ be N | a lL : x | ri | | | | i rsa it oS eho fe pi fopnensipenroree genase rT - lr i XX rE - ee 03 °F, the straight lines i df thet centre Con the cowex bisecting the chords the centre C on the concave side of the are y sude of the arc are parallel THE COLUMNS, : 121 Tue Errirse. yo ” Definitions. - TE If two points, I and f, be given in a plane, rr | "oh : . 7 Lo gz , and a point, D, be conceived to move around 7 5 i 3 them in such a manner that Df+DF, the sum i —hiermen pr ame 1B Ld... of its distance from them, is always the same, ord di oo i \ 5 wl Fy the point D will describe upon the plane the -. A iB line ABVB, which is called an ellipse. Er. : Tale 4 po a SR TIT The given points, F' and f, are the foci of z 3 the ellipse. "The point C, which bisects the straight line between the foci, is called the centre. The distance of either focus from the centre is called the eccentricity. The diameter which passes through the foci is called the major axis. The diameter perpendicular to the major axis is called the minor axis. 1st. The arc of an ellipse being given, the centre C is determined by tracing and bisecting the parallel chords. 2nd. Assume any point, P, in the curve, and from C, as a centre, with the radius CP, describe a circle cutting the ellipse in Pp. Bisect Pp at right angles by the line ACY, which will be the major axis. The minor axis is obtained by drawing BCb perpendicular to AV. 3rd. The foci, F and f, are determined by the intersections with the major axis of a circle, whose centre 1s B, and radius CA. 4th. The straight line which bisects the angle adjacent to that which is contained by two straight lines drawn from any point in the ellipse to the foci, is a tangent to the curve at that point ; then let D be a point in the curve, let DF and Df be straight lines drawn to the foci, the straight line DE which bisects the angle FDG is a tangent to the curve at D. | To Describe the Ellipse by Points. With radii CV and CB, describe the two ares of circles Vo and Bo ; then from any point, i 2 | M, in the major axis draw an ordinate, MQ, to 7 : | § the circle Vo; join CQ, cutting the circle Bo in [ Rye | q; through q draw ¢P parallel to CV, meeting shivtsdiemomatdyfinisnaboalile MQ in P, then P will be a point in the ellipse. Other points are similarly determined, and the arc traced through them. 2 2 ——5 (a — 2) The equation to the ellipse referred to its centre, C, and principal diameter, is 2 122 | . THE COLUMNS, The ellipse is a curve not much employed in the forms of the Doric order, but it is frequently met with in the Ionic order, and there are many examples of it in the Erechtheium. Also the curved lines connecting the volutes of the Ionic capital in the Vestibule of the Propylea are elliptical, and the curved surface on the return side of the volute 1s generated by an ellipse with a variable minor axis. Whenever this curve is employed, the axis major and the axis minor are invariably the given quantities, and the arc is easily traced by points. Tae HYPERBOLA. # / i 7d ’, / i 1 fon I ; wl / \ / \ EE , On | NY / \ oe? ho. ~ ~ . trayusverse ; 'M / ar AX ea slo y >. [ axes — a — ti a hon = —_ - — — — — — dan © — ti + mle + Noe + = cd errer © te reer me =) Zo) me + emt en = oer mmm e Ie i 1 SO ms 3 a 4 mm er en ng he AG —— ! | ’ \ J ; ry | - - “ — — a c—b a— { NN A / : ‘ 3 / Et 3 § g h ; St BY A Gf oH \ bt J et / y 3 ‘ Seer? 4 a SN. \ 1 / 3 BN | N Ii / \ log / y NG N TE Fo J y / yd \ N rt b ¢ 5 $ / od ~ 7 | / | \ / ry $ Sp oS Li J x ; \ x ’ d 4 % / N J | \ 2 | \/ D ™ fx x ' Na N S ; pi \ J P=. A » 7 Ny Definitions. If two points, I' and f, in a plane, and a point, D, be conceived to move in such a manner that Df — DF, the difference of its distances from them, is always the same, the point D will describe upon the plane a line DAD), called an hyperbola. The given points F and f are called the foci of the hyperbola. The point C, which bisects the straight line between the foci is called the centre. The distance of either focus from the centre is called the eccentricity. A straight line passing through the centre and terminated by the opposite hyperbolas 1s called a transverse diameter, and sometimes called simply a diameter. The extremities of a diameter are called its vertices. The diameter which passes through the foci is called the transverse axis. A straight line, BD, passing through the centre perpendicular to the transverse axis, and limited at B and b by a circle described on one extremity of that axis, with a radius equal to the distance of either focus from the centre, is called the conjugate axis; also called the second axis. 1st. The arc of an hyperbola being given, the centre, C, is determined by tracing and bisecting the parallel chords. THE COLUMNS, 123 2nd. Assume any point, P, in the curve, and from C as a centre, with radius CP, describe a circle cutting the hyperbola in p; bisect Pp at right angles by the line MACYV ; then ACV will be the transverse axis of the hyperbola, and the extremities A and V the vertices of the curve. 3rd. The second axis is found from the following proportion, as AM x MV : MP?:: AC? : BC?; then BC? = 3 the second axis. 4th. The foci are obtained by making CF and Cf each equal to AB. 5th. The straight line, which bisects the angle contained by two straight lines drawn from any point in the hyperbola to the foci, 1s a tangent to the curve at that point. Let D be the point in the curve, let DE and Df be straight lines drawn to the foci, the straight line DE which bisects the angle fDF 1s a tangent to the curve. To find any number of points in the hyperbola, having given the transverse axis and the focl— Construction.—Take H, any point in the axis produced both ways, except between F and f, the foci, and from F and f as centres, with the distances HA, HV, describe circles which will cut each other in two points, D and d, one on each side of the axis. These are points in the hyperbola. The equation to the hyperbola, referred to its centre, C, and transverse axis, is— VE + I? — a: 2the second axis, CB = b= “ Y 3 P=] 9 V 1? a re ——————————— b xr = When the elements are given, the curve can either be constructed by points, or the ordinates can be determined by calculation. 124 THE COLUMNS, This curve is the one most frequently employed both in Egypt and in Greece. In Egypt the outline of the shafts of some of the Columns at Thebes, as well as the sections through the cornices, appear to be traced as the arcs of hyperbolas. The outline of the Doric Column, both in the shaft and in the capital, is simply a combination of the arcs of the same curve, and in Greece it is frequently employed in the outlining of the Columns, in the profiles of the mouldings, and in the outline of the various ornaments, et cet. Cl Whenever the hyperbola is employed we shall find that the \ L given quantities are the vertex A, the tranverse axis AV, and one anh in aie point P in the curve. bid . : The second axis and the foci must be determined by calcula- 7 tion, and then the curve can be either geometrically constructed, or : 7 . o . 5 a few points determined by calculation. In the case of the entasis of the Greek Columns, the given quantities will be different ; but this subject must be separately considered. THE PARABOLA. Definitions. If a straight line, BC, and a point without it, I, be given in position in a plane, and a point, D, be supposed to move in such a manner that DF, its distance from the given point, is equal to BD, its distance from the given line, the point D will describe a line, DAD), called a parabola. The straight line, BC, which is given in position, is called the directrix of the parabola. © —— — — — + — — — =m, ’ y ' / ! . \ y é ' ' % : , : A / Ld + ’ : s \ axis M ! 4 ! x foes TAT me fen Te en te ee A em mt me = I 7 A : 1 ; 1 i” / ; | : / a digmeter The given point, IF, is called the focus. A straight line perpendicular to the direc- trix, terminated at one extremity by the parabola, “and produced indefinitely within it, is called a diameter. The point in which a diameter meets the parabola is called the vertex. The diameter which passes through the focus is called the axis of the parabola, and the vertex of the axis is ~ called the principal vertex. THE COLUMNS, 125 A straight line quadruple the distance between the vertex of a diameter and the directrix is called the perameter ; also the latus rectum of that diameter. The are of a parabola being given, the straight lines, or diameters, bisecting the parallel chords, will be parallel to one another ; then trace an ordinate, PP, at right angles to a diameter, and bisect it in M, and draw the line, MAC, parallel to a diameter. This line will be the axis of the parabola, and A will be the principal vertex. The axis and vertex of the parabola being given, the focus can be determined from the 2 equation to the parabola, y = 4 2 px, and p = = = FC, AF = py To DESCRIBE THE PArABoLA BY POINTS. Given the directrix, CB, and the focus I; through any point, M/, of the axis draw DD’ parallel to CB, and from the focus, F, with radius equal to CM/, describe a circle to intersect DD' in the points D and DY, then will the points D and D' be in the curve. The straight line which bisects the angle contained by two straight lines drawn from any point in the parabola, the one to the focus, and the other perpendicular to the directrix, 1s a tangent to the curve at that point. There are some very good examples in Athens of this curve. Thus, the soffit of the Pediment Cornice of the Parthenon is a very perfect parabola. We shall meet with this curve in other cases, but it is not very much employed ; whenever we do meet with it, the given quantities will be the axis, the vertex A, and one point, P, in the curve. TaE ProPoRTIONING OF THE CAPITALS, AND OTHER DETAILS. We have seen throughout the work how carefully the Greeks always adhered to the principle of dividing and of subdividing into aliquot parts, and of making all the quantities commensurable one with another, and the same principle will be found to apply to the proportioning and the arranging of the details and points required for the tracing of the carved outlines of the capitals, of the bases, of the profiles of the Cornices, and of the ornaments, et cet. Thus, in the capitals, the whole projection and the whole height are already given quantities ; these will invariably be made to subdivide nto some given number of aliquot 126 TOE COLUMNS, parts, and one of these parts being made a modulus, then each of the subdivisions in the capitals will be some multiple of this modulus ; it regulates the projections as well as the heights, and the given elements of the curves will also be multiples of the same modulus; and it will be, in every example, this exact dividing into aliquot parts, and all the required points falling simply and easily into their places according to this arrangement, that will afford the evidence in confirmation of this part of the theory. Every detail can be laid down without any reference to dimension, and, being thus reduced into aliquot parts, can be simplified both in the figuring and in the calculations. We may now proceed to consider in succession the designing of the Doric and of the Tonic capitals, and also the bases and the shafts of the Columns. The carved profiles of the mouldings, and the outlining of the ornaments, as well as the designing of the Entablatures, will all be considered in the next Division of the work, Part V. THE COLUMNS, 127 CHAPTER .111. THE CAPITALS. THE Dorie capital is composed of a few simple parts, and is rendered pleasing to the eye by the harmony of the proportions, by well-arranged light and shadow, and by mathematical accuracy in the outlines of the several curvilinear forms of which it is composed. But there is, I believe, in Athens, no example of any ornaments being traced upon the curved forms of the capital, or of any relief being imparted to it by variety of colour. Tt is thus the simplest of all the capitals, and yet the preference was given to it for two of the finest works of ancient Architecture in Athens, namely, the Parthenon and the Propylzea. The given mass of the capital is always Fig. 1. podueed into four parts, namely, the abacus, the echinus, the annulets, and the hypotra- chelium, and the curvilinear profile of the capital is composed of the ares of two hyper- oh bolas, the one convex to the eye, and the other concave, thus : the profile of the echinus, PAP), __.__ 1s always the arc of a hyperbola, and the pro- file of the hypotrachelium and annulets, PAT, is also the arc of a hyperbola. (See Fig. 1.) | | | | : NBT Besides these two curves, forming the CT TTT mmm me NN profile of the capital, there 1s also the vertical / / 7 , fe mn am ei — 7 mmm mmm — ee section through the centre of the flute, namely, the curve PAp (see Fig. 2), which is also the arc of a hyperbola. 128 THE COLUMNS. The consideration of the subject will naturally divide into two heads— 1st. The arrangement of the proportions of all the parts composing the capital. 9nd. The arrangement of the elements required to be given for the construction of the curves. The Parthenon Cap tal tn perspective. PLATE V. THE PROPORTIONS AND CURVES OF THE DORIC CAPITALS. The three examples selected in this Plate to illustrate the designing of the Doric capital were all laid down to the full size from sections taken in wax from the original marble, the outlines were accurately traced from the moulds, and the true proportions, as well as the elements of the several curves, were then recovered. In the Plate the capitals have been reduced to one-third of the real dimensions to suit the size of this work. In every example the whole height of the capital, OR, must be so arranged, that one common modulus will divide into aliquot parts, both the whole given projection, OP, and the given height, OR. This generally causes a slight correction to be made in the first given height of the capital, and then the heights and the projections of the several details will always be some multiples of this given modulus, and the given elements of the several curves will, to a certain extent, be regulated by the same modulus. There does not appear to have been any general law for assigning a value to this modulus, but in each example it was regulated by Part IV. Plate V. Propylea centre Portico Column The Fig. 2 R 174 Toe ProporTIONS AND Cundis of THE DORIC CAPITALS. 6-848 — width of abacus a" 34-24 Fig .1. The Parthenon Column. Height of Coleman ndon LL: 2 So bre 7 Z 2 lth. Castle 7 En 7 ore — 7 projection. 15 5369 30 3 | J a Tl 3 fe SENNA InN S YER RE u nu tang bo CS 3 I "Et—t— tt : fmm t + ft t + t —t—t—A—t— t frown] t T 1 a SE T 1 ' % | Ar | / 7” ei a > tr Hl oo i I J: 1 3 J J f t by ns 3 3 ht | +--+ . Mein Ae Sma sae ot et z = eran ay i : : ge : ik \ CLE a ee dl Yan J aq R 3 SL 7 pe : a a Rei / | + | S i \ I 3 <8 5 3 >, 4 ow | : i fs ME 4 ; | $ “2 } med : | ; a 3a jo AB = x ig abd 8 S x ; Xr seo k $ 2 t el JF x 2 I= 3 ol 5 Solin | 3 3 . ~ ho \ fe T = : NN J 1 XL 3 N b= v ie Soe n Fn - merry 3 | 2 = 1 Sho % 3 < ak xy Ss 1 Ts 3 : 3 by } 4% XN afd 3 «WB : ~ : od Lado ledetd oat, | . Ta : cles y Io 5 I il X SV 71 S Bree GD iad 3 N S ecb gel ¥ 3 N Tn a R S hepa bow = 3 3 3 A fe : 2 o}-4- » 2 Lod dn peel 1 mmeeSerenr ee ree ma 2) Srey 2? A 3 Foor a hr 1 3 =” | 3 | Zap. 4.4 I A Tr | i bd fs % oi 3 ni] 2 Stile We 3g pir 8 Fey pee Ss ly ; Bo : Hox 1 SN fogs bon S$ 5 ah / (is 4 So y & & & 2 3 | = | i | i a “1: x IX TS a8 8B 3 x Bs yell = x bal Dy sl 3 dol ey 3 | | Te jr ol (RP = ow 8 Fi] ob I oy S i AN ales RX Ws 00] 3 poak soloed oon 20 : : pe Iti ST § if da Td S 3 nN} SN { | Eh 3 = oa Te » : 5 os " i efuibuife nn) Rei i of -om-f-toe--- 8 ae / . doa aa 3 J oe Sr” / : E E ef Jriforethg _ a > z > Bo oa ood gs 0 3 S Ff a edo dd 3 | 1 3 Sad oft g 1] Ser lanl % i | S foe 3 ; ; a : os X be | o > NN QL } st erlfoertloe sm reBE I £3 Rd : : N = o f+ ! 3 L no § 2 5 3 0d 3 Lun foi 2 © > Zz Ss i * 05d o ~N E N | : 3 : SY wy L N : a ena Lo Ne S = = < = 5 Tp 3 : ET ! 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Pir I iz | N vo S11 / ' S | : ! : NEES oe bay, £ 1g = Sey J Sd 3 od ' yosu fe a IN ® haha eo LE Re sen We ST NS rE TSR Ar seh ve keane fd og A 3 = : Z i ‘ EL x 2) vole ~ 3H . y 1 i Ths 7 5) a > © ! * BN \ | 3 x i / ~ 1 <9 x : Nn yo is Th itr > Nv I) 7 7 a ——mmmm mE om == 1 A = oo SS ; “si 1. 0 x 7% Z i oo i) = = Q 7 : i : = : i RN Tn | N \ NS ho fe % a i | SE a . = IEE rr Praia le br * Sporto een Ce tr! 8 mrs cmon itm tds des HrpEns dnl pe Sennen mem enoe depemn ens dln re emer rr ee Pe nn UY: ape Sate Eases pe a see Ni 7 HK ---mms cms = aunRYIDROdNF -----— === i SOVQF SnUNYIST 5 i a 1) BOA] i etd ee maen ame 52 wpper doaseler meme 2 O1O226 1 5205 0 2 7... .. N upper 1584 x 18 John lnm. del. THE COLUMNS, 129 the judgment and taste of the Architect, still the variations in the proportions between one capital and another are generally slight : thus— Fig. 1. The Parthenon Column. Mod. for details 5 of capitals. The modulus of the Column — 04568 ft. ; divide this modulus into 16 parts, “4° — 002854 The projection, OP . . =2mod. X16 . =382 parts =002854 x32 . =0913{L. The height of capital, OR — (6m X16) + 3p = 99 parts = 002854 x99 . =2:825 Fig. 2.—The Propylea, centre Portico Column. Mod. for details : of capital. The modulus of the Column = 0-366 ft. ; divide this modulus into 18 parts, pe = 002033 The projection, OP . . =2mX18 . = 386parts=002033x 36 . =0732 The height of capital, OR = (6 X18) + 6p = 114 parts = 062033 x114 . = 2-3176 Fig. 3.—The Propylea, north wing Column. Mod. for details of capital. The modulus of the Column = 01534 ft. ; divide this modulus into 15 parts, py = 0010226 The projection, OP . . =. 7 A - 2 parts, = ph . = 05369 The height of capital, OR = 11 X15 = 165 parts, = 0010226 x 165 . = 1-687 THE PROPORTIONS OF THE DETAILS. Fig. 1..—The Parshonn. Fig. 2.—The Propyleea, Fig. 3.—The Propylea, central Portico. north wing. Heights. Projections. Heights. Projections. Heights. Projections. Hypotrachelium . 21 parts . . 3parts 23 parts . 3 parts | 32 parts . 52 parts Aomilels o. . 9 0 a goniae ug, cle) isi, Bchivaz. -. . 31 cL 86 ,. 9 , (B82 , .3L Abaenz . . . 40 ,, ew 2 47 -,, . 3 59 « B 4 Whole height, OR = 99 Projection=82=0P |114=0R 86=0P |164=0R 52: =0P This reduction of the proportions into aliquot parts, very much simplifies the figuring ; 1t satisfies also the ancient ideas of proportion, by making all the parts commensurable one with another, and multiples of a common modulus, and, as we shall see, it reduces the calculations required for the determination of the elements of the several curves into the simplest possible form. 130 THE COLUMNS. Tae GIVEN ELEMENTS oF THE CURVES. In the Doric capital all the curves of which it is composed are the ares of hyperbolas, and in each separate arc the given quantities will be the vertex of the curve A, the direction and magnitude of the transverse axis AV, and the position of one point, P, in the arc of the curve. From these given quantities the second axis, CB, and the eccentricity CF = AB, are determined by calcula- tion, and then a sufficient number of points in the arc of the curve can be determined by the descriptive geo- metry (see the construction of the hyperbola by points, page 123), or, if the case requires it, a few ordinates can be calculated from the equation to the hyperbola, referred to its centre, C, and transverse axis AV. a ee x= Vy + O — a; ay 92 =i IP ‘ Thus, taking for example the echini in the capitals of the Parthenon and of the centre Portico of the Propylea, Figs. 1 and 2, we have for— The Parthenon. (Fig. 1.) (y = MP = 29 parts 3 X 29 87 : o MA = 23 Ub ~/v32 5 may, Soe Given quantities AC G=80 = 3 » AR (OF = VAT BC = #05 1154 — 45009 (2 = MC =26 ,, The Propylea, Centre Portico. (Fig. 2.) y = MP = 33 parts MA =-=242 4 x33 132 w Bo aa kBS 132 Given quantities na C VRE —F ~ 05d 4-679 z=MC = 28% ,, With these quantities determined, the arc of the echinus is geometrically traced. THE COLUMNS. 131 In the curve of the hypotrachelium and annulets, Figs. 1 and 2, the sides, PS and ST, of the right-angled triangle, PST, must be given ; then bisect the hypothenuse, PT, in M, and divide MP into some given number of aliquot parts, and let AM and AV be multiples of one of these parts; thus, in the case of the Parthenon, let PS =15 parts, and ST = 35 parts, and, in the Propyleea, let PS=12 parts, and ST = 34 parts; then in both examples divide MP into 7 aliquot parts. | y = MP = 7 parts Vh=2 CB — =t — gly — 247 a=AC =1 ,, w=MC=8 , In the vertical section, through the centre of the interior of the flute, the are, PAp, is also traced as the arc of a hyperbola, and in this case the sides, PQ and PR, of the right angled triangle, QPR, must be given, and the hypothenuse, QR, is made the direction of the transverse axis of the curve; then trace PM at right angles to QR, and divide PM into some given number of aliquot parts, and let AM and AV be multiples of one of these parts. The depth of the flute, PP), is already given; then, in the case of the Parthenon, and of the Propylea— The Parthenon. Let PR = 15 parts, and PQ = 23 parts Let.y = MP = 4 parts AM=3 , CB = 2x4 8 d= AC =2 V2 + 4 5385 33 e=M0=5 -, The Propylza. Let PR = 16% parts, and PQ = 25 parts Let y = MP = 4 parts AMbS a=AC=1 ,=2Y AY=i, In all these calculations, by reducing everything as much as possible into aliquot parts, and by using the constructed tables of squares and square roots, et cet., the arithmetical operations are reduced to the simplest forms, and it was probably for this reason that the Greek Architects employed the aliquot parts in the laying down of all the details. We meet with no two capitals in Athens that are exact copies the one of the other; 4 132 THE COLUMNS. the three examples here given all differ in the proportions and in the given elements of the curves. The capitals of the Columns of each Portico are separate designs, carefully worked out and executed; but all the capitals of the Doric order agree both in the general idea and in the methods of the laying down of the several parts. THE IONIC CAPITAL. The Tonic capital is more complex in its design than any other detail of Greek Archi- tecture, and presents considerable difficulties in the recovery of the original methods of laying down the curved lines, for, besides the several conic sections employed, which are all known curves, we have to consider the spiral lines of the volutes, and in this case there is nothing left in any ancient work to guide us to the method which was anciently employed in the proportioning and in the tracing of these architectural spiral lines; but we possess within the Acropolis of Athens three very perfect examples of the Tonic order, namely, the Tonic capitals in the Vestibule of the Propylaea, and in the East and in the North Porticoes of the Erechtheium. From these several examples we shall be able, I hope, to deduce inductively, both the method of proportioning the volutes, and the manner which was employed in describing the spiral curves, which are the distinctive features of the Tonic order. The separate details of the Ionic capital are as simple as those in the Dorie, but the capital is rendered more elaborate as a design, by the greater variety of the curved lines and surfaces of its component parts; it is enriched with sculptured ornaments and painting, and is also frequently ornamented with metal spirals and gilding, as in the case of the capitals of the Krechtheium. To explain the several parts of the order, we may take as one of the best examples the Ionic capital in the Vestibule of the Propylea. THE COLUMNRX, - 183 3 | ! | | | 1 | | | | | | | | | | | In this instance the capital, as shown in Fig. 1 has the following subdivision of parts, namely, the abacus, the volutes, the elliptical lines connecting the volutes, the echinus, and the hypotrachelium. The general proportions of the capital being given, then the design of the volute will be found to divide into two parts— Firstly. The volute is proportioned by means of a rectangular spiral line ABCD, A'B'C'D), AB'C'D! ; and Secondly. The boundaries of each spiral line being given, then the spiral curves are described within this rectangular spiral line by one simple and uniform method to be explained. Tar ReETurN SpE oF THE loNic CAPITAL. “On the return side of the capital we have in every example an elliptical curved surface, as shown in Fig. 2, the method of describing which, will be explained in Plates IX. and X., showing the return sides of the capitals. / Fic. 2.—TaE RETURN SIDE OF THE VOLUTE. 134 THE COLUMNS, The several details in each capital, namely, the section through the centre of the capital ; the front view, Fig. 1, showing the volutes, with the elliptical connecting curved lines; and the curved return side of the capital, Fig. 2, are all laid down by proportion, and the several curved lines are then mathematically traced, as in the Doric order, and the first given quantities are also similar, namely, the width of the abacus, the height of the capital, and the upper diameter of the Column. The capital of the Ionic Column in the Propylea is probably the best example for denoting the essential features of the order, as it agrees in the arrangement of the details with the Tonic capitals of the Columns of the Temple of Victory, of the small Temple on the Ilissus, and with the Temple of Minerva at Priene. The capitals of the Irechtheium have the same general features as the other examples, but they have, in addition, an increased number of spiral lines in the volutes, and two extra members are added to make the capitals harmonize with the extreme richness of ornament in the other parts of the Temple. The subject will be rendered clear by laying down the volutes in detail from the casts and tracings obtained from the originals of the capitals of the Propylea, and of the Frechtheium, commencing with— First. The general method of proportioning the rectangular lines, forming the boundaries of the No. 1 guiding spiral line. Then— Plate VI. Gives the general method of describing the spiral lines, when the parallelograms ABDC, ABDC, A/B'D'C'" are given in position and in dimension. Plate VII. Gives the general proportions of the capitals of the Ionic Columns in the Vestibule of the Propylea, and to an enlarged scale, the proportions and the spiral lines of the volutes. Plate VIII. Contains the proportions of the capitals of the Ionic Columns of the North Portico of the Irechtheium, similarly laid down. Plates IX. and X. The return sides of the Ionic capitals, showing the proportions, the curves, and the curved surfaces of the same. THE GENERAL METHOD OF PROPORTIONING THE VOLUTES OF THE IONIC CAPITALS. Before commencing to describe the method of laying down the general curves and proportions of the Ionic capitals, which present no serious difficulties, it will be advisable to THE COLUMNS, 135 consider whether it is possible from the existing examples in Athens, inductively to recover the ancient method of proportioning and of tracing the spiral lines of the Ionic volutes. The idea of the spiral line, as that of other curved lines, is suggested by many forms that we find mn nature: it may also be derived from the cone, by conceiving a continuous line winding round it from the base to the vertex. In the ancient geometry we have the spiral of Archimedes, and some of the spiral lines of the Greek ornaments will, perhaps, be found to be true examples of this form of curve; but in the case of the Ionic capitals, it is clearly stated by Vitruvius that the spiral lines are composed of the ares of circles, and the tracings taken from the existing Greek volutes show clearly that this is the case. It is easy also to derive from the marble the fact that each revolution of the spiral lines is contained within a given parallelogram, the sides of which are in some exact propor- tion, as 5 : 6, or 6 : 7, ete. Thus, in the volute of the Tonic Column of the Propyleea, taking as an example the No. 1 spiral line, see Fig. 3, then— The parallelogram ABDC, containing the first revolution of the No. 1 spiral line, the ratio of the sides, DB : AB areas 6:7 The parallelogram A'B'D'C), containing the second revolution of the No. 1 spiral line, the ratio of the sides, D'B' : A'B’ are as 6 : 7 The parallelogram A'B'D'C/, containing the third revolution of the No. 1 spiral line, the ratio of the sides, D'B" : A’B" are as 6 : 7 These are simply the observed facts, but beyond these observed facts there is still required some law for fixing in position and in dimension these several parallelograms one within another, and for this law I am indebted to the careful study of the subject by Mr. John Robinson, who discovered the relationship between the several rectangular lines con- taining the No. 1 spiral line. Thus, in— Fig. 3. The given proportions of the rectangular lines containing the No. 1 spiral line of the volute of the Propylea. A’ C | sl A C K | Is © Te The parallelogram ABDC is derived from Fig.3. ‘ Tr 4 hb . r 4 the general given proportions of the capital, i 1 1 1 and it is required to lay down the two inner of | phere parallelograms, ABD/C’ and A"B'D/C". i B fremsafmmmionrween D -} | B. + | : ; D 136 : THE COLUMNS, Given lines. AB, BD, DK 7 46 3 DK, AK, AB | 7. 6.58 | AB, BD, DK 7 6 Divide DK into 7 parts. Divide A'B/ into 7 parts. | Divide D'K’ into 7 parts. DK, AK ; Divide A’K' into 7 parts. AK, AB, | : | Divide A’B’ into 7 parts. AB, BD! | ; | Divide B'D/ into 7 parts. BD! DK! 7 6 And the three parallelograms, ABDC, A’'B'D/C/, A/B/D"C", within which the three revolutions of the guiding spiral line of the volute has to be described, are now given both in position and in dimension. TE VoLUTE oF THE CAPITAL oF THE CoLUMN IN THE EAST PORTICO OF THE ERECHTHEIUM. In the volute of the capital of the Column in the Fast Portico of the Erechtheium, we find that the first revolution of the No. 1 spiral, commences with the same ratio of diminution as in the case of the volute in the Propylea, and then the numbers change as the spiral approaches towards the centre: thus— AB, DB, DK | _ ; Given lines Divide DK into 7 parts. l 7.6 3 DR, AR, AD}. . | Divide A’B’ into 6 parts. 7 8 3 AB, BY, DK Divide D'K! into 6 parts. 6 5 DR, AK, ABZ}... : ~ Divide A"B/ into 8 parts. 6 5 4 ABI, BD! 8 7 And the three parallelograms, ABDC, A'B'D'C/, A/B'D'C', within the boundary lines of which the No. 1 guiding spiral line of the volute has to be described, are given in dimension and in position. THE COLUMNS, 187 Tae VorLuteE oF THE NoRTH PorTicO oF THE ERECHTHEIUM. Tn the volute of the capital of the North Portico of the Erechtheium, Fig. 4, three similar parallelograms, ABDC, A'B'D'C/, A'B'D'C/, are first given, as in the example of the Ionic capital of the Propylea, but varying from it a little both in the proportions and in the positions of the parallelograms. Thus, in the case of the volute of the North Portico of the FErechtheium— ? Big 2 A AB : BD :: 6¢ : 57 instead of 7 : 6 as in the Propylzea. iF 1 AD BD: 62: 5 4 . 5 3 I AMB:BDi6t:5 , : Sn ay { I . . A] + Or dividing AB into 52 parts to obtain a smaller modulus, 1 K il + ¥ then, in the case of the North Portico of the Erechtheium, + + Sr I 1 1 the three revolutions of the rectangular boundary lines of 1 | FP I 1 4 the guiding spiral line can be expressed in the following i WT 3 Prt Let AB — BD — DK = : : ; Ratio 8, the 1st revolution of the spiral line. 52 — 4 — 36 pp dB BD UL UB im | . 2 2 2 Ratio 4, the 2nd revolution of the spiral line. = 26 — 22 — 18 AB BD DK — AB — BY — DRY : bok 4 4 4 b Ratio 2, the 8rd revolution of the spiral line. = 13 — 11 — 9 pl Then DK, KA, A'B Let KA' = PR dp irs, Given quantities. 2 2 equal 36, 31, 26, | | Ip Then DK/, K'A/, A'B' Let KA" = PRE I Given quantities. 2 2 18, 15, 13, 1 The side, KA/, is the mean between the last side, DK, of the 1st revolution of the rectangular spiral line, and the first side, A’B/, of the 2nd revolution. The side, K/A’, is the mean between the last side, D'K/, of the 9nd revolution of the rectangular spiral line, and the first side, A’B, of the 3rd revolution. And these two mean lines, KA and K/A”, place the three similar parallelograms in 138 THE COLUMNS, position, and the entire series of the rectangular boundary lines of the guiding spiral line of the volute can be expressed in the following manner—- 1st AB, BD, DK : : | Ratio 8. revolution | 52 44 36 DK, KA, A'B' Given quantities. 36 31 26 j AB, BD, DK 2nd revolution 2 0 22 18 | Ratio 4, equal to half of the 1st revolution. DK, K/A/, AB! Given quantities. 18 15+ 138 . [AR BY, DK") Ratio 2, equal to half 3rd revolution : 13 11 9 | of the 2nd revolution. Then within these given parallelograms, ABDC, ABDC, A'B'D'C/, now fixed in position and in dimension, we have simply to describe the three revolutions of the No. 1 spiral line. I am indebted to Mr. John Robinson for the true solution of the arrangement of the rectangular boundary lines of the volute of the North Portico of the Krechtheium, as well as of the volute of the Propylea, and there can be no doubt that these two capitals are the most perfect existing examples of the Ionic order; they possess great value as combined works of Art and of geometry, and suggest to us a new method of describing the spiral lines, which will probably be found to have had a wide application anciently in the designing of the architectural ornaments and details. There still remain to be considered the elliptical curved lines connecting the volutes together, and the method of describing these lines, will be given with the method of describing the spiral lines of the volutes. Part1V PlateVi Tar METHOD OF DESCRIBING THE VOLUTE OF THE loNic CAPITAL. As proposed by M* John Robinson . /” 4 / The Par allelograms ABCD ABCH, ABCU.b emg given In position . A C ne Le LR es a a ee a Cs Se a SS EE ae Lh le ee are rs i | 50; \ ! ! I p i 48 “ ! | ! ; | } iy >. : #y oy : } 3 41 ; #21 : i \ | 0. | | 2 : | T , | 4 \ | t A 5 : id | K aa al 7 “3 5 7 9 7 73 5 77 79 zw C 27 29 Foo #4 CO he pe pn pes or ff = fd cb mb eo A ep ed fe % | | 7 i % | i = iid | po } + : $ 2) 224 ; 132 : : i : + 4 | } 30} 2] Tn Lao : “ : i - Sg N 1 ” | 7? ' | A RIES. 1B NY 9 7 g€ 3 7 J : 2) 7221 A ts ys et re opal mtr A d= bm ee At PE 1 28 | jis ™ er : 1 i 7 + ; 5 5 (5 v ! z 1 ' \ \ Ny ’ ol : i 26: 7% | %} >, SE 176 126 , N , So | ! : ; “J ol BBL. tn A eins hii Ol | in |2¢ | ; + : 20 72 71 iz | 22 : i | T ! 203 70 | 24 aX dian it a rnd : : x 784 81 “8 Ls 78 : i ' y | i : to 3 : | ; | ’ | |e i 76 7% | 6 y A ' | ! f i . + , 4 : Pfeotep- ; T y : 2 7 ; : 7 1 Zi 3 7 B ! 14 | #4 J ¥ : ; 2! 2} : i lz ij hi | . t 3 . oz | =a - ed QBs pon espn ofr ipieselps ot oepivsnspp sims spon RED ETT op epee fe fe —F 4 Lao ev > 9 5 7 9 7 73 5 77 79 In 22 : B , i he D 4 ! : | 83 : = +8 3 | . 1 de i | 6; : | 6 T & ! + 7 | . i y 1 ' * : iy i . r I zl) / je 7 : : N I te : Na } 7 7 GSEs vsount =p hs sp sl mi 5 es mf. se fi A it fp sts fp es ges Sef pm me TT SEPEEET om th sh Ah emit ot fo sf tee sie freon fh spn 0 spose an cts BL) B 3 4 é 8 70 14 16 18 20 22 24 26 28 30 a2 34 26 38 40 42 #1 c In the given parallelogram, ABDC, derived from the general given proportions of the capital, let the length of the rectangular boundary lines, AB, BD, DK, of the first revolution of the spiral line diminish in some given ratio; then upon the line, AB, construct the right-angled triangle, AEB, and upon the line, DK, construct the right-angled triangle DGK. The points, E and G, must always be in the same perpendicular line, consequently ap DR Then construct the square EF GH, and bisect each side of the square in the points 1, 2, 3, 4, and from each of these points of bisection as centres, and with radii equal to 1a, 25, 8c, 4d, describe the 4 arcs of the circle combining to form the first revolution of the spiral line a, &, ¢, d, e. In the second parallelogram, A/BD/C/, let the side, A'B/, equal 2% and let the ratio of diminution of the boundary lines, A/BD/K/, of the second revolution of the spiral line correspond with that of the first revolution, and let KA’ be made equal to TR LAR and in the third parallelogram, A’/B/D/C/, let the side, AB’, be made equal to 2 and let the ratio of diminution of the boundary lines, A/B/D/K", of the third revolution correspond with those of the first and second revolutions. Then repeating within the boundary lines of the second and the third revolutions the same operation for the construction of the arcs of the circles, the three revolutions of the No. 1 guiding spiral line of the volute are described, and the other spiral lines of the volute are regulated by the No.1 guiding spiral line, as shown in Plates Nos. VII. and VIII. in the given examples of the Propyleea and of the North Portico of the Erechtheium. is always equal to the side BD. P c/o, 72 C % vin ore del I ob TL ERR THE COLUMNS, 139 PLATE: VI. THE METHOD OF DESCRIBING THE SPIRAL LINES OF THE IONIC VOLUTES. With regard to these Architectural spiral lines, composed of the ares of circles, we have nothing left in the ancient geometry to guide us to a solution of them, as all the Greek works upon Architecture are lost, and Vitruvius carefully avoids all geometrical explanations in his work upon the subject; but we possess the original curved lines executed with wonderful precision in the marble, and with these data we may now proceed inductively to endeavour to recover the ancient method of describing the spirals of the volutes. It has been already stated that the designing of the volutes of the Ionic capitals is divided into two operations. Firstly, to determine the dimensions and the positions of the parallelograms within which each revolution of the spirals is described, and, secondly, to describe the curves of the spirals within these given parallelograms, ABDC, ABD'C/, A'B'D'C/; and it 1s the second part of the subject that now remains to be considered. The following method of describing the spiral lines of the Ionic volutes, when the dimensions and the positions of the parallelograms are given, was discovered and worked out by Mr. John Robinson, after several failures on my own part to lay down these curves correctly ; and the curved lines described by it agree so accurately with the tracings of the volutes obtained from the original marble capitals, that I believe there can be but little doubt of its having been the ancient method of drawing these spirals, whenever they are composed of the arcs of circles, as is the case in the Ionic capitals. To DESCRIBE THE SPIRAL LINES. Fig. 1. Given the parallelogram ABDC ; then upon the line, AB, construct the right- Fig. 1. angled isosceles triangle, AEB, and upon the line, DK, construct the right-angled isosceles triangle KGD. The points IE and G must always be in the same perpendicular line, therefore, 42 5 pn always equal to the side DB, for BO = ne and OD == therefore, AB DK AB + DK BO + OD = BD — 5 + 5° = 22228, 140 THE COLUMNS, Then construct the square, EFGH, and bisect each side of the square in the points 1, 2, 3, 4, and from each of these points of bisection as centres, and with radii equal to 1a, 2D, Be, 4d, describe the four arcs of the circles combining to form one revolution of the spiral line, abede, within the given parallelogram ABDC. Repeating a similar operation upon the parallelogram, A'B'D'C/, we describe a second revolution of the No. 1 spiral line, and the third revolution is also contained within the parallelogram, A'B"D'C/, and is similarly described. By the same method, the spiral lines Nos. 2 and 3 are traced, as likewise the remaining spiral lines which form the finished design of the volute. (See Plates VII. and VIII.) The elliptical curved lines connecting the volutes together, namely, the lines hbh, ete., Fig. 2, might be composed of the ares of circles, combined with either the ares of hyperbolas or of parabolas ; but in the examples of the Athenian Ionic capitals we find from observation that these curved lines are composed of the ares of circles, combined with the ares of ellipses. Fic. 2.—TaE Ernvmrricar. CuRvED LINES CONNECTING THE VOLUTES. Tn the two examples of the Ionic volutes, in the Vestibule of the Propylaa, Plate VII., Fig. 3, and in the North Portico of the Erechtheium, Plate VIIL., Fig. 3, these elliptical curved lines appear to be laid down in the following manner— From the centre point, No. 1, the arc of the circle, hl, is described, and from some point, No. 1, in the same vertical line the arc of the circle, hl/, is traced ; then bisect HC in P, and draw the vertical lines PW and PV, and let Bb be the minor axis of the ellipse. Bisect Fig. 1. height of coluumn 33. 989 — 1.12 == Widih of abacus DE KA AB) : : - dovede A'B’ tito 7 parts. Yiilonnd | divide DH’ into 7 parts. divide K'A" indo 7 parts. | dovivle 4"8" vido 7 parts. and the three parallelograms ABDC, AB'D'C, A'B'D'C’ are gwerw in donenston and. in position. hen i oe - i L Jon [O JEBLIE | CE Itoi Fig. 2. i pes oto g x The rectangular spiral line of the No.l. spiral. ° i K | i ray pm So Part IV. Plate VII. THE VOLUTE or THE loNic COLUMN IN mg VESTIBULE OF THE PROPYL ZA. one half of the Teal, size L | Jd 3 ’ 4 LO 2 6 EEA EEE EE a ea Ea ee Ee x : 7 ee + 7! 0) >< Lg i es es re ee ae es on ei a Vp, aE ’ ree ss ee. | Fr a eet reanat | Be ron a Ee eee 55. : Poe te) eee nl ae LR | 2 | > oe, | sh. Tos, | “on | i i Ye | 5, | ! : N : > . | 2 | i i duconsr senda aenel tiie tbh a ose amis estar ry | ike = | 8 | Es : | IC + | Bate grt Ri RT TE Bree NNN | | A asec gies | | Teh 7 6 Fie Nox Nam a : comme 2 gotten Tae | F | | | x) ks | / | | JA Ade 1/7 [BL | | 1 fil] i! (if) : i 1 i, } k / 7 1 | | AN | | ||| TH 1 i Ai | NN | i \ | LAN] AAA \ TN | AL 2 IN jb] —\ 41] il g | \ rd EN ett, RE etl fl ssi i | | B | | oi) | } |i eres i | A — EE T= — mm seme bie on 3 i i int eo tS | | | | by ii i] | | | po rn Tt : = | JE ~¥ 0 - — — — — —— — —— —— — BR — 7 0 _— nn on MMMM LLL AL LAU LAr, easton ot me sone = £ 2 i D B I 1 | | I | | A I { 4 i —— =r" 0% 0 x ———— & * fon oe hn 4 ein tr tnt mm smn 5 mens ain S SEE n cs oar oe sw Se we ny mre msm eia sina "3 : jo 5 GC Sot Trotinson, del, Et 15 9472 A 7 7 “ \ 3 No \ \ 6 _ —- > . : . ’ A ' \ \ x \ - ’ . | ’ : . ’ ' ' ' | ' I ' | I I / ea , I. ' / | / ’ . . ' ’ . N 3 : / | | | | | > 1 17 5 + ; 342 | ; ¥ | pt 1 ; i | 0. | \ | \ 4 | | \ | 1 | | | | 1 GI ill, Loth Conrtlone Lomedomi EC. HE COLUMNS, 141 the minor axis Bb in O, which becomes the centre of the ellipse, and through O trace the major axis WV, and with these given elements construct the ellipse BWDYV. The second elliptical line, 'V/, is the arc of an ellipse, similar to the one already described, varying only in the position of the centre O' and the axis major O'V', PLATE Vii. THE YOLUTE OF THE CAPITAL OF THE IONIC COLUMN IN THE VESTIBULE OF THE PROPYLAA. The designing of the Tonic capitals is found to vary in every example in the adjustment of the proportions and of the details, the same as in the capitals of the Doric order, for we find that the Greek Architects never copied the designs of each other in the arrangement of the details, but the leading principles, of laying down the masses of the capitals first in aliquot parts, of designing the spiral lines within rectangular lines given in position and in dimension, and of tracing all the curved lines of the capital as true mathematical curves, are found to be the same in every example. Thus, in the Ionic capital of the Propylea— Fig. 1. Shows the first given proportions of the masses of the capital, figured in moduli derived from the general proportions of the Column ; also the proportions of the first parallelogram, ABDC, within which the volute has to be designed, are also given in position and in dimension. The given ratio of the sides of this first parallelogram, PD: AB, was 6:7. Fig. 2. Shows the given proportions of the rectangular lines, forming the boundary of the No. 1 guiding spiral line of the volute. The method by which they are proportioned has been already explained. These rectangular lines fix, both in position and in dimension, the three parallelograms, ABDC, A'BD'C/, A/B'D/C/, within which the three revolutions of the No. 1 guiding spiral line of the volute are described, according to the method already given. (See Plate VI.) Fig. 3. Shows the volute drawn to one half of the real size. The No. 1 guiding spiral line being given, there still remain the No. 2 and No. 3 spiral lines of the volute to be described, and these appear in all cases to be regulated by the No. 1 spiral line; thus the ratio of the sides of the first parallelogram, ABDC, BD : AB is as 6: 7, reducing this ratio to a smaller modulus; and, in the case of the volute of the Propyleea, multiplying by 9 for laying down the details, then BD : AB is as 54 : 63 moduli. 142 THE COLUMNS, For describing the No. 2 and No. 3 spiral lines of the volute, the thickness of the outer spiral band, bounded by the No. 1 spiral line, appears to be 3, 8, 21, 24, moduli. The inner spiral band, terminating in the eye of the volute, bounded by the No. 3 spiral line, can be given as follows—3%, 83, 83, 3, 24, 2%, 1, moduli. Through all the points thus given the several parallelograms are first drawn, within which the several revolutions of the No. 2 and No. 8 spiral lines have now to be described, by exactly the same method that was employed for tracing the arcs of the No. 1 spiral line, shown in detail in Plate VI. We thus see that the No. 1 spiral line regulates all the other spiral lines in the volute, and that the parallelograms being once given in position and in dimension, then one uniform method describes each revolution of the several spiral lines. The laying down of the volutes requires great accuracy of drawing, but the method of describing them is simple. The designing of the Tonic capital denotes a refined and cultivated period of Art, and neither the Doric nor the Ionic capitals could be properly designed by Artists unacquainted with the geometry, and it is easy to see why these capitals were laid aside by the Romans, and the Corinthian order more generally adopted. PLATE ¥VI1i11 THE VOLUTE OF THE CAPITAL OF THE IONIC COLUMN OF THE NORTH PORTICO OF THE ERECHTHEIUM. The proportions of the capital and of the volute of the North Portico of the Erechtheium differ from those of the Ionic Column in the Propyleea, but the method of designing the details igs similay. Thus Fig. 1. Shows the first general proportions of the masses of the capital, and the proportions of the first parallelogram, ABDC, within which the volute 1s designed, are given both in position and in dimension. In this example the design of the whole capital 1s contained within the double square LFGH, that is, as EG : EF :: 9 : 18, and the given height of the volute, AB, is made equal to 71 moduli. Then let the ratio of the sides of the first parallelogram, ABDC, be as follows—BD : AB, is as 5% : 6%; or to obtain a smaller modulus, 44 : 52 moduli. Fis. I. height of column 2 we 3NBL ae wrdth of abacus &/ . 8 abacus 3158 ze 2m 14 upper dicometer.. _.....\. } LA 2-24 “aay height of capital fs aaa : 16 codinben ssn am sit § height of base... iy width of base __ - rf ion retreat a eee pee or hr 2029 am 103708 == picdilile Tor details of the base Smee he Sn madre ULI OF ADOTES BIBS To sii oe ssi J } 5 6 7 8 9 J 2 2 74 ” < 0 er een _ _ a LLL, YI 7 ] 7 | 0 2 10 cent ities upper diameter 2: oneeiieenain.. 3 nr 1 ' hd 1 1 1 1 1 a 1 ay 1 1 bed ' | boy ' vy ' ) ' 1 ol vd Vl a v Ag. 2. The rectangular spiral line of the N?1. Spiral C, 4 i C A The Parallelogram ABCD is given Fg A’ from the general proportions of the A Capital. D D B D B AB. BD. DX 150 revolution | divide D K into 9 parts 6b....50% ,. .. 4% DE. AL. AD 9... 7%... 6% AD. BD DE 222 volition | | dovide DK into 9 parts 6%... 5% ..... 20% DE. AR. AB 9.7%... 400 AL. B.D Fe revolution : 6%... 5%... 95 Ioton J Polernaon del. Tur Vorure oF THE Ionic Coruvny mae ERECHTHEIUM (Nori Portico) two third, ie real sie. Part IV. Plate VII. dalle dl Li Me i en ese Ll De ee i a a 2-076 xX 90 —— 020 - ES CT Tr rT rrr ie ee ee — < a a i. L — sie nm eg me ee tire = Ye (jeg Tem ro ml % 3 3 2 + 3 x S A FH lth Cable J Fondon lL Part IV. Hate IX. THE RETURN SIDE oF THE loNic CAPITAL OF THE PrRoPYLAZEA. jE me mm = a i re or = ee ee ee i ee en ee seen eee i ete see cr a ste a em ee om me or re on mr mer fe rn ree Fig. 2. E The Propyleea. [one quarter the real size.) Or I ~§] \ \ | a ] 2 a me operas; gl 2 grea Bh 1Y a Sl ard ¢ @. x. — fins : 0 wa frist ta 3 | G4 TH bb nD opm mmm ann me UEC TOT VOIR anne ee mm ip morn CORI ee ea he I ede imotcholion. of Foton Holirscr, det. : | CT Hel, Aih: Castle St. London EC Cart IN Faie X THE RETURN SIDE oF THE loNic CAPiTAL oF THE EREcHTHEIUM (NORTH PORTICO) Ts | EN CN a size.) (‘one third of real Jee XN 7 hr Yr AZ Rs NS The Erechtheium. North Portico. N N-———mmm mmm mmm mee Meee oi MU —— Lem AN \ NR — ee . dae | R NN NN . Rhee termes cen ee henna a, AREA AIRAIE one e a S \ Ny a Tt - lL \ Te ar Ji bt eh di bri i Sk. l tne) | Fl .. Pvpotrachelivm........ . ellgiical termination..._J i | en mee TROULENG echinus y % C.F Tl, Ath, Castle 52. London EC. THE COLUMNS, 143 Fig. 2. Shows the given proportions of the rectangular lines, forming the boundary of the No. 1 spiral line, with the three similar parallelograms, ABDC, A'B'D/C/, A'B'D'C', fixed in position and in dimension by the method which has been already explained, within which the spiral line is described by the rule given in Plate VI. Fig. 8. Shows the volute drawn to two-thirds of the real size, with the various spiral lines which form the finished design described uniformly by the rule in Plate VI. above referred to. The thickness of the outer spiral band, bounded by the No. 1 spiral line, appears to be as follows—34%, 3, 23, 25 moduli; and the thickness of the mmner spiral band, terminating in the eye of the volute, can be given thus—7, 6, 6, 5, 4, 3%, 2, 1, 1, moduli. PLATE IX. Ax» PLATE X. THE RETURN SIDES OF THE CAPITALS OF THE IONIC COLUMNS OF THE PROPYLZAA AND OF THE NORTH PORTICO OF THE ERECHTHEIUM. Prate IX. Fics. 1 ano 2.—THE ProPyLz:A. In the return side of the capital of the Ionic Column in the Propylea we have a combination of curves and of curved surfaces laid down with great precision, and we find freely employed in the design, the hyperbola, the parabola; and the ellipse. The details taken separately are simple, and we will first consider the section through the centre of the capital on the return side, Fig. 1, cut through the line ED, Fig. 2. The given general proportions of the details are the whole height OR = 80 parts, and the projection OH = 20 parts, and these are divided as follows— Fic. 1.—THE PROPORTIONS OF THE DETAILS. Hypotrachelium . Apothesis . FKchinus Space for volute Abacus Whole height = OR = 20 parts . 3 parts. 5 : . 0 3 9 89. : <9 16- 8 80 Projection =20 ,, = OH In this section of the capital there are four separate curves to be traced. Ist. The 144: THE COLUMNS, outline of the abacus, which is the arc of a hyperbola, and requires no explanation. 2nd. The curved section, PABd, through the centre of the return side, which is composed of the arc of a parabola, and the arcs of two circles. parabola. 3rd. The echinus, which 1s the arc of a 4th. The hypotrachelium, which is the arc of a hyperbola. The curved section, PABd, Fig. 1, through the centre of the return side of the volute is a species of spiral line, composed of the arc of a parabola, PDA, and the ares of two circles, DB and Bd, the curves connecting one with another by means of common tangents. 7 7 77 2 7% 7Z vo 7 7 7 ao = i 54 7 | 2 _ \ 1 | N | i Nh i “Roms Geo Nt I tN 1 | — T In the echinus also the profile, P'Ap/, is the arc of a parabola, and the only difference existing between the two parabolas is that the arc of the echinus is traced to a smaller scale, the elements of both curves being identical. Thus, commencing with the echinus, the given quantities are, z=MA'=9p, y=MP' =11p; then in the equation to the parabola— I a 0 a . y= 2px, and p=2-=—- = 6722 =FC,and AP = ak i Gil = 3'361, and the arc of the parabola is constructed by points. (See Chapter I1., page 125.) For the curve through the centre of the return side of the volute, trace the diagonal line, Pm, of the parallelogram, PMpm, and at right angles to Pm, trace the line M'MA, then divide M'P = y into 11 parts, and let M/A = 9 parts = x, and trace the curve from the elements already given. The arc of the circle, DB, must be a tangent to the parabola at the point D, and the two circles, DB and Bd, will have a common tangent at the point B. In the hypotrachelium, let the curve, HIK, be traced as the arc of a hyperbola, and in this case the sides, HQ, HO, of the right-angled triangle, QHO, must be given, and the hypothenuse, QO, is made the direction of the axis of the curve; then trace Hm at right bh T0000 22777 7/7, 0000 77 , / / 7 / : ? 7 7/7 _ 7 7 Xx . iinet aie) H. 0 beeline Bf enna angles to QO, and divide Fim into some given number of aliquot parts, which will regulate the elements of the curve; thus, in the Propylea, HQ = 21 parts, HO — 21 parts; then divide Hm into 5 aliquot parts, and let y = Hm ml a=1c x = Mme z= cb a = 1TH 9 VE—2 THE COLUMNS, 145 The return side of the Ionic capital is a curved surface, varying in different designs, but the method of tracing the surface will, I believe, be found to be generally similar. The given quantities, with which to commence the design, are— 1st. The spiral line of, the volutes, NNN’, Fig. 1. 2nd. The spiral line through the centre of the return side of the capital, PABd, Fig. 1. 3rd. The upper diameter of the Column, PP, Fig. 2. In the capital of the Propylea let the upper diameter, PP, be divided into 24 parts, go = 0rl175 feet ; then— = The upper diameter, PP’. . . .= 01178 x 24 = 2-827 feet. The width ofabacug, RR .. . .=01178x32 = 5760 Thewidthol volutes, ed . . . .=01178x28 = 539208 Let the axis major of an ellipse, AV = 01178 x 26 = 3-062 ,, Half the axis minor, BC, is already given (Fig. 1); then construct the ellipse, ABV, Fig. 2. Let the axis major, AV, be a constant quantity, and let it move upon the two spirals, NN'N? and N'N'NZ. Let the axis minor, BC, move at the same time upon the spiral line, PABd ; then # the axis minor, BC, becomes a variable quantity, corresponding in succession to the ordinates mn Fig. 1, namely, 1, 2, 3, 4,5, ete., which are traced at right angles to the tangents of the spiral, PABd. Describe a succession of ellipses, with the axis major, AV, and the ordinates, 1, 2, 3, 4, 5, ete., for + the axis minor, BC. These ellipses become a series of sections through the return side of the capital, and will trace out the required curved surface. Prate X. Figs. 3 and 4.—TuE NortH PORTICO OF THE HKRECHTHEIUM. The return side of the capital of the Ionic Column of the North Portico of the Krech- theium is designed in a similar manner to that of the Ionic capital of the Propylea, the only difference being in the enrichment of all the parts; on the front of the volute there are more spiral lines and sculpture, and on the return side there is more sculptural detail. 146 THE COLUMNS. Considering first the section, Fig. 3, through the centre of the return side of the capital, on the line AD, in Fig. 4, R . py 8 p = | 3 7 | 1 _ J Z 7 _ i oo 75 / T% 0 / 1 / oo 7 7 7 Z ~ 7 0“ 7 7 : 1: BJ ve | ll] NA 7 / 0 i Le ; RT Ze i i The given general proportions are— | EX iy pede } TTT 1 ! 1 : ' mm momo ed ! 1 1 1 1 1 y : i | : eo bo | ; : Loa : Con : i y | ; da | } Ly | | al L bails fo foil atecat do tot eb Sl] | ddd tbr ellos obit 1 1 i | | 1 1 I | i | i s | : D h I SI = ie nr im eh ie ee To ren a on mine 1 ded fod 3d bob hot LLL ffl tdente AeA eedeted The whole height of the capital, OR — 114 parts. OP = 20 parts. The projection of the capital, Fig. 3.—THE PROPORTIONS OF THE DETAILS. Hypotrachelium Apotheds .. . .. . 3 Eehinug, 0... . 11 Extramounlding . . 8 Space forvolmle . . 33 Abies... 0,8 rrr nt, 90 Elliptical termination of shaft of Column, 24 Whole height . . . 114 39 9 33 3 33 32 2 3) 27 parts high OR. 1 | i . 3 parts projection. 0 6 20 2 339 29 33 3 OP I In this section of the capital the principal curves to be described will be, 1st, the curved section, PAGB, through the centre of the return side of the volute, which is composed of the arc of a hyperbola, P'A, and the arc of an ellipse, AGB; and 2nd, the curved termi- nation of the shaft of the Column, which is the arc of an ellipse, PA. THE COLUMNS, 147 The given quantities for describing the carve P/AGB, are arranged as follows— Construct the right-angled triangle, QST, Fig. 3, so that QS: ST: : 3: 5, then divide the hypothenuse, QT, into 6 aliquot parts, and let CT be equal to 2 parts, and BA = the minor axis of the ellipse, equal to 3 parts; and let the minor axis BA : the major axis GV :: 10: 12, then the ellipse will be given both in dimension and in position. _ _ x / oo LL 7 7 _ 7 7 oc Ry For the hyperbola— Lety—=PM-=9 git MA=3 , C'B 4s AD = 2 | = Mp | B_5.. a Toxd 18 A _B UD = = ame y= rime 0D, x 1 | A | a a =p | ~The termination of the shafts of the iA Columns of the Erechtheium are elliptical, and in the North Portico the given quantities for describing the upper termination are—— o AC = } the axis major = 25 parts ; and | Ph=the axis mmor = 7 ,, Fig. 4.—Tar CurvED SURFACE oF THE RETURN SIDE oF THE VOLUTE. The method of generating the curved surface of the return side of the volute is nearly similar in this example to that described for the Propylea. The given quantities with which to commence the design are-— 1st. The spiral line through the centre of the capital, PAGA . . Yig, 3, 2nd. Instead of taking the spiral line of the volute, M'M*M?, as the directing line, an inner spiral line is traced, as NN'N? . : : ET 3rd. The upper diameter of the Column PP’ . hii .. Pig. 4. In the capital of the North Portico of the Erechtheium let the upper diameter, PP, be divided into 64 aliquot parts, thus— - = 0035 feet. 148 THE COLUMNS. The upper diameter . PP = 0085 feet x 64 = 2:24 feet. The width of abacus BB =0085 ,, x80 =280 ,, The width of volute . od =0038 , x72-=2533 Let the axis major of an ellipse AV =0035 ,, x 62 = 217 ,, Half the axis minor : . BC is already given. Then construct the ellipse, ABV, Fig. 4. Let the axis major, AV, a constant quantity, move upon the two spiral lines, NN'N?, and N'NVN?, and let half the axis minor, BC, move at the same time upon the curve, PAGd, and correspond in succession with the ordinates, 1, 2, 3, 4, etc.; then describe a succession of ellipses with the axis major, AV, and the ordinates, 1, 2, 3, 4, 5, ete., for half the axis minor, BC, and these ellipses become a series of sections through the return side of the capital, and trace out the required curved surface. THE COLOURING OF THE TONIC CAPITAL After the curved forms of the capitals had all been geometrically traced, it was then requisite to render all the ornamental details clear and distinet, by the introduction of colour as well as of bronze ornaments and gilding ; thus, in the capital in the Vestibule of the Propylaea, there was a painted ornament traced upon the abacus, also the sculptured ornament in the echinus was certainly relieved by colour, as the remains of the red are still visible. The ceiling of the Propylea was so enriched by coloured ornaments that it was essential for the interior capitals to be made to harmonize with it both in colour and in ornament. In another Ionic capital, found close to the Propyleea, all the ornaments were engraved on the marble, both in the front and on the return side of the capital. This also was probably an interior capital, and although the original colours have disappeared, except the blue on the fillet of the volute, still the ornaments remain very distinct upon the marble. In the case of the exterior Ionic capitals of the Frechtheium, I am not aware that any traces of actual colouring have been found, but the ornaments were all sculptured, and therefore relieved by light and shadow, and the spiral lines of the volutes were marked by the introduction of a bronze spiral and ornament, which were probably gilded, and must have given great relief to the volute, and the bronze nails still exist where this metal spiral was introduced. Also in the plaited torus above the echinus of the capital small circles are deeply cut, which were filled in with different coloured stones in rows, thus— The first row of circles was filled in with black and light blue, alternately | See Inwood’s Krech- The second . .“ yellow and dark blue, ,, thelum, page 5, The third . . black and light blue, | plates 4 and 5. Part. IV Plate XI. half the real suze. Fig. 2 Base of the lonic (olummn in the Vestibule of the Propyleea. , "THE PROPORTIONS AND CURVES OF THE BASES OF THE COLUMNS. hg 1B ase of the lonic Column in the north Portico Erechtheium . Fl Kaden s mrs mes oom neS ing = inne = Swinson Etaicne so te mmm DIV SO Fry = 990. 8 = 9% 19%. EE tT ERIS | Sr x Serra - Seer Cress sengnens rig rrnrenenriy) reese Fe TE gp === ane Yo Sima asees tet rar BT yw a i | oo ! a TT | | 5 © | ge Ea | ge | bol angel 3 ri | bol a 1 ni]. | $ 3 | i | 0 D : v 7 7 7 “1 i | Ly Li bo a, pe Ly : Tr i Lo | = 0.) x Hh nil) | 3 © Lf po Lg Lisl YY 3 ¢ ial Fol ot | : F / ) Sul aa ee | Lr TE lee Ae tone Sh len Ff { = s il 7 | an ee Nhs 3 Yr f 1 Lo A _ De 3 I Sr 4 3 Zr ] £4 1 2 Jia A oa oo per RR oy 0 3 ; | | ; . / id Ne mp We g he oh 5 J ’ 2 / a / 3 ®- 1 3 S i Xo £4 mmm? | : 3 i 2 2. / \ / = S . 3 $ 3 LL ky at L”. Be 3 bt al fr 3. ble ale deb eli ot vd) ! x T oy TT eR) £7 ? oS I ih = Ne Ee : 7 rr 1 oo T i | i = i ? | IF ny” 7 | 9pamd zt opn 3 es wi ; 0 oo % RINT eg a 7 Ye | JO Srp nung) numa) 2p) 5 bs | JO PSDG AY} JO SYIDPP 217 MO] fom mmm mm mmm mm mm mm mm mee PIVG JO PYDIIY == §IT = X Py == === = == mmm =m ; ‘ en Cre Seer a. RE eT ETT * Lene 6 ToT % Lx ae a 7 i - TTT A.” | Ll 7 for — E Ig 3 | Ld J fA Lay Lf fie A | ne od “ | [oF | Cd] iL Sl Jo! A “rr ye | i > ie Lon se | _ 3 | tt” 5 Pag id 7 Fy | } 2 J | 3 | i $333 syn ey Ly JL ox / 1s nb: ol 2a: i en Fy i Ih re “gf 4d Ty 1 bf Ieee, P TT Se IA 1 AL sd... i RE A Ne 3 | » R84 $ | lh. ay ea 7 o 1A ay vy yee x wa | EY estonia tl A | A = 1 g > i 3 3 3 5 3 x eter ZI NY fo 2 or ) i mm 3 x. 1 LLL, : 2 hy \ : , = of 7) | ; | ll | | 3 Ts Reel mn paar Ei fennel It re x i ol : S ’ i ; | | : ] § of 4 = 0 | | pd Is i | je . 1 fren A ol = : ie | Pes | | i § 3 3s 3 | I ne > y | 2 | i N 3 . T | Hn red rr eee Sade {8% £ feds ; | 5 “8 4 [ ® SR ih Ql. yoo J | | 9 3% = AOUANTI YY) 0, % s, / v | suppor 9200007) 00 P04] 3 ol be i | osmg pg. 10 Sprvp Spa] es vy ty Wa nn ! Nn 7 2 8 3 o! ; KR © ii 3 S 8 Te or | Jed “x ! fre . x fom © © + © ® ~ Q! -8-344 257 x 77 — heh TF. Doll TH, Farstlo Fodor £6 X78 = 4-626 - R57 X 73 - 2857 7 Lower Diameter Wedtty of Base ......... THE COLUMNS. Ao CHAPTER 1V. THE BASES. THE first given quantities with which to commence the design of the base of the Column are the whole height, OR, and the whole projection, RP. (Fig. 1.) Then this mass is broken into separate members, and 1s generally composed of the following parts. (Fig. 2.) Fig, 2 1st. The apophyge, or termination PoE Ee of the shaft of the Column apaphyge. | y A LL LL XN — a froursins cen by a curved outline. separated from ee A 2nd. The upper torus. each other by rt aK fillets. wires lf ~ 3rd. The trochilus. th... : 4th. The lower torus. 5th. The plinth ; sometimes omitted. PLATE XL THE PROPORTIONS AND CURVES OF THE BASES OF THE COLUMNS. The principles of design for the bases of the Columns are in all respects similar to those for the capitals : the whole height and the projection divide into some given number of aliquot parts, so as to have a common modulus, and this modulus will regulate all the details of the base. Fig. 1.—THE Base oF THE loNic CoLuMN IN THE NORTH PORTICO OF THE ERECHTHEIUM. The given modulus of the Column in this example is 0-224 feet. Let this be divided into 6 aliquot parts, and the projection PR = 3 mod. = 3 X 6 = 18 parts ; the whole height OR = 7 mod.'= 7 X 6 = 42 parts. 150 THE COLUMNNS, TaE PROPORTIONS OF THE DETAILS. Heights in parts. Projections in parts. The apophyge, including the fillet . . 12 : . 5 The outline of the apophyge in The upper torus . : . 9 this example is elliptical, The fillet : ; : 1 : . B and all the other curves are The trochilus : : 9 arcs of circles. The fillet . : : 1 : . B The lower torus . ; : . .. 10 . 5 Whole height, OR = 42 18 = PR, whole projection. Fig. 2.—THE BASE oF THE Ionic CoLUMN IN THE VESTIBULE OF THE PROPYLZZA. In this example the given modulus of the Column = 0-257 feet. Let this be divided into 12 aliquot parts, and the projection PR = 2 mod. = 2 X 12 = 24 parts ; the whole height OR = S mod. — 8 X 12 — 96 parts. Tare PROPORTIONS OF THE DETAILS. Height in parts. Projection in parts. The apophyge . .. . 24 . 9 The fillet . : : wid The upper torus . : : . 1% The fillet . : , ; , 3 : oid The trochilus : +19 The fillet . : ; 9 ; . 1 The lower torus . : : . 29 : 10 The plinth : ; , 18 The whole height, OR = 96 24 = PR, whole projection. Let the curve of the apophyge, PAp, be a hyperbola, and let PQ be the diagonal of a square, whose side equals 24 parts ; then bisect PQ in M, and trace the line CAM ; divide PM into 9 aliquot parts; let y = PM = 9 MA-—- 6 A= A( = J T= MC =11 The outline of the trochilus is an ellipse, whose major axis : minor axis :: 9 : 5. The outline of the plinth is an ellipse, whose major axis : minor axis :: 32 : 14. The upper and the lower torus are the arcs of circles. "THE COLUMNS, 151 CHAPTER V. THE CURVED OUTLINE OF THE SHAFTS. TaE evidence is, I think, conclusive that all the curved outlines that we find in the details of the Columns, and also in the entablatures of Greek Architecture, are true arcs of one or other of the conic sections, and the question naturally arises, whether the properties of these curves were first discovered and applied to Art by the Greeks, or whether there exists sufficient evidence in Egypt for assigning a very much earlier date to the discovery and to the application of them to the purposes of Architectural design. The principal curves that we meet with in Egyptian Architecture are the curved outlines of the shafts of the Columns, and the curved sections through the cornices. The horizontal curved lines of the entablatures have already been noticed. THE EGYPTIAN COLUMNS. The capitals of the Egyptian Columns appear to be simply a combination of the straight line and the circle, and they require no explanation beyond what is given in Plate 1., Fig. 4, and in the annexed diagram, Fig. 1; therefore, our attention will be exclusively confined to the curved outline of the shaft of the Column, and the example I have selected 1s taken from the Outer Court of the Temple of Medinet Haboo. From the actual measurements, we are able to trace the arc of this curve to a large scale, and by means of parallel chords to recover the centre, C, and the original elements, and with these recovered elements to recalculate the dimensions, and we find the measured and the calculated dimensions so nearly agreeing that we may, I believe, identify the curve as belonging to the arc of a hyperbola, laid down in a similar manner to many of the Greek curves. THE COLUMNS, 15 jenn m mmm mmmm od ffoe=cene : | L 6. 393 Seip a Yao 14 2 F | 2 ! Eh ! o iz | : 3 | x at97 3 i. 13 bo ? * I ~ il a | ~ i X& ? -487 8 ee y Sel AC Le 8 i. Toe 3 I og ! / | > y | [ | © > +6 (9 12 ffir fen iri | ri v it | kro2ld I ita i ! | | v ' +2 y | i 1 ! J | 1.52.4 {7 | I 4 ! | I 1 | een rir om cerns | g x Liisi Pi i 8.890. nt Creer. | 1 {4 | I ! d I | ld 1 ! 1 | | i 1 | i La] ! b ; / | 5 ; ! Jt | 2 Ww J | \ 1 1 i | | ’ ly : fide of ' | / 3 | i J | 1! I ; | ‘ ! | | i | 5 ) peed | 4 2 1.600, JB | A | 4 | : | i 3 | Eo | 4 | iy % 7 | | 4; ~ | 7 / ' ' x Su 8 oY / \ t 1 = [ © 7 | ol § © 7 NE § ¢ wr Sof J g S | Pe hn es a ~f Ee Eo pe / 9 Lo | 7, ghey | ! = | ’/ A 7 | | y I I o I x | wl AE 7 | i 4 2 [ x ee i] ! | 1 / ’ 1 1 1 | | | A an | V | | | | | ! / foul : | | ! | | 7 4 | : | Wr 2 a £ | No | ZO 1/7 | i | ie 7 | IB i /% a adds \ QA | 7 J Lh | | = i A El [| ® I Ae } OX. | 7 ' vei | Vi =n me ak FAIR ol ye one yor en Pop TE rede cm eeeen . | EA / Sh { i ! EA J. Jo rE | ! ) ne / AR | | YL, iki Sr AP ’ . y | 22 or 70 JN ” > ’ J 4 | Foy | | nl DE LLB y { eer BE Fen ’ we 1 # p / i *| SE ir “ | ri /8 \ & wr hen | | PY Yar | a i oN : By \ a | v P AK Fao & : 97 i : Gon yn i of 1962 ,/& | | i fone AE > x oe oA SN *¥ ! i 2 Ge . PD) / ii we 7 [3 / BN y ~ / \ Ly E sade BE ie al 8%. 7897 i Ris Vv y ge L / | 0 = xX od 1 > aldomgid aiid le RE nd - 1 T RE ETO W t T 1 T T T T SESE ayy : Let : J At i PET UR, te eo oiesnrenint se Be BOE oiiiiiainns ; er 1 } ii i ' | ONT CLOIAET ee onlin si os BOY ciiinnernin) Le ! | 1 eT . 1 y | greatest diameter ee DEI. ci nd : = 1 y * i ; 1 3 | | I 1 Wh: OF GHSE ..... onsen oe mii fr onic B.I895. 0 iets 5 i i TAG OF COPUOY s oenimpiene beinni SAO eon 1 i ; height of abacus _....... 1.664. I hetght of base... ........ &--7.86%.-. 5} \ . ; i width of capital ....... fokonhen in tout or tases: ET ooh tienda) i i 29.841 gen height —7—=2.151 2.131 x 3=6.3935 — width 6.393 of* abacits —7z —0.5327=modulus of column Thus, bisect the chord line, AP, in Q, and trace QR ; then through R trace the straight line PRS, and at right angles to PRS trace the line MA : we then have given in position the right-angled triangle PMA. Let A be the vertex of the curve, and divide MA into 10 aliquot parts ; then let MA =10, a= AC =1, y= MP = 16256, z — MC = 11; ay 1X 16:256 16-256 AEC 1 112-12 ia . = 1-484; popes =z yx —a b=CB let =2 8, 4 6,11, ei cet., in succes- sion, and, by calculation, y = 2:57, 41968, 5747, 8779, and 16-256, et cet., in succession, and the measured and the calculated outlines of the shaft so nearly correspond, that we can identify them as belonging to the same curve. The outlines of the shafts of the Columns at Karnak, and also at the Memnonium, ap- pear, from my own observations, and also from Sir Gardener Wilkinson’s drawings, to be the arcs of similar curves, and to be described in the same manner. The subject of these curves 1s worth examination, for, if we find the outlines of the shafts of the Columns at Thebes to be well-defined arcs of hyperbolas, there is little doubt that similar Columns of a very much earlier date, as we find them drawn in the interior of the tombs at Beni Hassan, were designed with the same geometrical accuracy, and we shall be unable to assign any known date to the origin of the conic sections, and the early history both of geometry and of Art fades from our view in the extreme distance. The curved outlines of the Egyptian cornices will be investigated when considering the entablatures of Kgyptian and of Greek Architecture in Part V.; but they appear also to be traced as the arcs of hyperbolas. Part IV. Plate XIL The Propylaa . Fig. 2. Tor Extasis OF THE COLUMNS, THE GREEK COLUMNS. kg. }. The Parthenon. iy = % oy i, 3 - F Re oe os 3 4 Se A mn a rm 5 a1 Sa Si hai La pr RB 2 | y v | Oi | 1 I | shi eee =R4 NN rete Lgl nivel reve 69° ¢=N ope wo TT | : | £ : i | i | ' : iol | s 2 & SRE Ee 29°C 5 ree 98: 5/ Jotrssccnnin dentin erpriie eure 08 ToL Troe RW) 9 Lane : i 3 : : bong | : | ! ' i A 3] | 3 | % ol : I : | : i i 3 : 3! ; x! : I | | § : | 3 1 1 i | | i a \ | 3 2 | | : , 3 5 | : Ya : S i 2 3 : 3 : S : . [ ee : S i I | 3 i d s Jd _'s eebury wnab ‘Ry = = 4s ur, GAR go al ———————— Ee “gh | ~TT ay i ; ; | : ; : | ] i 1 | 4 y \ } | : I | : : | | } : 1 . 9 ; : ; 3 " | 3 + 3 Bi g:] B 5 | 3 3 § | | | ! | y \ RN! | Ny R| ] | wl 3, 5 | 3:3 Sig Sig 3 ghge——nmemezase ae somoeoosooo le nity EE meme Sree mr mm eee Ree] 3 : FIC TEIZL TIA 1. ro x, : ; ue Nd em—e——n - - - mmx = efi me ore =e me eae cn ee elon ef a en ee om oe rt a Ye ie mn a se ns mk fe es | a Se me Bp mE me mE ET TEE v Eh he a ale oe TE a WU) DT JP JIPYS T= 49 92 0)109LAAF Jo oun quot) urn hb BM N?s5. 183 183 00 ly? + b2— a ay I03......... A NA. —l........ x b b All lett. Castle St Tondon il] 044 @ 2.55% 06... 5 ...... 067... 8565 . 5025 062... ¢ w be— Nr Mrs. METS... L655 ..... O173...... o%0....... 055 ........- NZ A. A853 (lg E= — 2. 8365175 72.887 5 72.704) 6.35% 2a a Hoasuiremenis. ....... ............ Amount: of Enlasts.......... KEguation to the thperbola referred to the from tangent to hordRP..0%0........ From tangent to carve (o)...00...... . BM= 72.704 +.783 Mayor Azxs AB. 471 AH 0 Nes. 38 . 702 = 7867.9 12 03 bh? NA. O00. NIE... 045% coos Moe... OFGE ore cb3B rer 039 N73. HTX E. log. ¥=—2. 6464630 3.93 x 26.498 H556...... Ne2, 0630...... un sPl03........ lO 52H....... 27% The are of the given Hyperbola from _AtoP of "the Coliumns . 18Y Part of the tangent Une R A . G23........ The outline of the shaft 3.93 $.43 > 0.777 Ne. Ll. 029..... 26.948 > > z . 2 .! 4 5, Bt sm dee set Ff os imo SRA. LR a an eli ES DA Hl ' ) I | | : : fri spies mere ender corsage] ssi mnendianeenennssees ype ff tnt cmateee ation | gl ff ree nee eee ae Dp etedhenenee Senate pp rte siete ol py | etree eniecnnenas fir orestenss bed-any oo 5 3 5 hy RQ | 3 ® i 0 i i S! i Sh | oh | Xi | 3 | 3 I | I 3 1 3 Ts R IR 3 RN Ya iS 53 IQ S iz § : ¥ | N a 1 3 I 31 i: 3 mh : - & Quarry UID LB > 3 = me = ay 000g UAH JO ID : * Ye Sa le re TT BBE DIOL) gins meme me : : ef pe Te | | = : y i : ! | 1 | \ ! : | ; J | | 1 1 , ! 1 ! : | | | i ! | | | | | = = eins i cai si Sh hn es Ey nena eS 3 1i 3 3 1 : i 3 i ; 5, Ry! N: R! % lio ©! 2 2:4 3 Si SR : Ay . aot $2 ®is SN ! or ren. re = edn ree = =e mms See sme asso iY ET Ta 5 Ry £ ! yrrfr [L277 mug’ vrs 3 dq aT Zong : RE we : 8 2 : Eee es wm i em a td i en wl A me BEET eee qe Ty rrr le reer AID JO SINUS SEO yp tree fans eidsarna nt restr ens dessins vpn peer one ie Hors set eine se mwa eof a x Jur AM PM =— v HMeasuremenits...................... Amount of Entasts.. .... the From Lament to ord R.P..C27......... Major Jais AD == 2 a == 7.86 BM =.7.86 +.777 From tangend to curve.(x). upper & lower diameters Sohn Folengon del. B Part IV. Plate JULI THE ENTAasis oF THE COLUMNS. THE ROMAN COLUMNS. Fig. 1. The Temple of Jupiter Olympius. I | | I | I | | | I | 1 1 ' Delhi ie iL asa y meet od aaa GENS Ce ag Ee 7 Cc AB 0 » A a@ Km — —— —— 1 I 2a-10.99 325 XX = Z.22 Fig. 2. The Pantheon. I : 0 | 1 i | i I 1 ' t | | I 1 1 | I 1 i I 1 | | 1 | 1 l | 1 | 1 1 1 | 1 | | 1 | | I | | | | [om mm mmm mmm mmm mee I mm mm Emm em mm me em ee pm mmm 7 a 1 | | 1 | I ! 1 weno) AD 2LTYS = yg © Jo cis i rp 89.824 b 8068 . 3 Ze log $=—2. 786540 +. 9... | ee NOS ———— ' | | | I I I ew oie ms md de oe oo i i 30 al re i hi i poo 70.92 2a — Mayor Aas AB 5.495 @& = 107 - 39 5.86 x 37.38 35 X 12.06 b BM_70.97 + 328 7.305 > 11532 .0 b> 0.325 XX == AM — log §=— 2. 7369459 ~ fo AB rd en ce GE ) : % 3 ™ 5 » ol | oS is & % IN 14 is x 2 i © Nl 3 Al § A I I GC 8 RY oo uc oom 3% x 48 Ar S ahi tresses ea rsa rent tde en: ns Seneche nnd sh res nets RE fiSsnrcesmssthee | y ! i = | : ! i a) > | | ! | | ! } I | 3 4 | | 23 | I : : : \ : 1 ' } 1 ! | | y 1 ® | [ ' x | J | | : 3 | teat Ai a eh he LS et at mie hn Lc TR ie eats sea sen EEL UY) PLOY yy Tress rete -_ Jurbarry usnb Se ! © © IN : 5 8 2 r 11.72 Major Aarts AR - 24 5. 86 a@& == H.I2 4045 = 12. 05% AM 37.38 qq == PM Ne2 N23 Neg Nes Nel N22 Ns Ne 4 NCS Nez 325 152. BD O54 ..... From tangent to chord... . OFS ARB ......nine oF on LG ........ From tangent to chord. .._. From tangent to curve. ...... From tangent to curve... _. emetic IT J543 . 052........... M208......... H88..........4%............0%5 022 irinsnn.. B72 eres 0 AOL ........-.. JL ......-. G5. uae Amount of Entasts ... ssret OF snes HIE ans oi nia 057...... Amount of Entasis ..... wien ss ¥75........ Measarements.................. EIR lith. Pastle TE Tandon ZC. hm Sivbinaon del. THE COLUMNS, 153 PLATE X11. axp PLATE X111. THE ENTASIS OF THE GREEK AND OF THE ROMAN COLUMNS. \ In all the ancient Columns, instead of the outline of the shaft of the Column being executed as the frustrum of a cone, AAPP (diagram, Fig. 1), it is always slightly curved, and the increment given to the shaft of the Column is called the entasis. Fig. 1. | Bacall Thus, Fig. 1, instead of the centre diameter of the shaft being executed equal to ee, it 1s made equal to bb, and the given increment 1s equal to twice be. Feet. In the Parthenon the increment given to the centre diameter of the shaft amounts to : . 0114 = 2be hme In the Propylaea the increment given to the centre diameter of the shaft amounts to : e125 = In the Temple of Jupiter Olympius the increment given to the centre diameter of the shaft amounts to . 0236 = |, &e., &e. P lwediam Pp The variations thus observed between the diameters of the shaft of the Column conceived as the frustrum of a cone, and as 1t 1s executed with a delicately curved outline, are considerable, and if we could compare two Columns together—the one executed as the frustrum of a cone with straight sides, and the other with a mathematically curved outline—the eye would probably at once give the preference to the shaft with the curved outline. The question may naturally be asked, whether this curved outline of the shaft can be traced according to any known optical laws, or whether it was simply a mathematical curve, experimentally adjusted in each case to suit the refined eye of the Greek Architect ? In the case of the horizontal lines, Philo seems to refer to the concave appearance of the lines when he says— ““ For some things, although with reference to themselves they are both parallel and ““ straight, seem not to be parallel or straight, on account of the deception of the eye respecting ““ such things as it views them from unequal distances.” But he refers to no optical laws for accurately correcting the deception, but simply remarks—— 154 THE COLUMNS, “ Therefore, by the method of trial, by adding to the substance and reducing it, and “by experiments in every possible way, they (the ancients) made them regular to the eye, “and to appearance of good symmetry.” And we have seen that all the horizontal lines in the Parthenon were not corrected according to any accurate optical laws, but were traced as the arcs of two circles only—the one for the horizontal lines of the Porticoes, and the other for the return sides . and I am not aware, even with our present knowledge of optics, of any law by which we could accurately correct the optical deceptions that are to be observed in a building like the Parthenon. Vitruvius, when referring to the entasis, does not notice any concave appearance in the shaft of the Column, but simply says— “ The method for giving the proper increase to the shaft towards the middle, which 1s “ termed entasis by the Greeks, so as to render it gradual and easily applicable, 1s explained “by a figure at the end of the book.” In the case of the horizontal lines, we have seen that whatever the concave appearance of the lines might have been, the outlines of the Steps and of the Intablatures are traced as true mathematical curves, namely, as the arcs of circles; and there is no example in Greek Architecture of any curve being executed otherwise than as a conic section, and these curves will, I believe, be found to have been employed in the outlines of the shafts of the Columns. The outline is, I conceive, a true mathematical curve, traced so as to be agreeable to the eye, and, if this be the case, accurate measurements will give the nature of the curve, and will enable us to restore the original given elements, so as to recalculate the true outline of the shaft of the Column in each example. We may now proceed to give (1st) the observed facts, derived from careful measure- ments, and (2nd) to suggest some general method for recalculating the entasis in each example. The following amounts of the entasis in the shafts of the Columns, measured from the chord line, RP, to the arc of the curve, RAbLP, are taken from Mr. Penrose’s measurements— Lower deam?” = Te WN NN \ N\ NN N N ig 7 = Length of Parthenon . 9. . 083 . . O54 . , 939. ..Q . 31-148 ft. Propylea 0. 085 . . 0637. . His. . O .. 20846 , Yuplicr Olympitte 20 52 0 Al oo oo HIS 0, 06: 0 eG, &e. &e. &e. &e. &e. &e. THE COLUMNS, 155 The entasis of the Athenian Columns has been frequently measured by different observers, and there is no practical difference in the amounts derived from these various observations, but I have given the preference to Mr. Penrose’s measurements, as he is the last accurate observer, and has also studied the refinements of Greek Architecture more scientifically than has previously been done; and, with regard to the entasis, he says— “1 have found the entasis in every case so nearly resembling one of the forms of the ““ conic sections, namely, the hyperbola, that I cannot doubt that this was the curve used in ‘““ the Columns of the Athenian structures.” From observation, I arrived also at the same conclusion; but before the arc of the curve can be calculated we must ascertain accurately what were the original given quantities, viz., the positions of the vertex A, and of the axis major AB, and the given values in each example of x and y. We may observe in all the measured Columns that the lower parts of the shafts, from R to A, are executed as straight lines. In the Parthenon, RA equals about 5 feet; in the Temple of Jupiter Olympius, 9 or 10 feet ; and in all the Columns this straight line, RA, appears to vary from 1 to 5 of the height of the shaft. This given line can be indefinitely extended to S, and we may assume RS to be the given tangent to the arc of the curve at the vertex A. The inclination of this tangent line to the horizon will vary in the different Columns, being greater in the Doric than in the Corinthian order, and in some of the Roman Columns this line, RA, might be perpendicular to the horizon. Besides this given tangent line to the vertex A, which is assumed to be at # or § the height of the shaft, we may assume also the major axis, AB, to be always equal to the inter- columniation of the Columns, and with these given quantities we may proceed to suggest a method for describing the entasis, and the calculations must prove in each case whether the given elements of the curve have been correctly assumed. ProrPoSED METHOD OF CALCULATING THE KNTASIS oF THE GREEK AND RoMaN COLUMNS AS THE COMBINATION OF A TANGENT LINE wirH THE ARC OF A HYPERBOLA. Draw the perpendicular line Re, and let Pe = 4 the diminution of the shaft of the Column ; then let PS = x be made some aliquot part of Pe, such as i, or 4, or 4, and in some of the Roman Columns PS might equal Pe. Then draw the given line RS, and let this line be made tangent to the curve at the vertex A. The height of the vertex, A, above the lower diameter may vary in different 156 THE COLUMNS. Columns, but in the given examples the straight line, RA, appears to be about + or ¢ the height of | | hs | the shaft of the Column. CIT acs osmasd She Co | Let the major axis AB = the intercolumniation Lo | between the Columns, and draw PM parallel to the \ MM 5 $ . = nL L : ; given tangent RS, and let PM = y, and PS = x, and on Is | : with these given quantities we can proceed in any \\ Nk i : at y | example to calculate the entasis of the shaft of the Lo | | Column. Thus, Plate XII. | NOON \ | bs AN 12. 1. The Parthenon— \ | | 685 3 igs] NOAA | z= —— =-171,y = 2644, major axis = 24 — 7-86 \ 0 a i Fig. 2. The Propylea— \ \ \ | i . 1 == oe = 183, y = 22:37, major axis = 2a = 12:704 NN \ \ \ | \ a Plate XIII., Fig. 1. The Temple of Jupiter | 1 | Olympius— a 7 — 222 345, y — 37-38, major axis — 2a — 11-72 N\A i B XX XX \ a Ee : &e. &e. &e. NN rotation | The results of each calculation are given on the Plates, and are compared with the measured er 1 | ~ dimensions, and the two appear to agree as closely ° as possible. Whether this is the true method or not of describing the entasis I cannot positively assert, but it is a combination, of a tangent line with the arc of a hyperbola, that the Greeks would not have objected to, and, if the suggestion is correct, the entasis of the Columns becomes an interesting practical example of the ancient theory of the conic sections. Part IV. Plate XIV. THE FILUTING OF THEY SHAFTS OF THE GREFK COLUMNS. 20 Flutes aT TTT ] Ionic Shaft. 24 Vlutes. Doric Shaft. TTT mag an JO On BY BRT TTT Te X Upper du b = z ‘ | a 1 f NE P ¥ : i jo. | i t 3 i 2 3 +3 3 E 3 2.811] z L x x § S £ T 133% ™, = i al 3 - 7 7 . a) : § oo i! ; . pe < 7 —- of circles, as the ais major and the aais manor of the Ellipse could not be givery but simply the five pots trv Aluting buat trv pracice the flhating was described, by arcs each curve. Flating is uiereased towards the upper part of the shaft, to produce a deeper shadow. Arn Ellipse might be traced ulerdtical with the actaal The Tluting is described from three centres, the depth of the / ’ ’ 3 ’ wl | g 3 Sm | > 8d a een fb il E281 | : bmn hE r iE 5 3 z > o BE § S 3 2 breil i‘ $ £14 ¢ = -— > Qo : Syd = 7 _ / 2... H. CanlleS London. EC. 7 782 GIR, THE COLUMNS. 157 CHAPTER VI, THE PLUTING OF THE SHAETS. In Plates III. and IV. of the proportions of the Greek Columns the height of the shaft of each Column, with the widths of the lower and of the upper diameters, are given ; and if the shaft were simply the frustrum of a cone it would now be complete, but, as we have seen, the profile of the shaft in the Greek Columns, and also in some Egyptian Columns, is traced as the arc of a hyperbola, and in Greece, to make the Columns harmonize with the other parts of the design, it was requisite to enrich each shaft with flutings. And it will be, firstly, the tracing of the fillets on the smooth surface of the shaft, and, secondly, the outlining of the interior curved surface of each flute, that we have now to consider. PLATE X1V. THE FLUTING OF THE SHAFTS OF THE GREEK COLUMNS. In Egypt the circumference of the shaft containing the lower diameter is generally divided into 16 sides, but at Athens— In the Doric order, the number of flutings in the shaft of each Column is 20, and of the fillets, 20 In the Ionic order . ' - 24 o 24 In the Corinthian order ,, .“ » ’ 24 " 24 In the Doric order the fillet is almost imperceptible, being merely of sufficient thickness to mark with accuracy the line of separation between one flute and another. Inthe Parthenon and in the Propylea the width of the fillet is not more than j; of an inch. In the Tonic and Corinthian orders the fillet becomes a marked feature in the shaft, and the ratio between the width of the flute and the width of the fillet, that is, between the arc aAb, and the arc be, is always a given rational quantity ; in the Ionic order as 10 : 1 or 8 : 1, or any other whole numbers, as the case may be; or in the Corinthian order as 5 : 1, as In the example of the Monument of Liysicrates. 158 THE COLUMNS, The width of the fillet between the lower and the upper diameters of the shaft remains a constant quantity——that is, the arc bec = are blé—Dboth in the Ionic and in the Doric orders. The arc, aAb, being given, the chord, adb, is also given, and this line in the Ionic shaft is always the major axis of an ellipse, and will vary in magnitude between the lower and the upper diameters of the shaft. To DESCRIBE THE INTERIOR OF THE FLUTE oF THE IoNIC SHAFT. The outlines of the interiors of the flutes, FE both in the Columns of the Erechtheium, and also - \ SN pt ih NN MON in the Vestibule of the Propylea, are true semi- NN X C | in ibule o pyleea, are nce oP ANNE aS . ellipses, the axis major and the axis minor being, FTEs in every example, the given quantities. Thus, the arc, aAb, in the circumference containing the lower diameter, is divided into a given number of aliquot parts, as 10, 8, etc., according to the example ; then from A as a centre, with a radius Ae, describe the serainclvelo Ee, and E 1s the vertex of the minor axis; then the major axis will equal the chord, adb, and half the minor axis will equal dE, and the outline of the ellipse is geometrically constructed. In the Corinthian order the outline of the interior of the flute is simply a semi-circle. To DESCRIBE THE INTERIOR OF THE FLUTE OF THE DORIC SHAFT. The outlines of the interiors of the flutes in the shafts of the Doric Columns are less than semi-ellipses, and the axis major and the axis minor could not be given. The arc is, therefore, described from three centres, thus— In the circumference, containing the lower diameter, let the chord, adb, be Ln fi divided into some given number of aliquot be { = 7 % parts, as 14,13, ete., and let dE, the depth a, hh of the flute, equal 2 parts; then construct : : the equilateral triangle aBd, and divide \ / YE NV it into 4 parts, and from B as a centre, with radius BE, describe the arc MEN ; THE COLUMNS. 159 trace the chord Nb, and bisect it in ¢; draw the line, gD, at right angles to Nb ; then D, D/, are the two other centres required for completing the arc of the flute a MEND. In the fluting of both the Doric and the Ionic shafts the depth of the flute is made to increase, when compared with the width of the same, towards the top of the shaft, thus— Width of Depth of Width of Depth of flute. flute. flute. flute. In the Erechtheium North Portico : lower diameter. 10 : 4 Upper di ameter 9 : 4 In the Vestibule of the Propylea “ . 36 : 5 . 12 4 In the Parthenon . cit 2 - 12 = 29 This merease in the depth of the flute increased also the depth of the shadows, and must have given relief to the appearance of the shaft. By a variety of light and shade it might also have apparently added to the convexity of the outline. 160 THE COLUMNS. CHAPTER Vil. THE INCLINATIONS IN THE AXES. THE varying inclinations observed in the axes of the shafts of the Doric Columns appear to result from a variety of causes, which must separately be considered. We have seen that the Column was first designed as a square mass, of which the abacus alone remains in the finished design, and that the shaft of the Column, as well as the details of the capital, are all arranged within this first given mass. It will, therefore, simplify the subject if we consider— Firstly. The varying inclinations given to the axis of this square mass of the Columns in the Doric Porticoes. Secondly. The final inclination given to the axis of the shaft of each Column in the Doric Porticoes. PLATE XV. any PLATE XVI. THE VARYING INCLINATIONS IN THE AXES OF THE SHAFTS OF THE GREEK COLUMNS. 1st.—THE INCLINATION GIVEN TO THE SQUARE MASSES oF THE COLUMNS. Fig. 1. In the Doric order the planes ABCD, ABC'D/, containing the Upper Step and the abaci of the Columns, incline, as we have already seen, slightly inwards. In the Parthenon the given inclination inwards of these planes amounts to.. 0-077 feet. In the Temple of Theseus ' o v % . 0062 In the Propylzea “ .“ & “ . 0082 The original idea of giving the whole mass a slight inward inclination was probably Part lV Plate XV. THE VARYING INCLINATIONS IN THE AXIS OF THE SHAFTS OF . THE COLUMNS. Fig. 2. The Temple of Theseus. line of” upper step pony —7 = EJ th of ardlattave leng 68-22 = 69 ‘138 = = lon glly vi’ abacus ...... ¥ 19 i. The Propyleaea . (centre Portico.) 77 pl fi um 2 ; ™n ; Seay N | . Ts a i Ca, N g h | oR = : x TE EE oe er Tr tr ew 7 A 5 1 2 | EE er ~ « S : NX ; >. < = S ALE i 2 | Fig. 4. The Pr opyla 2 gd X — Lo architrave upper Step > 3:607....---- <0. Of lr ———— aires lon lo. C. 7 O7Lc UA, Bortloc Be Hele ~r 5 oS John, Teodiinm del Part IV. Plate XVI. IN THE AXIS OF THE SHAFTS oF THE (CoruMys. THE VARYING INCLINATIONS 3 _ JE f Bb ey yy wl fe Z 75.471 Tr EE ISTIC Tome mmr adeeo RR cc — = re mm nn 3 me ' 1 ' ' 1 | ) Be ci hos iets. Sein ' ' ¥ 1g . 1. The Parthenon. J | ffs : | i I | : re of ilertnediate cOLITE + co ooiooeoninsonaina — 1 | | | l [ | } 4 | I I! |: ] I i 70. 513 2 Tago oh = co 1 20 | K 773 —— mmm — = 74 from centre to centr 4 | | | . | | ; rR TT TE I TL a SL . ene 70.667 = width between the marble beams A.B’ ee] i I = On Ce. . HL LoTR 02 Lr | | o |] 3 | | | ; i > er 0. OCT } cake 3.29 x 7.876 TIE 1.102 Home . 3 i Se i Am tk oe di mb se nm em oe A te dt i | x. De N\ N Se NN Xx rr ——— ul a7 each lapilal is al right angles to thes surface at the pond pp. de. consequently the axes of the shafts of the Columns rw, rw,’ are variable as well as the acces of the Capitals piv, pu, and the axis of the Shaft and (apital are not the edge of the step than the centre of the masses v,r,’ &o. wn the same straight line sleght nclination tv the masses of the ndermediate colivmns Z L3- 282 » LOTT diff: v 33775 3rd. Zhe softit of the Architrave ts a portion of a carved surface, and the axis of 1st. The columns N° 71 and NP 2 incline towards each other - 077 this causes a 2nd. The centre of’ the lower diameter of the (olumns Bh Le. is.077 nearer to AN Ye. OFF i C.F. Kell, lth. Gastle St. London. F.C. Firmen Adel. Q hn S ~ i rt te a Ee el ie ea te a nt Le i i Ms SET iy AN | i THE COLUMNS, 161 derived from Egypt, but in every Greek example of the Doric order the first mass within which the Column is designed has this inward inclination. Again, the square masses of the Columns in the same Portico are so arranged as either to incline towards the centre line of the Portico, NM, or to incline from it, and towards the outer Columns, No. 1, No. 1. Thus, in the Porticoes of the Parthenon and of the Propylea— Plate XVI, Fig. 1; Plate XV., Fig. 8. The square masses of the Columns, No. 1, No. 1/, mcline towards each other at the same given angle. The square masses of the Columns, No. 2, No. 2/, incline towards No. 1 and No. 1, at the same given angle as the outer Columns. And the other square masses of the Columns, No. 3, No. 3/, and No. 4, No. 4/, incline less and less from the centre of the Portico, NM, until the square mass of a Column, placed exactly in the centre of the Portico, as is the case in the north wing of the Propylsea, Plate XV., Fig. 4, would be perpendicular. The inclination towards the centre line, NM, of the square masses of the Columns, No. 1, No. 1'= 0-077 Parthenon . 0-082 Propylza. The inclination from the centre line, NM, of the square masses of the Columns . No. 2, No. 2/ = 0-077 5 0082 ° The inclination from the centre line, NM, of | the square masses of the Columns . No. 3, No. 3/'= 0-046 5 0044 The inclination from the centre line, NM, of the square masses of the Columns . No. 4, No. 4 = 0-015 ’ In the Temple of Theseus, Plate XV., Fig. 2, the square masses of the Columns all incline towards the centre line of the Portico, NM ; the inclination diminishing as the Column is situated nearer to the vertical line in the centre, NM. The inclination towards the centre line, NM, of the square masses of the Columns . . No.1, No.1'= 0062 Temple of Theseus. The inclination towards the centre line, NM, of the square masses of the Columns . . No.2, No. 2 =0081 v The inclination towards the centre line, NM, of the square masses of the Columns . . No. 3, No. 3' = 0-000 ” 2nd.—THE INCLINATIONS OF THE AXES OF THE CAPITALS AND OF THE SHAFTS OF THE Doric CoLUMNS. The soffit of the Architrave, Plate XVI., Fig. 3, is generally a curved surface, and the centre of the square mass of each abacus, p, p', p’, p’, ete., is now given upon this curved surface. 162 THE COLUMNS, Then let the axes of the capitals of the Columns, pu, p'u', p*u®, p’u’, ete., be traced at right angles to each part of the curved surface of the Architrave, and the centres of the upper diameters of the shafts of the Columns, v, u', u?, u°, ete., will be fixed in position, and a curved line traced through the points, uw, w,u® u’, ete., will be similar to the curved line of the Architrave p, p', p*, p°, ete. Plate XVI., Fig. 2. In the Doric order the centre, R, of the lower diameter of the Column is always nearer to the edge of the Upper Step than the centre, r, of the first given square mass, within which the Column is designed. In the Parthenon, the difference between the two centres, R and », amounts to . . 0088 ,» Temple of Theseus > v “ 5 » Propylea ” b " The reason for this variation is, that the effect was rendered more pleasing by the springing of the shaft of the Column from the edge of the Upper Step, and possibly also by the increase of light thrown upon the shaft of the Column by an additional inclination being given to it externally. These two adjustments determine the positions of the centres of the upper and of the lower diameters of each Column, and the straight lines, ru, 1'u', ru? 1*u’, ete., Plate XVI., Fig. 3, become the axes of the shafts of the Columns, varying in inclination ; and the axes of the shafts of the Columns, ru, etc., and the axes of the capitals, up, ete., are not in the same straight line; and the measurements of Mr. Penrose at the east end of the Parthenon show this to be the case. We thus see that the true inclinations of the axes of the shafts of the Columns and of the capitals in the Dorie order result from a combination of varying causes. 1st. The arrangement in the Portico of the inclinations of the first square masses of the Columns. 2nd. The curvature of the soffit of the Architrave influences the positions of the centres of the upper diameters of the Columns. 3rd. The centre of the square mass of the Column and the centre of the lower diameter of the Column are made to differ for the reasons given. In the case of the Ionic and of the Corinthian orders, the square masses, within which the Columns are designed, are set out perpendicularly, and the only cause that influences the inclinations of the axes of the shafts of the Columns is the curved soffit of the Architrave, when the axes of the capitals are made at right angles to this curved soffit. But when the THE COLUMNS, 163 horizontal lines are executed as straight lines, instead of delicate curves, then the axes of the Columns become vertical lines, and the inclinations of the Columns quite disappear. The curvature of the horizontal lines, combined with the varying inclinations of the shafts of the Doric Columns, rendered it necessary that mathematical accuracy should be observed in the execution and in the fitting of each block of marble used in the Columns, in the Entablatures, and in the Steps, for none of the angles were right angles, and each stone was required to express the design in the marble, and a working drawing for each separate Column, as shown in Plate XV., Fig. 5, had to be traced upon three co-ordinate rectangular planes, XY, XZ, YZ, to show the true dimensions of each block of marble composing the Column. THE END OF PART FOUR, 165 PART VY. THE ORNAMENTS, THE MOULDINGS, AND THE ENTABLATURES. THE ORNAMENTS, MOULDINGS AND ENTABLATURES,. 167 INTRODUCTION. Tre methods employed by the Greeks for the designing of the Ornaments, the Mouldings, and the Entablatures appear to have originated in Egypt, and then to have been developed and perfected in Greece; they apply in a degree to the designs of the Egyptians, the Greeks, and the Romans, but are more particularly used in the outlining of the Ornaments and Mouldings of Greek Architecture ; and there is no reason why these same methods should not at the present time be employed in the designing of the details of important works of Architecture and of Art. The Greek Artist was always guided by the geometry in the laying down of the forms of the Ornaments and of the Mouldings, while he studied carefully the perspective effects of the Entablatures; and if all the refinements of the Greek cultivated mind were effaced from their Architecture, then the beauty that now exists in it would disappear, and it would become the work of a common workman, instead of the design of an educated Artist. In Part V. no new mathematical forms are required to be introduced, as the designing of the Ornaments and of the Mouldings is in all respects similar to the designing of the details of the Columns given in Part IV. The elements of the several curves are first given in aliquot parts, and the outlines are then all traced as the arcs of the several conic sections, combining together to form the varying outlines of the Ornaments and of the Mouldings, and the Ornaments are afterwards rendered clear by being relieved either by colour or by sculpture, and sometimes by both combined. For the Entablatures, the projections are all given in Parts I. and II., as well as the whole apparent heights, measured upon the arc of a great circle, with the point of sight for a centre ; the subdivisions into architrave, frieze, and cornice, with their separate details, are then all arranged in apparent aliquot parts upon the arc of a circle, and the true heights are trigonometrically calculated exactly in the same manner as in Part II, and the Mouldings and the Ornaments forming the Entablature are geometrically outlined and relieved either by colour or by sculpture. Lastly, the important works of sculpture are mtroduced mto the frieze and the Pediment, and the whole Entablature, in such a design as the Parthenon, becomes a highly finished work of Art. 168 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, This subject will be treated exactly in the same manner as that relating to the Columns ; showing—— Firstly. The Egyptian origin of the several Greek Ornaments, and then the geometrical methods of outlining the several forms of the Greek Architectural Mouldings and Ornaments with the colouring restored. Secondly. The Egyptian origin of the Greek Entablatures, with the ancient method of designing perspectively the Entablatures of Egypt, of Greece, and of Rome, and showing also the restored colouring of the Doric Entablatures. : Part V. Plate]. THE EGYPTIAN ORIGIN OF THE GREEK ORNAMENTS. Fig.1. Lotus and Papyrus Offerings from the Temple of Medenet Haboo . ig. 2 Offering of Grapes and Papyrus Fig.7. Offering of Grapes and : Pomegranates from the Tombs of the Kings at Thebes. R220002200822008222022220228Y Fig. 4. Lotus and Papyrus from the Temple of Dendera.. Fig. 5. Offering of Lotus and Papyrus from the Tombs of the Kings atThebes. Fig. 5. P apyrus from the Temple of Dendera . Fi g.06. Ornam ent from the Temple of Theseus. SPT ovine TATE 14, 17 THE EeypriaN ORIGIN OF THE GREEK ORNAMENTS. F 1g. 10. Greek elliptical Ornament. Fs. 8. Fig. a The Grape as a line of’ Ornament from the Temple of Medenet Haboo. Fig. 11 Fig. 12. Grapes and Lotus flower Fig. 13. Lotus flower and leaf Lotus Leaf [rom the combined with the Lotus Tombs of the Kings. leaf’ underneath. hg 16. Greek hyperbola Ornament. HS |R <5 : Ss nt. . Fig. 15, Egyptian Ornamen * ATH. e ET o o i of Wa ; A Nod / a 2 = Fg. 17. Egvptian Maander from the Fig. 18. Greek Meander {rom the Temple Fig 19. Painted Dental Cornice from the Tombs of the Kings at Thebes. of’ Theseus. Tombs of the Kings at Thebes. ty ohn Solunson del C.F Kell Sth Castle t London tk. C, THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. 169 CHAPTER 1. THE ORNAMENTS AND CEILINGS. PLATE 1. ax» PLATE 11, THE EGYPTIAN ORIGIN OF THE GREEK ORNAMENTS. WaEN commencing the theory of the Columns, the points of resemblance between the painted offerings of the papyrus and the different designs of some of the Egyptian Columns were noticed, as well as the close relationship of the Grecian Doric Columns with the earlier types of the Egyptian Capitals and Columns, and the same remarks will apply to the Ornaments of Grecian Architecture. The original ideas, as we shall see, were derived partly from the natural plants, such as the lotus, the papyrus, and the vine, growing in the valley of the Nile. These were at a very early period arranged and presented as Offerings before the several FKgyptian Deities, and these Offerings were copied in painting and in sculpture, and were combined, architecturally, to form the several Kgyptian Ornaments; and in Greek Architecture the general features of the Ornaments, upon examination, appear to resemble those in Egypt; but in Greece the ideas are so refined, and so translated into the language of pure geometry, that the original Egyptian forms are nearly, but not altogether, effaced, and the design of each separate form of Ornament in Greece becomes simply a geometrical combination of curved lines—generally outlines of the different conic sections, with the colours harmoniously arranged, as in Kgypt. We can carry back the monumental history of Egypt for a period of 2000 years B.c., and the earlier the monument the more perfect does it appear as a work of Art; but it is beyond our power to define the number of ages that must have passed between the first simple arrangement of these natural Offerings, such as the lotus, the papyrus, and the vine, that were presented to the several Deities, and the conception of the architectural Temple, with its Columns, Entablature, and Ornaments, suggested by these Offerings. The origin of Art appears to be the same as the origin of language, or of mythology : 170 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, it can be traced back to pre-historic ages, and the ideas first suggested seem never to be quite effaced. The proof of the very close connection between the Ornaments of Egypt and of Greece need not rest upon the mere assertion of the fact, for the works in both countries remain, and we have the power of comparing them together, and for this purpose, when in Egypt, I made a selection of a few of the painted Offerings and Ornaments that appear to have suggested the first early ideas of the several forms of the Grecian Ornaments ; and with this data, and some examples copied from Mr. Owen Jones’s work, “The Grammar of Ornament,” I shall now proceed to institute a comparison between the several Egyptian and Grecian Ornaments, commencing, first, with what may be called the lotus and papyrus Ornament ; both these Nile plants were held sacred. The lotus plant was sacred to Isis and Osiris, and was regarded as an emblem of the creation of the world from water, and considered symbolical of the Nile; the papyrus plant had a similar signification, and is frequently combined with the lotus in the painted Kgyptian Offerings and Ornaments. Tae Lotus AND PAPYRUS ORNAMENT. Before comparing together the lotus and papyrus Ornaments painted on the walls of the Temples in Egypt and in Greece, it is necessary first to observe the distinction between the Kgyptian and the Greek symbols for water. 7 ¥ In Egypt the symbol for water is always NIZIN denoted by zigzag lines, drawn either horizontally ZN or vertically, as shown in the figure annexed, copied | ZIN from an Egyptian drawing of the lotus and of the = apyrus growing in the Nile NA IR papyrus g 8 OA In Greece the symbols for water, as frequently shown upon the fictile vases, are always represented by curvilinear lines. First. A simple curve, with an aquatic bird SO swimming towards it. Second. A double curve, with genii hovering C0) (NO round it. Third. A double curve, with an aquatic plant CANO between the curves. ~ THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. 171 These different symbols will serve to explain painted Papyrus flower painted Lotus flower . . : some of the differences that are observed in the designs of the same Ornament in Egypt and in Greece. The lotus and the papyrus flowers are painted in Egypt in every variety of combina- tion, as Offerings to the different Deities, and as lines of Ornament. In Plate I., Figs. 1 and 3, are given copies of these painted Offerings, taken from the tombs of the Kings at Thebes. In these examples the lotus and the papyrus flowers are distinctly marked, and the difference in their characters is clearly defined. Plate 1., Fig. 4. Is a line of Ornament traced from the walls of the Temple at Dendera, executed during the age of the Ptolemies. The lotus and the papyrus are here evidently intended to be springing from the water. Plate I., Fig. 5. This Ornament, traced also from the Temple at Dendera, shows the papyrus above the water. Comparing this Ornament architecturally arranged in Egypt, and where evidently the lotus and the papyrus are intended to be represented as springing from the water, with the similar Ornament on the walls of the Greek Temples, the points of resemblance are sufficiently striking. Plate I., Fig. 6. Is a copy of the painted Ornament on one of the beams of the Temple of Theseus. Here, also, we see two distinct flowers alternating and resting on the curvilinear lines, symbolical of water, and, comparing together the two outlines, Figs. 4 and 5, with this Ornament from the Temple of Theseus, the points of resemblance appear to be sufficiently close to allow of our claiming an Kgyptian origin for this Greek Ornament; and the change worked by the Greek mind on the original external forms is not greater than in other details of Greek Architecture where the original idea has become moulded into a perfect work of Art. This Ornament is employed in all the Greek Temples ; painted along the cyma in the cornice of the Pediment of the Parthenon, on the beams of the Temple of Theseus, sculptured in every part of the Erechtheium, and everywhere preserving its essential features of the two flowers alternating and resting on the curvilinear lines. In these three examples the outlines only of the Ornaments now remain perfect, so that I am unable to give with certainty their original colouring. 172 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. In the next three forms of the Greek Ornaments, which I have named respectively— The elliptical Ornament The parabola Ornament The hyperbole Ornament . J ra 1] from the character of the curves that generally form the outlines of these Ornaments, the , ( | 1 “original ideas appear also to be derived from Fgypt; but in Greece the outlines are always traced as pure mathematical curves, composed of the arcs of the several conic sections, and are outlined upon the curved surface of the Mouldings, instead of being painted on a flat surface, and the Ornaments are not literal copies of the Offerings, as in Kgypt. Tae Ervrrerica. ORNAMENT. Among the Offerings painted on the walls of the Egyptian Temples we frequently meet with clusters of grapes, combined with other fruit, as shown in Plate I., Fig. 7, in which is represented an offering of grapes and pomegranates ; sometimes the grape, as an offering, as in Plate I., Fig. 2, is trained around the stem of the papyrus, and there are examples of the lotus flower and of the grape arranged as a line of Ornament (see Plate II., Fig. 12). Again, both at Medinet Haboo and in the tombs of the Kings at Thebes we find the outline of the grape by itself, arranged as a line of coloured Ornament (see Plate IL., Figs. 8 and 9), approaching so nearly in design and in colour to what is called the egg Ornament, or the Elliptical Orna- ment, Plate, II., Fig. 10, in Greek Architecture, that we are led to believe that the original idea was borrowed from HKgypt, and was then by the Greeks translated into a simple mathematical elliptical outline relieved by colour. Tare ParaBorA ORNAMENT. In the Egyptian painted Offerings of the Lotus, the leaf is always combined with the flowers, as shown in Plate I., Fig. 1, and there are many examples of painted cornices, such as Plate IIL, Fig. 12, in which we find an arrangement of the grape and of the lotus flowers with the lotus leaf underneath, and again, in Plate II., Fig 13, of the lotus flower and leaf alternating ; and in Plate IL, Fig. 11, is given the form of the lotus leaf, traced from one of the Offerings in the tombs of the Kings, which approaches so nearly in outline to what I have called the Greek Parabola Ornament, that I am inclined to believe that the idea of this Orna- suit was also derived from Kgypt, and was then transformed by the Greeks into a combination of geometrical curved lines, traced upon a curved surface, and relieved by colour. | | | | “a en SECC EEE = Bl coxmit j=X 2 V EEEEEESE -T< HEN. /6. 31 28243 Sl WW HEEEEESE ) c-3 oo 3% Nr EERE REE {OI SAE LPT THE GREE CrinaNgs. SS HEEEBEEEL CVI TTIIS LON EERE EEE S22 US 223 Lz BE = = 39172 X= 75 35 Sw BEE WZ \te 222 - Cu SN a rani FS cso [EEE EEE SE TY) Tear Eat | | | | | | x EERE BE ZZ B37. P33 =o J SN I LR a SEs C eiling from the Tomb N° 1 at Thebes. OR JUN NIN JN J LL TS 2 CROC CCRT ATE AC 8 ft AION [OL ZO ZC OL RO SO X20 LOR AUR ZUR RU JR Rt JU JCS AOE 0 TK ATR JX TS C200 JO ZOE XO XUN JO A ZX OR ICR TN ATS 0K JK 08 0 RT RC TCE OK EX Tar Loyprian OriciN or AAO XX ZX HERE SEER — TSAR RSMAS YEEREEEEREE ot EEL Tey EN es = Vx MR EEE <5 2 fo IF = Ss % BH EE 50 iy So Tet oo SEER REE ps; BREE EEE 2 Y oe (HIP &hie Ytevo NS REF X29 EEE \- 3 RSE ET SENN | | | TEER 3G rte Sto ERE a RRO F Ur EERE "7 3 75 3 A Es HEE ov Sr Eres Pua Xie a 73 A = § Fig.l. Portion of Dane n n he - ll tr i : Li 71 od Fig. 2 2. Sketch of small Ceiling in Tomb N° 2. KC / Fig 4. Detail of small Ceiling in Tomb N°? 2. Fig. 6. Detail of band on ig. 7 £ the Navil The Ceilmg 0 oe | Cree on RE SP pos yp a Sp 1] : yy ie So) EA 2 8 Fig. 5. Detail of Ceiling from the Temple of Theseus. EAN NEN Meo eMiid A Portico Portico Erechtheium. The Ceiling of the South IS (dA AS VY. Plats 111 OD DY DN BO OD OV OVO OF DD OO DF BD DD OO OO Oa FECT IF I x rf nr Or He NY yo [1] XX YIT YIY XX (1) 3 SISIVIVIVIVIVIVEvIVaL {hal ed 3 IE I 1) Erechtheium. Sob . Botos SOT, Ae 7 CFA, Loh ted rn 7 Condon G4 THE OBRNAMERTS, MOULDINGS, AND ENTABLATURES, 173 Tae HypErBor.A ORNAMENT. The Hyperbola Ornament, as shown in Plate II., Figs. 15 and 16, is a simple outline filled in with three colours, alternating in red, blue, and yellow, and is frequently employed both in Egypt and in Greece, the only difference being, that in Egypt, as in Fig. 15, it 1s always outlined with straight lines and painted on a flat surface, and in Greece, as shown in Fig. 16, the same arrangement of the colours is found with the curved lines of the hyperbola traced upon a curved surface. TaE MEANDER. The Meander, Plate II., Figs. 17 and 18, painted in two colours, belongs both to Egyptian and to Greek Architecture; the example, Fig. 17, is a painted dado copied from the tombs of the Kings, and Mr. Owen Jones suggests that it might be intended to represent, in diagram, a papyrus grove. Fig. 18 is the Greek Maeander traced from the cornice in the Pronaos of the Temple of Theseus. Ideas approaching to the beading and to the dentils of Greek Architecture are also frequently found forming parts of painted cornices in Kgypt. Plate II., Fig. 19, 1s an example of a painted dentil cornice from the tombs of the Kings. We thus see that the first ideas of the several forms of the Greek Ornaments are all of them found painted upon the flat surfaces of the walls in the Temples and in the tombs of Egypt, and in Greece these same Ornaments, translated into the language of the Geometry, are mathematically engraved upon the curved surfaces of the mouldings, and in the Doric order are simply relieved by colour, the same as in HKgypt. The only exceptions to the above statement are the spiral lines of Greek Architecture, such as the volutes of the Ionic capitals, the volutes of the consoles, and the spiral lines of the Ornaments; and of these no trace appears to be found in Kgypt—they belong to a later period of Art. PLATE-111. THE EGYPTIAN ORIGIN OF THE GREEK CEILINGS. The designs of the ceilings of Egyptian Architecture were generally suggested by the ancient ideas of astronomy, and were either composed of the signs of the zodiac, or of stars fixed upon imaginary lines, as in Fig. 1, which is a portion of the painted ceiling in the tomb of Rameses at Thebes. Sometimes the ceilings are divided into squares by black lines, and one star is painted in each square, or else they are divided nto compartments 174 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES,. by painted beams, and each compartment is filled with light stars on a blue ground, with an Ornament around, painted in the alternate three colours—red, blue, and yellow—forming a cornice encircling the whole, as shown in Figs. 2 and 4; and when we compare the Greek ceilings of the Temple of Theseus, as shown in Figs. 8 and 5, or of the Krechtheium, as shown in Figs. 7 and 8, the same idea of the beams, with the light stars on a blue ground, is seen to exist; but in Greek Architecture the parts are all carefully arranged and proportioned, so that, instead of a copy of the firmament, the design of the ceiling with the stars is made a part of a perfect work of Art. This slight comparison of the coloured details of Fgyptian and of Grecian Architecture, as shown in Plates I., IL., and IIL, is, I believe, sufficient to prove that in the early Egyptian painted Offerings and Ornaments are to be found the types and the models of the ornamental details of Greek Architecture, and that the change between the designs of the Ornaments in Egypt and in Greece, is not greater than would naturally occur, when the mind sought to express its ideas with mathematical accuracy of outline, and with perfect geometrical forms and proportions. In Egypt the Ornaments are generally traced upon a flat surface, and the ideas of the colouring are derived from the natural colours of the Offerings; but we meet with nothing to suggest the outlines of the several Mouldings of Greek Architecture. In Greece the Ornaments are traced upon the curved Mouldings, which are mathe- matically described as combinations of the several conic sections, and are relieved by a variety of colours; and, taking the forms of the Mouldings and Ornaments as we find them in Greek Architecture, we may now proceed in the next chapter with the consideration of— Firstly. The outlining by the descriptive geometry of the several forms of the Mouldings. Secondly. The outlining by the descriptive geometry of the curved Ornaments traced upon the curved Mouldings, and the colouring of the same. THE OBNAMENTS, MOULDINGS, AND ENTABLATURES. 175 CHAPTER 11. THE MOULDINGS. In Egypt we meet with scarcely any traces of architectural Mouldings, and the Ornaments are outlined and coloured upon flat surfaces; but in Greece the curved outlines of the Ornaments, as we have seen, are generally traced upon curved surfaces, which become the Mouldings of Greek Architecture ; and before considering the general designing of the Kntab- latures, which is one of the most important features of Greek Architecture, it is essential to give some idea of the profiles of the several classes of Mouldings, and of the Ornaments engraved upon them, as the Entablature is composed of these several elements combined into a work of Art. When designing the capitals and the other details of the Columns, we found that the whole height and the whole projection in each example was always divided into some given number of aliquot parts, measured by a common modulus, and that the required elements of the several curves were all multiples of this given modulus ; and the same curves, namely, the arcs of the several conic sections, and the same methods of laying down the capitals and the other details, namely, in aliquot parts, and with whole numbers, will be found equally applicable to the designing of the Cornices, of the Mouldings, and of the Ornaments of Greek Architecture. From direct observation we find that the curved profiles of the Mouldings can be reduced into the arcs of a few simple mathematical curves, and can then be classed according to the number of curves which combine to form the profile of the Moulding. Thus— The first class of Mouldings is formed of one mathematical curve. The second class of Mouldings is formed of two mathematical curves. The third class of Mouldings is formed of three or more mathematical curves. Besides these three distinct classes of Mouldings, the sections through the fascia are frequently curved surfaces, the section being either elliptical or hyperbolic, and the sections through the soffits of the cornices are also the ares of the conic sections, either of the hyper- bola, of the parabola, or of the ellipse. 176 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, In the following Plates, IV., V., and VI., are given a few of the varying combinations of the conic sections found in the Mouldings, and some examples of interior cornices, ante capitals, and mouldings, traced from the marble to illustrate the method of laying down the curved profiles which combine to form these details. PLATE 1Y. THE DESIGNING OF THE MOULDINGS. Tar Fmst Crass oF MOULDINGS. Composed of a single mathematical curve, and generally enriched with an Ornament formed by a combination of ellipses. In the first class of Mouldings, i composed of a single curve, Fig. 1, the : | point P, the direction of the axis MA, 77 ’ and the ordinates, MP and MA, must be : / given ; then, if the curve is a hyperbola, f AC—a, MC =a, MP —y, will all be = given in aliquot parts, and with these given quantities the second axis, b, and the two foci, F and f, are determined by : % a short calculation, and the curve of the ; hs Moulding geometrically constructed. If the curve is intended to be the arc of a parabola, then the axis MA =z, and MP = yg, are given in aliquot parts, and with these given quantities the focus, F, is determined by calculation, and the required arc of the parabola is geome- trically constructed from these given elements. TaE SECOND Crass oF MOULDINGS. Composed of two mathematical curves, and frequently enriched with an Ornament formed by a combination of the arcs of parabolas. In the second class of Mouldings, composed of two curves, Fig. 2, we meet sometimes Pp moray ugiy BG PE 1 IY, IVE WED Fig 11st Class of Mouldings composed of a single curve, an Hyperbola or Parabola. . kg 2 . 2nd. Class of Mouldings composed of two curves. / combinations of the Ellipse Hyperbola and Parabola 7 2 Fig.3. 3rd. Class of Moulding S$ composed of three curves generally arcs of cir "P “ and the arc of an Ellipse . dL ESTE ~ ~ ~ ~ ~ ~/ two arcs of circles and) arc of ipsa, . K emp es mp sen vs SG mim AN mmm mmm ————— — — Yo two arcs of creles %; and of ell; 0 are of ellipse . / / / / / ’ / / / / J / t / / / 4. / i \ / N i / | . | I . rf iY * x . Hg 4. Section through a Facia . 7’ na NV 5 Ste iag 5 | io 4 5 5 : TT Se B- RX . I Se J %, ru | Tah Xe J Foe oe ol i ™ g 7 pee 0 | Tonite | 2 wd] Rr mL ’ MM be 2 7 7 o in A PC ) Z Fe PN oo 3 Fig. Te Afledtion of the Soffit of a Cornice. 8 iid Bnertates 0 | o al >, : iE pwd] wl» : pe | | : Ss LE — A eX vA ! SW N/ Hyperbola | 7 two arcs of crcl \ \ i om ve or fo eri rele fo De oh ee oe em Fe SONIATAON dHL JO HNINODISAA AH], ‘Al S¥eld A wed THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, 177 with the combination of the arc of a hyperbola and an ellipse united by a common tangent, or of a parabola and an ellipse united by a common tangent, or of the ares of two B ellipses united by a common tangent. When the Moulding is composed of the oc v ares of a hyperbola and of an ellipse, then in re the hyperbola AC = a, MC =x, and MP = y, will be given in aliquot parts, and the second axis, b, and the foci, F and f, are determined by calculation; then draw a tangent line, PT, to the point P, and trace PC’ at right angles to PT, and A/C’ at right angles to PC’; then let PC = i the axis minor of an ellipse, and A/C! = & the axis major, and with these given quantities the Moulding is geometrically con- structed. When the Moulding is composed of the arcs of a parabola and of an ellipse, then MP =y, and MA =, are given, the focus, F, is determined, and a common tangent, PT, drawn to the point P, and the axis major and axis minor of the ellipse are determined as above. When the Moulding is composed of the arcs of two ellipses, then the axis major and the axis minor of each ellipse are given both in position and in dimension, and they are made to unite by a common tangent, PT. Tae THIRD Crass oF MouLpINGS. Composed of three or more mathematical curves, and generally enriched with an Ornament formed by a combination of the arcs of hyperbolas. In the third class of Mouldings, com- posed of three or more curves, Fig. 3, the combinations are generally the arcs of circles and the arc of an ellipse. Thus, the curve, PAN, is most frequently the arc of a circle, but in the example of the ante capital of the Parthenon it is traced as the arc of a hyperbola. The curve, PQA, is composed of either one or two arcs of circles, and the curve, AB, is i of an ellipse. 178 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. Besides these three classes of distinct Mouldings, the section through a given fascia is frequently a curved surface, similarly described to the termination of the flutings of the Columns. Thus, in Fig. 4, the given quantities will be the line PP, the diagonal of a given a parallelogram. Bisect PP in M, and draw MAYV at right angles to PP’; then, if the curve is a hyperbola, MAV will be the direction of the axis of the curve. Divide MP’ into some - given number of aliquot parts—for example, 8; then let MA=71, and AV=3, and the foci, I and f, are determined as usual by calculation, and the curve 1s geometrically described. Sometimes the curve is elliptical when + the axis major, CN, and # the axis minor, J CP, are the given quantities. The curved soffits of the cornices are another very important class of curves, executed with great precision, and upon a large scale, but they will be better explained in detail when | considering the Entablatures. We shall then see that the curved soffit of the Pedi- ment cornice of the Parthenon is the arc of a perfect parabola, and that the same curve in the Propyleea is the arc of an equally exact hyperbola. In both cases the chord, AP, is given, and in both a right-angled triangle, AMP, is described, making the chord, AP, a | the hypothenuse of the triangle, the same 7 3 NN Mn NN) NAA \ AL nk : N St ; as in the case of the entasis of the Egyptian ’ vi Columns ; then A is made the vertex of the 3 gl : curve, AM the axis, MP the ordinate y, and | the other elements are either given or found by calculation. In the Erechtheium the soffit of the cornice is elliptical, and the axis major and axis minor are the given quantities. The number of different combinations that are possible, with three curves and a few elementary forms of Moulding, is almost endless, but the same principles of making all the parts commensurable one with another, and all the curves arcs of one or other of the conic sections, and of tracing the several curves by fixing one or two points in position, and of giving Part V. Plate V. EXAMPLES OF INTERIOR CORNICES, MOULDINGS AND ANTE CAPITALS TRACED FROM THE MARBLE. Fis. 1. Dsterior Cornice south Portico Erechtheium. Fig. 2. Stylobate west Portico Trea, EE pe | Nl es aa Te \ ! ; y « i ? A 5% / 33 \ : Me 9 3 | : 45 ™» 20 x 5 » A x ™ ar | i 5S \ / ’ = 7 | > v »30 fo wa Noh 7 K 5 i \ ff 10 Ae NN / , / \ 7 \\\\ . Ci wns 27 | | | 1 1 1 | ; ; : . ! oi oo 4 eS. Las | pl jitsu! XT , / z : | | FA ; : 35 r 1 J ; i ! £ : . | ' centre I ’ oh mR male Cte = £354 pe . - a z Se ie Tar Yee of 1 ' 1 IE ft 8 ae K I N 7% } X J 1 0 1 ’ 3 \ | S gee i 7 ' ) le N10 | >) 1 I N 8 \ 4 EE aes NAR NAN a a ete a WN xg 3] 39.539 Berra mere eee Se i = gr wae WY es ee el ee 1 1 1 \ | sgn pase ; en ENS wm BVA « on Desmarais \ | \ a \ Lx a 1 : 2 fol oh | 10 |e cya i | = =’ \ ' : 7 : : pet ® 3 Ly thn Hr rb ene barn anrnanngna sudo uns ANE NT Aa Nery a p pS , owe | | 1 Nm BY ar gor . am Ror ! NA ese fromm mmm mek meth HO ee LL DE ttt tt] S RN rt A ~The 0 TT . \ LY B giver iru position the kypotheneuse 4 B Hetght of (ornice.......... = 46 ports of a triogle whose sides are Projection of Cornice...= 22 + mans rl Y Fig. 3. Interior of south Portico Erechtheium. ig. 4. Interior Architrave Cormice south Portico Erechtheium. 7% - a ier \ \ NW N \ I | ! \ “N\ | 1 I | \ \ 29 be \ | | NN 25 / / Hyperbola. | No A | / a = 3 Cia ue rl 7 Yom [rosa : {27 / ax = 1 | Ty oe LT | 1 1s I: I, I 0 Iotire Rotynaon; dol. CIV Sotho, bonito Sone ond PaxrtV. Plate V1 EXAMPLES OF INTERIOR CORNICES, MOULDINGS AND ANTZ CAPITALS TRACED FROM THE MARBLE. Fig. 1. Interior Cornice Parthenon. Fig. 2. Interior Cornice Propylaea. Bk AM N\\ : Ellpse. t NN \ 1 5 ea \\ magor axis — 5 ~~ 664 & \ 0 fe 78 75 Bia muauor acts 63 = ord . fa Ae ; | {a 3” Class of" Moulding Tetrion ptf 2 arcs of Circles and ¥ nd : : 60 x 7 arc of Ellipse. 37 nny oF Neslding arcs of Circles 60x 1 arc of Ellipse 5 57% 54 54 57 \ 5% 78 ¥ Bx 45 3 Woy \ 1 N\ Rx 3x 36 x / 7 2 / \ N) | LS f SE ‘ NY Fig. 4. Antee Capital Parthenon. Fig . 3. Anta Capital Propylwa. | EL - - “7 i . i . NNT LL = 1 a ho : a da £0 ea BL Lf Np 4 2 — La rt | 4. 4B eda il gq an NY = ry dae ua ae pint Freie wets p ads turd —N ~ en hmm em = mm eee \ gb bret oo] | ve B18 - 0 2.98 Lo rrp pple, | tate \ Bld r arp tee pron hn TT belts Sootor Dettori: glad EF Holl, Seth bartteS Sonor. 2G THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. 179 the required elements of the curves in aliquot parts, are alike applicable to every detail in the architectural works of Athens. To establish this classification of the Mouldings, it is only requisite to take every curved profile in Athens, either by tracing the form direct from the marble, which can often be done with great accuracy, or by cutting a section through a wax mould and then by tracing the outline, and upon this form correctly traced, to reconstruct in each example, by means of parallel chords, the points and the given elements that were originally required to fix the profile in position and to trace the curve, and it will be at once perceived that the profiles of the several Mouldings will decompose into one, two, three, or more separate arcs of curves belonging to one or other of the conic sections, according to the example that may be selected. In Plates V. and VI. several examples are given, traced from the marble, of interior cor- nices, ante capitals, ete., showing in detail the designing of the Mouldings, and how they were combined together to form either a cornice or a capital, and it at once becomes apparent how, even for the smallest Moulding, the Greeks invariably reduced everything into aliquot parts, and then the elements of the several curves being given in whole numbers, avoiding all fractional quantities, the foci and axes were determined almost by mental arithmetic, and the elements of the curve being thus given or calculated, the arcs of the curves were described by the descriptive geometry. PLATE VY. asp PLATE VI. EXAMPLES OF INTERIOR CORNICES, MOULDINGS, AND CAPITALS OF ANTA, TRACED FROM THE MARBLE. There are many examples in Athens of interior cornices, ante capitals, &c., designed in exactly the same manner as the capitals and bases of the Columns, that is, some multiple is found to divide the whole height and the whole projection of the cornice into aliquot parts, and then all the details of the cornice and the elements of the several curves are multiples of this common modulus; thus— Plate V., Figs. 1, 2, 3, 4, are examples taken from the Erechtheium, and show the designing of the curved Mouldings combining together to form the cornices. Plate VI., Figs. 1, 2, are interior cornices from the Parthenon and the Propylea ; the curved Mouldings and details are all regulated by the division of the whole height and pro- jection into some given number of aliquot parts, measured by a common modulus. Plate VI., Figs. 3, 4, are two ante capitals from the Parthenon and the Propylea, in all respects similarly designed. 180 THE ORNAMENTS, MOULDINGS. AND ENTABLATURES, All the examples in these Plates were traced from the marble, and it is possible to multiply the illustrations, as all the interior cornices and details in Athens are similarly designed, by first reducing the heights and the projections into aliquot parts, and by giving the elements of the curved Mouldings in these aliquot parts, and, lastly, by describing by the descriptive geometry the varying conic sections of which the Mouldings are composed. In the designing of the Doric and of the Ionic capitals we found the principles to be always the same, but the capitals vary in detail one from another: so with the cornices and the ante capitals, the principles are always the same, but one cornice is never the exact copy of another. THE GEOMETRICAL OUTLINING OF THE MOULDINGS. When all the plane and the curved surfaces which combine to form the masses of the design were given, the Architect had still to consider the mathematical outlining and the colouring of the Ornaments on the three classes of Mouldings, on the fascize, on the ceilings, and on other parts of the design, as well as the arrangement of the sculpture, of the painting, and of the inscriptions. Hverything that was requisite to give variety of form and of colour, as well as to satisfy the mind when contemplating the design as a finished work of Art, had still to be considered ; but in the present chapter we may confine our attention to the geometrical outlining and colouring of the Ornaments. In the Temple of Theseus, in the Parthenon, and in the Propylaea, the outlines of the Ornaments are simply engraved upon the curved surfaces of the Mouldings, and then the colours, red, blue, yellow, etc., were applied so as to render the geometrical forms clear and distinct to the eye. In the case of the Erechtheium, which was executed at a later period than the Propyleea, the Ornaments were first engraved, and then sculptured upon the Mouldings, and were, therefore, relieved by lights and shadows, and in the interior of the Portico by colour also; but I believe that in the Erechtheium no colour was applied to the Entablatures of the exterior Porticoes, and that the Architect trusted for the general effect to all the Mouldings being enriched with sculptured Ornaments, and in the Ionic capitals to the deep shadows, and blending of the metal volutes, probably gilt, with the marble volutes; in the Entablatures the frieze is also executed in the black marble from Eleusis, to which the bas-reliefs were attached and relieved by the dark ground of the marble. If we are correct in supposing that the Porticoes of the Erechtheium were not relieved by colour externally, but depended entirely for effect upon the lights and shadows of the 1 perbola GEOMETRICAL METHODS SEVERAL - — r-— 131 H 7 3 / i ; v ve / x Hl = vy Sy 2 ~~ J 3 Ti > 3! 3 N| ~ : 3 XX Pe a 0 ~ 31 S 9 : -3 : | 3 QS v KX 5 Z| % 8 % - 3 0 Parabola given Xie 72 77 70 parts 9 73 be 2 LE ) NON \ es ol } L$ ox “1 x \ I A als x “= i | 3) i Ry OUTLINES OF CLASSES OF GREER MounLniNegs. THE ORNAMENTS =) Q on, Sz Bs + = 8 ANN 2 = a > / N ‘+ SR 7 <“N NY SR 72 ¥ 3 3 / =. pI . OR 4 Ly 5% ’ Rr A - | F Ix 41 be iE f= T t + T 1 3 + f + ~~ = &N N 2 = R RR AN KS D So =~ Q a =~ oy x w~ S x fs 1. yaks 3X 7 TM \ T I T I FILS vii ON stye ) ig. 2. From the interior Cornice of the Propylea ( the real 7 7) John hb ION del - 2 Eo 3 ig | w £ > / ™ ™ —— He be ge lg : / % x TT il frnf= rm =n. mmm te fe =e or Eee c {i > \ Lf Pg r—-——52 EE medat or ¥*—>-—> edu a : rT boa ’ A f ir lS ae | / J | ~ ; sC0 bo! / | “k - in | > | Fe | | 5 / A | I. E Bev 1 | : £ ars i 13 tr a, | : Pi Te a —} [= J el [ T Tr 4 | : A \ TS mene 2 y i { ko \ EN pig 1 N — 1X = e® Yom Te ) wa i 4 +o 1 rm fs nit i + : oN : > y L! ~ bh in We a * = oy | on FI “= \ | — f A FA \ " oe \ 4 + Q x = Q = vo 5 vy C 7. of lL lth, Castle 7. Londen EC. 3 Plas, UM Part V ; is Le Vii. THE GEOMETRICAL METHODS OF TRACING THE OUTLINES OF THE ORNAMENTS ON THE SEVERAL (Cirassrs or GrEER Mourpincs. he © N : 3 8 = NY Q AM ed 5 R < = Q ne ~ A + ~— = © 3 ; = # & ¢ S Fo ~ S 3 ~ 1 3 to > ® Sanat Scie len peel ~ 2 a J A ot i eg 8 A re en Lis : +5 1s + ~ Sl et ; ; ; & = 3 3 3 © 9 <+ oy x ~ = _ nament on the cyma of the Pedime » = Cv = Somat ™ ~ i i oe > - OL ~ I Lan N] $ ~~ Q No oo] rene > pz tee o Cu A o = : QO Come = © 0 . pl © = = — = ~ =» r= 2 O A, = D = -— = oo Oo o E o — ~ ’ oi S o LD) oo < 2 3 jy © Sd : . pened ¢ = OL & 2% S —- 2. sod = = pu] jo Be | - | - | | a1 | 0 | x | \ \ \ oy | \ ¥ 2 > | Sa Lo : | oA } | > fy of ~ < oN Zz Ee 8 - | | ; > 3 1 | | 7 ~k NY 3 7Z “ y 72 > = R I | of 2 RN N | ft x Zz = N | / NT Ser | 7 > wr - TE > I i Sag] Fr i Lh | es my FR . pr | [| S Hl B > | | | Ee ot | 5 oR fe : a | ; i? | J | Soh 27 olvnson del £5 voll, 7 ¢ astle Sreel London ou Evil Fi THE OBNAMENTS, MOULDINGS, AND ENTABLATURES, 181 sculptured Ornaments, and upon the introduction of metal and of coloured marble (and no clear traces of colour have been found externally), then it would prove that the Greeks before the close of the best period of Art had laid aside the external colouring of their Temples, and that the Romans were only copying Greek ideas in trusting the effect in their Corinthian Porticoes entirely to the sculptured Ornaments, without the relief of colour. The exterior colouring of the Porticoes appears to have been confined by the Greeks to the Doric order, and when the Doric was laid aside for the Ionic and the Corinthian orders, with their sculptured Ornaments and bas-reliefs, then only the interior of the Porticoes was enriched with colour and with gilding, and of this we have evidence in the coloured ceilings of the North and South Porticoes of the Erechtheium. The examples selected to illustrate the geometrical methods of tracing the outlines of the Ornaments are taken either from the Propylea or from the Parthenon. The Ornaments were first engraved upon the smooth surfaces of the Mouldings, and afterwards relieved by colouring and by gilding. I obtained the outlines of these several Ornaments by fitting transparent paper to the smooth surfaces of the curved Mouldings, and then by tracing the outlines which were engraved upon the marble and which still remain visible, although the colouring has in most instances almost disappeared. The designing of the Ornaments becomes complex, owing to the multiplication of the curves one within another, but, when any single outline is taken, the curve is found to be simply the arc of one or other of the conic sections, easily traced by the descriptive geometry from the given elements of the several curves. PLATE ¥Il. avo. PLATE, VIII. THE GEOMETRICAL METHODS OF TRACING THE OUTLINES, WITH THE COLOURING OF THE ORNAMENTS, IN THE SEVERAL CLASSES OF GREEK MOULDINGS. Before considering the geometrical methods of outlining the curves composing the Ornaments, the several curved surfaces forming the Mouldings must be unfolded into plane surfaces, and the required Ornament must then be traced upon the plane surface, which can be again exactly folded to the original curved form of the Moulding : thus— The width of the plane, NM, Plate VII., Figs. 1, 2, will correspond in dimension with the length of the profile of each Moulding when it is unfolded into a plane surface, and this straight line, NM, is always divided into some given number of aliquot parts, which will regulate the dimensions of the required elements of the conic sections composing the Ornament. 182 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, Tar ErnrrpricA. ORNAMENT TRACED oN THE 1sT Crass oF MOULDINGS. Let the unfolded line, MN, Plate VII., Fig. 1, be divided into a given number of aliquot parts, according to the example, and let one of these parts be the modulus both for the horizontal dimensions, measured along the line NP, and the vertical dimensions on the line MN ; then the proportions of the Ornament and the elements of the curves are all regulated by this given modulus: thus— Let MN be divided into 16 aliquot parts, and let the Ornament be a combination of the ellipse and of the parabola. Then, for the outside ellipse, let the axis major = 29 parts, or AB’ = 14% parts. 9 5 ,, Axizmimor=13 , orAD = 6% And for the parabola, given the vertex A, and one point, D, in the curve, and let the chord, AD, be the hypothenuse of a right-angled triangle whose sides, AF, FD, are 7 2 4 wir llr=1y=0p=Cw= 2 g=0-=2=0 Tae ParaBorA ORNAMENT TRACED oN THE 28D Crass or MOULDINGS. This Ornament in the ceiling of the Propylea, where it 1s engraved and painted, and also in the cornice of the North Portico of the Erechtheium, where it is sculptured, is found to be a combination of parabolas. Other combinations of the curves might, perhaps, be found, but the parabola is the curve employed in the examples given. Take, for example, Plate VII., Fig. 2, the outline of the painted Ornament engraved on the interior cornice of the Propylea ; let MN be divided into 9 aliquot parts, and let the Ornament be a combination of 3 parabolas. Then, in No. 1 parabola, given A the vertex, and one point, P, in the curve, so that AM : MP as 3:5, let x =3,y = 5; p =o = 5 = 4166, AF = ©°% _ 9.083, Then, in No. 2 parabola, given the vertex and one point, let x : y :: 1 : 4; 4 p=1=8 AF —4. Then, m No. 3 parabola, given the vertex and one point, let z : y :: 1:5; p ==> = 125, AF — 6:25. In each parabola the vertex and one point in the curve are regulated by the given modulus, and the ordinates, « and y, are separately regulated to suit each case, simply taking care to keep them in aliquot parts or in whole numbers for the sake of the calculations. Tae HypERBoLA ORNAMENT TRACED oN THE SRD Crass oF MOULDINGS. The example selected, Plate VIIL., Fig. 1, is taken from the Pediment cornice of the THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, 183 Propyleea. Let MN be the profile of the upper part of the moulding rectified, and make MB equal to MN ; then trace the diagonal line NB, and bisect it in C, and draw CM at right angles to NB, and divide CM into 4 aliquot parts, and let the curve be the arc of a hyperbola, with M for the centre, AM=a=1,CM=xz=4, CB=y =4; b= > m= py = ors = 1408. The two foci being given, the ewive iv geometrically constructed. Besides the Ornaments formed by the combinations of the ares of the conic sections traced upon the three classes of Mouldings, we have also the Maander and the lotus and papyrus Ornaments frequently engraved and painted on the cornices and on the ceilings of the Temples. Thus— Plate VIII., Fig. 2. Is the Maeander Ornament engraved and painted on the interior cornice of the Pronaos of the Parthenon. This Ornament is simply a combination of straight lines, the same as the Ornaments traced on the Mouldings are combinations of curved lines. Plate VIIL., Fig. 8. Is the lotus and papyrus Ornament traced from the cyma of the Pediment cornice of the Parthenon. In this example the Ornament appears to have been enclosed within a semi-ellipse, with the axis minor CB = 6, and 4 the axis major FD = 4, and terminated by small volutes. In Plate I. a similar Ornament is given traced from a beam of the Temple of Theseus. THE COLOURING OF THE ORNAMENTS. The evidence still to be found on the remains in Athens is certainly conclusive that, after the Architect had designed the whole as a perfect work by the united aid of many separate branches of geometry, and after the works of sculpture had been designed and fitted into their appropriate places, both the Architecture and the sculpture were still further relieved by painting. Our attention at present is confined to the relief of the Ornaments by painting, and we have already seen that the first ideas of the Greek Ornaments with the colouring were derived from Egypt, where the colours still remain perfect. When excavating at the east end of the present Parthenon, in 1836, fragments of the Entablature of the earlier Parthenon, B.c. 800, destroyed by Xerxes, were found with the colours—green, blue, red, &c.—preserved in great perfection on different parts of the frieze and cornice, and on the earliest Doric Entablatures in Agina and in Sicily traces of colouring are everywhere visible. All these examples are earlier than the Athenian designs which were executed during the administration of Pericles, but in these later works the evidences of the colouring exist both internally and externally. 184 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. From the actual remains in Athens it is easy to restore the design and the colouring of the ceilings of the Temple of Theseus, of the Vestibule of the Propylwa, of the Parthenon, and of the North and South Porticoes of the Erechtheium ; also sufficient of the remains of the engraved Ornaments, and of the traces of colouring upon the interior cornices and upon the ante capitals exist to enable us with some degree of certainty to restore both the out- lining and the colouring of the Ornaments, and in Mr. Penrose’s work a few examples are aiven of the Ornaments thus restored, taken from the Vestibule of the Propylea, and from the Parthenon. We have seen that the combinations of the three arcs of the conic sections in the designing of the Mouldings and of the Ornaments might be almost endless, so likewise the combinations of the colours—red, blue, yellow, &e.—which were applied to relieve the outlines of the several geometrical Ornaments might vary in every example. Plate VII., Fig. 1. The elliptical Ornament traced from the beam of the Propyleea. Plate VII., Fig. 2. The parabola Ornament traced from the interior cornice of the Propylea. In both these examples no actual traces of the colours exist, but in the same Ornaments in the ceilings and in the cornices the traces of the blue, red, and green, are still visible, and from these data the colouring has been added to the engraved outlines. Plate VIII., Fig. 1. The hyperbola Ornament traced from the Pediment cornice of the Propylea. For this Ornament we possess ample evidence of the colouring in the cornices and in the ante capitals of the Theseium, of the Parthenon, and of the Propylaea. Plate VIIL., Fig. 2. The Maander Ornament. In the Parthenon this Ornament only remains as an engraved outline, but in the same Ornament in the ceiling of the North Portico of the Krechtheium the blue ground remains, and in the Temple of Theseus the blue and the red colours are still visible. Plate VIII, Fig. 3. The lotus and papyrus Ornament. This Ornament is found as an engraved outline both on the cyma Moulding of the Parthenon and on the beams of the Theseium, but all traces of the colouring have, I believe, disappeared. When endeavouring to restore the colouring of any one Ornament some degree of uncertainty must exist, for the actual remains of the colours after 2200 years are, of course, slight ; but comparing the Ornaments of all the Temples together, the remains of colour are amply sufficient to prove that the engraved outlines were relieved by means of the positive colours, red, blue, green, ete., and although these colours appear strong when drawn in detail, yet mn execution they were intended to be seen at a distance from the eye, as 1n the ceilings and In the cornices, where the light was subdued, and the strength of the colouring was toned down by distance and by shadows. — papgapen. Bruappopy go uy peasy Part V. Plate IX. THE ORNAMENTS SCULPTURED ON THE MOULDINGS AND FASCLZL. = __ 7 / B IE HITT mB Ere " . | Soe = Fig 1. Elliptical Ornament sculptured on the let Clans of Mouldings’ * | - E IR OR ei PE I form snteramanscsfe sone san dech on < 8 A > / VQ ISSA { o> £ / \ / &F Aen | / 3 3 . a / | | & > | A J he aa i L A NN | J J . Re: Ly C+ T | | | | doen | | | | 3 GAH SK, Grotto SSL ondon. EF. Cornice North Portico Erectheium. exterior Parabola Ornament sculptured on the 2nd Class of Mouldings Pig. 2. Iotor Fotonson, del. Part V. Plate X, THE ORNAMENTS SCULPTURED ON THE MournnpiNngs AND Fascism. ea hides rane 15 14 | 73 IR 14. 70 LOTUS FLOWER. i PAPYRUS FLOWER, ° \ \ 5 Ellipse Axvs major — 16 L Axcis manor =— 9 Ellipse. Axis major =—— 1 Aris mover == 4 Ais major == 15 +2 Ais minor = 4} TTI Ni ARCS NN a \ N A AS KEES BLES 4 $5 SERRE 2 ROR Wh WAN TR XR SR Ao 3 KS 0 SSS SSS RS Sa = | rier NIE I litte ~L nt! I i —_— Te Bie, 0 Fié . 4 . Lotus and Papyrus Ornament on the interior Cornice of the North Portico, Erectheium yT dr VFIKU Lith, rte London £¢. THE ORNAMENTS, MOULDINGS, AND ENTABLATURESR. 185 PLATE TIX. ax» PLATE X. THE ORNAMENTS SCULPTURED ON THE MOULDINGS AND FASCIA. The Ornaments that have hitherto been selected as examples are all engraved and painted on the smooth surfaces of the Mouldings and fascize, but the same Ornaments in the later designs, as in the Erechtheium, while preserving the geometrical outline of the Ornament that has been already traced, are more elaborated, and the parts, instead of being simply engraved on the Moulding, are also sculptured, so that the Ornament is relieved by light and by shadow, and the colouring was then dispensed with, as it was not required. Taking as an example the elliptical Ornament, Plate IX., Fig. 1, engraved on the 1st class of Mouldings, and continuing the design by outlining the horizontal section, AB, as a succession of semi-ellipses, with three lines between each ellipse, the design of the Ornament becomes a series of ellipsoids, which has caused the name of the egg Ornament to be given to it; and the Ornament being thus relieved by lights and shadows, the colouring was no longer essential. As a second example, take the parabola Ornament, Plate IX., Fig. 2, engraved on the 2nd class of Mouldings, the outline on the smooth surface of the Moulding remains the same—a combination of parabolas. Then trace the horizontal section, AB, as a series of ellipses, with a space between each, and the Ornament is thrown at once into relief and made distinct by lights and shadows, so that the colours were dispensed with, which, I believe, was the case in the example given, traced from the exterior cornice of the North Portico of the Erechtheium. The hyperbola Ornament engraved upon the 3rd class of Mouldings was never relieved by sculpture, as it probably was not considered a suitable design for the purpose, and where sculptured Ornaments are introduced, as in the case of the Irechtheium, this form of Moulding and the Ornament upon it were altogether dispensed with. The Meander Ornament, which we meet with both in the Doric and in the Ionic Temples in Athens, is also engraved and painted, but in the Acropolis it is never introduced as a sculptured Ornament. The lotus and papyrus Ornament appears at first sight to have been traced without any reference to the guiding lines of the conic sections, but when more closely examined this is found not to be the case. We have already seen that on the cyma Moulding of the cornice of the Parthenon, this Ornament was traced within a series of semi-ellipses, and in the same 186 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, sculptured Ornament in the Erechtheium the first outlines of the masses of the Ornament were evidently geometrically described. Thus, taking for an example the sculptured Ornament traced from the Erechtheium, Plate X., Figs. 3 and 4, we find the papyrus flower to have been described within a perfect semi-ellipse, with axis major = 16, and axis minor = 9. And the lotus flower to have been 1st, with axis major = 18, and axis minor = 11. described within two semi-ellipses 9nd, with axis major = 11, and axis minor = 4. These ellipses were proportioned and arranged according to a given modulus, the same as in other examples; then the separate flowers were outlined and engraved on the smooth surface of the marble within these given curved lines, as shown in Fig. 3, and afterwards relieved by being sculptured in detail, as shown in Fig. 4. The Erechtheium never having been quite finished, this Ornament is seen in progress, some portions being finished, and other parts merely executed in the first masses, and the same gradual steps are observed from the smooth surface of the work, simply outlined, to the finished sculptured Ornament, the same as is seen in the Ornaments executed on the 1st and 2nd classes of the Mouldings. The sections of the Mouldings, and of the Ornaments outlined upon them, are invariably combinations of the conic sections, and in practice it is probable that these curves were first traced upon thin lead ; that the forms were then cut out and bent into the form of the Mould- ing, and the Ornament traced on the marble, and made clear to the eye by being relieved with colours strongly contrasted, or by sculpture and colour sometimes combined. In the designing of these details the Greeks were evidently guided by the laws of geometry, and although the first ideas might have been sketched by hand, so as to be pleasing to the eye, yet their executed curved lines are always arcs of one or other of the conic sections, executed with the oreatest precision. THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. 187 COHOAPTER 111. THE ENTABLATURES. THE EGYPTIAN ORIGIN OF THE GREEK ENTABLATURES. A comparison between the Entablatures of Egypt and of Greece points to Egypt for the | original type of the Doric Entablature; but the Entablatures, as well as the Columns, of Grecian Architecture are so altered, that the original ideas are nearly lost, and the design of each order of Architecture in Athens becomes a purely intellectual work, and is a geometrical combination of lines and of surfaces, rendered pleasing to the eye by a variety of mathematical forms in the Mouldings and in the Ornaments, and by a variety of lights and of shadows, and also, when required, by the additional relief of colours. The Egyptian Entablature is always composed of two members, namely, the architrave and the cornice, which bear a close resemblance to the architrave and the frieze in the Dorie order of Grecian Architecture. Taking as an example the Egyptian Entablature, Plate XIa, Fig. 1, the cornice is ornamented with a series of coloured stripes, arranged in threes, and the intermediate spaces are filled in with the name of a King, cut in hieroglyphics, and the whole is relieved with colours. In the Grecian Doric Entablature, Plate XII., Fig. 1, the triglyphs in the frieze are very similar in design and in colour to the coloured stripes in the Egyptian cornice, and the sculptured metopes correspond closely with the hieroglyphic name of the King in the Egyptian Entablatures. The architraves in both cases are simply flat surfaces, inscribed with hieroglyphics in the Egyptian, and frequently with some inscription in the Grecian examples. The difference between the Entablatures of Egypt and of Greece is the addition in Greek Architecture of a third member, namely, the cornice, which is enriched with Mouldings and with coloured Ornaments, and is surmounted by a Pediment and a cornice equally enriched, and within the enclosed Pediment, as well as in the frieze, groups of sculpture were frequently placed ; the whole in the Doric order being relieved with colour. This additional third member 188 THE ORNAMENTS, MOULDINGS, AND ENTABLATURENS. of the Entablature, the cornice, with its Mouldings and its Ornaments, originated probably in the difference of climate, which made it essential to protect the Temples from the winter storms of Greece, and the design of the Doric cornice, with the mutules, would seem to indicate that it was first constructed of timber, and that the design was afterwards copied in marble and in stone. This division of the Grecian Entablature into its three distinct members—of architrave, frieze, and cornice—belongs equally to the Doric, to the Ionic, and to the Corinthian orders, and it exists in the earliest Greek, as well as in the latest Roman Architecture. The agreement between the Entablatures of Egypt and of Greece extends beyond the mere fact of the first idea of the design having an Kgyptian origin, for we find the same general principles of designing the Entablatures perspectively, and of tracing the curves as the arcs of one or other of the conic sections, applicable equally to the Egyptian Kntablatures at Medinet Haboo, B.c. 1200, as well as to the Entablature of the Parthenon, B.c. 430. In both designs the Architects were guided by the laws of perspective and of geometry, and the same general principles of design that were laid down by the Kgyptian Architects passed onwards to Greece, and then to Rome, through a period of 1000 years, with only the slight variations caused by climate and by intellectual cultivation. The earliest examples of the Doric Entablature have all disappeared, and possibly the first Temple of the Parthenon, built about B.C. 800 (which was destroyed by the Persians, B.C. 470, and of which large portions of the Entablature were built into the walls of the Acropolis by Themistocles, and other fragments of the frieze and of the cornice, with the colours—green, blue, etc.—perfectly preserved, were found, in 1836, buried under the platform of the existing Parthenon, which was constructed by Pericles), is the earliest example of the Grecian Doric order of which we possess any data. In the first Parthenon the design and the colouring of the Emtablature are in all respects similar to those of the Temple which was afterwards designed during the age of Pericles; and from the time of the earliest existing examples of the Doric Entablature, either in Athens, or in Zgina, or in Corinth, until the order was laid aside, no real change was made in the arrangement or in the colouring of the details. The Doric order is evidently the connecting link between the Architecture of Egypt and of Greece. In the lonic Temple of the Frechtheium the traces of any connection with Egypt have nearly disappeared ; and although the principles of the design in the Entablature are the same as in the Parthenon, yet the painted Ornaments are dispensed with externally, and sculptured Ornaments are substituted in the cornice and in the architrave. Variety is produced by lights and by shadows in the Ornaments, instead of by coloured combinations, therefore in the Ionic Entablatures we possess a connecting link with Rome, where also the effect 1s produced by sculpture instead of by colours. THE DESIGNING OF THE EGYPTIAN ENTABLATURES. Tueres. B.C. 1220. | | | I | 1 | | | 1 | | I i ; ef a — and Outer Courts of the Temple of MedenetHaboo Fig.1. Plan of the Inn I esn oa i hel i) | TTT PF 70 9 a. 7 6 & 9.8 2 4 0 | | emma Saciimiod | EN 1 TG 5 4 JF 2 oA 0 i 7 _ arid) A - Tae COLOURING OF THE I B.C. 1220 ES. THEB ABLATURES X ENT YP TIAN 3 LG Haboo. J edenet .1. The Entablature of the Outer Court of the Temple of M bi g | J 9 7% | === = 9 mma in mah NN NN N e-~ ht" a cr mmm mmm mm mm em mm mmm] 9% : 7 | 2 | J | 4 J 6 $.2.3 and 4 18 ons FI Medinet Haboo, are traced as the arcs of Hyperbolas. The Secta Fig. 2. Section of the Cornice of the Outer Court. 7 707 Fig. 3. \ er fo Sa Sy ; ey \ 2 | a i 118 A or . : w= Let , 6358 ee Ny 7 © \ rr < < = \ — \ ho Lr \ Ce ard \ - = = = 2a \ - - \ \ eT \ \ wa / \ ¢& i ; \ N | Lorideore, dol, "ry C 2 dove, z 7 SY loth. Bartle Er & Goto) > a Ea THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, 189 We thus perceive that the subject of the designing of the Entablatures can be divided into periods, namely— The 1st period. The designing of the Egyptian Entablatures, and the colouring of the same, B.C. 1220. The 2nd period. The designing of the Grecian Doric coloured Entablatures of the time of Pericles, B.c. 450, with the Ornaments engraved on the Mouldings, and relieved by colour. The 3rd period. The designing of the Grecian Ionic Kntablatures of the time of Pericles, with the Ornaments sculptured on the Mouldings, and the colouring dispensed with. The 4th period. The designing of the Grecian and Roman Corinthian Entablatures. This last period will be considered in connection with the subject of the Roman Corinthian Architecture in Part VI. The several designs of the Entablatures—the Igyptian, the Dorie, and the Ionic-— may now be considered in succession, showing the points of agreement and of difference between the earlier and the later designs. PLATE XI. Ax» PLATE Xla. THE DESIGNING AND THE COLOURING OF THE EGYPTIAN ENTABLATURES. When considering, mn Part I1I., the horizontal curvature of the lines in the Inner Court of the Temple of Medinet Haboo, I referred to the points of sight, Nos. 1, 2, 3, 4, and it appears probable that the heights of the Columns and of the Entablatures, as well as the details of the cornices, were designed to suit these given points of sight, in the same manner as they were afterwards designed in Greece. Sir Gardner Wilkinson remarks how different the Egyptian Columns appear in execution to when they are simply laid down geometrically on paper; and, speaking of the capital of one of the Columns, he says—* The under part of the overhanging rim, being seen “and forming part of the general effect, gives them an aspect still more different from that “ conveyed by an elevation. The Egyptian Architects consulted position, the size of the ““ buildings, and other conditions.” These remarks apply equally to the curved projections of the cornices, and to the Entablatures generally, which were evidently intended to be seen perspectively, as well as the capitals of the Columns. To unfold completely all the early traces of the Egyptian geometry that are to be found at Thebes, will require far more careful measurements than have as yet been applied to 190 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, Egyptian Architecture, still my own observations at the Temple of Medinet Haboo lead me to believe that the Greeks derived not only their ideas of Architecture from Egypt, but that their leading principles of design, such as the “additions and diminutions” made in the first given heights, the curvature of the horizontal lines, the application of the conic sections to the outlining of the curvilinear forms, were all of Egyptian origin, and were only | more fully developed by the Greek Architects. Taking for example the Outer Court of the Temple of Medinet Haboo, Plate X1I., Fig. 2—— The whole height is a given quantity = 38-781 ft. Lo =2'98— the given modulus of the heights. The whole height : . = 298 X 13 = 38-781 feet. The height of Column . : : , = 208 X 10 = 20841 The height of Kntablature . : , =O8X B= BOUL Height of Column . 2° = 2181, 2-131 X 3 — 6:393 — width of abacus. Width of abacus oa ik. = 0'5327 = modulus of the horizontal dimensions. Calculated apparent whole height = 82658", Ry = 6358" = apparent modulus of heights. Calculated Given Additions and heights. heights. diminutions. Apparent whole height . = B3587x 13 -— 82658". , 88-7814. . .38781ft... 00 Apparent height of Column .=6358'x10= 63580". .29-805 ,, . . 29841 ,, . .— 0036 Apparent height of Entablature = 6358'x 8 =19074'.. 8976, .. 894 ,, ..+0036 The Details of the Entablature. The apparent height of the Entablature . = 6358" x 3 =19074/ . i . Architrave . , = GRB8Y XD — 1271067 w Cornice ,=0358/X 1 = 635% For details of the cornice fy = 1059" = modulus for details of cornice. The fascia of the cornice ; : : .=1059" x 2 = 2118" The curved soffit of the cornice : : = 1059" x 4 = 4286 The torus of the cornice : ; . .= 1059" x 1 = 1059 The Inner Court of the Temple of Medinet Haboo. Plate XI., Fig. 3. The proportions in the Inner Court are very similar to those in the Outer Court, except that both the real and the apparent heights are divided into 14 instead of into 13 aliquot parts, thus making the Column = 11 parts, and the Entablature — 3 parts. The given height of the Column is divided into 15 parts instead of into 14 parts, and the width of the abacus = 3 parts. THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, 191 By calculation the “ additions and diminutions ” in the Inner Court amount to — 0-142 feet in the Column, and + 0142 feet in the Entablature, and the details of the Entablature are arranged similarly to those in the Outer Court. The measured curved soffits of the cornices, Plate XIa, Figs. 2, 3, 4, selected from the Temple of Medinet Haboo, appear to be all traced as the ares of true hyperbolas, the elements of the curves being given in aliquot parts, and the arcs geometrically described, the same as in many examples already noticed in Greece. The sections through the torus Mouldings are semi-ellipses, with the axis major and the axis minor as the given quantities. The Egyptian Entablatures being thus trigonometrically designed, and the curved forms all geometrically outlined as ares of the conic sections, then the colour was introduced into the Architecture to render the hieroglyphics and the architectural details clear and distinct when seen perspec- tively from the favourable points of view, and also to produce those combinations of geometrical forms and colours which were considered the essential elements of a perfect work of Art. Thus, in the designing of the Kgyptian Entablatures, B.c. 1200, we find all the elementary principles of design to be the same as those in the Grecian works of the time of Pericles, namely, the horizontal projections are given in aliquot parts; the heights of the mem- bers of the Entablature are reduced into apparent aliquot parts, which are measured in seconds upon the arc of a great circle ; and the curved forms are traced as the arcs of the conic sections, with sufficient colour introduced to relieve the details; and there can be little doubt but that in the first Parthenon, designed about B.c. 800, and in the Doric Temples at Aigina, at Corinth, in Sicily, ete., the same principles of design will be found to exist. The Greeks were guided intellectually by the earlier civilization of Egypt, and evidently borrowed from the Fgyptians their ideas and principles of Art and of geometry. THE DORIC ENTABLATURES. It has been already stated that in the Grecian Doric Entablatures we meet with the same principles of design as in the earlier Egyptian ; in both cases they are perspectively designed and calculated ; the horizontal dimensions are given in lineal aliquot parts, and the several heights of the members of the Entablature are determined trigonometrically by the visual angles, and the curved soffits, the forms of the Mouldings, with the Ornaments engraved upon them, are all combinations of the ares of the several conic sections, and the colouring is arranged to suit the perspective design. In many respects the Doric Entablature is a more finished work of Art than the Doric 192 THE ORNAMENTS, MOULDINGS. AND ENTABLATURES. Column. The same cultivated minds designed both, but the Entablature 1s, of course, more enriched with Ornaments, with sculpture, and with colour ; every detail composing it bears the impress of scientific thought, and it is essentially a combined work of Art and of geometry. Before entering upon the consideration of the more general subject of the Entablatures, a few observations seem to be required upon the harmonizing of the triglyphs, of the metopes, and of the Columns in the designs of the Doric order. Vitruvius, when referring to the subject in Book IV., Chapter III., says— Some “ individuals amongst the number of ancient Architects have contended that the Doric order “ ought not to be adopted in sacred edifices, because its peculiar character, if strictly observed “in the construction of Temples, would be inconvenient and at variance with the purport of “the building. ““ Not, indeed, that the order is considered as inelegant or deficient in majesty, but ““ the manner of placing the Columns is thought to be inconvenient, inasmuch as it renders ““ the just distribution of the triglyphs and the lacunaria difficult.” These remarks of Vitruvius are confirmed by the remaining works in Athens, and as there must always have been a slight difficulty in arranging the Columns, the triglyphs, the metopes, and the lacunaria in the Doric Porticoes, we may take the three Doric examples of the Temple of Theseus, and of the Porticoes of the Propylea and of the Parthenon, and we shall see how the Architects adjusted these details in each Portico. Tae TempLE oF THESEUS. In the Temple of Theseus the triglyphs are arranged centrally over the capitals of the Columns, and the relation between the triglyphs and the metopes is as 2:3; then 11 triglyphs and 10 metopes in the Portico divide the length of the frieze into 52 parts. e vnserranne cases. YE 263 == Tongth of wrekitrave .................... chia isn hen ities Te deh L | ak | | | L | | | | i } | | | { | | | | 1 T T T T T ™ T Re § T + Te ¥ ¥ 1 T T T ; (SE, § 1 1 T 1 1 20.530 S26 33 5047 WW 40 48 50 a2 bee te Ld faa) Se he eat L | rr T T T T TT == al | ST EL T t t T Tt @¢ 2 + 6 8 70. 72 14 16 18 20 22 26 28 r= 0851 = modulus. Triglyph ~~. .—0851x 2—1-700ft. Measurement 1-69. Metope . . .=085Ix 3-3853. ; 2-539. From centre to centre : of capital . = 0851 x 10-8510 ,, THE ORNAMENTS, MOULDINGS, AND ENTABLATULRES, 193 TaE CENTRAL PORTICO OF THE PROPYLZA. In the central Portico of the Propylea the triglyphs are central over the Columns, and there are 12 triglyphs and 11 metopes in the width of the Portico. In this example the length of the frieze is divided into 29 parts, and 1 part is made equal to the width of the triglyph. In the North Wing of the Propylea the triglyphs are central over the capitals of the Columns, and there are 9 triglyphs and 8 metopes in the width of the Portico. In this example the length of the Entablature= 35-006 feet, is divided into 43 parts, thus: gre = 0-814 = modulus ; triglyph = 0'814 xX 2 = 1628. This gives the width of the metope = 2:544. In both these examples of the Propylea the ratio of the triglyphs to the metopes is incommensurable, but the central lines of the capitals of the Columns and of the triglyphs coincide. Centre Portico. 0 2 4 6 8 10 12 14 16 is 20 22 R4 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 3 i | fal id | a) bt tt 0 1 2 3 4 5 6 7 8 9 10 11 12 13 4 5 16 17 18 19 20 21 22 23 24 23 26 27 28 29 coronene BES HUAI OF PU oatyiabesiitaressivarn ie sm stain Bondon noni pcb mds eh int ina itn negseoiod i : I ] T 3 { F ——— pre Ca ref RR | ei vy | TE PorTICO OF THE PARTHENON. In the Entablature of the Parthenon the regularity and the harmony of the Architecture are made subservient to the sculptured metopes, which are increased in size towards the centre of the Portico, and are found to vary in width, between 4:066 feet and 4-373 feet, to suit the different designs of the sculpture. Again, the difference between the centres of the capitals of the Columns and the centres of the corresponding triglyphs varies between 1 inch and 5-3 inches. In design the Entablature is irregular, and the centres of the Columns and of the triglyphs do not harmonize. If all the metopes had been alike, the relation between the triglyphs and the metopes would have been as 2 : 3, the same as in the Temple of Theseus, and this would divide the whole length of the frieze — 100°012 feet, into 72 parts : thus— 100-012 72 — 1-388 feet = modulus. Triglyphs . = 1-388 X 2 =2776. By measurement 2:765 and 2-780. Metopes ., = 1-388 x 3 == 4-164, uo 4-066 ,, 4373. 194 THE ORNAMENTS, MOULDINGS. AND ENTABLATURES. In the Parthenon we find that the centres of the Columns are all made to depend upon the arrangement of the lacunaria or marble beams of the ceiling of the Portico. These beams regulate both the dimensions of the Inner Portico (namely, the length of the Upper Step), and the centres of the two capitals, A and A/, of the Outer Portico, which correspond with the faces of the two marble beams BB. x S | 1B a Se Lfleietio Ye he Jeu half width of marble bears Q ge T pp I i === T i= forth | bo | os | | | | y | i | : RTE %-- # TE -— ¥F 066% || Xx R067 -%RV6- K+ 05-%R U6 NF RI5-¥ +2200 | $2.90 | | id | bd : J } T 1 centre of por tico | a Le wenn half width of upper step of the tnner Portico mmm PLATE X11, avn PLATE XI11. THE DESIGNING AND THE COLOURING OF THE DORIC ENTABLATURES. When considering the details of the cornices (see Plates V. and VI.) we found the whole height and the whole projection of any cornice being given, that these quantities were divided into some given number of aliquot parts, and that all the subdivisions were made multiples of a common modulus. The same principle of dividing everything into aliquot parts is found to exist in the general designing of the Entablatures. The projections of the details of each Entablature have been already given in Part IL, as well as the whole apparent height of the Entablature, measured in seconds upon the are of a great circle. Then dividing this whole apparent height into some given number of aliquot parts, measured also in seconds, the apparent height of the architrave, of the frieze, and of the cornice will, in each case, be a multiple of this given modulus. Again, by dividing the 1st modulus into a given number of apparent aliquot parts a second modulus is obtained, by which the apparent heights of all the details of the cornice, of the architrave, and of the frieze will be regulated, and the true lineal heights are then all determined by trigonometrical calculations. In the proportioning of the Egyptian Entablatures the whole apparent heights were first divided into three equal parts, two being given to the architrave, and one to the cornice. Then i Fi PartV. Plate XII. THE DESIGNING AND COLOURING OF THE DORIC ENTABLATURES. 0 4442 feet. of projections on the AD line __ horizontal modulus Q © Q NS 5 g 3 > | 3 > | : I 2 | 3 N id ~N ~~ | > » Q 3 > 2 FE 9 N I ! $ 3 prea N oN Nl - : 8 NN Le Ss Nor NR : A D0 ms N\ \ \ QS \D 3 : ; NN N NN \ N\ \ 7 3 \ © I | N NN 0 Ly Q <3 © . Q : LAMM NN 3) : ~, = 3 bi > Nn \ a ; No» = ~ ~ NN \ NN \ > QU \ NW 5 © N = N 2 3 \ ON 3 I ™, \ N NITInni nnn ATi oe BRN Nr ee- Dp. em vene readied] AN NN NN NN 1 1 1 I N i X \ Xx i I \ NS XT fy oN 0B AN x 5 Fol a a. | NY MON NN WW : \ ! § DIAN \ nnn ! nnn \ ) \ 1 1 1 N PB YZ \J | ey | f : | | 4 z | | : | i Na / = i \ : SE : £3 Es E : i COR : | i Tr © § | pt | 0 i ; i 1 dna zt : oh i oxy Err ri y 29 Q ov a “eo dr bt 09 r Trae ad <1 § = aN r+ - fii gph loll honreas gem 3 5 i QO NNN 0 NA $ WN \\\ A 2 - | Ls ) iL 3 1 = , mens ee mr NEY : A 13 3 X : . \ \ \ > . \ hoe i $ 3 od el I 1 5 of, \ : \ \ 9 NNN i - Ann N\ TT TT TT te N alana NN \ NN NN NR \ \ N NNN nN NN NN NN AN \ NN NN NR N N \ NR NN ee 3 Rae mE i JE ll a i NW NN ; N \ l / \ | i / \ nnn h \ N NN ni nk 1 / \ nN NN Vr NNN ND nuannnmaeg 7 N Naan NNN N |v / Ninna NN \ NN \ NN \ | NN N NN NNN NN | / NR \ \ nn the true Joint of” View. Fntablature determared by calculation and the complete omy perspective Design, as original #7 3 +9978 7 Ing 1. The northwest angle of the Parthenon . The heights and parogections of the several parts of ‘the FHI, aotle S Indoor. F.C ip. « 7 Jo Part V. Plate XII. THE DESIGNING AND COLOURING OF THE DORIC ENTABLATURES. 24% 7072277777777 . 1 ft a re __ i SA Z i 7 Er ll Lill ells NEN N . yy s ’ ar 7 7: of 2g 7 7 Mane _ _ | mmm mm Ye 2 oo = a =k Si 5% > =] prtppau anand hui T \\7 2% VL fm api ele ait gion oct er me ome eee ti ir i i me Be im em nm em mo oi ee ee mr mt ee ee ee ee me = em ef em mm hm mm et me fn te di fn nm er a Nee ey a \ mmm mmm mmm eee ee re mmm mm meg 1 | 4——-- EET rT GOL mre mee UOXALOY 0} 99 - 6¢ TTT a RA : A z i | & r | | I I I | | I I I | | I I I | | I I I 1 I | | A ! I 1 1 I | i 1 | I I | : I —*3 1 | 1 7 N= a RSS eer Zs ry — ——— x Wn N N \ x y 91-875 to point of sight a 5 Boe re me em i ef ie es st is os ks tea rs Si Zz : HP 8 7 6 57 3 2710 4 » « \ 4 48 Y2\%1 4 B® ] ’ / z 7 ; / rl ’ Xo / / ; / D> / # of the real size) Fig. 2. The Pediment Cornice of the Propylzea . x A t Let A be the vertex of anv Hyperbole, and A.B. the diagonal of the square A.B.C. let AC. 3 TD ie 2 £ 2 . $ os °C i | | 2 ~ $ rm — 2 » B 1 B00 O ®R ’ / / / , v, , / 7 7 S AL, Castle Se Lordon 2 .C. Soto Teotersorn del : THE OBRNAMERXNTS, MOULDINGS, AND ENTABLATULRES. 195 by dividing the 1st modulus by 6, a second modulus is obtained, which regulates the details of the cornice ; and in the proportioning of the Greek Entablatures the whole apparent height is generally divided into three apparently equal parts, namely, the architrave, the frieze, and the cornice, and the whole apparent height of the cornice being divided into some given number of aliquot parts we obtain a 2nd modulus, which regulates the details of the cornice, ete. Thus, taking for example— Prate XII., Fig. 1..——THE NorTH-WEST ANGLE OF THE ENTABLATURE OF THE PARTHENON. The given apparent height of the Entablature from the abacus) — 13984/, Rs w= 1748 = let given apparent modulus of to the fascia above the corona Entablature. Apparent projection of the abacus = 237" ‘Whole height of Architrave. Frieze. : cornice. Apparent modulus 1748" x 8 = 5244" = 5244" — 5244" + 237! Nore.—The projection of the abacus apparently cuts off a small portion in the height of the Entablature, and this quantity = 2377 is thrown into the soffit of the cornice. Then for the horizontal} 4.4040 details of the Entablature| 3 0-148 = hori- =(-4442 ft. let this given modulus be zontal modulus for the ~ details of Entablature. The 1st given horizontal modulus, which regulates the projections measured upon the line AB . divided by 3 . Then for the apparent SA SM re The given apparent height) + heights of the details of 12 $57 = approval je 5244" ,, the dovtien lob 594A he modulus for the details divided by 12 of the cornice of the cornice. Having determined the values of these two moduli, 0'148 fect for the projections, and 437" for the apparent heights, then all the details can be figured in aliquot parts, as shown in Pig. 1. | The apparent heights of the cornice . = 14+34+1+5+2=12 apparent parts in seconds. The horizontal projections of the Entablature=18+3+2+2 ~~ =25 horizontal aliquot parts. Prate XIII., Fic. 1.—TuE CENTRAL PORTICO OF THE PROPYLZA. 03/ The given apparent height of the Entablature =18093, Loo = 1206-2" = 1st apparent modulus of the Entablature; 1206-2" x 5 = 6031" = frieze; 6031"=architrave ; 6031" = cornice. The first given horizontal Then for the horizontal Liar ? ou — 00914 ; modulus, which regulates op details of the Entablature _ 100914 feet = horizontal the projections measured let this modulus be divided| [modulus for the details upon the line AB . as follows , , .| of the Entablature. 196 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. For the apparent heights Lo = 201" = apparent — 6031" of the details of the cornice, modulus for the details let 6031" be divided by 30. of the cornice. The given apparent height ) of the cornice : : J Having determined the values of the two moduli, 0:0914 feet for the projections, and 201" for the apparent heights, then the details are figured in aliquot parts, as shown in Fig. 1. The apparent heights of the details of the cornice =8 + 2 + 5 + 6 + 9 = 30 apparent parts, measured in seconds. The horizontal projections of the Entablature = 8% + 174 + 3% + 3% + 32 = 31% horizontal aliquot parts. Plate XII., Fig. 2, and Plate XIII., Fig. 2, are sections of the Pediment cornices of the Parthenon and of the Propylea. In these sections we possess two very perfect examples of a described arc of the conic sections. Plate XII., Fig. 2. The soffit of the Pediment cornice of the Parthenon being the arc of a parabola, with A for the vertex, then let AB be the diagonal of a parallelogram, whose sides, AC, CB, are as 9:2; let AC=9=x, CB=2=y, and from these given elements the parabola is described. Plate XIII., Fig. 2. The soffit of the Pediment cornice of the Propylea is traced as the arc of a hyperbola, with A for the vertex; then let AB be the diagonal of a square, whose sides AC=CB; let AC=5, AD=1=a, DC=6=2, CB =5=y, and from these given quantities the arc of the hyperbola is described. The outlines of the Mouldings and of the Ornaments are all geometrically described as the arcs of the conic sections, and have been already given in Chapter II. THE COLOURING. Colonel Leake, in his introduction to the ““ Topography of Athens,” says—* There can “be no stronger proof of the early civilization of Athens than the remote period to which its “ history 1s carried in a clear and consistent series. We have some reason to believe that “ Cecrops, an Egyptian, who brought from Sais the worship of Neith, was contemporary with “Moses.” And the close connection between the designs of the coloured Entablatures and Ornaments of Kgypt and of Greece, as shown in Plates I., IL, and III., seems to confirm the idea that an early mtercourse existed between the two countries, and to lead us naturally to expect that the early Doric Entablatures were relieved by colours, the same as the Entablatures in Egypt, even if no remains existed ; but on all the Doric Entablatures the traces of colours are found, thus, on portions of the Entablature of the early Parthenon (possibly B.c. 800), now THE ORNAMENTS, MOULDIXGSE, AND ENTABLATURES. 197 built into the walls of the Acropolis, the red and blue colours still exist, and in the excavations made at the east end of the present Parthenon, in 1836, other fragments of the early cornice were found, with the colours, green, blue, red, ete., perfectly preserved: also on the Entabla- tures of the Doric Temples at Algina, at Corinth, in Sicily, ete., B.c. 600 and B.0. 500, the remains of colours are everywhere visible ; but our attention will be more immediately directed to the Doric Entablatures of the time of Pericles, namely, the Parthenon, the Theseium, and the Propyleea. In these three examples the engraved Ornaments upon the Mouldings still remain perfect, thus evidently showing that they were prepared to be coloured; and Colonel Leake says (page 335), “In the hands of Phidias and his colleagues the Doric order imposed no “limit to the decoration applicable to the upper parts of the edifice, and hence (as we find “ proofs in many traces still existing in the marble) the statues and reliefs, as well as the “ members of the Architecture, were enriched with various colours, rendering them pictures as “ well as groups of statuary ;” and these remarks are quite confirmed by my own observations, and also by those of Mr. Penrose, and of many other observers. Prate XII. Fig. 1.—THE PARTHENON ENTABLATURE AND THE REMAINS oF COLOUR. In the Entablature of the Parthenon, at the east end, and over the second Column from the south-east angle, the mutules are painted blue, and are relieved by a red ground ; also on the fascia over the capital of the triglyphs a Meander is visible. The capital of the triglyphs is blue, and the interior channels appear also to have been blue. On the Mouldings of the third class the alternate coloured Ornament is engraved, and occasionally traces of colours are found. On the cyma of the Pediment the lotus and papyrus Ornament is engraved, and on the cornice of the Architrave there are the traces of an engraved Ornament, as shown. In the cornice of the Pronaos the engraved outlines of the Ornaments on the second and on the third class of the Mouldings, and of the Maeander on the fascia, are distinctly visible, and traces of the usual colours are found on the Moulding of the third class. In the capitals of the ante the outlines of the Ornaments are clear, and the remains of the colours, blue and green, are very perceptible. Mr. Penrose found similar remains of the colours upon the several parts of the Entablature, which he has described in his work on the Parthenon. Tar TEMPLE oF THESEUS. Colonel Leake says (page 511), “ All the sculptures of the Theseium, as well of the “ metopes as of the friezes, were painted, and still preserve some remains of the colours. ““ Yestiges of brazen and golden-coloured arms, of a blue sky, and of blue, green, and red “ drapery, are still very apparent. A painted Meander is seen on the interior cornice of the “ Peristyle, and painted stars in the lacunaria ; similar painted Ornaments are seen in the ““ Parthenon, in the Panhellenium of Afigina, and in several other Temples.” 198 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. This Temple, although of an earlier date than those in the Acropolis, is one of the best examples for studying the arrangement of the colours. The ceiling exists in its place, and in all parts considerable remains of colour are still to be found. Fxternally the colours appear to have been similarly arranged with those in the Parthenon; the mutules in both Temples are blue, relieved upon a red ground, and on the third class of Mouldings is found the usual coloured Ornament. On the interior cornice of the Peristyle, composed of a fascia with a Meander traced upon it, and a Moulding of the third class with the usual Ornament engraved, the colours blue and red in the Meander, and blue, red, and green in the Ornament, are visible. On the ante capital at the west end large portions of colour are still remaining—Dblue, red, green, and white. In the lacunaria the engraved outlines of all the Ornaments are perfect, and large portions of blue remain; also a painted beading, and lines traced in green, formed a part of the ceiling. On the sides of the marble beams the lotus and papyrus Ornament is beautifully engraved, but no colour remains. Some of the colours from this Temple were analysed by Mr. Faraday, and the results were as follows— ““ Portion of coating taken from the soffits of the mutules of the Theseium. The blue “is a frit, or vitreous substance, coloured by copper. Wax is present here. ““ Portion of coating taken from the Columns of the Theseium. I am doubtful about “ this surface. I do not find wax, or a mineral colour, unless it be one due to a small “ portion of iron. A fragrant gum appears to be present in some pieces, and a combustible ‘““ substance in all. Perhaps some vegetable substance has been used. “ Portions of coatings from the lacunaria of the Theseium. The blue is a copper frit, “or glass, with wax.” Pirate XIII, Fie. 1.—TaE PrROPYLEA. The Entablature of the Propyleea is nearly destroyed, but on the remaining fragments of the cornice and of other details, the engraved Ornaments, as shown in Fig. 1, are clearly seen, and Mr. Penrose found traces of red between the mutules, and that the mutules bore distinct traces of blue. Pausanias says, “The roof of the Propyleea is of white marble, and excels all other “works mm Ornament (executed in painting) and in the magnitude of the stones.” The Ornaments traced on the first and on the second classes of Mouldings taken from THE ORNAMENTS, MOULDINGS, AND ENTABLATUREN. 199 this roof have no remains of colour, but the sizes of the stones, the arrangement of all the architectural lines, and the outlines of the engraved Ornaments, are still to be found sufficiently perfect for the design of the roof to be restored with certainty. On the ante capital in the Pinacotheca the outline of the Ornament on the third class of Mouldings is very distinctly marked by a dark line, and portions of green colour still remain. The results of an analysis by Mr. Faraday of some of the colours taken from the Greek Temples are given in a letter to Mr. Donaldson, published in the Transactions of the Institute of British Architects for the year 1842, and, in regard to this Temple, are as follows— ““ A portion of the coating taken from the ante of the Propylea—the blue produced “by carbonate of copper, wax being mingled with the colour. “ Portions of coating from the Northern Wing of the Propyleea—the colour a carbonate “of copper. Wax 1s present.” The restored colouring of the Entablatures of the Parthenon and of the Propylea, as shown in Plate XII. and Plate XIII., is founded upon the oeneral evidence derived from the actual remains of the several Kntablatures and Interiors, one example supplementing what may be wanting in another ; but the fragments of the colours still remaining on the Entablatures of the Parthenon and of the Temple of Theseus are sufficient to enable a restoration to be made with some certainty of its being correct, and, in the case of the Propylsea, sufficient exists to show that the colouring was the same as in the other two examples. The evidence still to be found on the remains in Athens is conclusive, that after the Architect had moulded his ideas in the marble, and had designed and constructed the whole by the united aid of the many separate branches of geometry, and by the known laws of Art deduced from observation, and after the sculptor had designed and fitted into their appropriate places all the separate subjects of sculpture embodied in the archi- tectural design, then both the architecture and the sculpture were still further enriched by painting ; or in the words of Plutarch, when speaking of the works of Pericles, “ A bloom ““ was diffused over them, which preserves their aspect, untarnished by time, as if they were “ animated with a spirit of perpetual youth and unfading elegance.” To collect all that is found to exist on this important subject of the ancient painting in Egypt, and in Greece, at Pompeii, and at Herculaneum--all that may be found in the writings of the ancient authors relating to this third branch of Art——chemically to analyse the remains of the different ancient colours that we possess—to reduce all this information into order, and to deduce from it any laws of colouring applicable to ancient Architecture—would be a work both of great labour and of much time, though it would be repaid by revealing to us the ideas of those eminent in 200 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, ancient times who were devoted to this branch of Art. My own attention has been directed alone to the architectural science of the Athenians, and it would render the present work too voluminous to enter upon the consideration either of the painting or of the sculpture. In the architectural designs we have found that one point of view was selected, for which all the proportions and the lines were adjusted, and that on a plane given in position, the entire outline of the design, as stated by Vitruvius, was supposed to be perfectly traced in perspective ; and this given perspective outline was the foundation on which the painter had to arrange and to harmonize the colouring of the work ; and it appears to me to be impossible that any correct idea could have been formed for the colouring of these designs from merely geometrical drawings, on which the colours must be introduced in all their brightness and their purity, and in which the soffits cannot be shown. Position and distance, both entered into the consideration of the Architect when arranging the lines of the design, and the same considerations were equally essential to the painter when designing the colouring of it; and whether it is for the colouring of only a portion of the work drawn in detail, or for the entire design made up of these several portions, the perspective outline must always be traced from the same given point, and the representations of the colours must be toned down, by supposing the atmosphere to be interposed between the eye and the design, and this will at once remove the apparent harshness of the colours, and the erroneous impressions which a geometrical drawing of the colouring conveys to the mind. It appears probable that when the marble was all sculptured and finished that some method was then employed for softening the glare of its whiteness in every part of the design, and that when the entire design was thus subdued, then the Ornaments and the other enrich- ments were relieved by more positive colours. Pliny says ‘that milk and saffron, mixed with ““ lime, were used to produce a delicate colour in frescoes,” and the Greeks must have had some method of harmonizing the extreme whiteness of the Pentilic marble. The Interior Court of the Temple of Medinet Haboo at Thebes may be taken as an example of the general tone of colour required for the masses, and the effect of this colouring when contemplated from the point of view is In no way overpowering, and only sufficient to relieve the details of the design; and in the Greek Temples, on the Steps, on the Doric Columns, and on the plane surfaces of the architraves, one tone of colour seems to have prevailed, and in the cornices and in the Ornaments this same tone was blended with richer colours. It may be observed in the Temples of Egypt that, in proportion as the light was subdued, the colours were introduced in larger masses. Thus, in the tombs of the Kings at Thebes, where they are lighted from the entrance, the ground tint of the walls is of the same tone as at the Temple of Medinet Haboo, and at the Memnonium ; but in the tombs receiving no natural light the bright colours on the walls and on the ceilings are applied in broader masses, and the same was probably the case in the Greek Temples. In the Part V. Plate XIV THE DESIGNING OF THE loNIC ENTABLATURES. I1g.1.The North Portico of the Erechtheinm . + + 1 = + Hessssntesd iil ftp hpi: uz. __ = 4 Fee ne— ne WEL Ce Re ETT BEE ca #X rey. ~~ 0 | od x i J ie 7 __ ne a NN a ; x EE aE Ry a itt \ ¢ pi rh i 2 8 i i. . o 2 x " | = meee « EB HINT eee SN : i En RnR ey 1 1] i Pe Lil | ! | | ners e bill: 3B ky 0 scsivisioiossusenenioies Lr 1H Rain RE 1 B rrr A rs ys HE 2 23 22 21 206 18 11 16 15 14 13 12 1 40 9 k7 Bbabalby 0 en a R tempat omen creo cunt muon == Co 2 go : fenitidiicammnie | 5M Gsmomainmnn ey A mmm mn tm tm mmm fmm mm mm nm mmm mm a Fig. 2. The Cornice of the North Portico . one half of the read sve. iL - ; ~ Ter J i 4 CN oR CE of ~~ N Ti To Ve rrr Segre freee i meres rose Greenford SL : ei | fuflsfuton fer ideden shod infos - F ig. 3. The Architrave Cornice. JE fd Fo a ee, L one halt of the real size. +r _ SIohon Rolunson, del. Part V. Plate XV. een dI9E 5, OD Point of sight. DON NYY YY YY YY YY YY YY VY ALNNINSINNNANNINNS NNN ANN ANNI NNN AANA F ig 2 Plan of the South Portico. x i UIUULL em ———t me mr mr reed NR A — - gL HT 1 UOXLIY UROL" * Pl SAAS AN ( LAD IN J X ( A ON ) NA {I UII NA The South Portico of the Erechtheium . (one sucth of the real sxe.) Fig 1. THE DESIGNING OF THE IONIC ENTABLATURES. - - ” Li a SER pee x TAVAN Moree mm A OI <3 b { 7 77 / os . / St 7 7 $2 5 L Z 7 7 “ Te NET in er et a ee ee ino br z \ 3 \ A NX \ | O 7 : \ > re a Bit he ea Cs ee RS el el eS tN Sa ea a Te so : 7 \ 2 x EE Tn ororrreeErens nd errr Sra tas En san saan te SEE SEES SEER SE Te an med rmt ken Seed tte mg mr amis 7 : : : 3 N 1 ; /; \ » 7 ridin be ne tention tne i Mmm de po i NE i orm th de em me hn a a A eo einen tne a Ee i \ \ N \ } - v r X 7 \ 3 \ \ \ | 5 by \ | 2 \ > mmm ee Na) LOTR el Ee PR a LS me RL EL ee GL Le LE a a : \ \ \ \ \ \ ER RE rr \ \ ! \ \ \ \ 3 \ I i 5 \ \ A \ \ | i \ \ N \ \ \ \ i : \ A N iN \ \ | 1 \ i» 5 \ % \ % ! § J 5 : : 5 \ y: Y 2 \ 5 5 § i i NY \ \ \ } | \ \ \ \ \ \ | | \ 5 yybroy oY — * by Y : Y 3 \ 3 f ) AM. sur Goo ! o : Ep Arm ee mmm Nh CL AN ee Ge a Bi RE ht mm een ee ef ey eh eee i ei ns es mi mt Sm me it en mn ee] ele i : : 5 \ A 2 \ \ \ NS RE EE Fer rr rr Em ee eT rs eC C merce E nr eee rs re oye x ---s—1 ; \ \ \ \ \ \ 3 A ® | 7 \ \ x \ x 4 = | i ! 1 \ \ X S \ > \ \ 3 : ST \ \ > > \ \ Le \ © \ \ \ 3 Ne 3 N \ A \ \ \ \ A 1 8 \ \ \ \ \ A s+ |! \ \ \ \ 3 \ \ \ \ ) fi i Ct i i et me a) ee od 2 oe Se en ee 20 te on ff fe rr dm ce te ee ee 8 fe) dt me i ne ot Ee a i me eee oN LLL Ne NR = 372 - 8 ns to point of sightt..........ow.tee.e-.....} THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, 201 Theseium, and in the Parthenon, externally, a large proportion of the surface was only the colour of the marble softened down, but in the Pronaos the colouring in the upper parts was in larger masses, and internally the walls and the ceilings were much enriched with painting. It has been already supposed that the painter was supplied with a detailed perspective outline of the design made from the point of view from which all the parts were corrected, and by taking this given perspective outline, and by filling in the colours existing in each design into the places in which they are found, little more would be required, in some instances, to restore the original coloured drawing from which the design was finished, and from what exists in the Temples and in the tombs of Egypt, combined with the information that can be collected in Athens, and from other sources, we might with some certainty add to the Athenian works the last finish that was given to them, and which has been the first almost totally to disappear, and again present these designs as they were conceived by the ancient Architects, and show the combined Art and geometry which exists in every detail, and which must have required centuries of scientific cultivation to bring to perfection. PLATE X1V. axp PLATE XV. THE DESIGNING OF THE IONIC ENTABLATURES. Comparing together the Doric and the Ionic Entablatures, the variations in the propor- tions and in the arrangements of the several parts of the Entablatures are slight. In both there are the threefold equal divisions into the architrave, the frieze, and the cornice; but in the Ionic, in place of the mutules in the cornice, we have a curved soffit, the same as in the Pediment cornices of the Dorie order. The arrangement of the architrave and of the frieze varies in the two orders, but the principles of design are the same; in both, the Mouldings and the engraved Ornaments are composed of the ares of the conic sections, laid down in the manner already described when considering the subject of the Mouldings and the Ornaments; but in the Ionic order the Ornaments are sculptured as well as engraved upon the Mouldings, and are, therefore, relieved by lights and by shadows, and the external colouring of the Ornaments appears to have been dispensed with in the Ionic order. Thus, take for example— Plate XIV., Fig. 1.—The Ionic Entablature of the North Portico of the Erechtheium, seen from an angular point of view. The given apparent height of the Entablature from the architrave | = 26886/, we to the cymatium : : of the Entablature. = 2240" = 1st given apparent modulus 202 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. The apparent modulus 22405" x 4 = 8962" architrave ; = 8962" frieze ; — 8962" cornice. The given horizontal projection a the Entablature measured on the |= 2-217 ft., pot — (0°088 ft. = horizontal modulus for the line AB | details of the Entablature. The given apparent height of the cornice = 8962’, = 373! = apparent modulus for the details of the cornice. The values of these two moduli being given, 0-088 feet for the projections, and 373 for the apparent heights of the members of the cornice; then the details are figured in aliquot parts, as shown in Fig. 1. The apparent heights of the cornice = 4% + 5 +41 + 2 + 7 + 1 = 24 parts measured in seconds. The horizontal projections of the Entablature =1+2+4+2+11+ 2+ 2+ 5 = 25 horizontal aliquot parts. Plate XV., Fig. 1.—The Entablature of the South Portico of the Erechtheium, seen from a central point of view. The Entablature of the South Portico of the Erechtheium is an example of a different class of designs, the Portico being simply arranged in aliquot parts, without any corrections being made in the 1st given heights, and the horizontal lines are executed as straight lines. It is, therefore, the Entablature alone which is perspectively designed to suit a central point of view, which is determined by the Lower Step being exactly embraced within the visual angle of 45°. This fixes the point of sight at a distance of 3728 inches from the line of the architrave, and 135 inches below it. The whole given projection of the Entablature is found to divide into 12 aliquot parts, and the whole apparent height into 36 apparent aliquot parts. An inspection of Fig. 1, showing a section of the Entablature drawn to a scale of 7 of the real size, will explain the details. Plate XIV., Fig. 2 1s a section through the cornice of the North Portico of the Erechtheium, drawn to a scale of + of the real size, showing the curve of the soffit to be # of an ellipse. Plate XIV., Fig. 3. The detail of the architrave of the same Portico + of the real size. There are no remains of colours externally on the Entablatures of the Erechtheium, but on the ceilings, both of the North and of the South Porticoes, there are traces of the engraved Ornaments, and also of the colours. In the ceiling of the North Portico the THE OBNAMERTS, MOULDINGS, ARD ENTABLATURES, 203 Ornaments are partly engraved and partly sculptured, with evident traces of colour, and in the Maander, outlined between the lines of the beading, the blue is very distinct; the stars in each inner square appear to have been formed of metal gilt, and the Msander also was probably relieved with gold on a blue ground. In the ceiling of the South Portico there are distinct traces between the lines of beading of simple lines having been drawn, probably relieved in gold, and there are also marks of blue on the engraved elliptical Ornaments. 204 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, CHAPTER 1Y. THE SCULPTURE, PAINTINGS, AND INSCRIPTIONS. GREEK Architecture harmoniously blended the geometrical lines and forms executed in the marble, with the works of Sculpture, of Painting, and of Inscription. In the purely architectural parts of the design every branch of the ancient geometry is found to be applied, namely, the trigonometry, the perspective, and the calculations of the arcs of circles, and of the arcs of the several conic sections, and all these calculations and forms are expressed in the marble with geometrical precision. But into this geometrical framework there still remains to be introduced the celebrated works of Sculpture and of Painting, as well as the Inscriptions, before we can form a general idea of such finished works of Art as the Parthenon, the Propylea, the Theseium, ete. For a detailed account of the Sculpture and of the Paintings I must refer to the works of Pausanias, of Colonel Leake, and of Monsieur Beulé, who all treat upon these subjects, and I will simply tabulate a few of the principal works of Sculpture and of Painting that were introduced into the finished designs of the several Temples, so as to convey a general idea of their intellectual completeness, and to show how fully they must have satisfied the refined taste and the cultivated minds of the artists and of the philosophers of Greece. Tar PARTHENON. Sculpture.— Leake, page 336: “ Probably no Greek Temple of any order was ever so lavishly “adorned with Sculpture as the Parthenon. In the eastern or main apartment of the “cella was the colossal figure of the invincible virgin goddess, from whom this “ chamber m particular, and the building in general, received the name of Parthenon, “and which was an example of chryselephantine Sculpture, having but one rival in “ Greece, and that by the same master. Tn the Pediments were two compositions, no 1) THE ORNAMENTR, MOULDINGS, AND ENTABLATURES, 0 “near eighty feet in length, each consisting of about twenty-four entire statues of ““ supernatural dimensions, the eastern representing the birth of Minerva ; the western, “the contest of Neptune and Minerva for the Attic land. In the exterior frieze were “ ninety-two groups, raised in high relief from tablets, four feet three inches square, “relating to a variety of actions of the goddess herself, in which her favoured ““ champions had prevailed by means of her influence ; and lastly, along the outside “of the cella and Vestibules reigned a frieze of three feet four inches in height, and “520 feet in length, to which a relief, diahily raised above the surface of the wall “which 1t crowned, was considered most applicable, as it was seen from a nearer “ distance than any of the other Sculptures, and by reflected light. This great work “ represented the procession on the quadrennial festival of the Panathensea, when the “new peplus of Minerva was carried through the Cerameicus, and from thence to the “ Acropolis.” Painting.—Page 561 : “The prodomus and hecatompedum were adorned with Paintings, but ““ concerning them we have no knowledge, in consequence of the loss of the works of ““ Polemo and Heliodorus, except that the prodomus was partly painted by Protogenes, “of Caunus, and that in the hecatompedum were pictures of Themistocles and ‘““ Heliodorus.” Pliny says that in the pronaos of this Temple, Protogenes, a celebrated painter of ships, had represented the triremes, “ Paralus” and “ Hammonias,” together with several other vessels on a smaller scale. The painting of the Paralus” is praised by Cicero. Leake, page 151: ““ Another subject of the Paintings in the prodomus of the ““ Parthenon, according to Philostratus, was the rock, Aornus, and the fissure, which “was said to attract the birds flying over it.” Tae THESEIUM. Sculpture.— Leake, page 499: “ The eastern fronting of the Temple, marked by the greater : ““ depth of the pronaos, 1s shown still more strongly by the Sculpture. In the eastern “ Pediment only are there any traces in the marble of metallic fastenings for statues, « and the ten metopes of the eastern front, with the four adjoining of either flank, are “ exclusively adorned with figures, all the other metopes having been plain. “In the Theseium the cella was adorned, as the Temple of Jupiter at Olympia “appears from Pausanias to have been, with a sculptured frieze over the Columns “and ante of the prodomus and opisthodomus. The Sculptures over the prodomus “and opisthodomus of the Theseium are in much higher relief than the frieze of the 206 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES, ‘“ Parthenon, and, although now for the most part in a state of extreme degradation, ““ they were evidently—that of the prodomus at least—works of greater merit and “ perfection. As Micon, who painted the walls of this Temple, was a sculptor, as well ““ as a painter, there is every reason to believe that these are not only from his designs, “but that, being not very numerous, all the best of them were finished by his own “ hands.” Painting.—Pausanias, Chapter X VIL. : “Near the Gymnasium is the Temple of Theseus. Here “ are pictures, one of which represents the battle of the Athenians with the Amazones. “ There is a Painting, also, in the Temple of Theseus of the Fight of the Centaurs and “ Lapithee, where Theseus alone is represented as having slain a Centaur ; the others “ being engaged in an equal combat. The picture of the third wall is not very clear “to those who do not understand the subject, partly because it is injured by time, ““ and partly because Micon has not expressed the whole affair.” He then enters into a detailed account of this third picture, but it is too long to extract. Polygnotus was probably the colleague of Micon in the painting of this Temple. (Leake.) Tae ProrpyLZA. Sculpture.—No Sculpture appears to have been introduced into the Pediments or the metopes of either the east or the west fronts of the Propylea, but there were some separate groups of figures in the Vestibule, as we find from Pausanias. ‘In the very entrance ““ of the Acropolis are Mercury Propylaeus, and the Three Graces, said to be the work “of Socrates, son of Sophroniscus, whom the Pythian priestess declared to be the “wisest of men. Here 1s a brazen lioness in honour of Leena, the mistress of “ Aristogeiton, who was tortured to death by Hippias; besides which stands a Venus “by Calamis, dedicated by Callias. Near it is a brazen statue of Diitrephes, pierced “ with arrows; and not far from the latter (for I do not wish to speak of the portrait- “ statues of persons of little note) are a Hygieia, called the daughter of Aisculapius, “and a Minerva, surnamed Hygieia.” Painting.—* On the left of the Propylea is a building containing pictures. Those which are “not obliterated by time represent Diomedes bringing from Lemnos the bow of “ Philoctetes ; Ulysses carrying off the statue of Minerva from Troy; Orestes slaying “ Kgisthus, while Pylades kills the sons of Nauplius, who came to the assistance “of Algisthus; Polyxena about to be sacrificed at the tomb of Achilles; Achilles “ disguised among the virgins of Scyrus; Ulysses encountering Nausicaa, and her “ attendants washing clothes at the river (as described by Homer); the two latter by “ Polygnotus.” Pausanias mentions the names of several other pictures that are in the same chamber. THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. 207 INSCRIPTIONS. In the works of Egypt, after the surfaces of the design were all prepared, the hiero- glyphical Inscriptions formed an important part of the ornamental details; but as both Sculpture and Painting attained in the hands of the Greek artists a higher degree of perfection than that which we find in FEgypt, so they were employed to express much that in the earlier designs of Fgypt would have been hieroglyphically written; yet, even in the remains of Greek Architecture, the Inscriptions form an important division of the Art, and add considerably to the general interest of the design. In the Acropolis of Athens there is ample evidence of different Inscriptions having been executed on separate stones, and placed with the sculptured groups within the enclosure, thereby adding much to the mental interest which is excited by this repository of the Athenian mind ; but the artists of the time of Pericles do not appear to have introduced so many Inscriptions upon the surfaces of the architectural designs, as we find to have been the case in Egypt, or in the Ionic Temple at Priene. At the east end of the Parthenon gilded shields, with Inscriptions between them, were arranged along the architrave, but, according to Colonel Leake, these were introduced long after the building of the Temple. In Francoeur, ¢ Traité d’Astronomie,” page 90, is the following passage :—* Si l'on avait une serie de 19 anneés d’observations lunaires, les phases “reviendraient périodiquement dans le méme ordre, et T'on pourrait prédire les dates des ““ retours de ces phases dans chacune des périodes suivantes. Le cycle lunaire de 19 ans fut ‘“adopté des Athéniens I'an 433 avant notre ere, pour regler leur calendrier luni-solaire, et “ils en avaient fait graver le calcul, en lettres d'or, sur les murs du Temple de Minerve.” In the Erechtheium, the Propylea, and the Theseium there are no Inscriptions on the surface of the work, but in the Monument of Liysicrates one is found on the fascize of the architrave, so that in general the Athenian Architects seem to have preferred making the Inscriptions together with the separate groups of statuary, blend with the design, but form no part of the surface. This was reserved more particularly for the dass relieve and for the Paintings. 208 THE ORNAMENTS, MOULDINGS, AND ENTABLATURES. CHAPTER YY, THE SPIRAL ORNAMENTS. Besmes the Greek Ornaments to which we have already referred, there is another class of Ornaments, composed of spiral lines, which appear to have been suggested to the Greeks by the many beautiful spiral forms that are found in nature, such as the spiral shells, &c. Thus, taking for an example the section of a spiral shell, the Ammonite, Fig. 1, traced full size from nature, we find that the curved spiral lines can be described within a rectangular THE ORNAMENTS, MOULDINGS, AND ENTABLATURENS, 209 spiral line, the same as in the Ionic volute ; and that the ratio of diminution of one side to the next is throughout as 4:3. Within these rectangular lines the curved spiral can be described very nearly as the ares of circles, but in nature the spiral is a curve, approaching uniformly to one common centre. In the above spiral shell, and in the Ionic volutes, we have examples of these curved spiral lines, described within rectangular spiral lines, diminishing in some given ratio; and in the consoles to the doorways of the Erechtheium, and on the roof of the Monument of Lysicrates, we have other examples of spiral lines, combining with the arcs of the conic sections to form an Ornament, which is equally geometrical with the other Ornaments, and which probably originated in the Greek schools of geometry. a rags Sim ime Fig. 2. | i Is the console ofthe doorway of the Krech- theium laid down in a similar manner. | There may be an endless variety of the combinations of spiral lines, and they are probablyall designed in a similar manner, but to do justice to the subject of the designing of the Greek Ornaments would require a separate work. The same principles that we meet with in the designing of the Mouldings, and of the several varieties of Ornament in the Architecture, will apply equally to the designing of the vases, of the works in bronze and in metal, of the furniture, and to every branch of Greek manufac- tured art. The Greek ideas of art appear always A i to have been controlled and perfected by — C the laws of geometry, and where geometry | 7 + was absent the decline of art was rapid, | DR r as we find was the case in the Roman de- 4 signs of the Ornaments. | | iH | ’ mens Seb ano SE Erni id THE EXD OF PART TIVE. 211 PART V1 ROMAN ARCHITECTURE. ROMAN ARCHITECTURE. 213 INTRODUCTION. Arr that we meet with in Roman Architecture applies as much to the buildings of modern Europe as to the Monuments of ancient Rome, and Mr. Fergusson truly remarks that we “feel in Rome we have to deal with a great people, who for the first time in the world’s ““ history rendered Architecture subservient to their many wants.” In Greece the Portico is the leading feature in the Architecture, but in Rome, in addition to the Temples, we find Basilicas, Baths, Palaces, Tombs, Arches of Triumph, &e., &c., many of them works stamped with great originality of thought, and worthy in conception, although not in execution, of the designs of the Greek Architects: but in every Greek architectural design we have the pure geometry combined with the best sculpture and painting, and such a work as the Parthenon will always remain unrivalled as an example of true Art, and will be studied as the Grammar of Architecture. In Rome we see the decline of a pure taste, the geometry in a great degree laid aside, and coloured marbles and rude ornaments substituted for the more refined architectural forms and sculpture of the Greeks: still the Roman Monuments take rank next to the Greek in point of excellence as works of Architecture, and more than bear comparison with any buildings that have been erected in the modern capitals of Furope, and they are, therefore, well worthy of the careful study of all those who follow Architecture as a pursuit. When we pass over the period that elapsed between the meridian of Athenian Art and Science, in the age of Pericles, B.c. 450, and approach the consideration of Roman Art, about the commencement of the Christian era, we shall perceive that the natural characteristics of the Greeks and of the Romans are clearly to be traced in their works of Architecture. In Rome we meet with the remains of Temples and of Palaces more extensive, and, when taken collectively, more costly, than were ever erected in a single city by the Greeks. Augustus boasted, with truth, that he found his capital of brick and left it of marble, and certainly, if we compare the number, the extent, and the costliness of the works executed during the administration of Pericles with those erected by the command of Augustus and of his successors, the balance is, perhaps, in favour of Rome : but if the Romans encouraged the 214 ROMAN ARCHITECTURE. construction of costly works, they also discouraged the cultivation of the sciences of Greece, which alone were able to stamp their works with the marks of true intellect. In the words of Montucla, page 406— ““ Lies sciences ne firent jamais chez les Romains des progres proportionnés a ceux “qu'on leur vit faire dans la Gréce. Ces conquérans de 'Univers uniquement occupés du “soin d’etendre leur domination, ne s'avisérent que fort tard d’aspirer a la gloire d’étre “scavans et éclairés; il-y-eut méme a diverses reprises des décrets du Sénat pour chasser ““ de Rome les philosophes et les rhéteurs qui apportoient dans cette capitale les sciences de “la Grece; si ces ordonnances ne parvinrent pas a detruire dans I'esprit des Romains le gout “ des lettres et de I'éloquence, elles influerent du moins tellement sur la philosophie et les “ mathématiques moins attrayantes par elles-mémes, qu'on ne compte parmi eux qu'un fort “ petit nombre d’hommes qui aient eu des connoissances plus qu'ordinaires dans ce genre. “ Les mathématiques surtout furent extremement negligées a Rome, et la géométrie a “ peine connue ne 8'y éleva guere au-dessus de Art de mesurer les terres et d'en fixer les “ limites.” Gibbon also bears testimony that this lowered intellectual standard was not alone confined to the mathematics, and to Art. He says— “The love of letters, almost inseparable from peace and refinement, was fashionable “among the subjects of Hadrian and the Antonines, who were themselves men of learning “and curiosity. But if we except the inimitable Lucian, this age passed away without ‘““ having produced a single writer of original genius, or who excelled in the art of elegant ““ composition. “The authority of Plato and Aristotle, of Zeno and Epicurus, still reigned in the ““ schools, and their systems, transmitted with blind deference from one generation of disciples ““ to another, precluded every generous attempt to exercise the powers or enlarge the limits of ““ the human mind. “ A cloud of critics, of compilers, of commentators, darkened the face of learning, and “the decline of genius was soon followed by the corruption of taste. ““ Longinus, who in somewhat a later period, and in the Court of a Syrian Queen, ““ preserved the spirit of ancient Athens, observes and laments this degeneracy of his con- ““ temporaries, which debased their sentiments, enervated their courage, and depressed their “talents. In the same manner, says he, as some children always remain pigmies whose “ infant minds have been too closely confined, thus our tender minds, fettered by the prejudices ROMAN ARCHITECTURE. 215 ““ and habits of a just servitude, are unable to expand themselves to attain that well-proportioned “ greatness which we admire in the ancients, who, living under a popular Government, wrote ‘““ with the same freedom as they acted.” Vitruvius, in his work upon Architecture, says, Book I., Chapter I.—¢ Arithmetic, “assisted by the laws of geometry, determines those abstruse questions wherein the different ““ proportions of some parts to others are involved.” And this is quite true of Greek Archi- tecture ; but when Vitruvius is treating practically of Roman Architecture he makes no allusion to the problems of Iuclid, to the trigonometry, or to the conic sections, all of them branches of the ancient geometry, and without which no Greek design was ever laid down and prepared for execution: but many of the finest works of Roman Architecture still remain, and the principles involved in the designing of them can be inductively recovered, the same as in the designs of Egypt and of Greece, and when this is done we shall be in a position to compare the Architecture of Greece and of Rome, and to mark the existing points of agreement and of difference between them, and thus ascertain from actual observation whether the Roman architectural remains bear their own testimony, added to that of history, to the general neglect by the Romans of the cultivation of the ancient geometry. For this purpose, without entering minutely into Roman Architecture, which would require a voluminous work, it will be sufficient to consider in detail the remains of the four existing Corinthian Porticoes which were designed and constructed during the best period of Roman Art, namely— The Porticoes of the Pantheon, of the Temple of Jupiter Tonans, of the Temple of Jupiter Stator, and of the Temple of Antoninus and Faustina, all of them executed in marble, and erected between the time of the Emperor Augustus, B.c. 50, and that of the Emperor Antoninus, A.p. 161. Our attention has hitherto been confined to the Doric and to the Ionic orders; but all the Roman Porticoes are of the Corinthian order, and we shall, therefore, connect together the Greek and the Roman Corinthian examples by commencing with the Monument of Liysicrates, executed B.c. 335, the oldest example of the Corinthian order, and one which possesses more- over a peculiar value, as an example in which the first given aliquot parts are the executed quantities, the same as in the South Portico of the Erechtheium, and as we shall find to be the case also in the Roman Porticoes. In all these works the apparent magnitudes for the determination of the small ““ additions and diminutions ” were not trigonometrically calculated, as in the larger Greek designs. For the sake of comparison, it will be convenient to follow, in the consideration of Roman Architecture, the same arrangement of the subject that we have already made in the calculating and in the laying down of the designs of the Greek Architects: therefore 216 ROMAN ARCHITECTURE. Chapter I. contains—1st. The proportions of the Monument of Liysicrates, compared as a Greek example of the Corinthian order with the Roman Corinthian. 2nd. The positions in the Roman Forum, with regard to the Sacred Way, of the Temples of Jupiter Tonans, of Jupiter Stator, and of Antoninus and Faustina, to ascertain whether these positions were at all considered in the Roman designs in respect to any fixed points of sight. 3rd. The lineal given proportions of the Porticoes of the Pantheon, and of the Temples of Jupiter Stator, of Jupiter Tonans, and of Antoninus and Faustina. 4th. The designing of the masses of the Roman Porticoes, to which the calculated apparent magnitudes, and the curvature of the horizontal lines of Greek Archi- tecture do not apply. Chapter II. The designing of the Roman Corinthian Columns. Chapter III. The designing perspectively of the Roman Corinthian Entablatures, with a few short notes on the interior Architecture of Rome. Note.—The dimensions given are all taken from Taylor and Cressy’s ““ Archi- tectural Antiquities of Rome,” published in 1821. Fort Vi. Plate 1, THE CORINTHIAN MONUMENT OF LYSICRATES. Designed B.C.335, 2 $f 3 3 3 3 i 8 r 3 Fa an I i ee 3 3 I yf 3 i] ¥ 13 a fornsnge Bi tnnan ns 3 R oo. 2.025 X 49=399. 225 Architrave..... i . i 3 ir } 3 ; l(a Wr ] x i 5) SA el =) 3 3 S i 5) er 77 3 = fede by i | EL Bl > ; L 2 & 3 | Li 13 58 4 ¥ | | S00 y | 2 i 3 hi Fd 4 EEE hirer | & a Te 2.025 X 69 =719.475 =middle step of Corona ...._..., Fig. 1. Let AB The square Cornice of the Plinth =129-59 be divided into 64 aliquot parts 129.59 = 2.025 = modulus for the horizontal : ahd. vertical dimensions jess 2.025 % 63=127. 57 = Lower crcl SLeP ooeeeu een nnnnena Let C D The diameter of the Lower circular step = 2.025 x 63=127.57 : 4 Let C E The whole height of the circular Monument — twice the lower diam - wn ater == 3.025 *126 == 255.14 = 127.57» 2 et 2-025 x 64=129 57 = square cormce of Phndb gs Let the whole height of’ the circular Monument mcluding the Tripod 2 ! anal 156 Moduli. 150 Modnk a 2.025 x 96 = 113 4 — square mass a" FPlanth.... 5 Let the height of the square plinth equal 5 = 75 Moduh Heights . Sotntl Znvmsdons Siylobate = 2025x 8 = 16.200... 16.25 | Colarnn = 2025 x69 =130.725....... 130.65 | Fotablobwre..... oie = 2025 = 16 = 32.400........ 32.42 ree ROGE..ooooereo 0 = B00» Dw R225 18.25 Stand for Tripod .................. = 2.025 x 2) = 45.600....... 48.85 = 2.025 x126 =255.150 Tripod. =2.025 x 24 = 48.600 Height of square Plinth = 2.025 x 75 =151.870 : Horizontal Dimensions. Square Cornice of Phnth = 2.025 x 64 =129.59 Lower circular Step ........... = 23025 x63 =127.570... 128.3 Middle circular Step. = 2025 x BY ==119.475....... 119.8 Corona .........iceeeeeen....™ 2.028 x 83 =H 475 2 Avclitrava.................0c... - 2025 x49=099 ...... 99.8 / Lower diameter of’ Column: = 2.025 x 49 = 99.9 / 3? In thas example no corrections are made in the Vertical heights but the | . Entablature 1s designed perspectively from the given point of sight 0 meetin DTI sed mmm 00 embracing the whole height of the de s16n within the given angle of : 1 = 45° pegtatr?? ROMAN ARCHITECTURE. 217 CHAPTER 1. THE PROPORTIONS. PLATE 1. THE CORINTHIAN MONUMENT OF LYSICRATES. (B.C. 335.) TaE inscription upon the Monument of Lysicrates shows that it was raised in the archonship of Evaenetus, who held that office when Alexander the Great passed over into Asia, or about the year B.C. 335. It is probably one of the earliest specimens of the Corinthian order, and possesses a special interest, as being the only existing Monument in Athens of the Corinthian order executed during the best period of Grecian Art. It is also an example of a Greek design, the same as the South Portico of the Erechtheium, in which the vertical corrections upon the first given design are omitted, and the Entablature alone is perspectively designed to suit a given point of view. The ornaments also are sculptured the same as in the Erechtheium, and, I believe, no traces of colour have been found to exist externally upon them. In both these respects it is similar in design to the Roman Corinthian Porticoes, and thus becomes, with the South Portico of the Erechtheium, a connecting link between the Architecture of Greece and of Rome, and serves as an introduction to Roman Architecture. Tae GENERAL GIVEN Proportions or tHE MoNuMmENT oF Lysicrates. (Fig. 1.) The circular Monument rests upon a square plinth, the cornice of which, AB, = 129-59 ins. in length ; then divide AB into 64 aliquot parts. 218 ROMAN ARCHITECTURE. 129-59 64: = 2025 = the given modulus for the horizontal and the vertical dimensions of the design. Let CD, the diameter of the lower circular step, = 2:025 X 63 = 127-57. Let CL, the whole height of the circular Monument, = (0D x2 = 127-57 X 2 = 255-14 inches = 2:025 x 126 parts. The whole design of the Monument is, therefore, contained within a cylinder two diameters in height. The proportions given on the Plate, along with the description, will explain themselves without a second repetition. SUMMARY OF THE HEIGHTS. The arrangement of the Steps. Column. Entablature. Roof. i oa Tripod. heights in aliquot parts} 8 + 69 +16 + 9 + 24 + 24 =150 aliquot parts. 18 The given dimensions in : : 16:2 + 139-72 + 82:4 + 18-225 + 48:6 + 48:6 = 30375 mches. inches are . : The height of the square plinth is made equal to half the height of the Monument, 30375 : : “= = 151'87 inches. 9 CoMPARISON OF THE HEIGHTS wiTH THOSE oF THE lIoNi¢c Portico oF THE NoRTH PORTICO OF THE KERECHTHEIUM. Comparing the height of the Steps + the Column + the Entablature, 188-32 inches, with the given height of the North Portico of the Krechtheium, which divides into 35 aliquot parts, we shall perceive that the proportions are almost identical : thus— on — 5'88 = modulus. The Monument of Liysicrates, The arrangement of the heights in aliquot parts | Steps. ~~ Column. Entablature. : : 8 + 26 4+ 6 =2385 aliquot parts. in both examples 1s 1 | The oj di in inches in the Monu- e given dimensions in inches in the Monu 16-14 + 18088 + 32-98 13532 inches. ment of Liysicrates are It, therefore, appears that, without altering the proportions of the masses of the Ionic Porticoes of the Erechtheium, they might be changed into Porticoes of the Greek Corinthian order. The designing of the details of the Columns, and also the perspective designing of the Entablature, will be considered, in connection with the Roman Columns and Entablatures, in Chapters II. and I11. ROMAN ARCHITECTURE, THE POSITION OF a 7] °e RC TITUS 219 THE ROMAN TEMPLES. When considering the Architecture of Egypt and of Greece, we found that the spectator was always led by the artificial arrangement of the roads and of the enclo- sures, to view the designs from certain favourable points of view. In Egypt, avenues of Sphinxes led to central Propylsea, which formed the entrance to a series of Inner Courts. In Greece the Temples were generally approached so as to be seen from angular points of view, as shown in the plan of the Athenian Acropolis, and the question may naturally be asked whether, in the Roman Forum and in other designs, the positions of the Temples were at all considered with reference to any fixed points of view, the same as in Kgypt and in Greece. Tae Roman Forum. (See Figure.) In the Roman Forum, the line of the Sacred Way can be traced with certainty from the Arch of Septimus to the Arch of Titus, and supposing the Temple of Jupiter Stator and the Temple of Antoninus and Faustina, to have been viewed from central points of sight, embracing the Lower Steps within the usual angle of 45° then both these Temples were so arranged in position, that the given points of sight appear to be exactly in the centre of the Sacred Way. In the case of the Temple of Jupiter Tonans, the central point of sight seems to be on a line of road almost at right angles to the Sacred Way, and central with the Arch of Septimus. 220 ROMAN ARCHITECTURE. THE PANTHEON. With regard to the Pantheon, which is situated in the Campus Martius, we can form no opinion as to the enclosures, or to the roads of approach ; but the Portico, which is one of the | finest in Rome, appears to have been designed to be seen from a central point of view, the same as the other Roman Porticoes, and it was so arranged, with regard to the circular part of the building, by giving to it greater width and depth, and increased height to the Pediment, that from the given central point of view, the Portico only was seen as a distinct and perfect design ; then, passing underneath the Portico, and entering the circular portion of the Pantheon, we have a second design, namely, the interior of the Temple, with a magnificent dome ; this dome was quite unique at the time it was designed, and was a work worthy in conception of taking its place along with the best designs of the Greek Architects. We thus have combined in this building two distinct designs—an exterior Portico, complete as a design, and an interior circular design; the latter has never been surpassed for originality of conception; and the two designs are so arranged as not to be seen together, in the same way that the Propylea and the Erechtheium, in Athens, are each of them combinations of three separate designs. The Temples in the Roman Forum were certainly not enclosed in the same manner as we find to have been the case with the Temples in the Acropolis of Athens, and with other Greek designs, and it was evidently intended that they should be seen from central, and not from angular, points of view, still they appear to have been so arranged that the eye exactly embraced each Portico within the angle of 45°. The evidence 18, I think, in favour of the conclusion that in the designs of Egypt, of Greece, and of Rome, the position of the design with regard to the roads of approach and to the eye of the spectator, was always carefully studied and adjusted. In the case of the Roman Porticoes, the Entablatures being perspectively designed, the same as in Greece, establishes the fact of their having been designed to suit certain given points of view. We may now proceed to the consideration in detail of the several Roman Porticoes, commencing first with the given general proportions of each Portico. PLATE 11. ax PLATE 111. THE DESIGNING OF THE MASSES OF THE ROMAN PORTICOES. In Athens we are able to decide at once what the general proportions of any Doric or Ionic Portico are likely to be, but in Rome each Portico appears to be an independent design, PartV]. Plate ll THE DESIGNING OF THE MASSES OF THE ROMAN PORTICOES. io 7 y { | 2 BIEL § yr 3X 3 PI ose > F 233% yr 2 3 - Tx > ~ ~ xX 3% 11 ious 3 13. Zi ai aii 3 i] 212 2538s 5 3 Fa 3 i 21 3 12: goo « } Bo 3 1 3 1 2 %e83 4 aw = 2 > > X= $i. : §§ : Fi. F134 2 iz G i 3. 5.37 2 3 3 s 2 883% 3% 1 3: 31. a E ! Lo ru i ~ 12 % dogs I 404 5 5 : ! S 1g! 3 vse 3.3 83 = 2 L021 dius Fi 3 4 it 3 ® . Xx Be = I x x Q XN : : : Tn 3 : PT gE 1 grEar Fora B ERR RE) 1] 1 £3 RYE 3 2 8 Ax ‘3 1 x : RS 133 1 | 3% ¥ : 3 #3 iS | | | ES £3 14d AY | FF : S A 1S be < ” 3 : 0 ; 3 13 3: {4 77] % Tes 388333 °C §.V IE 13 alals 131.3 | iT AAR iii S RS ® < : . ; 23 WE) 1 N : ~ * R | ikke I iil 51 jee TRE Y IGiET 3 ‘| £Xs3 2% SRS TFSI SE 2" 3 53 CE RCRTI EIN ~~ NE 2.3 2% 3 9% v9 $F Fawn | $ ® ¥ x yr 2 5 un 3 WE | remind be bo ai | os 3 + hie nn +t free} ! ZR fetrrpememerers eben wy Fare 2 > ay TL TE oe. Ea , Pes am 7 sary ig aL Cw ga gpgEthrceterrsecnceninieenasies Lise Toro we .. Ay LHe a : -spavd : resin sod pon a} TTT sud : 2 7 a a 2 S NN EY] S | L A *1 \ $1 N N 3 N N S 3 IN Ny mb = ON SE ed \ NN N 7 ’ ’ ’ ’ ” 7 s ’ ’ ’ ’ / ’ ’ 7 / ’ \ ’ ’ - Z . 1 ' 1 I 1 i | I I I 1 | | 1 \ i \ \ \ Ee & 20 72 evr 1 78 20 22 2 C2 28 30 30 9 50 38 40 © oo» fretless eee reeset rae peepee fei ; 66.6.4 80.2 5 66.6 5 80.2 566.6 5.80.2. 5 71.7 4 80.2. 566.6 ; 802 , 66.6 80.2 566.6 4 80.2. : ; : | i ! Ge A 67 Eo L L \ NN \ 2 4 6 2 2 os so gr gg 0 I 4p ttt te fesse emerson], | 8.35 ey. DBD. 88 58. Lye OB VD ny. 53.28. I5ND 33. 05.20. oe 85.95 OF NEy B5 35 IF ND B88 2G ope VEN oo 85.28 uy 7 5 22 30 37 a 62 61 68 76 83 97 98 70: i 1 1 I 1 | 1 I 1 | 1 ' 1 ' ’ ' | ' I 1 I 1 I 1 J 1 1 | ! 3 1 1 SE SAN o . 0.2 op \ eee] | Bh hiss 1 L 1004. i EET oe Vv a di - Call] Sotth. Croll SE mon LL Lon inners. Ad, k----80 798. 66. ® y—-80 798 x. 66. 1__y._. 80.79 OO 2 I. _.x---.80 THE DESIGNI Tae M oF THE RoMaN Porrico Figl. The Jup ans hh oo co ng db 1 fon i — containing the \ | i A Y | | Hrtorandl, dnmsions ! In Rr eR Sema boom) 2.5. A id = LL _ _ i Get ne o 00 0 0® rz re | s lumnia Tie Ems YY spar tm ws. 4" di he : | BR | _ | | | nt AB—829. 826 ins. be divided into A ? : BC_ 509 52 _ 21. 53 — guven, modulus BB h | | 1] as CB 3 A hm E . | | i a rm ee en cn may 38 1 : ae > - 7 M e © ge -80 798g 66. 1...4...80 TIE sp... 5 gz #1 + fue + + JT. + 8 SK 66 Pr © N 13 . . \ rg T A BL 61 a rm 154 48 v | | ' 67 124 | . } ph; . hadi ——_-——-——— + + " | a pe FE | ERY ! | 1 1 Wl bl lung TT | | \ 5 e Columns and the Intercolumniations John Jiotinaon del. ¢ F Hell. Lith Castle F ¥ London J. { 3 A ROMAN ARCHITECTURE. 221 although in the arrangement of the heights the proportions agree very closely with the given proportions of the Ionic Porticoes in Athens. There is an agreement also in the divisions of the heights and of the widths of the Porticoes into some given number of aliquot parts, and in one of these parts being taken as a modulus, and the heights of the Steps, of the Columns, of the Intablature, and of the Pediment, being made multiples of this given modulus. In Greece these first given heights in the larger designs, as in the Parthenon and in the Propylea, underwent a correction, so that when they were viewed perspectively from the given point of view, they should still all appear to be exact multiples one of another. This correction in the smaller designs of the Greeks, as in the South Portico of the Krechtheilum and in the Monument of Lysicrates, was omitted, and these designs were executed as they were at first laid down in the lineal aliquot parts; and in the Roman Porticoes, also, the small “additions and diminutions ” found in Greek Architecture were omitted, and the masses of the Porticoes were executed as they were first designed in the original aliquot parts. The Upper Step of the Portico was not so clearly defined a quantity in Rome as it was in Athens, still some general width of the Portico was always given, such as the line of the Architrave, or the width of the Stylobate, &c., and in each example some common modulus was determined which regulated all the heights. The examples that have been selected to illustrate the Roman methods of designing the Porticoes are the two octastyle Porticoes, known as the Pantheon and the Temple of Jupiter Stator, and the two hexastyle Porticoes, called the Temple of Jupiter Tonans and the Temple of Antoninus and Faustina. Tae Panraeoy. (Plate II., Fig. 1.) The Pantheon consists of two designs—I1st. An exterior Corinthian Portico ; 2nd. A circular interior, with a domed roof; this interior was mentioned by Pliny as a novelty in his time. The Portico is one of the finest in Rome, and measures 109 ft. 11 ins. in length, and 81 ft. 11 ins. in height; it is constructed of a combination of polished granite and marble ; the shafts of the eight front Columns are of grey granite, and those of the ner ones of red oriental granite, each shaft is formed of a single block, 38 ft. in height and 5 ft. mn diameter. The bases and the capitals of the Columns, as well as the Entablature and the Pediment, are of white marble; therefore, in size, and in the costliness of the material employed, this Portico is not inferior to that of the Parthenon at Athens. 222 ROMAN ARCHITECTURE, The proportions of this Portico differ from those of other Roman examples, the inter- columniations being wider, consequently the height of the Pediment is increased, and the reason for this might have been that, when looking at the Portico from the central point of view, it should be seen as a complete design in itself, without either the circular walls of the Temple or the dome appearing externally ; then, passing underneath the Portico, the spectator entered into the circular Temple, designed to be seen only as an interior architectural work ; but our attention is now confined to the proportions of the Portico, which may be laid down as follows— Tae DESIGNING OF THE PORTICO OF THE PANTHEON. Describe the parallelogram, ABCD, containing the mass of the Portico, with the sides, AB and BC, as 5 : 4. Let AB = the length of the Architrave = 131144 ins. ; AB: BC::5:4::1311'44 ins. : 1049-15 ins. = BC = whole height. The whole height BC = 104915 ins. = 32786 = given modulus for the heights and for the projections. 32 32 The Given Heights. Inches. Measurements. Steps : : : : =U X 3 =~ (5572 Column . : : : . == 892786 X 17 = 557-360 55720 Entablature ; : : , , = S786 X 4 = 131'144 131-60 Pediment . : : : : . = 82786 X 9 = 295-070 294-80 The Horizontal Dimensions. Inches. Inches. Length of the Architrave . : ; ; . == 32-786 X 40 = 1311-144 id Length of the upper diameter of the Columns . = 82-786 x 40 = 1311-144 Length of the Cornice : : . = 82786 X 43 = 1409-798 Length of the line, MN, measured along the base = 82-786 X 41 = 1844-2 of the Columns | The Arrangement of the Columns and Intercolumniations. The given length of the base line of the Columns, MN, = 82786 X 41 = 1344-2 ins. ; then along this line, MN, are set out the widths of the bases of the Columns and of the intercolumniations, as follows—— MN 1344-2 Divide MN into 113 parts, Bm = 11'89 = the given modulus. Inches. Let the square plinths of the bases of the Columns = 7 parts = 11:89 X 7 = 83:23 Let the intercolumniations, except the centre one, = 8 parts = 11-89 Xx 8 = 95-12 Let the centre intercolumniation . = 0 parte = 11-80 X 9 = 10707 ng: . : = 086 = given lower diameter of the Columns. BOMAN ARCHITECT URL, 293 Tae DesieNiNg oF THE Portico or THE TeEmpLe or Jupiter Stator. (Plate II., Fig. 2.) The octastyle Portico of the Temple of Jupiter Stator is perhaps one of the best examples of the Roman Corinthian order. It is built of white marble, and was intended to be seen from a central point of view. A marble staircase, 22 ft. 8 ins. in height, led up to the base of the Columns by two flights of Steps. The width of the mass of the Portico, AB, appears to have been 98 ft. 3 ins., the same as the whole height of the Portico BC. The design was, therefore, embraced within the given square ABCD. The Portico of this Temple, nearly 100 ft. square, built of white marble, must have been one of the principal works erected in the Roman Forum during the best period of Roman Art. | The proportions of the Portico may be laid down as follows— Describe the square, ABCD, containing the mass of the Portico, and let AB = BC =1179-2 ins. be divided into 52 parts. oe Bn 22677 ins. = modulus regulating the heights. 2. Wm The Given Heights. Inches. Inches. Let the basement, designed as two flights of Steps . = 22-677 X 12 = 272-124 Height of the Columns : : ; ; . = 22-677 X 24 = 544-248 Height of the Entablature : ; ; .=22:677 X 6 = 136062 Height of the Pediment . : : : , = DBT7 X10 — 226-77 The whole height . : . = 22-677 X 52 = 1179-204 The Horizontal Dimensions. : Inches. Inches. Given length of the Stylobate AB : ; . = 22-677 X 52 = 1179-204 Given length of the base line of the Column MN . = 22677 X 49 = 1111-173 Given length of the line of the lower diameter of the = 22-677 X 48 = 1088-496 Columns Ap ws Ru = 3'77 = modulus for the projections. Given length of the Architrave : . = 108849—3'77 X 2 =108095 Given length of the Cornice , = 108093 + 377 X 80 — 1194-05 224 ROMAN ARCHITECTURE. The Arrangement of the Columns and of the Intercolumniations. Inches. Inches. The given length of the base line of the Columns, MN = 22-677 X 49 = 1111-173. Let the line, MN, be divided into 101 parts, MY _ NUIT 11-0072 = modulus 10 = 1; for setting out the Columns and the intercolumniations. Inches. Inches. Base of Columns . ; : : : =11:0072 X 7: = 798 Intercolumniations . : : . : ‘ = 110072 X 6 = 6604 Centre intercolumniation . : . ; . =11'0072 X 7 =T705 Inches. Height of Column, 544-248 : Sah of Coven, © = 57-289 = given lower diameter of the Columns. 9} Tae DesioNixa oF THE Portico or THE TEMPLE oF Jupiter Tonans. (Plate III, Fig. 1.) The Porticoes of the Temples of J upiter Tonans and of Antoninus and Faustina are built of marble. In the case of the Temple of Jupiter Tonans the Columns are composed each of three blocks of white marble, and in the Temple of Antoninus and Faustina the shafts of the Columns are of Cippolini marble, each in one piece, 4 ft. 10'3 ins. in diameter, and 38 ft. 3 ins. in height, and the rest of the design is executed in white marble. In these several Porticoes the heights of the Columns only slightly vary. Thus, both in the Pantheon and in the Temple of Jupiter Tonans, the Columns are 557-2 ins. in height ; in the Temple of Antoninus and Faustina they are 559-7 ins., and in the Temple of Jupiter Stator 544-248 ins. in height. | Tae Given PRrRoPORTIONS. Describe the square, ABCD, containing the mass of the Portico, and let AB = BC = 798 ins. be divided into 20 aliquot parts. Inches. BO _ T° _"899 — the first given modulus of the Portico. 20 ~ 90 The Given Heights. Inches. Inches. The Columns . . : : : : , = 309 X14 = 5586 The Entablature ; ; .=3899X 3 =1197 Mheloliuent © a. oa. a S=200% 3. 107 Thowlole bel BO. . .. . . i. = 800%00 = 7050 The height of the Stylobate : : , = 399 X 4% = 1795 The Given Horizontal Dimensions. The length of the Stylobate AB : ; : . = 899 X20 = T7980 The length of the Architrave . es . . = 899 X 191 = 7680 399 5 = "798 = the given modulus of the projections. ROMAN ABCHITECTURE. 225 Inches. Inches. From the Architrave to the lower diameter of the Columns = "798 Xx 5 = 3:99 From the Architrave to the edge of the Cornice : .="TI8 X55 = 4389 Whole length of the Cornice = Architrave . = 7680 + 43:89 X 2 = 85578 The arrangements of the Columns and of the intercolumniations are given on the Plate. Tae GivEN ProprorTIONS OF THE PORTICO OF THE TEMPLE OF ANTONINUS AND FAUSTINA. (Plate I11., Fig. 2.) Let the given width of the Steps, measured along the line AB = 839'826 ins. = whole height BC; then describe the square, ABCD, containing the first masses of the Portico. Let the given height, BC, be divided into 39 aliquot parts— bd oi Lo = 21'534 = modulus for the heights of the Portico. The Given Heights. Inches. Measurements. The height of the Steps above the Pedestal . = 21534 Xx 1 = 21-534 ” - Columns . ; . = 21'534 X 26 = 559-884 5597 " Entablature : .=215834 Xx 6 = 129-204 1292 Pediment : ; = ABB x 6 = 1200204 The whole height ; , ; . = 21534 X 39 = 839-826 The height of the Basement ; : m= 584 X B= 172272 The Horizontal Dimensions. The length of the Stylobate AB . : ] : . = 21-534 X 39 = 839-826 ” Architrave : : . = 21'534 X 87 = 796758 i? Cornice . : ; : . = 21-534 X 42 = 904-428 Ee = 2691 — the given modulus of the projections. The length of the line, MN, measured along the | Stylobate. : = 839-826 — 2691 x 5 = 826-371 base line of the Columns . : : | The arrangement of the Columns and of the intercolumniations is given on the Plate. 226 ROMAN ARCHITECTURE. A COMPARISON BETWEEN THE GENERAL PROPORTIONS OF THE GREEK AND OF THE ROMAN PORTICOES. The heights and the widths of the masses of the Greek Porticoes were all laid down according to certain general scales of proportion, and in Greece the variations from these first given proportions are very slight, and are only made for some special reason, so that, the Upper Step being given and the nature of the Portico known, we can tell almost with certainty what the first proportions will be. The Roman Porticoes differ from the Greek, and are designed within a given paral- lelogram or square, ABCD, and then the whole height, BC, is divided into a given number of aliquot parts, and these parts regulate the heights of the Columns, of the Entablatures, and of the Pediments ; and when we compare the arrangement of the heights of the several members in the Greek and in the Roman Ionic and Corinthian Porticoes it is seen that the Roman Architects were evidently influenced by the earlier Greek proportions. Thus the whole given height, BC, of the Greek Ionic Porticoes is divided into 35 or 36 aliquot parts, according to the example; then 26 or 27 parts are given to the height of the Columns, 6 parts to the Entablature, and 3 parts to the Steps; and taking this scale of parts as a standard of comparison, then the heights of the several Greek and Roman Porticoes may be given as follows—— The Heights of the Greek Porticoes in Moduli. Columns. Entablature. Steps. The East Portico of the Erechtheium . . : : 7 = 85 + 3D The Ionic Porticoes at Priene . : : . 2 + 6 + 3 The North Portico of the Erechtheium : 28 + 6 + 3 The Corinthian Monument of Lysicrates : . : 2 ..+ 6 + 3 The Heights of the Roman Porticoes in Moduli. Columns. Entablature. Steps. The Corinthian Portico of the Temple of Jupiter Tonans . 28 + 6 + 3 The Corinthian Portico of the Temple of Antoninus 2% + 6 + 1 and Faustina . ; The Corinthian Portico of the Pantheon 25 + 6 + 3 The Corinthian Portico of the Temple of Jupiter Stator . 24 4+ From this we see that the variations of the proportions between the Greek Ionic Porticoes and the Roman Corinthian were not very considerable, and that the same general proportions would have suited either the Ionic or the Corinthian order. ROMAN ABCHITECTURE. 227 In Greece the first given height of the Pediment was always made equal to ; the length of the Cornice, and was then corrected to harmonize with the apparent magnitudes, but this rule does not apply to the Roman Pediments, which are given in aliquot parts, and which vary very slightly from what is stated by Taylor and Cressy (at page 48)— “ The height of the Pediment seems to have been determined by striking the segment “of a circle from the two extremes of the Cornice, having the centre at the line of the ‘“ pavement of the Portico.” Thus— Calculated |Given by from the calcula- Differ- aliquot parts. | tion. ence The Pantheon . PK=PH=983-57 9850 1:45 mm mmm meme ee mm me mmm mm mn meme mm mmm mm mem me mee meee —eee oof - The Temple of a Yoltis | PR=PH-90702 904-0 8:0 The Temple of Pp | PK-PH-7051 801-0 2°9 Jupiter Tonans | The Temple of Pi Antoninus and } PK = PH =839-81 839-1 0-81 Faustina . These general proportions of the Porticoes being all arranged, we have only to consider the proportioning of the Columns and the method of designing the details of the Roman Entablatures. THE APPARENT PROPORTIONS. The several passages already quoted from Vitruvius clearly prove that the Romans were acquainted with the Greek theory of the apparent magnitudes, namely, the method of determining trigonometrically the amount of the small additions and diminutions ” always made to the first given heights of the Steps, of the Columns, and of the Entablatures of the Greek Porticoes; but, when we examine carefully the Roman Porticoes, this part of the ancient theory of design appears to have been omitted, and the true executed heights to have been at once given in their final dimensions, the same as in the smaller designs of the Greeks. In the case of these Porticoes, which were intended to be seen from central points of view, the calculated variations from the first given dimensions would have been very small, and the Roman Architects probably considered that these ““ additions and diminutions ” might be omitted : but in Trajan’s Column, erected by the Senate and the People of Rome, A.p. 114, recent observations appear to show that the apparent magnitudes were here considered, for 228 ROMAN ARCHITECTURE. in Mr. Augustus Hare's <“ Walks in Rome,” Volume I., page 135, speaking of this Column, he says— “It is composed of 34 blocks of marble, and is covered with a spiral band of bas- ““ reliefs, illustrative of the Dacian wars, and increasing in size as it nears the top, so that ““ it preserves throughout the same proportion when seen from below.” And in Mr. Davenport Adams’ © Temples and Monuments of Greece and Rome,” page 161, also referring to Trajan’s Column, we find— “ These bas-reliefs are 23 in number; the lower are 2ft. high, but they increase ““ to nearly double the size at the top, thus conquering the effect of distance, and presenting ““ the figures to the spectator’s eye of uniform dimensions throughout.” Not having any recent measurements of this Column, I can only direct attention to the subject ; but we find that the principle of the apparent magnitudes is never lost sight of in ancient Architecture. It is found in Egypt; it is applied to the inscriptions on the ante of the Ionic Temples of Priene in Asia; to the correction of the Greek Porticoes; and, in the later example of Trajan’s Column, to the correction of the sculptured bas-reliefs, which are made to wind round the shaft of the Column ; and no doubt it will be found to apply to many Greek and Roman works that have not as yet been carefully investigated. THE CURVATURE OF THE HORIZONTAL LINES. The words of Vitruvius are sufficient again to prove that the Romans were acquainted with the fact of the curvature given to the long horizontal lines of Greek Architecture ; but we have seen that in Greece this correction was only applied to designs intended to be seen from angular points of view, and that in the case of the West Central Portico of the Propyleea, which was seen from a central point of view, the line of the Upper Step of the Portico is set out quite level. We should, therefore, not expect to find any curvature in the horizontal lines of the Roman Porticoes, which were also intended to be seen from central points of view, and, I believe, it will be found to be the case in these Porticoes that the horizontal lines of the Steps and of the Entablatures were set out perfectly level, and without any convexity. In the Roman Temple of the Jupiter Olympius at Athens, a.p. 120, Mr. Penrose has observed a certain amount of curvature in the line of the Upper Step and of the Architrave at the south-east angle of the Temple, both on the return side and in the Portico (see Plan). ROMAN ARCHITECTURE. 229 uth East arg = S ae ry 1@ N basi iis. ' i oy iy J@) N 1 5 1 i : ' DN «@ ire RK | eo o . - moist sm snes nn tic smn ceod LG I Re In the centre of the Portuco at B* suppose the rise of curve =0.3feet Trace the square BD and set out the diagonal lune B*c B2 perfectly level, then Bon the return side will be the gwen thard point in the carve . [] gagkgtog ies non Plan of the bases of the Columns of the Temple of Jupiter Olympus. giving dafferences of level above that at the SE. angle . The position of the Arch of Hadrian shows that this Temple had an angular approach, and although the enclosure is too small to allow of the Temple being seen within the angle of 45°, either from an angular or from a central point of view within its area, yet it appears, from the above plan of the levels taken by Mr. Penrose, that the Upper Steps in the Porticoes and on the return sides, were set out as the arcs of circles, exactly in the same manner as in the Pantheon and in the Temple of Theseus. From the measurements on the return sides, the rise of the curves at B® in the Porticoes might be 0-3 ft. ; describe the square BD, and draw the diagonal line, B’¢B? quite level, then the three required points will be given in the lines of the Porticoes and on the return sides, and the curves of the Upper Steps can be calculated. Mr. Penrose remarks at page 70, ““ These differences of level are quite in accordance “ with the account that this Temple was built on foundations laid by Pisistratus, for we “ have no reason to suppose that at the time of Antiochus Epiphanus, when the Corinthian ““ structure was begun, these refinements continued to be practical even at Athens. We are, “ therefore, probably safe in supposing that at the time of Augustus these refinements in “the horizontal lines were laid aside as involving difficulties of calculation, and also of ‘““ construction.” The calculations required were simply the laying down of two arcs of circles—one for the Portico, and the other for the return side, and this did not involve any calculation more 230 ROMAN ARCHITECTURE, difficult than that which was requisite to determine the entasis of the Columns which, in the case of the Temple of Jupiter Olympius, is a delicate curve, 45 ft. in height, traced as the arc of a hyperbola, and in the time of Augustus there were evidently geometricians in Athens quite capable of calculating and of tracing accurately any of these curved lines. We are, therefore, I think, safe in considering that the horizontal lines in this Temple were inten- tionally made convex at the time that the present design was executed, A.n. 120. Thus, in the Column of Trajan we have a late Roman example, A.n. 114, of the theory of the apparent magnitudes, and in the Temple of the Jupiter Olympius also a Roman example, A.D. 120, of making the horizontal lines of the Upper Step convex, and traced as the arcs of circles. These refinements in Art are, therefore, found to extend from an early Egyptian period until after the commencement of the Christian era; they can be monumentally traced for 1300 years. ROMAN ARCHITECTURE, 231 CAOAPTER 11. THE CORINTHIAN COLUMNS. WaEN considering Greek Architecture, our attention was confined to the Doric and to the Tonic orders, as the Corinthian order is not employed in any existing Greek Portico, and it may be doubted whether the Architects of the time of Pericles would have introduced it as a leading feature into any important design. The Athenian Doric and Ionic Columns are works of pure geometry, executed in marble ; but in the Corinthian capital, although the masses in the best Greek examples were first geometrically designed, the same as in the other orders, yet these masses were afterwards sculptured to represent foliage, and the geometrical lines and surfaces in a measure disappeared in the finished capital, while the Architects who designed the works of the Doric and of the Ionic orders in the Acropolis trusted for architectural effect to purely mathematical lines and surfaces. The Corinthian Columns of the Monument of Lysicrates were designed and executed about 335 B.C. ; they are, consequently, some of the oldest examples of the Corinthian order, and although the Columns are only 11:64 feet in height, or 1 the height of the Roman Columns, yet they are designed and executed with all the care and the refinement peculiar to Greek Art, and the capital possesses a special interest, as the details of it within the enclosed part of the Monument, which were not seen, are left in the original masses, without the foliage being indicated ; so we have this capital, first as a geometrical design, the same as the other capitals, and secondly, in the finished state, with the sculptured leaves, &e.; it has, therefore, been selected as one of the best Greek examples of the Corinthian order. ~The Roman examples that have been taken to illustrate the Corinthian order are, the Columns of the Temple of Jupiter Stator, and of the Pantheon, respectively 45 ft. and 46 ft. in height, each of them executed in costly materials, and designed during the best period of Roman Art, from B.c. 25 to A.p. 150. 232 ROMAN ARCHITECTURE. Besides these two examples in Rome, there is the Corinthian Temple of the Jupiter Olympius at Athens, which was completed by Hadrian about A.p. 130; it was composed originally of 124 Columns, 55 ft. in height, in the Porticoes and in the Peristyles, 16 of which are still standing. One of these Columns was measured by Mr. Penrose with his usual accuracy, not only to obtain the general dimensions, but to ascertain also the entasis of the Column and the curves of the details of the capital ; it has been, consequently, more accurately measured than any Roman Column ; it is executed in Pentelic marble, and equals the best Roman examples. These four examples of the Columns of the Corinthian order are sufficient to illustrate both the general proportions and the method of designing the details, and the subject may be considered under the same heads as in the Greek theory of the Columns, namely— 1st. The general proportions of the masses. 2nd. The designing of the capitals and of the bases. 3rd. The entasis. PLATE 1V. THE GENERAL PROPORTIONS OF THE MASSES OF THE CORINTHIAN COLUMNS. In the proportioning of the Greek Doric and Ionic Columns, it is invariably found that the width of the abacus was derived from the height of the Column, and that by dividing the abacus into some given number of aliquot parts, 12, 13, 14, 15, 16, &e., according to the example, and by making one of these given parts into a modulus, the lower diameter of the Column, the upper diameter, the height of the base, the height and width of the capital, &e., are always multiples of this given modulus. But in the designing of the Roman Corinthian Columns the arrangement is different ; the abacus is not so clearly defined, and the lower diameter of the Column is made the regulating quantity, instead of the abacus; and this lower diameter is derived, in the Roman examples, from the given height of the Columns. Then, dividing the lower diameter into a given number of aliquot parts, 12, 13, 14, 15, 16, &e., according to the example, and making one of these parts into a modulus, the lower diameter and the upper diameter of the Column, the height of the base, the height of the capital, and the width of the abacus, are all multiples of this given modulus, the same as in the Greek examples of the Doric and of the Tonic Columns. The Corinthian Column of the Temple of Jupiter Olympius in Athens may be taken as an Part Vl Plate TV THE ARRANGEMENT OF THE MASSES OF THE CORINTHIAN COLUMNS. te hin i Sed I J 099 g gs C i 1 - y | aon ! CC Fs i c : Ce : ol = % =X ig. Jupiter Olympius Fi UID JO, YPN D)OYM QE ptr G i Ae RE I Ae NRE gl DORR 3 i er NT Al aa ] = d | ! ’ | bre 8 I to . I 8 | | ~~ ~~ mm mm mmm rm mmm mm mmm | i Z8 "Ctt a 03 = a 9 fio Il -|| 67 Ly ay. EEL NYC SCR iS 3 . E > we 4 No = " ®» 5 Nd on os > p= QC By Be rs oo Be fermenannainenunanennntle~ pnmynn yng MOY SELES TTT LER eR say oa rer esses rao ge" oT | MA CA ’! # , : ; ; | : i y | S i | ! : | ® . | : 5 I 5 or y ! SH 4) . ; a N 52 o > Q is S aN : : id 5, en ee nee WAND Jo PYBPY BIOYW PEL LCL TTT TT ean as PL Ly Torr roirridssenciens yng agg) tezesmas ale 900) The MY ; ri 7 ¢ nti) Sd ’ S 5 = N ’”° et e L F. se ZF / Pt 5 = 3 2.82 =Modulus for detals or ol > T 31 | Nf rye | 3 Xd. 00 3 ~3 : T 25 t=] || 3 TEE fF | ; 1st ¥ RB 8 nhl rl I fp oily be. 5. ei i ned = > i Sy | dl dl Eo ; SB % Q 3 Q 3 | I 83 > i 3 8 3% Ty 4 § 55 3% 1 3 % < : S 3 3 3 39% S82 8 fer ae rer 31 3 81 3 | : 3 | 3 filreemaeiie egy ff T 8 1 § 3 : 2] itors 3 | 5 1 ‘3s NY od Mr ME : Fe WE 8 3 a Rio inl 2 1] } 1:1 5 : 2 : $= os 2e 1 ET 1% «1% SR ; if NS 0 3 s os : : ie je ET 5 ~ iv 0 $l : : NN 3 3 *t: 11 hs it JR 5 & al! {101 BIT {bi ~ 1a iS oti dbld viditl 5 = 1 tle LE £ : iid 11 3 oq Lo I> $f 353i 8 2 Lh I i$ 3 : $11 3 i 3 § SR 3 3 =< details of Moog : ®1 -§ x ~N i" it 3 r Sora | = 3 ®t 1 I - is SF < > § S R = xt ! BIR > 1 : P Ne § 2 Qit-rx | a I P19 He 5 Sl i ; Ss | > | sal |i8ls Ys |! ols X wis + Baetsnn 3 HM RB» ee Nh Ry ts y \ I 2 IaiRelR 1 I od Ns : NN] ; | +R 5 ! Rie © yb ps hl : 1 ! 1 Gita ob. Tae dd LS Diameter of Abacus derived from ime MN Govern Width of” base 9% Given lower diameter Upper dvameter .___. H. of l= 557.36 Height of Capital | dpm ~ 3 1) #] ry ol... op Li ii wl 21 33 § SQ {1+ ; |] : NE Hi 8 '¥ I 5 os 3 N Jey : : TAH $B Fog lilt S$ L & . SoH » Ne iti i+ 1 33 J | : l SE Ls ll nn o i : = He » oe liye ono EE sede ds LS 5 i EEA I to tiie} : 3 s Ye 3 1R he) oS D . n 9 2 ~ { T3833 iis 3 S28: 2 $4334 3% I$ 3 > SLADE BS. S $F 8] zg [ X bt 7 Sok enson Adel. CF Koll, loth. Gaalle St. Sondon LC hie, visi cand SEGRE ee I Se IOI Sa Sn of SR VE SRI GAY, On Uh Eis Sule Se Sn Seas SE pT Se NI SH oll A DRE ee nti hE af oS A eS Sa Se al SS Sst Lo SRE DEI TE Ai Se FE (Le Sha I A MA a a de ERR a FL Sa le he a a ROMAN ARCHITECTURE. 233 exception, as, in this case, the width of the abacus is derived from the height of the Column, the same as in other Greek examples, and the regulating modulus is then derived from the abacus. The following Table shows the lower diameters of the Columns, derived from the given heights, and the value of the modulus in each example— Given width of the b : of oe ind CH ope : ey from the line MN. : ne Ins 139-725 : 1397 : . 20-952 Monument of Lysicrates — —= 13-97, 5 = 1'164 = modulus for details. 3395. Pantheon: oon uBR ums, Ep, 798 Jupiter Stator 57289, 358 — s ; | ol Wig of upiter mpius at | gao- Abacus. : B gl oo =1018, E08) i, " Athens . : a 20 The proportions of the masses of the several Columns are given in the Plate worked out from these given moduli, and are summed up in the following Table— Tar PrororTiONS OF THE MASSES oF THE COLUMNS IN ALIQUOT PARTS oR MODULI Lower Upper Height of Width, AB, of Height Value of moduli diameter. diameter. capital. the abacus. of base. for details of Parts. Parts. Parts. Parts. Parts. Column. The Monument of Liysicrates. 12 10 20 24 62 1-164 Pantheon . : : , 14 12 16 28 8% 4-185 Jupiter Stator . ; 16 14 18 32 94 3:58 Jupiter Olympius at Athens . 27 23 27 36 16 2-82 Then, multiplying the value of the given modulus in any example by the numbers in the Table, the dimensions of the upper or of the lower diameter, and of the other details of the Column, are obtained. These numbers and proportions are derived simply from observation, the same as in the Greek Columns, and no attempt is made to give any laws for regulating the proportions of the masses of the Corinthian Columns. In the Greek Ionic and in the Roman Corinthian there is always a difference of two moduli between the upper and the lower diameters, and the width of the diagonal line of the abacus, AB, in these examples of the Corinthian order is nearly equal to twice the lower diameter of the Column. The number of aliquot parts into which the lower diameter of the Column was divided and the arrangement of the details appear to have been left, within certain limits, to the 234 ROMAN ARCHITECTURE. judgment and feeling of the Architect, but the examples given vary only slightly, either in their proportions or in their dimensions. There appears to be a certain agreement in the methods of designing the Columns in Greece and in Rome, and the number of aliquot parts into which the abacus or the lower diameter are made to divide appear to be much the same in the Greek Ionic and the Roman Corinthian, namely, 12, 13, 14, 15, 16 parts, according to the example. Also, comparing the upper and the lower diameters together in different examples, we sometimes find them very closely agreeing : thus— In the Ionic Portico of the Erechtheium, and in the Corinthian Monument of Lysicrates. The lower diameter . . = 12 parts, | i ’ . = 12 parts. The upper diameter . . w= 1 ol 5% 2 5 =10. In the Ionic Column of the Propylea, and in the Corinthian Column of Jupiter Tonans. The lower diameter . . = 13 parts, - “ == 18 paris. The upper diameter . *. =11 ,, ” " = 11 °, The variations in the proportions between the Greek Ionic Columns and the Greek and Roman Corinthian Columns are very slight, in the same way that there was a certain amount of agreement in the division of the heights of the masses of the Porticoes between the Ionic Porticoes in Greece and the Corinthian in Rome, thus showing that in the arrangements of the general proportions there was no real difference between the Architecture of Athens and of Rome. THE ENTASIS OF THE ROMAN COLUMNS. The entasis of the Greek Columns has been already considered in Part IV., Plate XII., and there is no reason to suppose that there was any real difference in the method of describing the entasis of the Roman Columns, but these Columns have not yet been measured with the same accuracy as the Greek, therefore any remarks upon the subject can be offered only as suggestions. First, the Roman Columns of the Pantheon, of the Temple of Jupiter Tonans, and of the Temple of Antoninus and Faustina do not vary in height more than 3 ins., and, comparing these Columns with those of the Temple of Jupiter Stator, the variation is only 15 ins. Again, the intercolumniations, agreeing with the major axis, AB, of the hyperbola, are also nearly similar, and the variations in the entasis will probably be found to be quite im- perceptible in these several examples. It was, therefore, not requisite to calculate the entasis of each Column separately, and it may well be doubted whether the Roman Architects troubled themselves to calculate with ROMAN ARCHITECTURE, 235 precision the arc of a delicate hyperbola, but probably in the Greek works upon Architecture the entasis was carefully laid down for the shafts of Columns, say, from 35 to 40 ft. in height, and from this data it would have been easy by simple proportions to lay down the entasis of any given shaft. Vitruvius, speaking of the entasis of the Columns, says (Book III., Chapter ITI.)— ““ Concerning the augmentation that is made in the middle of the Columns, which by “the Greeks is called entasis, the manner of forming it just and gradual is shown by the “ draught at the end of the Book.” 1 would, therefore, offer as a suggestion, the possibility that Vitruvius in this passage simply refers to a Greek diagram, which he might have copied, giving the entasis in detail to a certain scale, which might be enlarged or diminished to suit any given Ionic or Corinthian Column : thus—Supposing, as shown in the annexed diagram, the entasis was calculated to suit the shaft of a Column like that of the Pantheon, then by proportion the parts could be easily reduced or enlarged, as required. In the case of the Roman Columns given in Plate IV. no variations in the entasis would be required. For the entasis of the shaft of the column of the Temple of Jupiter Olympius an increase of about ; in the dimensions would be required. In Part 1V., Plate XIII, is given the calculated entasis of the Columns of the Pantheon and of the Temple of Jupiter Olympius. The calculations for the entasis of the Borvei a Doingret Fo ho’ Boreani Olen, Roman Columns are similar to those for | Fi the Greek, the only difference being that : 'S S! : I . ° ° . I ¥ im the Ionic and Corinthian orders the ' Lh ddameter i Cf | tangent lines, RS, are made perpendicular = 3 J to the horizon, and in the Grecian Doric iz | Ti : cn : | 3 |. these lines incline slightly at some given 1A Sf i 5s i 2! bo] i183 i Fy angle. iis bid S Hes eg : ; 3 k ; | & The Perpendictidar tangent Lies = RS ili | i ¥ The, Upper and, Lower diameters = PF RE | 1 2 | The Intercobiumaaation — AB major axLs | Hs | : The hexght from R tod, the vertex of the hyperbola = RA | | 15 | A AM = | i | § PM = » : | | S The space bevweerv the Chord) tine RP and the are of the | | | 3 hyperbola 4 Pts called the Entasts u mao jaceis | [ | 4 Arne wr Is a i's $ | i's ; | | | | aan R lower dicaneter R Intercoluumnialion R lower dicumeter = 236 ROMAN ARCHITECTURE. CHAPTER 111, THE DESIGNING OF THE ROMAN CORINTHIAN ENTABLATURES. TrERE appears to have been no difference in the general method of arranging the proportions of the Greek and of the Roman Entablatures; they are both designed perspectively to suit certain given points of view, and the general ideas of the forms of the Mouldings and of the Ornaments are very similar; but in Greece these forms were traced mathematically by geometricians, and in Rome they were probably designed by Artists, who seem to have been unacquainted with the curves of the conic sections, and it is this total absence of the descriptive geometry in the executed designs of the Romans, which marks the real difference between the Entablatures of the Temples in Athens and in Rome. When considering the Greek Architecture, we found that the proportions of the Entablatures were invariably regulated by two scales of aliquot parts— 1st. The horizontal scale of parts for arranging the projections. 2nd. The circular vertical scale of parts with the point of sight for the centre, for arranging the apparent heights. Then the true heights of all the details of the Entablature were determined by tracing visual rays from the given point of sight O, to pass through certain given points in the circular vertical scale of parts until they intersected the given perpendicular lines of the several projections. The Greek Intablatures were thus perspectively designed, and such we find to have been the case also with the Roman Entablatures—they were all designed to suit certain fixed central points of view, and the given projections and the heights of the details were arranged by the two given scales of aliquot parts, exactly in the same manner as in the Greek designs. The Greek Porticoes were generally designed to be seen from an angular point of view, but the Roman Porticoes were intended to be seen from central points of view, and the Part Vl]. Plate V. THE DESIGNING OF THE CORINTHIAN Fig. 1. The Pantheon. 7777777777777 en Fig . 2. The hs of Antoninus and Faustina. : 7 0 _ — — ee THA 729:2 - oofbon db iid dra TT i i. A 4 N __ J j 2 2 | 7 i yi & 7 N ou | ’ ; Ef | © | oe = : ol ZO : Fe ? z 1 = : _B ime oe : LL whmmwswmmmwesiebebiog 3 { | 53-839 lien | if srareintennsres a 1299 93 to the point of sight. 1 24 | x 33 $ iL $3 £3 == = Lf ¢ r = 17 v $ 1 4 ) =. : & A. 1.3 pot, of sight or g ] 5 Rms ™ L iin a rr i he aa 0p LE : > 3s ee 1745 + 5 to point of sight. ®-._ Fig. 3. The yy of’ i Tonans. ENTABLATURES Fig.k. The Pantheon GH 0 i sy Fs en J & __ | = = Tr ll wt 7 i | z | 2 § » af oy LI J fhe “eo I= i | ; | | So'9 = = V9" ses Modulus | | a) TT rgetion oes | | Rie--- 39 9 =1 Modulus _. i 9 \ : 3 : Ni we§ 3 JF Reema 1367 - 2 to the point of sight SN 3 be L450 ; oon. Btorarorn Wolds LTA ot Lorton i omni BL, ROMAN ARCHITECTURE, 237 centre of the road was usually at a sufficient distance from the given Portico to allow the eye of the spectator to embrace the whole width of the Portico within the visual angle of 45°, and from this given point of view we shall find the apparent proportions of the details of the Entablature to have been regulated. In the Roman Entablatures there appears to be no necessity for minute trigonometrical calculations, as the descriptive geometry will be found to be quite sufficient, both for the determination of the points of sight O, and for the regulation of the heights of the details in each Entablature, and it is easy to trace the Entablatures upon a plane to 1 or 1 of the real size, and then to enlarge them to the full size. With these few general remarks, we may now proceed to lay down the FEntablatures of the Pantheon, of the Temple of Jupiter Tonans, and of the Temple of Antoninus and Faustina. PLATE VY. THE DESIGNING OF THE CORINTHIAN ENTABLATURES. In the Doric and in the Ionic Greek KEntablatures the apparent heights of the Architrave, of the Frieze, and of the Cornice, measured on the circular are, are invariably made equal to each other; but in the Corinthian KEntablature of the Monument of Lysicrates an increase of height is given to the Cornice, and the apparent heights are—the Architrave = 4 parts, the Frieze = 5 parts, and the Cornice =5 parts; and the same is the case in the Roman Corinthian Entablatures—an apparent increase is made in the height of the Cornice, as shown in the several given examples. The given positions of the several points of sight for the designing of the Entablatures may be tabulated as follows— Tae PosiTION IN EACH EXAMPLE oF THE GIVEN PoINT OF SicHT. From the line Below the of Architrave. Architrave. In the Monument of Lysi- (The position of the| Inge 4 gions : . { 511:0.—The plane of the horizon 191-79 crates . . ; . | point of sight, O, is In the Portico of the Pantheon 5 » 17455 " 3 . © 5506869 In the Portico of the Temple 5 AS : . ome of Jupiter Stator In the Portico of the Temple ; : AD ; : 6888 of Jupiter Tonans Portico of the Templ In the Por a of the i e : : an . : 68013 of Antoninus and Faustina 238 ROMAN ARCHITECTURE, The varying proportions of the details of the several Kntablatures are best explained by a reference to the Plate, but the following Tables give in a summary form the division into aliquot parts of the arc of the great circle, showing in‘each example the apparent heights of the Architrave, of the Frieze, and of the Cornice, and serve to illustrate the amount of the variations in the proportions of the several given examples of the Entablatures. The Architrave, the Frieze, and the Cornice again divide into smaller parts for the arrangement of the appropriate details, as shown in the several figures on the Plate. TABLE sHOWING THE RELATIVE PROPORTIONS IN EACH EXAMPLE, OF THE ARCHITRAVE, oF THE FRIEZE, AND oF THE CORNICE, MEASURED ON THE ARC OF THE CIRCLE. Architrave | Frieze Cornice Total “| Division of the parts. | paris. parts. parts. horizontal line of | the projections. In the Entablature of the North Portico of the Erechtheium, the arc 16 |, 16 16 48 25 parts. of the circle is divided into 48 parts . | : In the Entablature of the Monument of Liysicrates the arc of the circle is 16 20 20 56 10 divided into 56 parts 53 In the Entablature of the Pantheon ) the arc of the circle is divided into 17 164 234% 57 25 57 parts. 35 In the Entablature of the Temple of Jupiter Tonans the arc of the circle 7 8 93 24% 55. 1s divided into 24% parts . In the Entablature of the Temple of Antoninus and Faustina the arc of 9: 104 14 34 20, the circle is divided into 34 parts ~~. | In the arrangement of these first general proportions there is very little difference between the Fntablatures of Greece and of Rome, and the same divisions of the parts would have answered equally, either for a Greek or for a Roman Corinthian Entablature ; but it 1s when we approach the designing of the forms of the Mouldings and of the Ornaments that the real intellectual difference between the Greek and the Roman details becomes apparent. ROMAN ARCHITECTURE. 239 THE MOULDINGS AND ORNAMENTS OF THE ROMAN CORINTHIAN ENTABLATURES. We have already seen that the Greek Entablatures, with their Mouldings and Orna- ments, were works of pure geometry, and that every curved line which is found m them is mathematically traced. The Ornaments were also relieved, either by colours or by being sculptured in relief, and carefully executed works of sculpture were also introduced into the more important designs, so that every Entablature when complete became a highly finished work of Art, with the ideas expressed as much as possible in the language of the geometry. But when we enter upon the consideration of the Roman Mouldings and Ornaments we find that the geometry is absent, and that there is a want of refinement in the designing of all the details. The Mouldings appear to be either the arcs of circles or curved lines traced by hand, and the Ornaments were evidently designed and executed by inferior workmen, and an examination of the details of Roman Architecture quite confirms the remark of Montucla (page 406)— “ Les mathématiques surtout furent extremement négligées a Rome, et la géométrie a ““ peine connue.” If the designs conceived by the Romans had been executed in Athens during the age of Pericles they would have exhibited greater excellency as works of Art, for the ideas of the Architects would have been expressed geometrically in the marble, and it is improbable that an Entablature, with its Mouldings and Ornaments, such as we find in Rome, would have been erected in the Acropolis of Athens. The conception of a work of sculpture or of painting may be spoilt by the manner in which it is executed, and the same remark applies to Archi- tecture. If the details of Roman Architecture had been as carefully studied and worked out as those of the Greek, then the Roman Porticoes would have taken their place among the finest works of ancient Architecture ; but they fail, not from the general proportions, nor from the material in which they are executed, but simply from a want of mathematical knowledge in the Artists who designed and executed them. SUMMARY OF THE COMPARISON OF THE GREEK AND ROMAN PORTICOES. Having now completed the comparison between the Greek and Roman Architecture, we find that the Roman in all its essential features must have been derived from the Greek, and the only difference between them that we discover 1s, such as we had every reason beforehand to expect, namely, a certain degree of absence of the calculated, and also of the descriptive geometry in the Roman designs. 240 ROMAN ARCHITECTURE, Proportion.—The positions of the Roman Temples with regard to certain fixed central points of view appear to have been studied, and the first proportions of the masses of a Greek or of a Roman Portico only slightly differ from each other. But the Romans did not consider it necessary, in the case of the Porticoes which were intended to be seen from central points of view, to make all the parts apparently commensurable to suit a fixed point of sight, therefore the small ¢ additions and diminutions ” trigonometrically calculated in the Greek Porticoes are not found to exist in the Roman Porticoes: in these the first given lineal magnitudes are the same as the executed dimensions. The corrections in the heights would have been small in amount, and would have been trigonometrically calculated, but we find them to have been altogether omitted. In such a work as Trajan’s Column the apparent magnitudes of the sculpture were considered and allowed for, as the spiral band of bas-reliefs increases in size as it nears the top of the Column, so that the figures when seen from below preserve throughout the same apparent proportions. The Horizontal Curves.—The horizontal lines in the Roman Porticoes were all executed as straight lines, and under similar circumstances, when the lines were intended to be seen from central points of view, they were executed in the same manner in the Greek Temples, as we find to be the case in the West Central Portico of the Propyleea. Whenever the horizontal lines in the Greek Temples were made convex to the eye the design was intended to be seen from an angular point of view, as in the two designs of the Parthenon; and in the case of the Roman Temple of the Jupiter Olympius at Athens, which appears to have had an angular approach through the Arch of Hadrian, the lines of the Upper Step, both in the Portico, and also on the return side, were made convex to the eye, the same as in the Parthenon. The Corinthian Columns.—In the Athenian Doric Columns the width of the abacus is derived from the height of the Column, and the given abacus being divided into a certain number of aliquot parts, 12, 13, 14, 15, 16, &ec., then these parts regulate all the proportions of the masses of the Columns ; but in the Corinthian order the abacus is not so clearly defined as in the Doric and in the Ionic orders, consequently in the Roman Corinthian Porticoes it is the lower diameter of the Column which is derived from some given width of the Portico, which is divided into a given number of aliquot parts, 12,13, 14, 15, 16, &ec., and these given parts are made to regulate the proportions of the masses of the Columns. With this exception, there is no difference between the Greek and the Roman methods of laying down the masses of the Columns, and the Roman proportions would serve equally well for examples of the Greek Doric or Ionic as of the Roman Corinthian. ROMAN ABCHITECTURE, 241 With regard to the details, comparing first the bases of the Greek and of the Roman Corinthian, we meet with more refinement and variety in the curved lines of the Greek base than of the Roman, which is simply a combination of the arcs of circles. In both cases the entasis of the shaft of the Column is the arc of a hyperbola, but in the Roman examples the elements of the curve are the given quantities, and the calculation of the curve is very much simplified, and agrees more nearly with the Fgyptian examples. The Entablatures.—In the proportioning and perspective designing to suit a fixed point of view, there is no difference between the Entablatures of Greece and of Rome, and when we compare the proportions of the Corinthian Entablature of the Monument of Liysicrates with the Roman examples of the same order we see that the Roman proportions were probably derived from Greek authorities. In both an increase of size is given to the Cornice when compared with the Doric and Ionic orders, and it is only in the Mouldings and Ornaments that the absence of the Greek refinement becomes apparent. In Greece we find that the original ideas of the Ornaments (which were derived from Egypt) were all translated into the language of the geometry, and that the Grecian Mouldings and Ornaments become simply combinations of geometrical forms ; but in Rome the designs of the Ornaments nearly agree with the original Egyptian forms, and differ only in the manner in which they were executed, namely, in Hgypt they were sketched and coloured on a smooth surface, and in Rome they were sketched on the marble and sculptured in relief, but there was no attempt to trace the curved lines and surfaces with mathematical precision. The result of this absence of the geometry in all the details of Roman Archi- tecture, is to give to the Roman designs an inferior appearance as works of Art when compared with the earlier productions of the Greeks ; but if the Pantheon and other Roman designs had been laid down by the Architects of the age of Pericles, and had been executed by Greek Artists, they would have equalled the best designs of Greece ; and, if the Parthenon and the Propylea had been executed by Roman Artists, the absence of the geometry would have caused every trace of the beauty which exists in the curved lines of the Capitals, of the Mouldings, and of the Ornaments entirely to disappear. 242 ROMAN ARCHITECTURE. INTERNAL ARCHITECTURE. Our attention has been hitherto confined to external Architecture, for with the Greeks their religious ceremonials were external, and their Architecture was naturally adapted to their climate, and to an external worship. The cella of the Greek Temple was small, and only suited for the reception of the statue of the Deity, and the Architecture became subordinate to the sculpture. Although our information with regard to the interiors of the Temples is limited, owing to the ruined state in which we now find them, still it would be possible, with some degree of certainty, to restore the interiors of the Parthenon, and of the Krechtheium, and the Vestibule of the Propylea could be perfectly restored from the parts that remain. We know, however, that the interiors were carefully designed in every detail, and far more enriched with colour than the external parts of the Temple, and that the same principles of design were applicable to both alike, except probably the “ additions and diminutions” in the first given heights, and the curvature of the horizontal lines. In Egypt the Architecture has more of an internal character than in Greece, and the interior appearance in the series of Courts and Halls that were enclosed within the outer walls of the Temple was more studied than the external effect; the interior of many parts of the Memnonium at Thebes and of the Temple of Karnak must have been impressive, and the well-proportioned chambers in the Tombs of the Kings, with the vaulted roofs highly enriched with colour and ornament, show an advanced state of architectural design, differing in nothing from later works, except in being impressed with an Egyptian character, both in the ornament and in the hieroglyphics. But it is in Rome, as Mr. Fergusson truly remarks, ‘that we find we have to deal “with a great people, who, for the first time in the world’s history, rendered Architecture ‘““ subservient to their many wants.” “It thus happens that in Roman cities, in addition to Temples, we find Basilicas, ‘“ Baths, Palaces, Tombs, Arches of Triumph, &ec., all equally objects of architectural skill, “and the best of these, in fact, are those which, from previous neglect in other countries, are “ stamped with originality.” It is especially the internal Architecture of the Roman designs that is worthy of study, and that approaches more nearly to the requirements of modern civilization. In such works as the Vestibule of the Pantheon, the Basilicas of Trajan and of Maxentius, the Christian Basilicas of St. Peter at Rome, and of St. Sophia at Constantinople, we possess ROMAN ARCHITECTURE, 243 early and valuable examples of internal Architecture, all of them executed at a time when the School of Geometry and the Library at Alexandria still existed, and when probably few of the Greek works upon ancient Architecture were lost, and although we find a great decline of Art in the execution of the details, still it is possible that some of the general principles of design were followed out in all these structures, and that the perspective designs were to a certain extent considered, and 1t would have been easy for a Greek Artist of the age of Pericles to have rendered them worthy of the best age of Greece without destroying any of the characteristic features, either in the construction or in the general conception of these really beautiful interiors. I have spoken of all these works as interior designs, for there is no external Archi- tecture in any of them worthy of the name, except to mark the entrances to the interiors. Thus, speaking of the Pantheon, Mr. Fergusson remarks— “ Kixternally its effect is very much destroyed by its two parts, the circular and the ““ rectangular, being so dissimilar in style, and so incongruously joined together. ““ The Portico especially, in itself 1s the finest which Rome exhibits,” and in the interior, “ notwithstanding these defects and many others of detail that might be mentioned, there is a ‘“ grandeur and a simplicity in the proportions of this great Temple that render it still one of “the very finest and most sublime interiors in the world.” "The Entablature of this Portico was, as we have found, perspectively designed from a central point of view at a distance of 144 ft. from the Architrave, and from this point nothing was seen either of the dome or of the brick walls and arches of the Vestibule, which in the geometrical drawings destroy the harmony of the external appearance. The Portico was a distinct design seen by itself, and probably the space in front of the Portico was originally enclosed like other designs of a similar kind: thus, the Vestibule, with its interior dome of 145 ft. span, and 147 ft. high, enriched with bronze ornaments, was not seen at all as an external design, to which it has no pretension, but, passing under the Portico, the whole interior then opens to view as a second design, worthy of any age and of any Architect in its general conception and boldness of execution, failing only in details that might be easily rectified. The Pantheon may, therefore, be considered as two distinet designs, both of their kind the finest in Rome, and neither of them have yet been surpassed, nor even equalled, by any modern designs in Europe. 244 ROMAN ARCHITECTURE. THE BASILICAS OF TRAJAN AND MAXENTIUS. Without careful drawings and restorations it is difficult to speak with certainty of Trajans Basilica Basilica of Maxentius. ORCRORORORORCRC Il ee I Wf © Peo ®® 66s Es Ee ETs Ew © | yy C Tees usansssnasrae 7 a I = Ol o @ / i f T 1 | apse =| al i. Centre aisle nr iL) © © [eo 1H vw \\ | © = § ® \¢ cers svrvsevvareves tk _— eee eee e ® ® © see 9 ee © | a : = . [o [0 these two Basilicas. I shall, therefore, for the present adopt Mr. Fergusson’s description of them given in Vol. I., page 316. He says— ““ It may be doubted whether, in any respect, in the eyes of the Romans themselves, the “ Temples were as important and venerable as the Basilicas. ““ The people cared for government and justice more than for religion, and consequently ““ paid more attention to the affairs of the Basilicas than to those of the Temples.” “ It happens, however, that the remains which we do possess comprise what we know “to be the ruins of the two most splendid buildings of this class in Rome, and these are “ sufficiently complete to enable us to restore their plans with considerable confidence. “It 1s also fortunate that one of these, the Ulpian or Trajan’s Basilica, is the typical ““ specimen of those with wooden roofs; the other, that of Maxentius, commonly called the “ Temple of Peace, is the noblest of the vaulted class.” Internally, Trajan’s Basilica ““ was divided into five Aisles by four rows of Columns, ‘““ each about 35 ft. in height, the centre being 87 ft. wide, and the side-Aisles 23 ft. 4 in. each. ““ The centre was covered by a wooden roof of semi circular form, covered apparently ““ with bronze plates richly ornamented and gilt. ““ The total internal height was thus probably about 120 ft.” ““ At one end was a great semi circular Apse, the back part of which was raised, being “ approached by a semi circular range of Steps. In the centre of this platform was the raised “ seat of the queestor or other magistrate who presided. On each side, upon the Steps, were ““ places for the assessors or others engaged in the business being transacted. In front of the ““ Apse was placed an altar, where sacrifice was performed before commencing any important ““ public business. | “ Externally, this Basilica could not have been of much magnificence. It was entered ROMAN ARCHITECTURE. ; 245 ““ on the side of the Forum by one triple doorway in the centre, and two single ones on either ‘“ side, covered by shallow Porticoes of Columns of the same height as those used internally.” “ The Basilica of Maxentius . . . . was rather broader than that of Trajan, being 195 ft. ““ between the walls, but it was 100 ft. less in length. The central Aisle was very nearly of the ‘““ same width, being 83 ft. between the Columns, and 120 ft. in height. There was, however, “a vast difference in the construction of the two; the side Aisles were roofed by three great ‘““ arches, each 72 ft. in span, and the centre by an immense intersecting vault in three compart- “ ments.” Externally, neither of these Basilicas presented any architectural magnificence. In each case the entrances were marked by a few Columns ; but, so far as relates to the Architecture, they were both internal designs, and as such are well worthy of study. CHRISTIAN BASILICAS. 4 : | 0000000 N0e 106000000. See BN Sets odie tr dh het ne SCE she ate BBO ot a St eS ay Rs LL 11 ara al = EE aa “lee eee ie a 00 0 0s so 0 0 eo eo 000} Plan of the Basilica of B-=:s ES nr ae St Sophia pT T | at Constantinople Plan of the Basilica of St Feter at Rome ““ There is no real distinction between the Emilian or Ulpian Basilicas and those which ““ Constantine erected for the use of the early Christian Republic.” ““ When, in the time of Constantine, this persecuted and scattered Church emerged from ““ the Catacombs to bask in the sunshine of Imperial favour there were no buildings in Rome ““ which could be found more suited for their purposes than the Basilicas of the ancient city.” ““ In the Basilicas the whole congregation of the faithful could meet and take part in the “ transaction of the business gong on. The bishop naturally took the place previously occupied “ by the praetor or quaestor. ““ The altar in front of the Apse” . . . . “served equally for the celebration of Christian “ rites.” ““ An atrium or courtyard in front of the principal entrance was considered at that early ““ age a most important, if not indeed an indispensable, attribute to the Church itself.” “ Tn the centre of this atrium there generally stood a fountain or tank of water, not only ““ as an emblem of purity, but that those who came to the Church might wash their hands before ““ entering the holy place.” 246 ROMAN ARCHITECTURE, “ The great Basilica (of St. Peter at Rome) was erected in the reign of Constantine, and, “as will be seen in the plan, it possessed a noble atrium or fore-court, 212 ft. by 235 ft.” “ The Church itself was 212 ft. in width, by 380 ft. in length, and the central Aisle was “about 80 ft. across;” internally the walls were panelled, “ each containing a picture.” ‘“ Externally this Basilica, like all those of its age, must have been singularly deficient “in beauty or in architectural design. The sides were of plain unplastered brick, the windows “were plain arch-headed openings. The front alone was ornamented.” (Vol. I., page 414.) The Church of Sta. Sophia at Constantinople was built in the time of Justinian, A.n. 532, by the Architect Anthemius of Thralles, and “neither the Pantheon nor any of the vaulted halls ““ at Rome equal the Nave of Sta. Sophia in extent, or in cleverness of construction, or in beauty “of design. Nor was there anything erected for ten centuries till the building of the great “ medieval Cathedrals which can be compared with it. Indeed, it remains even now an open ““ question whether a Christian Church exists anywhere, of any age, whose interior is so beautiful ‘“ ag that of this marvellous creation of old Byzantine Art.” ‘“ Externally the building possesses little architectural beauty beyond what is due to its “mass and the varied outline.” (Vol. II., page 443.) In referring to the Pantheon, to the Roman and Christian Basilicas, and to the Church of Sta. Sophia, Mr. Fergusson makes the same general remark, that externally all these great designs are left without any attempt at architectural ornament ; the walls are simple brickwork ; the windows plain arch-headed openings, and the front alone 1s marked architecturally by a Portico, or a few Columns, to denote the entrances to what are certainly interior designs of great architectural beauty and originality. Can any reason be assigned for this absence of external Architecture ? I believe there can, and that the Architects of these later ages designed to a certain extent perspectively in the same manner as the ancients had done before them, and that they made no geometrical drawings, except for the purposes of construction, and for the arrangement of the first given masses; the perspective designs were principally considered, and no ornamental Architecture was introduced, which did not add to the general effect. Thus, the Acropolis of Athens is entered by a small Doric gateway, between two towers, without architectural decoration ; then, ascending the marble staircase, the real entrance to the Acropolis appears in view—in the Portico of the Vestibule of the Propylea—and admits the spectator to the interior architectural designs, which are all of them external works of Architec- ture perspectively designed and suited to an external worship, and so arranged that the priests, the altars, and the sacrifices might be brought together upon the prepared platforms in front of the Porticoes of the several Temples. ROMAN ARCHITECTURE. 247 In the case of the Christian Basilicas of St. Peter and of Sta. Sophia, a gateway admits the spectator into an enclosed court or atrium, which was an essential part of the plan; then immediately in front is the entrance to the Church, clearly marked by appropriate architec- tural ornament, and passing through this entrance the real design at once appears, as an internal design, suited in all respects to a congregational and Christian worship, and it may well be doubted whether any Christian Churches have since then been designed to equal them, either in convenience or in beauty. If what is here stated be correct, the Architects of the time of Constantine and of Justinian when making their designs studied the proper point of sight, and did not consider it requisite to ornament architecturally those large external portions of the buildings that could not be seen from any favourable point of view; it is only in recent times that architectural designs, with all their details, have been laid down and studied simply as geometrical elevations, drawn in a manner in which they could never be seen, under any possible circumstances, or from any point of view. We have already observed that all the Roman Porticoes were proportioned in aliquot parts, but that no “additions or diminutions” were made in the first given heights, and that the horizontal straight lines were not changed into convex lines, as in the Greek designs, but that the Entablatures were all perspectively laid down ; and it is probable that the interiors of the Pantheon and of Sta. Sophia were designed, like these external Porticoes, in aliquot parts, and that no corrections were made upon the first given quantities; the Entablatures alone being perspectively laid down. But although these late interiors were possibly not perspectively corrected, like the more refined Greek works, still this does not prevent their having been perspectively designed, and they are worthy of more careful study than has yet been bestowed upon them. If they had been executed by early Greek Architects we may feel confident that they would have been as carefully designed for general effect, and that all the forms would have been as mathematically traced as any of the works of the Acropolis. To render justice to the interior designs of ancient Architecture would require much study and a separate work, but ample materials exist for investigation in the Sepulchral Chambers, the Halls, and the Inner Courts of Egypt, in the interiors of the Greek Temples, and in such works as the interiors of the Roman and Christian Basilicas, in the Vestibule of the Pantheon, and in the Greek design of the interior of Sta. Sophia. The Roman Architects down to the time of Justinian must have been influenced by the works of the Greeks, that were everywhere to be seen, and also by the writings of the ancient Greele Architects which were then in existence; besides, the traditions of Art are only slowly lost, and in all these later interiors we certainly perceive traces of influence, although the details and refinements in them are very inferior to the Greek, and the designs bear the marks of the lowlier intellectual stamp of the age to which they belong. 248 ROMAN ARCHITECTURE. Egyptian and Greek Architecture was not confined to straight horizontal unbroken lines if the design required any other arrangement of the masses. In Egypt the outlines of the Temples were very much broken by the Towers of the Propylea and by the Obelisks, and in the Tombs of the Kings at Thebes we have vaulted roofs of great beauty. In Greece the combination of separate perspective designs within the same mass of building 1s not limited ; thus, in the Erechtheium, there are three quite distinct designs in the Hast Portico, the North Portico, and the South Portico, forming together a very irregular mass. In the Propylea there are three perspective designs, namely, the Portico of the Vestibule, the North Wing, and the Temple of Victory, connected together without any uniformity. In the Temple at Eleusis, Plutarch speaks of two ranks of Columns, one above another, and informs us that Xenocles built the dome on the top; and in the Monument of Liysicrates there 1s the model of a small dome. The designs in Rome were many of them the conceptions of Greek Architects whose names are lost, although their works remain. We are therefore justified in including the domes of the Pantheon at Rome, and of Sta. Sophia at Constantinople, and the vaulted roofs constructed either of timber or of brickwork in the Roman Basilicas, among the forms which Greek Architecture might assume ; indeed there is no limit, within the powers of construction, to the varying forms of the masses that might have been employed by the Greeks without any departure from their principles. There 1s no reason why we should limit our ideas to what are known as the Three orders of Architecture, if any designs, either of Columns or of Entablatures, can be suggested more suitable for internal Architecture—there are no two Dorie, Ionic, or Corinthian Columns, alike in Greece, as the designs as well as the proportions were always varied. The Greek Architects, as we have seen, derived their first ideas from early Egyptian and Asiatic sources, and slowly refined and perfected them by the application of the geometry, but if they had been acquainted with any forms of Columns or of Entablatures, in India or elsewhere, which were suited to their designs, they would not have hesitated to take the ideas and to Impress upon them that intellectual refinement which would have rendered them at once purely Greek. If the Greek power had increased and grown into an Empire, instead of having to give way to the Roman Empire, the ideas and forms of Architecture would have multiplied as new wants had in each age to be supplied, but the same principles and the same refine- ments would have been met with in all the designs, for Architecture cannot exist as an Art without them ; although separate from Art, it can supply, as we find to be often the case, all the material building wants of a nation. ROMAN ARCHITECTURE. 249 The ancient Architects were unacquainted with what is understood in Europe by Styles of Architecture, and they never considered it requisite literally to copy any ancient work, or to adhere to the forms of any particular century, although they had present to their minds many varieties of Architecture, in the Egyptian, the Assyrian, the Pelasgic, the Etruscan, the early Greek, &ec., but whatever ideas the Greeks derived, either from Egypt or from Asia, they impressed upon them the marks of their own higher scientific cultivation, so that in the smallest fragment taken from the Parthenon, or from any other work of the best period of Art, we at once perceive that it has received the marks upon it of a cultivated mind, and is not the rudely executed idea of a common workman. It was this intellectual and scientific character that rendered the stream of ancient Art, that commenced in Kgypt and flowed onward with varying degrees of strength and depth, through the best Greek and Roman periods, so different to that of any other country in the world. The Arts were then united with the geometry, and with the highest intellectual culture, whereas, we find in India, in Assyria, and, in the middle ages, in Europe, that Archi- tecture everywhere attained a certain degree of excellence, suited to the climate and to the wants of society, and then became stationary and decayed, for without the geometry it could not advance beyond the first elementary state, and there was no power to refine and perfect the first ideas. In the investigation of the works of nature, either with the telescope or with the microscope, the fact that nature is always working by the laws of geometry, both upon the largest and upon the smallest scale, 1s continually made apparent to us, and it is this perfection and accuracy of design and execution, that we admire in all the works of nature, that true Art should strive to attain, by being guided by the same mathematical laws and principles. It was not until the European mind, in the fifteenth century, was linked again to the ancient stream of geometry and philosophy, that a real advance was made in any branch of modern science, and probably no real progress will be made in Architecture until we can completely recover and freely use the accumulated knowledge of the ancient world in all that relates to the science of Art, and make it a basis and a starting point. But there 1s no ‘reason why the designs of modern Furope should be in any degree inferior, either in concep- tion or in execution, to those of the best ages of the ancient world; or why, with the civilization of the nineteenth century, we should impress upon our public monuments the marks of the twelfth, or of any other century that has preceded us. FINIS. Sa ae £4 Fi > (nt deka fie rl \ \ 7 7 00 4 7 a, i 3 7 be 77