few minutes. Other references will be found on the plate. Mr. Robert Mylne was the archi tect, and the foundation-stone of the bridge was laid in 1760.

164. The lower figure in plate XXXVI, is a section through the piers and one of the arches of Waterloo Bridge, London, built under the direction of Mr. John Rennie, Civil Engineer. In this section the piling for the piers, the construction of the arches, and the centring for turning the arches upon, are shown. The spandrils over the piers were formed by parallel brickwalls, with blocks of stone, from wall to wall, for supporting the road-way. The dotted line on the arch, near the middle of the depth of the arch-stones, shows the direction of the pressure in the arch when the whole load is upon it. This line is called the curve of equilibrium, and, when it passes every where at the middle of the depth of the arch-stones, the arch is of the best possible form. It will be seen that it is nearly in the middle in this case. It was formerly considered, that the soffit of the arch should be made of the same form as the curve of equilibrium, but the error was corrected by Dr. Young in his valuable treatise on Bridges, in Napier's Supplement to the Encyclopædia Britannica.

The centring was composed of eight frames or trusses, and was abundantly strong for the purpose. The disposition of the timbers will be seen by the elevation, in plate XXXVI, but a more perfect idea of the nature of the work will be obtained by a reference to the frontispiece.

Description of Plate XXXVII, (the Frontispiece.)

165. The principal object is the Centring of one of the Arches of the Waterloo Bridge, with part of the arch-stones set, and the work in progress. The framing, seen under the centring, is that of a temporary bridge for the use of the workmen. To the left, the coffer-dam, pile-engines, and machinery used in forming the next pier, are shown. The view of the work was taken at that period of its progress by Mr. Blore, an artist equally distinguished for his taste and fidelity of representation. This magnificent edifice has now been completed several years, and its simplicity of design, skilful arrangement, and solidity of execution, will render the Bridge of Waterloo a monument, of which the metropolis of the British Empire will have abundant reason to be proud, for a long series of successive ages.

OF GROINED ARCHES.

165. GROINS are formed by the intersections of the surfaces of two or more vaults, or continued arches, crossing each other.

GROINED ARCHES may be either constructed of brick or stone, and they are sometimes formed of wood, and lathed over for plaster.

When they are constructed of brick or stone, the arch-stones or bricks require to be supported upon wooden frames, boarded over, so as to form a convex surface, to fit that surface the groined vault is required to have, in order to sustain the whole during the time of building. This construction is called a CENTRE, and it is removed when the work is finished. The framing of the centre consists of equidistant ribs, fixed in parallel planes, perpendicular to the axis of each vault; so that, when the under sides of the boards are laid on the upper edges of the ribs, and fixed, the upper sides of the boards will form the surface required to build upon.

In the construction of the centring for groins, one portion of the centre must be completely formed to the surface of the principal vault, without any regard to the cross-arches, so that the

upper sides of the boards may form a complete cylindrical or other surface. The ribs of the cross-vaults are then set at the same equal distances as that now described; and parts of ribs are fixed on the top of the boarding of the principal vault at the same distances, and boarded in, so as to intersect it, and form the entire surface of the groin required.

Groins constructed of wood, in place of brick or stone, and lathed under the ribs, and the lath covered with plaster, are called plaster-groins.

166. PLASTER-GROINS are always constructed with diagonal ribs intersecting each other; then other ribs are fixed perpendicular to each axis, in vertical planes, at equal distances, with short portions of ribs upon the diagonal ribs; so that, when lathed over, the laths may be equally stiff to sustain the plaster.

167. When the axis and the surface of a semi-cylinder cuts those of another of greater diameter, the hollow surface of the lesser cylinder, as terminated by the greater cylinder, is called a Welsh groin.

WELSH GROINS are constructed either of brick, stone, or wood. If constructed of brick or stone, they require to have centres, which are formed in the same manner as those for other groins; and, if constructed of wood, lath, and plaster, the ribs must be formed to the surfaces. In the construction of groins and vaults, the ribs that are shorter than the whole width are termed jack-ribs

168. Cellars are frequently groined with brick or stone, and sometimes all the rooms of the basement-story of a building, in order to render the superstructure proof against fire. The surface of brick or stone, on which the lowest course of arch-stones, or of bricks, is placed, is called the springing of the arch or vault. It is evident that the more weight there is put on the side-walls which sustain arches, the more they will be able to sustain the pressure of the arches; therefore the higher a wall is, the greater the weight should be on each of the sidewalls and for this reason, in upper stories, where the walls are high, and not much weight over them, groins are often constructed of wood, instead of brick or stone, as not being liable to thrust out the walls, or bulge them, by the lateral pressure of the arches. The upper stories of buildings are therefore never groined with stone or brick, unless when the walls are sufficiently thick to sustain the lateral pressure of the arches. The ceilings of old Gothic cathedrals were generally constructed with groined arches of stone, which were obliged to be supported by strong buttresses, at the springing points in the arches; and, in a few instances, the same method has been adopted recently.

Geometrical Lines for Groined Arches.

169. Given the plan of a rectangular groined arch or vault, of which the openings are of different widths, but of the same height, and a section of one of the arches, as also the plan lines of the groins, to find the covering of both arches, so as to meet their intersection.

In fig. 1, pl. XXXVIII, let A, A, A, &c., be the plan of the piers, and ab, cd, the plan lines of the intersection of the groin.

Let the section of the arch, standing upon the lesser opening, BC, be a semi-circle: it is required to find the section upon the greater opening and the ends of the boards, so that the surfaces of the groin may meet in the given line of intersection.

The difference between the plan of any body and the plan line is distinguished thus: The plan is a figure upon which a solid is carried up, so that all sections, parallel to the plan, are equal and similar to that plan, and the surfaces are perpendicular; but the plan line is not in contact with the intersection itself; but a perpendicular erected from any point in the plan line will pass through its corresponding point of the intersection.