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3. Plato, 429, in Critias, descriptive of a former imaginary condition of Athens. 4. Æschines, 389. 5. Demosthenes, 385. It was remarked, that, during the Macedonian and Roman periods, the Pnyx was not used, and is only mentioned incidentally, or by way of allusion. 6. Plutarch, A. D. 40, in the Life of Theseus and Life of Themistocles, an anecdote of the Thirty Tyrants. 7. Lucian, 120, in the Fishers. 8. Julius Pollux, 183. 9. Timæus, 3d century A. D., in Lex. Plat. 10. Hesychius, 380. 11. Proclus, 412, Commentary on Plato. 12. Souidas, in the eleventh century. Then came the Crusaders, and the periods of the Dukes of Athens, and of the Turkish domination, during which the knowledge of Athenian topography almost disappeared.

The opinions of the early modern travellers were mentioned. In the seventeenth century, Spon thought it was the Areiopagos: Wheeler, the Areiopagos or Odeion. In the eighteenth century, Stuart and Revett believed it to be the Theatre of Regilla. Chandler, 1765, expressed the opinion that the structure was the Pnyx, or place of the popular assemblies of the ancient Athenians, and from that day to a recent period no doubt has been entertained that the levelled space, supported below by a heavy polygonal wall, was the Pnyx, and that the stone platform was the Bema, or stand on which the orators took their place when they addressed the people.

In 1836, the University of Athens was founded, and Professor Ulrichs, one of the German scholars appointed to a chair in the institution, began to entertain doubts of the correctness of the received opinion. In 1842, Professor Welcker of Bonn, one of the most eminent scholars of Europe, visited Athens, and, in company with Ulrichs, went up to the Pnyx. On examining the place, he found reason to coincide with the impressions of Ulrichs. Since that time he has carefully studied the subject, and in 1852 published in the Abhandlungen der Königlichen Academie der Wissenschaften of Berlin a very elaborate dissertation, in which he embodies the results of his studies, and arrives at the conclusion that the Bema is an

ancient altar to Zeus Hypsistos, or Jupiter the Highest, and that the levelled space, with the old supporting wall, is the ancient Pelasgicon. This essay was answered by Professor Ross, formerly of Athens, now of Halle, in a pamphlet, published in 1853. Welcker replied by another pamphlet in 1854.

Professor Felton gave a summary of the arguments on both sides, and stated that the subject had occupied much of his attention while in Athens; — that he had come to the conclusion that the received opinion is correct; — and, in confirmation of this view, went at some length into an examination of the authorities, especially Plato, Demosthenes, Plutarch, and Proclus, citing a passage from the last-mentioned author which had never been considered before, and which was pronounced to be almost, of itself, conclusive: and quite conclusive, as the last term in a cumulative argument, the expressions being precisely applicable to the shape of the supposed Pnyx, and to no other place or structure in Athens.

Four hundred and twenty-first meeting.

December 11, 1855. — ADJOURNED QUARTERLY MEETING. The PRESIDENT in the chair.

The following gentlemen were elected Associate Fellows; viz.: –

Rev. Moses A. Curtis of South Carolina, and Professor Charles W. Short, M. D., of Louisville, Ky., in the Section of Botany.

Drs. J. P. Kirtland, of Cleveland, Ohio, and J. C. Dalton, Jr., of New York, in the Section of Zoology and Physiology.

Professor Dennis H. Mahan, of West Point, in the Section of Technology and Engineering.

Hiram Powers, Thomas Crawford, William C. Bryant, and Washington Irving, in the Section of Literature and the Fine Arts.

Professor W. B. Rogers exhibited to the Academy a set of Schönbein's test-papers for ascertaining the amount of ozone in the atmosphere, and explained their use and the great importance of the observations based upon them.

Professor Rogers also exhibited a series of diagrams explanatory of certain conditions of binocular combination not hitherto described, and intended especially to demonstrate the form of the curve which results from the binocular union of a straight line with a circular arc, or of two equal circular arcs with one another.

“ First. Of the binocular resultant of a straight line and a cir. cular arc.

“ Assuming the optical centres of the two eyes as fixed during the act of combination, the centre of the eye directed to the circular arc may be regarded as the vertex of a cone whose surface includes all the positions of the optical axis of that eye as successively directed to the different points of the arc. This cone will of course be right or oblique, according to the direction in relation to the plane of the paper of the line joining the optical centre with the centre of the circle of which the arc is a part. The axis of the other eye, in ranging from end to end of the vertical line, vibrates in a plane which during the binocular combination intersects the conical surface in an attitude depending on the distance between the optical centres, the place of the diagrams, and the relative position of the component lines.

“ The two optical axes, directed each moment to corresponding points of the vertical line and arc, meet in the conical surface, forming optically a series of resultant points which together compose the binoc. ular resultant curve. This curve must, therefore, be a conic section, the nature of which will depend on the direction of the cutting plane in reference to the conical surface.

“ Considering the several cases in which the arc is convex towards the right line or concave towards it, and in which the combination is effected before or behind the plane of the diagram, all the results may be thus summed up.

(a.) When the arc is convex to the right line and they are united beyond the plane of the diagram, or when the arc is concave to the line and they are combined in front of it, the binocular resultant may be either an ellipse, a parabola, or an hyperbola ; but in either case it will turn its convexity obliquely towards the observer. .

(6.) When the arc is concave to the right line and they are united beyond the plane of the diagram, or when it is convex to the line and they are combined in front of the diagram, the binocular resultant is always an arc of an ellipse turning its convexity obliquely away from the observer.

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“Second. Of the binocular resultant of two circular arcs.

“In this, as in the preceding combinations, the optical centres are to be regarded as immovable during the experiment. Each eye, while viewing the successive points of the arc presented to it, revolves in such manner as to carry the optical axis around in a conical surface. Thus two conical surfaces are generated, having for their respective apices the centres of the two eyes, and including all the directions , which the optical axes assume in combining the successive pairs of corresponding points of the circular arcs. In general terms, therefore, the binocular resultant in all such cases may be described as the curve line in which the surfaces of the two visual cones intersect one an. other.

“It is only, however, under special conditions that the resultant thus formed is a plane curve. When the circular arcs presented to the two eyes are of unequal curvature, the visual cones by their intersection produce a curve which cannot be included in a plane, but lies in an inflected surface; and this accordingly is the form which the resultant takes whenever circular arcs of unlike curvature are combined either with or without a stereoscope.

“ The several effects of the binocular union of circular arcs of equal length and curvature may be thus summed up.

“ (a.) When the arcs are convex to one another, and are combined behind the plane of the components, or when they are concave to one another and combined in front of this plane, the resultant may be either an hyperbola, a parabola, or an ellipse ; but in either case it will be convex towards the observer and in a vertical plane.

" (6.) When the arcs are concave to one another, and are combined behind the plane of the components, or when they are convex to one another and combined in front of this plane, the resultant is always an arc of an ellipse concave towards the observer and in a vertical plane.

" Whenever, in any of the combinations referred to, the resultant curve takes the position of the sub-contrary section of the cone, it of course becomes an arc of a circle."

Professor C. C. Felton exhibited to the meeting a series of

silver coins of Athens, which he had lately received from Mr. George Finlay, of Athens, and made some remarks, of which the following is the substance.

“Mr. Finlay is the distinguished historian of the Byzantine Empire. He has resided in Athens for many years, occupied with historical studies and archæological researches. The ancient coins of Greece, and the coins of the Byzantine Empire, of which he has a large and valuable collection, have been much attended to by him, both on account of their intrinsic interest and for the illustrations they afford of numerous points in history.

“ The excellence of the Athenian currency has been often the theme of eulogy. The practical sense of the Athenian people was as remarkable as their genius for literature and art. We are apt to forget, in our admiration of the Parthenon adorned by the sculptures of Pheidias, and of the tragedies of Sophocles and the orations of Demosthenes, that the same people were equally eminent in commerce, manufactures, and agriculture; that they had devised a judicious sys. tem of public revenue, and well understood the theory and practice of credit in commercial and banking operations. At an early period, the silver coinage of Athens acquired a general currency throughout the commercial world. So well did the Athenians perceive the advantage of this, that they retained, even during the periods of the highest excellence in the fine arts, much of the rudeness of the earliest mintage : so that the coins of Macedonia, and of many of the colonial states, far surpassed, in beauty of design and execution, the coins of Athens. This adherence to the archaic style was intentional; it was the result of practical wisdom, abstaining from change, in order not to affect the established credit of the ancient currency.

“The principal authorities on ancient coins are Spanheim, Eckhel, Mionnet, Boeckh, Hussey, Cardwell, and Humphrey ; together with the lists of the coins in the public and private collections of Europe.

“ The silver coins now exhibited are, — 1. Tetpáðpaxmov. 2. Apaxuń. 3. Tpoßolov. 4. "Obolos. 5. Tpurnuópiov. 6. 'Hylobolcov. 7. Terapinuóplov. These coins have been carefully weighed by Professor Horsford, with the following results :

Troy Weight.

French Grammes. Tetpáðpaxuov (four drachmas), 255.99 gr. Apaxuń (drachma),

63.20

4.0929 Tpoßolov (three-obol piece, or half-drachma),

30.70

1.9883

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