" But although the total immersion, even of a lofty pier, will seldom require any great alteration in the thickness, there is yet another circumstance which well deserves atten tion. Bridges are often built, especially in a tideway, with the arches springing below the high waters ; we have in that case a diminution from the weight of the arch itself; but unless the keystone be under water, the horizontal thrust is unchanged; we must, accordingly, in our calculation, make the same diminution for that part of the arch which is thus immersed, as we did in the above example for the piers. The result will oblige us still more to increase the thickness of pier.
" On the whole, we may conclude from this investigation respecting the piers, that the increase of breadth which may be, and usually is, given to the pier, is of much less import ance, on account of the weight that is thereby gained, than by its increasing the length of that arm of the lever, whereby thg weight of the whole resists the effect of the horizontal thrust oversetting it.
" Instead, therefore, of building up the pier with perpen dicular sides, we should think it more advisable to begin the foundation Of the pier on a base much wider than usual, and from thence, by regular recesses, or otherwise, gradually to diminish it, until, at the springing of the arch, it does not exceed the depth of the two arch-stones, while the outline of the pier may be a curve of any shape that is most pleasing. Many advantages would, in our opinion, be obtained by this construction: the water-way will be enlarged ; the pier equally strong ; the stability equally great, nay, much greater than usual ; and the chance of the foundations being hurt in floods will be greatly diminished ; and all this with a smaller quantity of materials." It is manifest, that before an arch of equilibration can be destroyed, the pressure applied must be so great as to come the resistance offered by the friction of the adjoining voussoirs, or the adhesive power of the cements; and be it remembered, the greater the pressure, the greater also is the friction. We give the following as a method of discovering the extent of license allowed in practice, on account of this quality in the materials employed.
To find the quantity of friction in individual instances,— Place the stone to be used upon a platform of the same mate rial, and raise up one end of the platform, until the least additional elevation would cause the stone to slide down, and measure the angle of elevation so found.
Now the effect of friction is this, that instead of being compelled to place the joints of the voussoirs in the position assigned them by theory, we may place them in any position on one side of it, provided the joints fidl within an angle from their theoretical position, not greater than the angle of eleva tion, determined as above ; or if the joints of the voussoirs are maintained in their original position, we may allow a proportionate variation in their weight. On this account very great latitude is allowed in construction, for we may depart very flir from the rules laid down from theory, before we can endanger the stability of the (slide°.
Dr. Robison is of opinion, that the voussoirs may be con sidered as it solid mass, and that the principal object to be attended to, is that the arch should be made so flat, as to admit the same straight line being drawn in such a manner as to pass through some point in every voussoir on either side of the keystone, and where this is impractieable, he recommends that the straight line should be carried through as many arch-stones as possible, and that the arch should be carefully loaded at the intersection of such lines, considering each number of voussoirs passed through by one line as a separate block of stone. Generally, he supposes, that the pressure at the crown, is communicated in a straight line through as many stones as one straight line will pass through. All suggestions, however, on this subject, must be attended with considerable doubt and difficulty, as we are almost entirely ignorant of the method by which the communication and distribution of pressure is regulated, and even, in many cases, of the nature of the materials employed.
In accordance with the intention expressed by us in our article on BRIDGES, we now proceed to give a description of the principal stone bridges erected over the Thames, com mencing with Westminster, as being the oldest. The first stone for that bridge having been laid on January the 29th, 1739, by the Earl of Pembroke, and the bridge itself being entirely completed on the 10th of November, 1750.