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looked upon as one of the greatest performances of themasonic art: for if we compare the enormous weight of agreat arch, with the strength which the cohesion of thefirmest cement can give, we readily admit, that it is only bythe nicest adjustment and balancing of its parts, that they are| hindered from instantly falling to pieces.

I “ Though there can be little doubt that the Romans, andj latter Greeks, had paid some attention to this subject, from| the beautiful specimens of their architecture which existj even in our times ; yet, in none of their authors, either prac-tical or scientific, is the smallest light afforded us respectingthe principles upon which their practice was regulated.

“ The architects of the middle ages, who constructed thosegreat cathedrals, that are still the ornament of the chief citiesin Europe , and the delight of the architectural antiquary,seem to have fondly indulged in the balancing of arches,j They were, without doubt, directed by maxims which had| been elicited from a varied and extensive practice ; but wliat-| ever these were, they are to us unknown. None of thesearchitects, though many of them were men of learning, seemever to have committed to writing, either the history of anysuch erection, or the principles by which its construction wasregulated. Nay, this knowledge seems rather to have beencarefully kept secret, and regarded as a sort of mystery ; acraft which was only to be communicated to the brethren ,whose experience and skill had already qualified them to beinitiated into the mysteries of the sublime degree.

“ It does not appear that a knowledge of this subject couldbe acquired otherwise than by experience. The mathe-matical sciences were then little known, and we may see| from the construction of the bridges of that age, that the| priests, who were the only architects, have had in their eye,j rather, the successive vaulting of a Gothic cathedral, than toj have originally considered of the best way of forming a per-manent and convenient road. It was only about a century! ago, when Newton had opened the path of true mechanical| science, that the construction of arches attracted the atten-| tion of mathematicians. Since that time, volumes have beenj written respecting the equilibrium of arches. It has beenfound one of the most delicate, as it is one of the most impor-tant, applications of mathematical science. Yet with all duedeference to the eminent men who have prosecuted this sub-ject, we are much inclined to doubt whether the greater partof their speculations have been of any value to the practicalbuilder. He is still left to be guided by a set of maximsderived from long experience, and, as yet, little improved bytheory. In truth, his works seldom fail, even where theydiffer furthest from the deductions of the theorist; and at allevents, he finds that a much greater latitude is allowable thantheory seems to warrant. He is therefore surely excusablein doubting of the justice of such theories, at least until theyare more consonant to the approved practice.

“ It is our intention, in the present article, to point out anew mode of considering this subject, to which, with greatdiffidence, we request the attention of the intelligent prac-titioner. It may indeed still be deficient, if not in somerespects erroneous, but it will, we think, have this merit,that of being readily apprehended, and easily applied, with-out requiring much previous scientific information. Indeed,though we highly value the sublime geometry, we are inclinedto think that the unnecessary parade of calculus in the appli-cation of science to the arts, has been one of the chief causesof the dislike, which many able practical men of our countryhave shown to analytical investigation.

“ Nevertheless, as many of our readers are well qualifiedto comprehend, and will naturally expect that we should pointvut, the modes of investigation, usually pursued in this

interesting subject ; we shall previously, and in as c0 „j-a manner as possible, endeavour to lay before them j l£lV jngmonly received theory of equilibration. From which) a „ycleared away the useless rubbish, if we can ext g 0 odproper materials, we may, like economical builders, muse of them in our future structure. . . ; 3 tl>®

“ The first thing like a principle that we meet ’’^ifichassertion of the eminent Dr. Hook, that the figure m ^ a ta heavy chain, or rope, arranges itself, when sus P e ., e( j tl> ethe two extremities, being the curve commonly ca c jj;catenaria, is, when inverted, the proper form for anthe stones of which are all of equal size and weight- rP Ily“Now, as this idea, strictly just, has been very g® ff0r t)iadopted, and afihrds some useful hints, it may be wewhile to examine it. j,o<3i eS ’

“Figure 1.—Let a b be a string or festoon of heavy c!in -hanging by the points a, b, and so connected, that ^pgednot separate although flexible. These bodies having a r „ e dthemselves in the catenaria A c B, conceive this to jjjgd,exactly upside down. The bodies A and b beinthen each body in the arch adb, being acted on by o e q U jland the push of its two neighbours, with forces exaC - v g posi'and opposite to the former, must still retain its relation, and the whole will form an arch of equilib rat1 ®^ 1 ' *“This arch, however, would support only j tse i.u do' vn |mere breath will derange it, and the whole will * a a cub'f‘But if we suppose each spherule to be altered into ^ th eform, occupying all the space between the dotted jyot 11stability will be more considerable. And as the t;nr ^ t0 th®each spherule to its neighbour is in a direction p aia o j )V io aS ’tangent of the arch at the point of junction, it 1 jj cU iar 10that the joints of our cubical pieces must be perpenthat, so as to prevent any possibility of sliding. ,

“ Our arch is now composed of a series of trunca e t j jr0 og 1Jarranged in the curve of the catenaria, which pass or y,t°their centres; and we are disposed, with David *- rX *J>ec aUfleinfer, that when other arches are supported, it is 0 Jin their thickness some catenaria is included.

“ Figure 2.—The haunch, e, of the arch - 4 C B ’ ugtmuch greater depth of stuff than the crown, itcontrived as to resist this additional pressure, b •. • ° ne otr*?;

jf'V

proper for carrying a road-way of the form E G a 'j ig refloatupon a vertical wall, the points a, c', b, invertingfigure : suspend from A b an uniform chain or j di vl rf j, 1 g

its middle may hang a little below the point c > a | i( j di’ 11 "^'the span, A b, into any number of equal parts,the perpendiculars ab, c d, &c., suspend from jj ia t pe‘ ‘ ‘ ‘ ‘ ‘ ‘ so trimmed-

and, 11 1 >" !in

to

tions, e,f bits of chain, e b,f d, &c.,ends may fall on the line of the road-way; l 11 ,

observed, that as those pieces, which hang nea * j-ais® 11will bring it down, the crown, c,' will thereby u -jr

its proper position. . „ a a y ,iii‘J

“But although this mechanical way of ^ or, . g [,tTybrated arch be founded upon principles sufim 1 pi®be perhaps the simplest and best way in win®

ueu. an (if®

“ This curve is, indeed, the only one proper g jngjconsisting of stones of equal weight, and touching >v ]ii®points, but is not at all adapted to the arch of a .^^gtindependent of the varying loads that pass over i > t j•£>*filled up at the haunches, so as to form a conyen ^ eCO viway. In this case, some farther modifica 110necessary. __ . „ n be al ' inS s o

mo-tion of the line fGH, or extrados, will require < c0 „i... (

fication of the curve a c b, or intrados, and t 1 pop® ‘ 0Accordingly, M. De la Hire has suggested amode of investigating this subject. Let it * ,e ( j jjeigb^ offdetermine the form of an arch of the span a b, an lurk