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Let U 10, 20, &c. to 60°, represent the curve of intrados, containing 60°, and V, II, &c. to A, the extrados of the loading over it. The vertical distance between these curves being determined by the length of the lines I 10, I 20, &c. which may (as Dr. Hutton and our author both observe,) be obtained sec. 3XU V. rad. 3.

from this theorem, =110, I 20, &c. which lines, they admit, are sup posed to be indefinitely narrow parallelograms, standing close to each other upon indefinitely small equal parts of the arch; or, as Mr. Gwilt expresses it, indefinitely short voussoirs. Thus they say, that by this means the curve of intrados is balanced and kept in an equilibrial state; and all this is admitted to be very just, MONTHLY MAG, No. 226,

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he could not fail of doing,) there he should have dropped the inquiry, and rested satisfied with the discovery, with out imposing this ideal theory upon us, and attempting to establish it with all its show of fluxionary preparation, but which has since been admitted, even by its advocates, cannot be depended upon in practice; for Mr. Gwilt, in page 62, acknowledges, "while the voussoirs are considered as indefinitely short, and are held in a tottering equilibrium by the vertical pressure of the loading alone, as the theory requires, the arch would not be calculated to bear any extraneous weight," and, in the same page, "that the voussoirs should be as large as may be conveniently got ;" and Dr. Hutton implies the same, by recommending them to be of an extraordinary length, and to increase all the way downwards to the springing, "the more the better," as he observes under article Voussoirs, in his 66 Principles of Bridges."

It hath been observed before, that by this theory the arch is kept in equilibrio by indefinitely narrow parallelograms; but, notwithstanding their indefiniteness in a metaphysical sense, they must have inite dimensions in a physical one, and those well defined, as each must act upon its appropriate part of the curve; that is, if the curve be 60°, with a parallelogram to each degree, the number of parallelo grams will likewise be 60, and their horizontal breadth must be the difference of the sines of the angle, that each side of those makes with the axis GV, upon the intrados, (as at 30 in the figure,) and which difference, multiplied into the height, will give the area of that parallelogram, and so for each; and the Jum of those areas must be the area of the whole space between the curve of intrados and that of extrados.

This circumstance the Emersoniaus have not considered as of any conse quence; but, as the area can be obtained from the vertical, it is obvious the vertical can from the area, and as (according to La Hire and Parent) that may be found by multiplying the difference of the tangents by the depth at U V.

Therefore, when this area is thus obtained, it is only dividing it by the difference of the sines, and you have the vertical without the expression, sec. 3XUV.

&c. raised for that purrad. 3 pose only; and further, to adapt the extrados to an arch composed of voussoirs ́of definite value, (suppose in length 4ths

of UV, and one degree in thickness,) then it is but to deduct the area of a voussoir from that of a parallelogram, and dividing the remainder by the difference of the sines adjusted to the extrados of the voussoir, and the result will be the mean height of the loading over that voussoir, according to its place in the arch, and so for each of them; and then the line VB, traced through their extremities, will be the curve of extrados to the loading over those voussoirs u E, the extrados to the voussoirs.

Now, seeing that the curve of extrados to the loading, according to either the Emersonian or wedge theories, may be determined without having recourse to the Emersonian theorem, (which is all they have to boast of,) may it not be asked, what new light hath Mr. Emerson cast upon this "curious and useful subject;" or can a theorem, raised from fluxions, to perform what for every practical purpose can be performed without it, be called a light? Surely not, but the re verse, so far as it regards the practical bridge-builder, who is the most interested, and therefore to whose capacity this light ought to be rendered clear.

It hath before been observed, of the Emersonian theory, that, upon introducing voussoirs of finite value into it, this theory must fail; and now this is inade evident by inspection, for from that you will perceive that the loading designated for the 60th degree, by the first theory, is by the second partly intercepted by the voussoir at 54°, while those voussoirs, from thence downwards, are with out any loading at all by that theory; even in this case, where the voussoirs are only aths of U V; but, if they were to extend to the curve V E, which we may suppose to be what Dr. Hutton recommends, the curve of extrados would be VXC, and the loading would only reach to 490, and the other 11° be without any, while the piramidical part IIIAX, would act as an incumbrance. Upon the whole, there is not one force or pressure, except that of UV, that retains its original direction, or can act with a pro. per effect; and all this is caused by admitting voussoirs as auxiliaries, and not incorporating them in the theory. For, when they are so incorporated, as is the case in the wedge theory, they may be made of any length within bounds; and whether they are indefinitely short, or of definite dimensions; whether they be all of equal length, or vary in that respect; or the arch put in equilibrio by means of

them

them alone, as VD, the wedge theory is sufficient for determining the nature of a proper extrados to the loading over them, as hath been sufficiently shewn. To show that voussoirs of different lengths require different curves of extrados to their loading, is only to observe that this curve is dependent on the centres of gravity of the voussoirs, which is nearly in their centre of magnitude; and therefore, when they are indefinitely short, (which is the case in the Emersonian arch, being only a curve line,) the centres of gravity must be all in that line, and consequently the first extrados is the proper one to the loading over the same. But, as this extrados can be found without having recourse to Mr. Emerson's theorem, which has hitherto been considered as a theory, and as this theorem is only adapted to this solitary case, I cannot see with what propriety we can deem it a theory; or call it by that name, what is no other than a different method of resolving a particular case, in the general theory of the equilibriuin of arches, and which theory comprehends several other cases.

Nor can it easily be defined why La Hire's (as our author denominates it) should be called the wedge theory, in contradistinction to the other,) seeing all the pressures act in the same manner, and in the same direction, in both; for, notwithstanding their parallelograms of loading are indefinitely narrow, and are supposed to act upon indefinitely small voussoirs, yet, as they are admitted to act at right angles to a tangent to the curve at the point of contact, they cannot act in any other manner than as wedges, between the voussoir and a fixed abutment, while acting above, and as a weight (W) suspended to the centre of gravity when acting below, and that whether they are definite or indefinite.

Then, as to the voussoirs, although they certainly partake of the properties of the wedge from their wedgelike form; yet they are never considered to act as such individually in an arch, never entering into the calculation but as parallel sided figures, unless rectified afterwards; and are with more propriety considered as bodies upon an inclined plane, exerting a part of their weight by their gravity, in endeavouring to descend down that plane; and what they are deficient in, in that respect, and in counteracting the horizontal pressure, is made up by means of the parallelogram, or wedges of

loading above, or weight below, as before. But collectively, when they are all connected together, and properly. balanced, they form one great wedge be tween the abutments; and, by its weight or vertical pressure, tend to separate those abutments farther apart in a horizontal direction, or by its initial pressure (the resultant of the vertical and horizontal) give them a rotative motion, (not noticed by our author or Dr. Hutton,) and tending to upset them. And. all this would take place when the arch is a curve line only, if it were possible to form one of that sort; but that I believe will not be attempted, even by the mathematicians themselves; and therefore this theory, as it hath been falsely called, must no longer be considered as such..

Thus I have endeavoured to explain these two theories of arches, as they were called, by exhibiting them in various points of view, and contrasting them in such a manner as appeared to me most likely to be conducive to that purpose. How far I have succeeded, (whatever my own private opinion may be) must be left to the public to determine; but I trust, the practical bridge-builder will find several useful hints interspersed, which, if he takes care to foster, may be of advantage to him, and he will be the more inclined so to do, when he is informed they are the result of nearly forty years' experience, in the application of the laws and principles of mechanics to practical bridge-building, and where perseverance has, in some measure, made amends for the deficiency occasioned by a limited education; a deficiency that often falls to the lot of the practical bridge-builder, but which may, to a great degree, be compensated by a close application to the study of those laws:a study so pleasing and general in its application, that a late celebrated author, in a very popular work, has made use of it to prove the existence of the Deity, or grand First Cause. Yet this science is no more than what most, who are said to have a mechanical genius, are, with inclination and industry, capa ble of obtaining. And it is for such I write, not only for their instruction, but likewise to caution them, and Mr. Gwilt, from paying too implicit obedience to great mathematical authorities; for, however right they may be in their conclusions, when the subject is considered abstractedly, those only tend to mislead the practical builder, as all the circumstances U u 2

under

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O. 11, 21, and 22, are similar. Considerable difficulties, to me at least, attend the elucidation of this figure. Pignorius (Mensa Isiaca) has mistaken the head of a cat, belonging to lurus, for that of a lion; and at the Villa Borghese is a female with a cat's head in a chair, holding the tau, (now demonstrated to be a key, which unlocked symbolically the canals of the Nile,) which tau is however mostly, if not wholly, confined to Osiris and Isis. The heads of the lion and serpent recall to recollection Mithras; but there are other circumstances which oppose this opinion. Montfaucon says, that the lion was worshipped both under bis own form and under a human form, with only a lion's head, and he mentions monuments of both, especially among the Abraxas. The symbols, however, support the idea that this figure is intended either for Cneph, Phthas, or Vulcan, or perhaps for Osiris.* It is requisite to give the reasons for this opinion. The emblem of Cheph was at first the Greek, or, according to Eusebius, a serpent extended in a circle, which he touched upon two sides: secondly, a cross in a circle, which is similar to the tau. Cneph, or the divine goodness, was represented by a serpent not venomous. (Paw.) Lions, says lian, (de Anim. xii. c. 7.) were consecrated to Vulcan, among the Egyptians, which Vulcan was Cneph, or Agathodamon. In the bark of Marcia

* No uncontested figure of Osiris is known; (Monges, Rec. pars i, p. 5) wherefore the assertion of a figure of Osiris, in No. 20, ought to be qualified with a perhaps.

nus Capella, is a lion upon a tree, sym bolic of Vulcan. Plutarch says, (Simp. Quæst. 1, 4, 9, 5,) that the lion was consecrated to the sun. The relations of the lion to the sun, (says Horapollo, 1. 1. c. 21.) were more direct, because the inundation of the Nile happened whilst the sun was in the sign of Leo, that is, in July and August. Hence, adds Horapollo, the priests gave the form of a lion to the mouths and stops of the sacred fountains; hence, according to the same writer, (1. 1. c. 17.) lions were placed under the throne of Horus, to show the analogy which existed between this aniI am aware that this mal and the sun. figure does not coincide with the representation of Cneph, given by Eusebius in his Præparatio Evangelica (1. 2. c. 11.); but authors, though they may elucidate, cannot disprove, marbles. The grand objection is, that the worship rendered to Phthas, Cueph, or Vulcan, did not long subsist; and to this intellectual symbol were substituted celestial and terrestrial phenomena, Osiris, Isis, Hammon, Horus, the Nile, &c. Hence no feast was celebrated in his honour, and only one temple was consecrated to him, situate at Memphis. Hence, I doubt, whether this figure may not be an Osiris, with attributes of Cneph. At all events it is easy to give an hieroglyphic meaning of the figure. The Tau was the key that opened the Nile; the lion's head implied the solar influence; the serpent was the symbol, variously, of the sun, (Macrobius) divine goodness, good fortune, &c. But it is more to our purpose to know that Cneph, or Agathodæmon, appears, upon some bronzes and coins, as a serpent, erect, with his head with horns, supporting a discus, like that of Isis. Authors observe that the first Christians destroyed numerous representations of the Agatho-dæmon. According to the usual method of explain. ing Egyptian figures, this figure typifies the rise of the Nile, and the influence of divine goodness, and the solar power; bat, whether it represents Caeph, the Agathodæmon, or Egyptian Vulcan, others must decide for themselves from the above evidence, What an abstruse species of learning is Egyptian hieroglyphics, the public well knows, as well as also that we have no key to the hieroglyphics. According, however, to the evidence within my knowledge, the figure is either Cueph, or Osiris with the attri butes of Cneph. Learned men may still

find good grounds for dissenting from this opinion.

Nos. 12 and 14, are fragments of a column.

No. 13. A coffin.

No. 15. Part of the frieze of a temple, the upper part consisting of a row of birds, only the legs of which remain.

No. 17, is another frieze, the upper part consisting of a row of serpents. At Persepolis the figures are fac-similes, in attitude, costumes, &c. Is, or is not, this repetition of identical objects, in succession, a test of very high antiquity?

No. 16. An Egyptian Obelisk. It is much more slender and of finer proportions than the modern. Winckelmann has justly reprobated the absurd custom of mounting obelisks upon pedestals.

No. 18, is a small Egyptian figure, with a beard, a short apron, and a terrific aspect. He is standing upright, but holding his arms downwards, a little apart from the body. The ornament upon the head is peculiar to the representation of this figure. I regret that this figure escaped me. The Egyptian Typhon was not like the Greek giant of that name, a monster, but a human figure, of terrific aspect, and a part of his dress rising from the shoulders in an arch over his head, as if it had been blown up. See the figure in the Florentine gems. (Tom. ii. pl. 41, n. i.) Typhon was, in mythology, the evil spirit of Egypt; but, from the collected evidence, it appears that Typhon was not only a burning and desiccating wind, but moreover a wind which blew from the east, and, after ha. ving passed the scorching deserts of Arabia, the borders of the Euphrates, &c. deluged Egypt with torrents of fire. (Enc. des Antiq. v. Typhon.) Typhon thus symbolized a burning drought; in Egypt, a tremendous evil. No wonder therefore that the terrific aspect and arched veil accompany his figures. How far these remarks apply to No. 18 must be estimated by those who have examined the statue; but no other Egyptian figure of terrific aspect is known to me, and therefore I have risqued the above remarks.

*For instance, the Abraxas, with the lion's head and serpent's body, are inscribed, Cnoumis, Anubis, &c. See Chifflet, Capello, &c. One, a human form, with a lion's head, in a chair, is inscribed ΜΕΛΑΝΟΜΕΝΗ. According to the explications of the Isiac table, Isis appears with the lion's head and tau.

No. 19, is the head of an Egyptian Sphinx. The bottom of the nose is very broad. The Egyptian conformation of the face should be attended to by artists, who grecianise the faces of the people of all nations.

No. 20 to 22, include a kneeling figure supporting an altar, and fragments similar to No. 10.

No. 23, is the celebrated Rosetta stone. Antiquaries were elated, upon its arrival, with the expectation that it would furnish an alphabet of symbols, explanatory of the hieroglyphics.—Vain hopes!

Quibus si credideris
Expectare poteris

Arthurum cum Britonibus;

or that there does exist the famous pays de Cocagne, where fowls fly about readyroasted. This famous pye, in which fourand-twenty blackbirds were inclosed, was not set before the king, but the Society of Antiquaries; and, when the birds began to sing, it proved to be only a tomb-stone eulogium of Ptol. V. enNow this graved by order of his son.

said

very Potlemy, (as bad readers have styled him, or some wag,) is declared by Justin (2. 29, c. i.) and elsewhere, to have been a very infamous fellow, both as a king and a man. He murdered his father, mother, brother, and wife, kept woman after woman, and feasted and fiddled away almost all his time. (See The stone has been (. 30, c. i. 2.)

published in fuc-simile by the learned society, and it will be useful, as showing the forms of the Greek and Egyptian letters, in the year of the world 5021, when Ptolemy VI, or Philometor reigned.

No. 24 to 35, contain colossal heads, fists, &c. &c. of which last below.

No. 36 is a votive column, on which is an inscription in Greek, to the great god Serapis, at Canopus. This Serapis, wor shiped at Canopus, was Serapis of the Nile, and his chief temple was at the above town, near Alexandria. We are told by some writers, (Enc. des Antiq.

Serapis) that, when Ptolemy brought the statue of Serapis from Pontus, (Serapis of the Nile being represented in form of a pitcher or vase,) and placed it at Canopus, already consecrated to Seraps of the Nile, all distinctions were confounded. The Greeks spoke no more of Serapis, whom they confounded with their Pluto, and the traces of Serapis of the Nile were lost entirely. The presence of a Greek inscription upon this votive column, may perhaps denote its

antiquity

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