Chap. VIII.

BRITAIN.

419

rig. 421.

a weight proportionable to the height they rise, to keep their parts firm in the situationthey are first placed, for it is very reasonable to think, that the arches of London Bridgewould not have remained so entire to this day, if it was not for the weight of houses thatare erected thereon, which must certainly prevent those frequent shocks and shakings thatit must otherwise have suffered, by loaded carts and cars, and other vehicles of burden, thatdaily pass and repass thereon.

“ But to proceed to make some observations on the shape of arches in respect to theirduration. I think the most common sort that are to be found amongst our modernbuildings are either semicircles, segments, or semi-ellipses, which I must own have anagreeable effect on the eye, because they are part of regular figures, and make a good ap-pearance in a building if they are well proportioned and well introduced; but this is notalways observed by our modern builders, for I have often seen a passage of 3 feet wide witha semicircular arch, and a gateway of 10 with an elliptical one, whose height from thespringing hath not exceeded 20 inches ; such a one cannot be supposed to be of any longduration without very strong abutments, unless the weight be discharged by a concealedbreastsummer, or very little laid thereon : in such cases ornament is consulted more thanstrength, for the arch of 3 feet being a semicircle wdll bear above ten times more weightthan the elliptical one of 10 feet with the same abutments, by reason of its flatness anddouble centres, which must render it very weak and unfit to support a great burthen, Imean such an ellipsis whose transverse diameter is placed hori-zontal ; but if you take an ellipsis the other way for an arch, and letthe conjugate diameter be horizontal, then it will become altogetheras strong, and may very justly be esteemed the best sort to supporta great burthen, excepting those formed by the catenarian , which Ishall endeavour to prove the strongest of all, and the most durable.

But for the truth of what I have asserted in respect to the ellipticalarches, I must refer to a very easy and familiar experiment, whichis, to take an egg, and try whether it will not bear a great dealmore weight on the ends than it will on the sides before it burst;such an experiment, seems to me to put this matter out of the reach of contradiction, andwill justify the theory I have hitherto endeavoured to explain, namely, that all arches willbear a weight proportionable to the height they rise from their springing, if their chordlines or openings are the same, let the shape be what it will, although it must be allowedthat some sort of shape will bear more weight than another of the same height and abut-ments ; for if the elliptical arch was a segment of a circle of the same height, it would addmuch to its strength, by reason that a curve would be more uniform, and approach nearerto a catenarian than it was before, in the flat elliptical form, for it is my opinion that thestrength of all arches would be increased the nearer they approach that firm arch of nature,for so I must call it, by reason it is formed by action of gravity, which must be allowed tobe a natural cause.

“ This curve or arch may be discovered by suspending a chain, or flexible line, that is notvery light, from two horizontal points or nails; the curve or arch that such a line or chainwill form is called the catenarian. This line, as I before observed, is formed by the actionof gravity, which acts on all bodies according to their density or quantity of matter theycontain, if their form and shape are the same ; therefore, if gravity by its action on a slackline or chain form the arch a, it is very plain that if it were turnedupside down it would form the arch K, which, consequently,must resist that action in the same proportion as the other gaveway, that is, K would become an arch of equal strength in allits parts, and for that reason must be certainly the best shapefor any arch that is to bear a great burthen.

“ But as the properties of the catenarian arches are so far con-cealed that it w r ould be very difficult to assign any centres thatwould strike the same, for if they are very flat they appear likesegments of large circles, but if you endeavour to form a semi-circle by letting the line drop half its opening, it will then appearelliptical, and as you drop it lower, it seems to approach thehyperbola, so that the distant appearances it makes in these dif-ferent stations must render it very difficult to find out proper centres to strike them out.But those that have occasion to apply them to practice, may observe the following method,which may answer the purpose very well if it be carefully observed, that it is to take sucha line as before mentioned, and rub it with chalk or charcoal until it be fit to leave an im-pression ; then, on some flat plane or board that is large enough for the use, fix in two nailshorizontally, according to the width or span of your arch, and from thence let the line fallas far below the horizontal line as you would have the arch to rise above it; then carefullypress the line hard enough to leave the impression, and that will be the arch required ; then

e e 2

rig. 422.