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From (5) . . P . a='957 (134920) (4+5'5)+3'56745 (134920) = 129118'444+1191511'78; „ (6) . . F. c='4975 (134920) (4+5'5)—-4975(527854'4) = 67122'7 <+106567'28 ; „ (7) . . Q .5=101-22798 t 3 +186xl01'22798P. Adding and reducing, the equation for equilibrium (3) becomes <’+186< 3 +1938'6t—29373'24=0, whence 4=8'2 ft. for equilibrium. And the equation for stability (4) becomes 4 3 +1864’+I938'64—71570=0, whence 4=14'66 ft. for stability. In the construction of this particular dome, the values ob tained above for 4 will only apply to four points on the, walls which carry the dome; for instead of being built on a circular “ drum,” this dome is made to cover a square chamber by means of “ pedentives,” which are so arranged as to throw the thrust principally on the angles of the building, where the values of a and c will become very great, and it is only at the centre of each of the four sides that the above equations can be employed to compare the thrust of the dome with the strength of the walls. At these four points the walls are about 11 ft. thick, so as to be considerably more than sufficient to produce equilibrium; and the coefficient of stability at these points is 1'374 instead of 2. Had the dome therefore been built on a circular drum of 11 ft. thickness, in all probability the edifice would not have stood for any length of time. Much of the thrust of a dome may be counteracted by means of an iron belt placed round it at the point where the thrust is greatest. This point I have shown to be at 70° from the crown, or 20° from the springing. (To be continued in our next.} PAINTING AS A FINE ART; ITS PRINCIPLES AND THEIR FULL DEVELOPMENT IN THE WORKS OF THE ANCIENT MASTERS.* By H. Mathews, Abchitect. If we refer to an English Lexicon for a definition of the word Architect, we should read “ a Chief Builder,” and I believe that this is about the estimate that most people put upon those who are employed to design and carry out the works which are entrusted to them, being sufficiently satisfied if their interests, pecuniary and otherwise, arc well conserved. That no one can be an architect who does not understand the principles of construction, and will not allow his own pecu niary interests to be second to those of his client will bo admitted, but mechanical knowledge and integrity of purpose, are far from being the only requisites for an architect, even if he be clever in planning and accomplished in designing. Neither will his education be complete by a well grounded knowledge of period or style. His advocacy of one particular style to the disparagement of another may elevate him to a class leader or head centre, but it is the refined mind, the just appreciation of what is really good in every style, with a generous acknowledgment that what does not commend itself to taste, may, nevertheless, possess beauties which the superior learning and natural genius of others may qualify them to discern. These are graces which, being possessed by many, should be coveted by all. Not limiting himself to the study of the sciences, the archi tect should also cultivate an intimate acquaintance with art in each of its departments, and be as able to appreciate the beau tiful as to comprehend the difficult; to discover the exquisite touches in the engraving of a gem, as the stupendous grandeur and ample proportions of an amphitheatre. Delineation may be classed with the most ancient of the arts, and as having been employed by the inhabitants of many countries for the communication of their ideas long before they obtained the knowledge of the art of writing. The graver and the pencil may be said to write an universal language, easily and instantly understood by the simplest minds. We all know their effect upon the eye and mind of a child, and that in pro * Read before the Architectural Association. portion to the closeness of the resemblance to the object intended to be represented, so does the picture more or less operate upon the feelings of the beholder. Among the fine arts, that of painting has been more or less associated with architecture from its infancy; and if not so extensively employed as its twin sister sculpture, yet by the Romans and the Italians, both in classic and mcdiawal times, it was enlisted as an accessory in giving character and effect to the grandest productions of architectural genius; and as there is now a manifest desire for mural and pictorial decoration in public and private edifices, which doubtless will conduce greatly to the free and widely extended use of the pencil, I wish to put in a plea on behalf of “ Painting as a fine Art; and its principles, and their full development, in the works of the Ancient Masters.” A School of Painting does not mean merely an academy conducted by one or more masters, but it denotes a class of artists who have learned, some by the direct tuition by the founder of a certain method of painting, diverse from that hitherto practised, or which possesses peculiarities or charac teristics of a new or of a higher order—or of others who by study, display more or less of his manner from their desire of imitation, or from the habit of adopting his principles. The schools of painting since the revival of the art in the 14th century, may primarily be distinguished as the Italian School, the German School, the Flemish School, the Dutch School, and the English School. The Italian School is subdivided into the Schools of Florence, Rome, Venice, Bologna and Lombardy; the latter School comprising those of Parma, Cremona, Milan and Naples. The Egyptians carried the art of delineation to a very great extent, and by means of their wall pictures and hieroglyphical carving, the moderns are in possession of an intimate acquaint ance with the history, religion, arts, manufactures and other characteristics, not of Egypt alone, but of a great portion of the then known world at that remote period. The Greeks, although attaining to great eminence in the arts of Architecture and Sculpture, seem to have had a circum scribed knowledge of Painting, and until the age of Alexander the Great, we scarcely know of its existence as an art. The early Grecian masters, it appears, used only four colours ; an earth for white, an ochre for yellow, another earth for red, and lamp black : and it was with these four simple substances that Zeuxis, Polygnotus and others, executed their renowned works. By degrees new colours were discovered, so that at a later period, when Appellcs and Protogenes flourished, the art was brought to great perfection; and if we may credit all that ancient authors write of them, it may seem doubtful if the moderns possessed greater advantages in this respect than their predecessors. During the time of Alexander, Grecian art had attained great eminence, and the painters of that age had learned to express the emotions of the mind with such fidelity, that that universal conqueror grew pale and trembled upon beholding a picture of the betrayal of Palamedes by his friends: and on another occasion he rewarded Appellcs with the gift of one of his concubines, with whom the painter became ena moured, while, by the emperor’s command, she sat for her likeness. Pliny, the historian, tells of two painters each being a competitor for the prize. One painted grapes so naturally that the birds used to peck at them; and the other represented a curtain so artfully, that his opponent ordered it to be drawn aside in order that he might have a view of the painting it con cealed. None of the works of the Greek painters have been pre served to us, so that our estimation of their merits must rest entirely on the opinions entertained of them by their con temporaries and historians. The conquest of Greece afforded the Romans a grand opportunity of improving their knowledge and appreciation of the art which had to some considerable extent prevailed since the reign of the Tarquins, and at the time of the subjugation of Greece to the Roman power, that people had arrived at the zenith ot artistic eminence, and in consequence the victors reaped the full benefit of the mental culture which,’for three centuries, that enlightened people had been systematically bringing to perfection. Until the time of Augustus Caesar it seems to have been usual only to paint the internal walls of houses with a single colour, relieved in part with ornamental work. That emperor is said to have been the first who thought of covering these