1. Stone-Masonry is the art of building in stone. The word mason is derived directly from the French maçon, which signifies indifferently a bricklayer or mason. Du Cange attributes the origin of the word to the low Latin maceria, a wall; others have endeavoured to show that it comes from machina, because builders use machines for hoisting materials; but by far the most probable derivation is that of the French maison, a house; thus maisionner is to build houses, and the maçon, the man who builds them. Among ourselves, at present, we reckon three sorts of artificers—rubble or rag-stone masons, freestone masons, and marble masons. This last branch, however, is rather that of the carver or statuary. The art of working or reducing stone to the proper shape for the mason to set, or place them in the walls, &c., has generally been called stone-cutting, and depends very much on the nature of the stone for its details.

2. The art of building with stone is of very great antiquity; it was originally, no doubt, suggested by the holes in the rocks, or natural caves, in which our forefathers sheltered themselves from the inclemencies of the weather. The perishable nature of their wooden huts afterwards suggested an imitation of them in stone as a durable material; and the trunks of trees, and the beams laid across them, were probably the prototypes of columns and architraves.

3. Among rude and barbarous people there seems to have been always a great desire to erect huge masses of stones, either as memorials of some event, or for the purposes of religion, and the early history of almost every country treats of some of these structures. (See Cromlechs, Stonehenge, Architecture, p. 423, &c.) The treatises of Dr Lukis, and other papers in Archaeologia, give the fullest account of these structures.

4. The necessity for defence against predatory tribes seems to have given the next impulse to building with stone, and to this we probably owe those extraordinary walls, commonly called Cyclopean or Pelasgic (Architecture, p. 439). These are huge polygonal blocks of stone, carefully cut so as to fit exactly to each other without mortar, and forming walls which must have been impregnable at that time. An idea of their size may be gathered from the fact that in the Etruscan walls at Ruscello, Mr Dennis (Cities and Cemeteries of Etruria, vol. ii.) measured a stone 12 feet 8 inches long by 2 feet 10 inches high. Most of the blocks forming these walls would weigh from 6 to 8 tons. It seems very difficult to understand in that state of civilization how they were hoisted and set. Pausanias (ii. 25), describing those of Argolis, says—"The walls, the only remains of the city left, are the work of the Cyclops, and are made of rough blocks of such size that a yoke of mules would be unable to move the smallest."

5. At Nineveh the walls seem mostly of unburned brick, but they are lined with huge slabs of marble, or rather a species of alabaster, the working and carving of which show a very great advance in art. (See Nineveh.) The architecture of the Hindus, Persians, Phoenicians, and Jews, will be found under their respective heads. (Art. Architecture.) But there is nothing about their masonry differing from that of other similar structures on which it would be profitable to dwell.

6. The Egyptians, however, seem not only to have used gigantic masonry, but also to have had the power of working, carving, and polishing granite in a way which we certainly cannot at present attain to. The most marvellous fact connected with their masonry seems to be that the whole work was executed with copper or rather bronze tools, which seem to have answered their purpose better than even our best and hardest steel. Such seems to have been the facility with which they worked this, to us untractable material, that they were not content to cut and polish huge slabs and masses of granite, but they covered them all over with the most delicate and sharp-cut hieroglyphical inscriptions.

7. The masonry of the Greeks yet remaining is chiefly of beautiful marble. The workmanship is of the most exquisite character, the joints, &c., of the greatest truth. The artistic beauties of the carving, &c., have been unrivalled at any period. It seems difficult to believe that so enlightened a people were ignorant of the use of the arch, especially as it is clear it was known not only to the Egyptians, but was used at Nineveh. However, no example of a Greek arch exists at this time, as an architectural feature, although, as has been said before (art. Arch., § 8, p. 401), for necessary purposes (as covering drains), and concealed in the walls (as discharging arches), examples are to be found in Greek works. (See Ferguson's Handbook, p. 252; Architecture Suppl., § 2, p. 500.) It is probable that, as they had plenty of marble in blocks of almost any size, they preferred to use it in horizontal bearings, to working it into arch forms.

8. It was, however, the contrary with Roman masons; although it is true many of their temples were Greek in masonry, character, and most of them rivalled those of that nation in size and in the vastness of their material. But in general there was less of that ponderous strength that characterized the Egyptian and the Grecian Doric; and much more science in the construction, particularly as regarded economy; though in point of artistic beauty they were far below the Greeks. To what nation or race the invention of the arch may be attributed, it is clear the Romans were the first to bring it into general use; and though we read of a species of dome among the Greeks called θόλος, and though the Hindus delight in domical construction, it is clear the Romans were the first in Europe to use the true dome in covering their temples. Besides this, they had not only good lime but plenty of pozzolano, and therefore their mortar and cement were of first-rate quality. To these advantages we may attribute the vast works which to the present day amaze the spectator, who cannot view their cloaca, aqueducts, amphitheatres, basilicas, walls, towers, tombs, domes, harbours, without wonder at the enterprise of the people and the skill of their masons.

9. After the ruin of the Roman empire, and the irruption of the savage hordes over the whole of civilized Europe, the art of masonry, like all others, declined to the lowest ebb. In fact, except for the erection of rude forts and towers, it became almost extinct. In England we owe its first revival to the works of the Norman invaders; and next, no doubt, to the return of the crusaders, who had witnessed with admiration the marvellous lightness of the buildings in the east, and who brought back with them the arts and learning of the Arabians, especially their mathematical science. From these sources, no doubt, pointed architecture took its rise, and massive cylindrical pillars, composed of many small pieces of stone; small circular-headed windows; walls of vast thickness, with very shallow buttresses; and plain groining without ribs, gradually became changed to

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There are pieces of the architrave of the Temple of the Sun now lying on the Quirinal at Rome, measuring 16 ft. 6 in. long by 9 ft. 6 in. high, and about 6 ft. thick, or nearly 50 tons in weight. light shafted piers, and delicately moulded arches; windows rich with varied tracery; panelled walls, with bold buttresses, surmounted by niches, and crowned with pinnacles; and groined roofs, fretted with a net-work of ribs, and studded with richly floriated bosses.

10. The revival of classic architecture threw the arts into another channel, and the masons had hardly forgotten their old traditions when Jones and Wren introduced them to new details. The latter, in particular, formed an excellent school of masonry. The works at St Paul's, and his other public buildings, are executed in a very superior manner. He seems to have been very choice in the selection of his stone. Among all his buildings is scarcely a failure, or a defective block. Besides this, by the assistance of Gibbons, he formed an excellent school of architectural carvers.

11. The art of masonry was well upheld by Hawksmoor, Vanburgh, and Chambers; but shortly began to languish, when the inordinate use of cements, first introduced by the Adamses, came into vogue. Besides this, the heavy duties imposed on the transport of stone by sea, and the high prices which all materials bore during the war, threatened to reduce masonry to its lowest. The revival of Gothic architecture has renewed the use of freestone, and has taught our masons the art of working tracery, groined roofs, flying buttresses, and such use of stone as was supposed, scarce a century ago, to be one of the lost arts. Besides this, the abolition of duties, and the introduction of many facilities of transport by steam, both by land and water, has so reduced the price of stone, that in many places the use of cement is a false economy. Again, our intercourse with the Continent has brought us into more familiar acquaintance with the great works of classic antiquity, and of the Italian Renaissance. In addition to these causes, the vast engineering works, our docks, harbours, lighthouses, bridges, and, above all, our railroads, which have lately been constructed all over the country, have given a vast impetus to the study and practice of constructive masonry on the largest scale; and the consequence is, we now have in Great Britain a body of masons of higher and more varied skill than perhaps ever was known in this country at any time, both as regards constructive ability and elegant taste.

12. In Italy the old customs and traditions are still closely followed, and masonry is extremely well but slowly executed. The fine viaduct lately built at Albano is, however, a favourable example of Italian engineering in stone; and as railways gradually spread over the country we may expect still greater progress. In France masonry has always flourished, stone being so abundant, especially in the neighbourhood of Paris. The late works at the Great Exhibition, particularly the beautiful bridge over the Seine, and the noble buildings which unite the Tuileries and Louvre, form probably the finest palace in the world, and speak highly of the state of the art in France. In Germany we may note the fine works at Munich, particularly the Valhalla, the Pinacothek, and the Glyptotheke; at Berlin, the beautiful buildings of Shinkel; and in Russia the vast improvements at St Petersburg, particularly the cathedral of St Isaac, the dome of which is surrounded by twenty-four columns, each of one single piece, and each weighing more than 60 tons, and standing at the height of 150 feet above the ground. (See art. ST PETERSBURG, vol. xvii., p. 490.)

13. It is now proposed to treat this subject under the following heads:

I. Materials used in masonry.—1. The various kinds of stone. 2. Their durability and causes of decay. 3. Mortars and cements.

II.—Of the principles of stability and strength in masonry. Under this head it is proposed to give the whole of the scientific article written by the late Professor Robinson expressly for this work.

III.—Of foundations.—1. On land. 2. In the water.

IV.—On stone cutting and setting.—1. General. 2. Medieval.

V.—On artificial stones, and on the induration of soft stones.

L.—OF MATERIALS USED IN MASONRY.

14. In our article on MINERALOGICAL SCIENCE, vol. xv., Materials, p. 155, we have given an epitome of the various rocks which compose the fabric of the globe. We purpose to go through this list, showing those used in building as they occur seriatim, with some practical remarks upon each, which will give a complete epitome of the materials used by masons in all ages.

15. Of Igneous Rocks of volcanic origin, the varieties Igneous which have been used are those light stones called tufa and rocks of pumice, and that stone called peperino. The two former of volcanic origin, these were extensively employed by the Romans in the filling in of vaulting, on account of their great lightness. The latter stone, which is obtained in large quantities near Rome; and which, though of volcanic origin, resembles a sort of coarse oolitic conglomerate, was used by that people extensively, particularly for substructures, for which it is fitted, being obtained in large blocks.

Of the second division of igneous rocks, the trappean; Trappean, porphyry, and serpentine have been used, but chiefly as ornamental coloured stones, and have been generally classed as marbles.

Of this third division the granite alone is in use, and is Super-sill now very extensively employed, not only in bridges and other engineering works, but in public buildings and dwellings. It is got from the quarries by splitting the blocks with Granite, wedges, and is so hard it cannot be cut by any ordinary saws. It can only be worked first with large hammers, and then reduced by pointed chisels, and consequently is very expensive in building. Some very good specimens come from Cornwall and Devonshire, but by far the best are from Dundee and Aberdeen. A variety of the latter, called Peterhead, is only to be equalled by the finest oriental granites.

16. Of Aqueous Rocks—Mechanically formed, and of Aqueous the Arenaceous varieties.—Gravel is used by masons for rocks, concrete, and sand in making mortar. Sandstones and grit-Gravel and stones are very extensively used. These are either laminated, sand, as the York stone, and used generally for paving, as it can York pav readily be split into large surfaces of small relative thickness; ing, or compact as old red sandstones, which stand very well inter-old really, but perish sadly with the weather, as may be seen at Sandstone Chester cathedral. The new sandstones, the best of which is the Calverley stone, got near Tunbridge Wells. These Tunbridge stones are easily quarried, but, if sawn, the wet saw and sandstone, sand must be used. The finer grained compact sandstones, Compact which are comparatively free from iron, and form very good sandstone, building-stones, are very numerous. We name a few. These are the Bramley Fall, used by engineers for bridge copings, &c.; the Park Spring, Elland Edge, and Whitby, all from Yorkshire. Scotland can boast of some of the finest quarries of sandstone, the best of which, perhaps, is the Craigleith, much used at Edinburgh. The college, courts of law, registry, custom-house, royal exchange, national monument, and many churches and private residences there, are built of this excellent material, which has also been extensively exported to Hamburg, Altona, Gottenburg, and the continent. Humble stone has also been extensively used, Humble both at Edinburgh and at Glasgow, where it forms the Royal Exchange and bank. It is easier to work than Craigleith. Glamis is also a fine sandstone. The castle there, Glamis, as well as those at Inverguraphity and Cortachy, and Lindertis House, are built of this. In Fifehire, at Culcello, are Culcello. Materials quarries from whence the stones for the monument to Lord Melville at Edinburgh, and that to Lord Nelson at Yarmouth, were obtained. In addition to beauty and durability, these stones have the merit of being capable of receiving the finest and smoothest forms from the chisel of the workman. Another class of sandstones are commonly called firestones, as they endure the action of fire better than most others. Of these the best known is the Regate stone, which is the principal material used at Windsor Castle, Hampton Court, and in many old buildings round London.

Of aqueous stones classed as argillaceous, the Clunich clunch only is used in building. It may be seen in Ely and Peterborough cathedrals, and many other mediæval buildings, and is a beautiful material for carving, but will not stand the weather.

Chemically Of those aqueous stones, classed as chemically formed, and of the subdivision, the calcareous, we have none of Travertine, note but the Travertine, or, properly speaking, Tiburtine. This is a coarse grained stone, of warm colour, found in large blocks, and extensively used at Rome, both in ancient and modern buildings; the great cathedral of St Peter's may be cited as an instance; but it is unknown in England.

Calcareous. Of aqueous rocks, organically derived, and of the first subdivision, the calcareous claims our principal attention. The chief of these are the limestones, which are generally considered by architects as compact, magnesian, or oolitic limestones. Of the former the best, in the south of England, is that called Chilmark, of which Salisbury Cathedral and Wilton Abbey, and many other fine buildings, have been erected. In the midland counties the Tottenhoe stone, of which Dunstable Priory, Woburn Abbey, Luton church, &c., are built, is an excellent stone. There is also a stone of high quality got near Wirksworth in Derbyshire, used at Chatsworth, Belvoir, Drayton Manor &c., Anstone, or Bolsover Moor stone, used formerly at Southwell Minster, and lately at the houses of Parliament; the Tadcaster stones, used at York, Beverley, and Rippon Minsters, and very many other buildings; and the Roche Abbey, used at the building of that name, and very many other churches in Yorkshire and Lincolnshire. These stones contain a great deal of carbonate of magnesia, from which they take their name, and are of beautiful texture, and stand well in the country as building-stones; but fail in London, from a cause which will shortly be stated.

We now come to the most important subdivision of the limestones used in masonry—the oolitic—so called because they resemble, when broken, a conglomerate of globular eggs, also frequently called roe-stones, because they resemble what is called the hard roe of a fish. (See art. GEOLOGY, vol. xv., p. 146.) Very good examples of these are the Barnack stone from Northamptonshire, of which Peterborough Cathedral, Croyland Abbey, Burleigh House, &c., &c., are erected. Ketton stone, used at most of the colleges in Cambridge, and at Bury St Edmunds, Bedford, Stamford, &c., &c. But the principal English oolites used in masonry are the Bath and Portland. The former, as its name imports, is found in the neighbourhood of Bath. The chief quarries are the Box, Combe Down, Farleigh Down, and Corsham Down; all these quarries vary in quality at different depths. The Corsham Down is said to produce the finest in quality, and the Box Ground stone to be the hardest; but everything in the use of this stone depends on the judgment in selection. Large quantities of a similar stone are imported from Caen, in Normandy. They are more compact in texture than Bath, and therefore fitter for carving; but do not appear to stand the weather of our climate so well. The best variety of this stone is said to be D'Aubigny stone. Almost all these oolites can be sawn with a common dry saw, which saves a great deal in the labour of conversion. But, without doubt, the best of all this class of stones is that from the Island of Portland; for beauty of texture and for durability, it perhaps exceeds any stone in the world. It seems the only stone unaffected by the smoke of London; and therefore the greater number of its buildings, St Paul's among the rest, are of this Portland stone. It must, however, be sawn by the use of sand and water; and, being of hard texture, is much more expensive to work than the softer oolites. There are between fifty and sixty quarries on the island. The best are said to be those on the north-eastern side; but, like all stone, there is good and bad in every quarry, and everything depends on the selection. It is said, when Sir Christopher Wren built St Paul's, he had this stone quarried, and exposed to the weather on the sea-beach for three years, before he suffered it to be used. A very excellent limestone for walling, especially for Gothic work, is that called Kentish Rag. It is found in large quantities in the neighbourhood of Maidstone, and is very hard, and worked, like granite, with large hammers instead of the saw. Jambs, strings, and mouldings are sometimes worked out of it, but the hardness makes the work expensive. Of siliceous stones, Flint flint is sometimes used for rough walling; but in England this work is done by the bricklayer, and not the mason. (See BUILDING, p. 737.)

The Durability and Causes of Decay in Stones.

18. The causes of durability of stone, and the correspondent causes of failure and decay, are either chemical or mechanical, and may be described either as decomposition or disintegration. Durability also depends much on the power of resistance to wear.

19. Decomposition is caused by some of the elements of the stone entering into such new combinations with water, gases, or acids as render them soluble either by the air or water. Granite, though the hardest of building-stones, is liable to serious decomposition when the feldspars are alkaline (see art. GEOLOGY, vol. xv. p. 136), and will unite with water or acids. Some qualities of this stone are rapidly decomposed by the sea. The same is the case with many of the limestones, as is described in the article above quoted, page 151. Stones containing iron are also liable to decay. In its native state it is usually in a low state of iron oxidation, and is liable to be acted upon by additional quantities of oxygen or carbonic acid. This sort of decomposition is much increased by being alternately wet and dry, or by frequent changes of temperature. Stones, however, containing iron in a high state of oxidation, as rosso-antico, porphyry, &c., do not readily become decomposed. The most curious discovery of modern times is with regard to the magnesian limestones and dolomites. These Magnesia were chosen for the new Houses of Parliament on account of their durability. The work at Southwell Minster, 800 years old, bears every mark of the tool to the present day, and every circumstance seemed to justify its selection. It appears, however, that magnesia has a great affinity for sulphur; and the consequence is, the sulphurous acid which Sulphurous is present in such quantities in the smoke of London, has already caused serious decomposition in that building, as well as in the Lincoln's Inn Hall. This acid has also so much effect on the softer limestones, that the fronts of several important buildings, Buckingham Palace among the rest, have been obliged to be painted, to save them from decay.

20. Disintegration, as has before been said, is the separation of parts of stone by mechanical action. The chief cause is the freezing of minute portions of water which get into the freezing. Materials pores, or fissures, or between the laminae of stones, and swell slowly as crystals of ice are gradually formed, and consequently burst open the pores, or split the grain of the stone. The south sides of buildings, in northern climates, suffer more than others, as their surface becomes thawed and filled with wet in the day, and frozen again at night, more frequently than the others. A very common error in the present day, is the not taking care to set stones with their laminae, or grain, or, as the workmen call it, "bed," in a horizontal direction. If work be "face-bedded," the action of the weather will cause the laminae to scale off, one after the other, just as the leaves of a book fall over, if the volume be placed on its back in an upright position. For fuller illustration of the subject of decay and decomposition of rocks, we must refer our readers to the article MINERALOGICAL SCIENCE.

21. Resistance to wear is another obvious cause of durability; but this depends rather on the toughness than the mere hardness of material, a quality often attended with brittleness, as also on its situation. The crushing weight of Portland is about 10,000, while that of York is about 12,000, or one-fifth more; but in many situations Portland steps will last much longer than York. Again, the crushing weight of Peterhead granite is about 18,000, or not quite double that of Portland; whereas, if used as street-paving, it would outlast six sets of the latter.

Of Mortars and Cements.

22. The use of some material, not only to cause stones to adhere together in building, but to fill up crevices between them, and irregularities in bedding them, is of the remotest antiquity. The earliest mention of mortar is in Genesis xii. 3, where the builders of the Tower of Babel are said to have had "slime for mortar," which the LXX. called ἀργόλιον (bitumen) and πηλός. Herodotus (Clio, 179) tells us the walls of Babylon were built of bricks, cemented together by hot asphalt. The Egyptians used mortar of lime and sand, almost exactly in the proportions we do, as was proved from an analysis of some taken from the pyramid of Cheops. The Grecian mortars and cements are very fine and strong. Vitruvius gives careful directions how to make mortar (lib. 2, ch. 5), and his instructions are probably the best, and his observations the most sound, of any author, at least till the time of the researches of Vicat and the French chemists.

Definition.

23. Mortar is generally considered under two heads: as common mortar, or that mixture of lime and sand ordinarily used in building; and hydraulic mortar, or that which will set under water. Cement is a name given to the produce of certain argillaceous stones, after calcination, which will set rapidly in the air, and become a hard, adhesive substance in a short time; and which will also set under water, both without admixture of any other substance. The name is also given to certain artificial imitations of these substances, possessing the same properties; and besides, to various bituminous, or oleaginous compositions, used in building for similar purposes.

Lime.

24. Pure lime is an oxide of a metal called calcium, but does not exist in a natural state. It is, however, found abundantly in the conditions of carbonates and sub-carbonates, in chalk, and the various other descriptions of limestones. Its chemical qualities and analysis will be found under the proper heads. The first thing is to drive off the water, which all limestones contain in a greater or less degree, and the carbonic acid gas, which is done by calcining or burning in a kiln at red heat, which must be kept up for several hours, taking care, however, to avoid any approach to vitrification. By this process it is slightly diminished in bulk, and it loses nearly half its weight, and becomes caustic lime.

25. Limes are generally classed, since the publication of the work of Vicat, as—1. rich limes; 2. poor limes; 3. limes slightly hydraulic; 4. hydraulic limes; and 5. eminently Classifica-hydraulic limes. In treating of mortar, we have to deal with the first two of this division.

26. The lime must next be converted into a hydrate. Production This is done by a process called "slacking," or throwing of hydrates water over it from time to time till it hisses and cracks with considerable force, and some noise, gives off a large quantity of hot vapour, and falls into a powder. The rich limes, which are the purest oxides of calcium, increase to double their bulk in the process. The poor limes swell to a much less degree. The hydrates thus formed absorb water, and easily take the form of a paste. They contain rather less than one-third water to two-thirds lime. In this state, if treated with pure water, frequently renewed, every particle of rich limes, and very nearly the whole of the poor limes, will be taken up in solution. In the process of slacking, too much water should not be used, as it "drowns" the lime, according to the expression of the workmen. When in the form of paste it begins to absorb the carbonic acid, which, though no component part of air, is always present in it, in large quantities; and gradually to crystallize again, and so to harden. If the air be excluded from the hydrate of pure lime, it may be kept for almost any length of time. Alberti (lib. 2, cap. 2) says that he once discovered some in an old ditch, which, from certain indications, must have been there 500 years, and was as soft as honey or marrow, and as fit for use as it could be.

27. The rich limestones give a white lime, which easily Rich lime-slacks, and increases in bulk; but it is curious that, though stones, the stones differ so much in outward appearance and in texture, the lime, if they be well burned, is the same. The softest chalk, and the hardest rag-stone, or marble, yield an equally good lime, the calcium which they contain being the same mineral. But as chalk generally contains water, irregularly distributed in some places and not in others, and as it is does not exhibit the change that marble or stone does, it is frequently unequally burned, and therefore slacks imperfectly. It is said, however, that lime, made from chalk absorbs the carbonic acid more rapidly than that made from stone; but our own experience does not warrant this conclusion.

28. Poor limestones are those which contain silica, mag-Poor lime-nesia, manganese, or metallic oxides. In consequence of stones, this they are more liable to vitrify in burning, and do not slack so freely. The lime is generally of a browner colour than that from rich limestones, which is said to be a proof of the presence of the above-named metallic oxides. If, however, they be ground so as to facilitate the slacking of every particle, and if used immediately it is made up, poor limes produce a mortar which becomes harder than that from the rich limes, and which resists water better. In fact, works where the latter have been used, have been found to fail entirely by the action of running water, which, as before has been said, will continue to remove the whole of a rich lime, particle by particle.

29. It is found that the mixture of some kind of hard Use of matter in particles or granules facilitates the setting of sand, mortar, renders it harder and more adhesive than when used alone, besides the saving of limestone and expense of burning. The harder this material, and the sharper the particles the better, as the brick or stone has always some irregularities on the surface, into which these angles or sharp points may enter, and form what is called a key. The substance most generally used is sand, which is generally classed as river-sand or pit-sand. The former is Materials generally preferred, as it is more free from any earthy matters, particularly soft loams or clay. If pit-sand be used it should be well washed. Scarcely any material is better than crushed quartz, or flint, from the sharpness of the angles of the particles; in fact, it is said, that very sharp sand, with an interior lime, will make a more adhesive mortar than soft sand with the best lime. For observations on the practical mixing of mortar, see Building, p. 731.

30. Where sand is scarce, other materials may be used, the principal and cheapest of which is burned clay. The Romans used this extensively in the form of pounded brick. At present the custom is to throw up clay mixed with any fuel in loose heaps, and burn it slowly. The French writers at one time asserted that burned clay, if not equal to pozzolano, was very nearly so; and large quantities were used as hydraulic mortars at various public works. Where the water was fresh, as at Strasbourg, the work stood very well; but where these mortars were exposed to the action of sea-water, they failed and went to powder in three or four years. Vicat gave great attention to the subject; and though he attributed much of the fault to the imperfect carbonization of the materials, it appears with but little doubt there is some inherent difference between the pozzolanos and other volcanic products, which will be treated of shortly, and those produced artificially.

31. The vitrified refuse of furnaces, called slag, and the scorie from the iron-works, have also been crushed and used instead of sand; and with lime slightly hydraulic, produce good mortar. The former is preferred to the latter, as having sharper and harder particles, and containing much less iron. Coal cinders have been used, and seem to have some hydraulic properties; they should, however, be employed with caution, for it is considered they make the lime "short." Wood cinders are too alkaline to be used with safety. A very excellent mortar, much used by engineers in tunnels, is composed of one part of moderately hydraulic lime, one part of coal ashes, one part of burned clay, and two parts of sharp sand.

32. The vitrified and calcined products of volcanoes make most excellent materials for mortars, particularly where required to be eminently hydraulic. The principal of them is the Pozzolano, which abounds in Italy. It is called so from being found in great abundance at Pozzuoli, near Naples, and is, in fact, the basis of all the best Roman mortars, ancient as well as modern. It varies in colour from reddish brown to violet red, and is sometimes grayish. It is usually sent to England from Civita Vecchia. It has a roughly granulated appearance, and sometimes resembles a cinder in texture, and has frequently a spongy appearance. Acids have little effect on it, and it is not soluble in water. A similar earth is found in the centre of France. But one more familiarly known in this country comes from the village of Brohl, near Andernach, on the Rhine; this is called terrass or trass. These materials have a wonderful effect in rendering even the rich limes eminently hydraulic, and in less proportions improving the hydraulic limes. Vicat says, these mortars begin to set under water the first day, grow hard in the third, and in twelve months are as hard as the bricks themselves. The mixture of common lime with these materials, according to the French writers, should be 1 of pounded lime to 24 of pozzolano, or to 2 of terrass; or 1 of lime to 1 of sand and 1 of pozzolano. The analysis given by them is nearly as follows:

| Silica, per cent. | Terrass | Pozzolano | |------------------|---------|-----------| | Alumina | 12 | 15 | | Lime | 3 | 8 | | Magnesia | 1 | 4 | | Oxide of Iron | 5 | 12 |

1 After long investigation, Vicat was of opinion that this failure was due to the quantity of hydro-chloride of magnesia always present in sea-water; but in what way this affected the burned clay and not the volcanic products, he was unable to explain.

In addition to those which we have called hydraulic lines, there is a peculiar class of stones, which, when burned and pulverized, may be used as a species of mortar, without admixture of sand or any similar substance; and which will not only set rapidly under water, but will acquire an unusual degree of hardness and tenacity.

34. These are called natural cements. The inventor supposed to have been a Mr Parker, at any rate that gentleman took out a patent about sixty years ago for what he called Roman cement. His material were those argillo-calcareous nodules, or septaria, which are found in the Isle of Sheppey, and commonly called bald-pates. They contain about 70 per cent. of carbonate of lime, about 4 per cent. oxide of iron, 18 per cent. of silica, and 6 or 7 per cent. of alumina. The process is simply to break the stones into small pieces, and burn them in running kilns with coal or coke; they are then ground to a powder, and headed up into casks for use. The success of Parker's cement led to experiments in other places, and the same process was carried on with other argillo-calcareous nodules, as the septaria at Hawick; those in Yorkshire, which produce the cement called Atkinson's; and those in the Isle of Wight, which produce the Medina cement. Similar substances were also discovered, and the same processes carried on in France and in Russia. All these cement-stones effervesce with acids, and lose about one-third of their weight in burning. Parker considered the more the stones were burned short of absolute vitrification the better; but this is not the practice in the present day, though no doubt sound in theory. When taken from the kiln these stones will not slack without being pulverized; and if kept dry, and not exposed to the air, the cement will be good almost any length of time; but it rapidly absorbs both water and carbonic acid if not carefully closed, and falls back into a state of subcarbonate, from which it is said it may be recovered by fresh burning, but it is doubted whether it is ever so good as on the first calcination.

35. The great utility of these cements, and the expense of obtaining the stone, induced the manufacturers to endeavour to discover some method of making an article by artificial means which should resemble the natural cements. Mr Frost seems to have been the first who attempted it on a large scale; but though assisted by the talent and science of General Pasley, the results did not come up to the expected standard. Of course, the object was to produce an argillo-calcareous substance, containing the same chemical qualities as the natural nodules, and which might be burned in kilns as they are. The attempt to combine argil in the form of burned clay, to be mixed with lime instead of pozzolano, had partially failed, as has been stated before. Our space will not allow us to relate the various experiments by General Pasley here, nor by Vicat at Meudon in France. They were all based on the principle of mixing together, in a mill, with a quantity of water, masses of chalk and clay, just as the brickmakers do for the production of malm bricks, but in the proportion of about four of the former to one of the latter. The fluid mixture is run out into shallow receivers, and when dry is cut into small blocks or lumps, and burned exactly as the natural nodules are. The difficulty seems to have been to give the materials the full degree of calcination short of vitrification. This seems to have been at last attained by the inventors of the Portland cement, so called from its Portland near resemblance to Portland stone in its colour. It not cement only possesses the property of setting more quickly, and has greater powers of cohesion than the natural cements, but it may be used with a superabundance of water in the

36. A class of cements capable of taking a brilliant polish resembling marble, and consequently very suitable for internal decoration, had lately been invented. The chief of these is Keene's marble cement, and the Parian cement. They become excessively hard in a short time, and are capable of being painted in a few days. The principal component part is said to be obtained by the precipitation of alum by an alkali, which gives a white powder of great brilliancy. It is, however, more matter for the plasterer than the other building trades.

37. Cements made by the mixture of oil with various substances were formerly much used both here and abroad. The best known in England was called Hamelin's mastic, that in France the mastic de Dihl. These cements being very expensive, and requiring to be constantly painted, have now gone nearly out of use. For outside plastering they form a very fine clean surface, as may be seen in the quadrant in Regent Street.

38. The asphaltum, or mineral pitch (see ASPHALTUM), have lately come into extensive use for pavings, and for covering the backs of arches, or rendering the walls of basements where wet is likely to soak through. The best is said to be that from Seyssel, in France. For their chemical properties see BITUMEN. It is used thus—A bed of concrete, made of the best hydraulic lime, is first prepared, and made fair at top by a rendering of similar mortar. The asphalt will not dissolve with heat by itself, but will calcine in the caldron. A small quantity of pure mineral pitch is therefore first put in; when hot the asphalt is added, and soon dissolves; into this is stirred a quantity of powdered stone-dust, and a small portion of quick-lime. The mixture is then laid hot on the bed of concrete (which must be quite dry), and spread close and fair, some sand being sprinkled over the top and well trowelled in. The best proportions are said to be about 2 pints of mineral pitch to 10 lb. of asphalt, and one-fourth bushel of stone-dust. A very inferior imitation is made by mixing a quantity of sharp sand with gas-tar, heated in a caldron, and then adding some quick-lime. This may do for rendering walls, &c., to keep out wet, but is of very little use in paving.

II.—OF THE PRINCIPLES OF STABILITY AND STRENGTH IN MASONRY.

39. The strength and the stability of stone-work depends partly on its mass or weight, and partly on the resistance of the materials. And, since we cannot imagine incompressible fulcrum, nor that the materials of masonry are infinitely hard and inflexible, as writers on elementary mechanics consider them to be, therefore, it is essential that the resistance of materials should be considered, and the effect of their weight allowed for in estimating the power of the straining force.

The resistance of stones being dependent on their state of aggregation, and not on the hardness or density of their elementary parts, their comparative strength cannot be judged of by these qualities; indeed there are few kinds of materials of which the resistance is so uncertain as that of stone, and hence, it is not at all adapted for any support where its resistance depends on its cohesion only, unless it be very carefully examined, and abundant strength be allowed. The resistance of stone to compression is less affected by its irregular nature, particularly as it is usually employed in blocks of inconsiderable height; and, in general, there is scarcely any reason to be sparing of a material which it is often more expensive to reduce than to employ in large blocks. When, however, works of great magnitude are to be constructed, the weight of the materials themselves forms the chief part of the straining force; and, consequently, in such cases it becomes desirable to form a tolerably accurate estimate of their power.

40. This power is limited by a property of bodies that has not received that degree of attention which its importance would lead us to expect. We shall in this place make it the basis of an investigation of the power of materials to resist a force applied in any given direction, and show its application to some of the cases where a mason is most likely to need the assistance of calculation.

When any material is strained beyond a certain extent, every time the strain is increased to the same degree, there is a permanent derangement of the structure of the material produced; and a frequent repetition will increase the derangement till the parts actually separate. (See the article CARPENTRY.) When a small base rests upon a considerable mass of matter, as a pier on the ground, the quantity of derangement will increase only till the mass be compressed to that degree which renders the increase insensible; but in many cases a number of years will elapse before the settlement becomes insensible.

41. The strain which produces permanent derangement in the structure of a material varies from one-fourth to two-fifths of that which would destroy its direct cohesion. In stone the lower value should be taken, on account of its being subject to so many defects; and, for the present, let this strain be denoted by \( f \) lbs. upon a superficial foot.

42. Imagine ABCD to be a block, fig. 1, strained either in the direction EF or FE, by a force W; and let BDF be a line drawn in the same plane as the direction of the straining force, and perpendicular to the axis ab of the block. Now, if we consider the resistance of the block to be collected at the centres of resistance \( t \) and \( c \), then \( tF \) will represent a lever acted upon by three forces; that is, the resistance at \( t \) and \( c \), and the straining force at F.

If the angle FEG be denoted by \( \alpha \), then the effect of the force W, reduced to a direction perpendicular to the lever, will be expressed by \( \cos \alpha W \). (1)

Also, if \( T \) be the resistance at \( t \), and \( C \) the resistance at \( c \), we shall, in the case of equilibrium, have \( C - T = \cos \alpha W \). (2)

And, by the property of the lever,

\[ \frac{te}{eF} = \frac{W \cos \alpha}{C - T} \]

Hence, \( \frac{te}{eF} = \frac{C}{T} - 1 \) (3)

Without stopping to notice some maxims furnished by this equation (see the article BRIDGE), we will proceed to explain the notation used in the investigation which follows:— When the strain becomes transverse, or when EF is perpendicular to the axis, as in fig. 3, then \( \cos \alpha = 0 \) and \( \sin \alpha = 1 \), hence

\[ W = \frac{fbd^2}{d + 6y} \]

(14)

If the block be supported at the ends, and the load be applied in the middle of the length, as in fig. 4, the fracture will take place at BD; and \( W \) in equation (14) will be the pressure on either support, which is obviously half the load in the middle.

47. In any of these equations it is perfectly immaterial how the load be distributed, provided the line of direction be that which passes through the centre of gravity of the mass supported, and the weight be the whole weight of that mass; or, if the strain be the combined effect of several pressures, then the direction must be that of the resultant of these pressures, as determined by the principles of mechanics. (See the article CARPENTRY.)

48. If a slab of equable thickness and width be supported along two of its sides, as at AC, AB in fig. 5, and it be strained by a force acting at D, in a direction perpendicular to its surface, and DE made equal to DB, then the fracture will take place in the direction EB; for it may be shown, by the principles of the maxima and minima of quantities, that the resistance, according to that law, is a minimum. And since, in that case, EB = 2 FD, we shall have, by equation (14),

\[ W = \frac{fbd^2}{d + 6y} \]

(15)

A force uniformly diffused over the surface of the slab would fracture it in the direction CB, shown by a dotted line in the figure, and if \( w \) be the load in pounds upon a square foot of the surface, then the proper values being substituted for the leverage and breadth in equation (14),

\[ w = \frac{fbd^2(CD^2 + DB^2)}{CD^2 + DB^2} \]

(16)

The strength of a series of steps bearing upon one another, as in the perspective sketch (fig. 6), may be determined with sufficient accuracy by the last equation, supposing the depth to be the mean vertical depth of any one step; as, for example, taken at GH in fig. 7, the figure showing the ends of the steps.

49. The case to which equation (14) applies, affords the most convenient, as well as the most accurate, means of determining the value of \( f \) for any material; and, suppos- value for various stones, mortars, &c., in the nearest simple numbers under the calculated value:

**Table I.—Experiments on the Transverse Strength of Stones, &c., to the Case Equation (14).**

| No. of Exps. | Substance tried | Weight of a Cubic Foot | Length, L | Depth, d | Breadth, b | Breaking Weight | Values of \( f = \frac{1}{4} \) of the absolute Strength of a Sq. Foot | |-------------|-----------------|------------------------|----------|----------|------------|----------------|---------------------------------------------------------------| | 1 | Statuary marble | 169.12 | 15 | 1.075 | 1.075 | 23 | 65,000 | | 2 | | | | | | | | | 3 | | | | | | | | | 4 | | | | | | | | | 5 | | | | | | | | | 6 | | | | | | | | | 7 | | | | | | | | | 8 | | | | | | | | | 9 | | | | | | | | | 10 | | | | | | | |

Numbers 18, 19, and 20 are from Barlow's *Essay on the Strength of Timber* (p. 250), each being a mean of three trials. Number 23 is from Rondelet's *Traité de l'Art de Bâtir* (tome iii. p. 377), lowest result; the rest of the experiments were made by the writer of this article.

**Table II.—Experiments on the Direct Resistance of Stones, &c., to the Case Equation (13).**

| No. of Exps. | Substance tried | Weight of a Cubic Foot | Area of Specimen | Weight that pulled it Asunder | Values of \( f = \frac{1}{4} \) of the absolute Strength of a Sq. Foot | |-------------|-----------------|------------------------|------------------|-------------------------------|---------------------------------------------------------------| | 1 | Hard stone of Givry | 147 lb. | 96 lines | 164 livres | 8,400 lb. | | 2 | Tender stone of Givry | 130 lb. | 324 | 183 | 1,400 | | 3 | Mortar of sand and lime sixteen years old | 1 lb. | 1 | 53 | 1,800 | | 4 | Plaster of Paris | | 1 | 64 | 2,500 | | 5 | Adhesion of mortar to lime stone, joined six months | 4 lb. | 64 | 547 | 1,180 | | 6 | Adhesion of mortar to brick, joined six months | 4 lb. | 138 | 1,180 | | | 7 | Adhesion of mortar to tile, joined six months | 4 lb. | 141 | 1,200 | |

We have not here availed ourselves of the experiments of Gauthey (Rozier's *Journal de Physique*, tome iv.) on the transverse strength of stones; because those he fixed at one end appear to have been injured in fixing, and only a calculated result is given for the other specimens supported at both ends. As to this, see the article on the Strength of Materials.

50. Several experiments have also been made, with the intention of measuring the direct resistance to extension or compression; but theory indicates so nice an adjustment of the direction of the straining force as necessary in these experiments, that the reader may expect the results to differ as widely amongst themselves as they are found to differ from theoretical calculation.

The experiments, Nos. 3, 4, 5, 6, and 7, are extracted from Rondelet's *L'Art de Bâtir* (tome i. p. 312). Nos. 1 and 2 are by Gauthey (Rozier's *Journal de Physique*, tome iv. p. 414.)

51. In the resistance to actual fracture, from a compressive force, the joint effect of cohesion and friction is concerned, and, therefore, a much greater force is required to crush than to tear asunder the same quantity of material. The resistance to fracture might be investigated on principles analogous to those we intend to employ in determining the pressure of earth against retaining walls, &c. (See the article CARPENTRY.) But we conceive that it is neither prudent, nor useful, nor necessary, to load the parts of a structure beyond that limit we have made the basis of our investigation. (See § 34.) Rondelet has observed, that the load under which a stone began to split was nearly always two-thirds of that which crushed it; but that stone of some kinds began to split with half the load that crushed it (*L'Art de Bâtir*, iii. 86 et 101). The value of \( f \) should, therefore, not exceed one-fourth of the force which splits stone; and, supposing the splitting force to be always half the crushing one, we shall have \( f = \frac{1}{8} \) of the crushing force.

52. In this, as in the preceding tables, the reader will observe, that the results of all experiments are given in the original weights and measures; but that the value of \( f \) and the weight of a cubic foot are in English pounds avoirdupois, and for an English foot. The foreign weights and measures are distinguished by their foreign names.

The experiments, Nos. 1, 21, 22, and 36, were made by Gauthey (Rozier, *Journal de Physique*, tome iv. p. 406). Those numbered 3, 4, 5, 8, 9, 11 to 20, 30, 31, 32, 34, 37, 38, and 39, were made by Mr George Rennie (*Philosophical Transactions* for the year 1818). The others were made by Rondelet (*Traité de l'Art de Bâtir*, tome i. and tome iii.) We have selected those which will be most useful, with others of a more interesting and curious nature; such are Rondelet's experiments on the effect of ### Table III.—Experiments on the Resistance to Crushing.

| No. of Expts. | Substance Tried | Weight of a Cubic Foot | Area of Specimen | Weight that Crushed It | Value of f of the Crushing Force for a Square Foot | |--------------|-----------------|------------------------|------------------|-----------------------|---------------------------------------------------| | 1 | Porphyry | 179·44 | 20 lines | 5,268 livres | 640,000 | | 2 | Granite | 174·9 | 4 pouces | 119,808 | 500,000 | | 3 | Granite, Aberdeen blue | 164·06 | 2·25 inch. | 24,556 lbs. | 196,000 | | 4 | Peterhead, hard and close grained | 2·25 | | 18,636 | 149,000 | | 5 | Cornish | 166·37 | 2·25 | 14,302 | 114,000 | | 6 | Gray | 171·06 | 4 pouces | 39,168 livres | 165,000 | | 7 | Rose oriental | 166·32 | 4 | 52,764 | 220,000 | | 8 | Marble, white statuary | 172·5 | 2·25 inch. | 13,632 | 109,000 | | 9 | | | 1 | 3,216 | 57,000 | | 10 | Veined white, Italian | 168·37 | 4 pouces | 19,584 | 83,000 | | 11 | Variegated red, Devonshire | 170·37 | 2·25 inch. | 21,772 lbs. | 174,000 | | 12 | Dundee stone | 168·12 | 2·25 | 16,172 | 128,000 | | 13 | Craigleith stone, with strata | 163·25 | 2·25 | 14,918 | 112,000 | | 14 | Bramley Fall sandstone near Leeds, with the strata | 156·62 | 2·25 | 13,632 | 109,000 | | 15 | Portland stone | 151·43 | 2·25 | 10,284 | 82,000 | | 16 | Culello white sandstone | 151·43 | 2·25 | 14,918 | 67,000 | | 17 | Yorkshire paving stone | 156·68 | 2·25 | 12,856 | 102,000 | | 18 | Hard stone of Givry | 147·31 | 324 lines | 11,208 livres | 85,000 | | 19 | Tender stone of Givry | 129·43 | 576 | 5,880 | 25,000 | | 20 | Saillancourt stone arches of bridge of Neuilly | 141·31 | 4 pouces | 7,280 | 30,000 | | 21 | Portland stone pillars of All Saints at Angers | 160·68 | 4 | 62,600 | 110,000 | | 22 | Bagneux stone pillars of the Pantheon at Paris | 137·12 | 25 centim. | 6,125 kilog. | 62,000 | | 23 | Stone bridge of St Maxence | 156·25 | 4 pouces | 23,380 livres | 97,000 | | 24 | Caeretè stone, in Italy | 169·87 | 4 | 36,142 | 150,000 | | 25 | Stone of temples at Pestum | 140·87 | 4 | 13,720 | 58,000 | | 26 | Traverino, ancient buildings at Rome | 147·37 | 4 | 18,112 | 77,000 | | 27 | Derbyshire grit, a friable red sandstone | 144·75 | 2·25 inch. | 7,070 lbs. | 56,000 | | 28 | From another quarry | 151·75 | 2·25 | 9,776 | 78,000 | | 29 | Roe stone, Gloucestershire | 760·00 | 4 pouces | 3,520 | 15,000 | | 30 | Tufa, from Rome | 37·81 | 2·25 inch. | 1,127 | 9,000 | | 31 | Chalk | 37·81 | 2·25 | 2,140 | 8,500 | | 32 | Pumice | 37·81 | 2·25 | 2,140 | 8,500 | | 33 | Brick, hard and well burned | 130·31 | 324 lines | 5,290 | 34,000 | | 34 | " pale red, mean of two trials | 135·5 | 2·25 inch. | 2,255 | 10,100 | | 35 | " red, mean of two trials | 135·5 | 2·25 | 1,817 | 14,500 | | 36 | Stourbridge fire | 118·31 | 4 pouces | 3,854 | 30,900 | | 37 | Mortar of lime and sand 18 months old | 118·31 | 4 | 2,552 livres | 10,900 | | 38 | " 16 years old | 101·56 | 4 | 1,866 | 7,900 | | 39 | " not beaten 18 months old | 101·56 | 4 | 1,866 | 7,900 | | 40 | Mortar of lime and pit-sand, 18 months old | 99·25 | 4 | 2,475 | 10,600 | | 41 | " beaten together, 18 months old | 118·93 | 4 | 3,420 | 14,600 | | 42 | " of lime and pounded tiles, 18 months old | 91·06 | 4 | 2,895 | 12,300 | | 43 | " beaten together, 18 months old | 103·93 | 4 | 3,970 | 16,000 | | 44 | " 16 years old | 103·93 | 4 | 3,970 | 16,000 | | 45 | " from an ancient wall at Rome | 98·37 | 4 | 4,248 | 18,000 | | 46 | " from the Pont du Gard | 93·75 | 4 | 3,090 | 13,000 | | 47 | Lastrico, brought from Naples | 62·5 | 4 | 4,664 | 19,400 |

---

1 Gauthey, Rozier's Journal de Physique, tom. iv., p. 409; and Construction des Ponts, tom. i., p. 273. 2 Rondelet, L'Art de bâtir, tom. iii., p. 74. 3 Telford, Edinburgh Encyclopædia, Art. " Bridges," p. 505.

The last column in each of the three tables of experiments shows the greatest load that we suppose should be borne by a superficial foot of the different kinds of stone contained in those tables. We now propose to give the results of some calculations respecting the extent to which stone has in practice been loaded. The foreign ones are reduced to our own weights and measures, and the whole stated in round numbers.

The pillars of the Gothic church of All-Saints at Angers, of the stone, No. 24, Table III., support on each superficial foot a pressure of 86,000 lb. The pillars of the dome of the Pantheon at Paris, the lower part of which are of Bagneux stone (No. 2151, Table III.), support on each superficial foot 60,000 lb. The pillar in the centre of the chapter-house at Elgin, which is of red sandstone, supports on each superficial foot 40,000 lb. The piers which support the dome of St Paul's in London sustain a pressure on each superficial foot of 39,000 lb. The piers which support the dome of St Peter's at Rome sustain a pressure on each superficial foot of 33,000 lb. The pressure on the key-stone (No. 23, Table III.) of the Bridge of Neuilly has been estimated for each superficial foot at 18,000 lb.

In regard to these examples we have to remark that the calculators of them have considered the pressures as uniformly distributed over the pressed surface; but this can only be true when the direction of the resultant of the straining force coincides with the axis of the pier or pillar; besides, stones cannot be wrought absolutely level, nor bedded in perfect contact. From these circumstances, the strength of piers, columns, pillars, and arch-stones, Principles should be estimated by equation (19), and when the line of direction falls within the pier, always making \( y = \frac{1}{2} \) the least dimension of the section, an allowance which will include the effect of strength, the greatest possible inequality of action. We shall, in that case, have

\[ \frac{fbd}{d + \frac{fbd}{4}} = W \]

If the pressure on the Bagneux stone in the piers of the dome of the Pantheon at Paris be estimated by this formula, it will be found that it is sufficient to split the stones, and this has actually happened.

55. The chief elements of the theory of arches have already been given in the article BRIDGE (sect. ii.), to which we refer the reader, at the same time expressing a hope that the excellent article referred to will be useful in correcting some absurd notions respecting catenarian and other curves, which are too commonly entertained. The conical support of the lantern of St Paul's is a fine example of an appropriate form, whilst the catenarian dome of the French Pantheon exemplifies a scientific blunder of the first magnitude.

The principles of domes, of groins, and of vaulting of every kind, are the same as those of arches, excepting that each kind has its peculiar manner of distributing the load on the different parts. See prop. M and N, art. BRIDGE.

Of the pressure of Earth, Fluids, &c., against walls.

56. When a high bank of earth, or a fluid, is to be sustained by a wall, as it is often necessary to do in forming bridges, locks, quays, reservoirs, docks, and military works, the construction is very expensive, however economical the means employed may be; hence it is desirable to devote some space to an object of which the importance is manifest.

Let EC, fig. 8, be the line according to which the earth would separate, if the wall were to yield. In a small degree; then AEC will represent the section of the prism of earth, the pressure of which causes the wall to yield.

Put \( W = \) the weight of the prism AEC, when its length is unity.

\( R = \) the resistance of the wall, when its length is unity.

\( \alpha = \) the angle ECA, which the plane of fracture makes with a vertical line.

\( \epsilon = \) the angle ACE, which the back of the wall makes with a vertical line.

\( F = \) the friction of the earth when the pressure is unity.

\( h = \) the vertical height of the wall or C in feet.

and \( S = \) the weight of a cubic foot of earth, water, or other matter to be supported.

If \( g \) be the centre of gravity of the prism of earth, the triangles rpg, CogE, being similar, the effort of the prism to slide in the direction EC, reduced for the friction, will be

\[ W(1 - F\tan \alpha) \]

This effort is to be opposed by the resistance of the wall, which let us suppose to be collected at \( e \), the centre of pressure, and, reducing to the direction CE, the effect of friction being allowed for, it becomes

\[ R(F + \tan \alpha) \sec \alpha \]

Hence, in the case of equilibrium,

\[ W(1 - F\tan \alpha) = R(F + \tan \alpha) \sec \alpha \]

Or, \( R = W \left( \frac{1 - F\tan \alpha}{F + \tan \alpha} \right) \)

57. But, in the case now considered the radius being unity,

\[ W = \frac{ABS}{2} (\tan \alpha - \tan \epsilon) \]

Therefore, \( R = \)

\[ \frac{ABS}{2} \left( \tan \alpha - \tan \epsilon \right) \times \left( \frac{1 - F\tan \alpha}{F + \tan \alpha} \right)^{\frac{1}{2}} \]

And, from the state of the variable quantities in this equation, it is obvious that it has a maximum value, which determines the angle of fracture. By the principles of maxima and minima, the maximum pressure takes place when

\[ \tan \alpha = F + \left( \frac{1 + F\tan \epsilon}{F^2 + F\tan \epsilon} \right)^{\frac{1}{2}} \]

If the angle which the plane of repose (BRIDGE) makes with a vertical plane be denoted by \( i \), then

\[ F = \frac{1}{\tan i} \quad \text{and} \quad \tan \alpha = \frac{1}{\tan i} \]

\[ 1 + \left( \tan \epsilon \tan i + \tan \epsilon \tan i + \tan \epsilon \tan i \right)^{\frac{1}{2}} \]

If the back of the wall be vertical, \( \tan \epsilon = 0 \), and then this equation reduces to the simple form, which Prouy obtained, of \( \tan \alpha = \tan i \).

58. When we substitute in equation (21) the value of the tan \( \alpha \), which has been found in equation (23), it becomes \( R = \)

\[ \frac{ABS}{2} \left( \tan i + \tan \epsilon + \frac{2}{\tan i} \right)^{\frac{1}{2}} \]

And when the back of the wall is vertical, it becomes

\[ R = \frac{ABS}{2} \left( \tan^2 i \right)^{\frac{1}{2}} \]

The tan \( i \) being the co-tangent of the angle of repose, if the matter to be supported be of so fluid a nature that it naturally assumes a sensibly level surface when at rest, the tan \( i \) becomes equal to unity, and consequently,

\[ R = \frac{ABS}{2} \]

The same result may be obtained from the common principles of hydrostatics in the case of fluids.

Since the only variable quantity which enters into the calculation of the distance of the centre of pressure is the height \( h \), whatever the nature of the supported material may be; therefore that distance counted from the base will always be \( \frac{h}{4} \), as in the pressure of fluids.

59. Table IV.—Table of Constant Quantities necessary for calculating the Pressure of some Materials.

| Substance | Angle of Repose | Weight of Cubic Foot = S | Value of R in Equation (26) | |-----------------|-----------------|--------------------------|----------------------------| | Water | 0° | 62½ lb | \( R = 31\frac{1}{2}A^2 \) | | Fine sand | 33° | 92 | \( R = 13\frac{1}{2}A^2 \) | | Do. moist | 119 | | \( R = 17\frac{1}{2}A^2 \) | | Quartz sand (dry)| 33° | 102 | \( R = 19\frac{1}{2}A^2 \) |

In sand, clay, and earthy bodies, the natural slopes should be taken when the material is dry, and the clay and earth pulverised. When any of these bodies are in a moist state, the parts cohere, and the angle of repose is greater, though the friction be actually less. The preceding table shows that the pressure of water is greater than that of any of the other kinds of matter, and from the nature of fluids it is evident, that if water be suffered to collect behind a retaining wall, calculated to sustain common earth only, it will... Principles most likely be overturned. Such accidents may be prevented by making proper drains.

60. The preceding analysis will apply, without sensible error to the curved walls which have lately become fashionable. Fig. 9 is a section of one of these walls, as executed from a design by Rennie. The vertical height, AB, 21 feet; the wall of uniform thickness, with counterforts 15 feet apart; and the front of the walls described by a 69 feet radius, with the centre in the horizontal line DA produced. The wall is built of brick, and the uniform part is 4½ feet thick. The radius is usually thrice the vertical height of the wall; when this proportion is adhered to, the angle c will be ten degrees, for which the value of R is calculated in the table.

Resistance of Walls.

61. In the first place, we propose to investigate the resistance a wall offers to being overturned; and, in so doing, it appears desirable that the resistance of the mortar in the joints should be considered one of the elements of the strength of the wall. Good mortar adds much to the firmness of walls, and still more to their durability, and, all things considered, its first cost is less than that of bad; besides, the resistance of mortar to compression must be considered, for, in practice, we have no perfectly hard arrises to fulfil the conditions of common mechanical hypotheses.

Put A = the area of the wall. w = the weight of a cubic foot of masonry. y = the horizontal distance, y a, between the vertical passing through the centre of gravity of the wall, and the point where the axis cuts the plane of fracture, the same notation being applied to the other quantities as in the foregoing equations.

Let G, fig. 10, be the centre of gravity of the wall; and on the vertical Gp set off y, the height of the centre of pressure; also, let IK represent A × w = the weight of the wall, and HI the force R of the earth.

Then, completing the parallelogram, HI will represent the direction and intensity of the straining force; consequently, \( R_{aw} = \tan \alpha \) (28).

Which determines its direction, and its intensity is

\[ W = \frac{Aw}{\cos \alpha} \] (29)

But, we have found,

\[ W = \frac{fbd^2}{d \cos \alpha + 6i \sin \alpha + 6y \cos \alpha} \text{ and as } W = \frac{Aw}{\cos \alpha} \text{ (equa. (29))}; \tan \alpha = \frac{R}{Aw}; \text{ equa. (28)}; l = \frac{3}{4}, \text{ art. 51}; \text{ and } b = \text{unity}; \text{ the equation reduces to } fbd^2 - Adw - 6 Awy = 2Rh. \] (30)

If the section of the wall be a parallelogram, then \( A = hd \), and Principles \( \frac{1}{4} \tan \epsilon = y \); these values of \( A \) and \( y \) being substituted in equa. of Stability (30), it becomes \( -whd^2 + fbd^2 + 3Ahd \tan \epsilon = 2Rh \). (31.)

Or, \( d = \frac{h^2w}{f - hw} \left( \frac{-3 \tan \epsilon}{2} + \frac{\sqrt{2Rh(f - hw)}}{h^2w} \right) \) (32)

When the section of the wall is a rectangle \( y = 0 \), therefore equa. (31) reduces to

\[ d = \sqrt{\frac{2Rh}{f - hw}} \] (33)

This last equation is also correct for a wall of which the back is vertical, and the front sloping. We suppress the investigation, to afford the young student an opportunity of proving that the diminution of weight is exactly counterbalanced by the alteration of the distance of the centre of gravity from the axis.

The tendency of a wall to slide forward may be easily prevented, by giving an inclination to the joints.

62. To illustrate these rules we shall give two examples, and in these show the construction of a table, which the reader may enlarge at his pleasure.

Example I. Let it be required to determine the thickness of a rectangular wall for supporting the front of a wharf 10 feet in height, the earth being a loose sand, and the wall to be built of brick.

The weight of a cubic foot of brick-work may be estimated at 100 lbs., and the resistance of mortar being valued at 5000 lbs. per superficial foot, the experimental value being 7900 lbs., Table III., Experiment 42, and the difference an allowance for any irregularity in building, consequently, \( f = 5000; w = 100 \); and by Table IV., \( R = 13-84 \); hence equa.

\[ d = \sqrt{\frac{2Rh}{f - hw}} = \sqrt{\frac{2 \times 13-8 \times h^2}{5000 - 100}} = \sqrt{\frac{h^2}{181-362}} \]

When \( h = 10 \) feet, then the thickness of the wall \( d = 2-644 \) feet. If \( h \) be made successively 10, 20, 30, 40, &c., feet, the numbers under the head of dry sand in the following table will be obtained, observing that they are only calculated to the nearest tenth of a foot.

The proper thickness being found for supporting one kind of material, that for any other may be easily determined; as the thickness varies as the square root of \( R \), equa. (33). Let the thickness for dry sand be \( d \), then

\[ \sqrt{13-8} : \sqrt{31-25} :: d : 1-5d \] the thickness for supporting water.

\[ \sqrt{13-8} : \sqrt{17-85} :: d : 1-14d \] the thickness for supporting moist sand.

In this manner, by means of Table IV., the thicknesses for other kinds are easily calculated.

Example II. If a retaining wall be intended to support a sandy and loose kind of earth, to be constructed of brick, and to be inclined 10 degrees from the vertical, the thickness being uniform; it is required to determine that thickness for any given height.

By equa. (32), \( d = \frac{h^2w}{f - hw} \left( \frac{-3 \tan \epsilon}{2} + \frac{\sqrt{2Rh(f - hw)}}{h^2w} \right) \) and as \( \epsilon = 10^\circ \), \( \tan \epsilon = 0-18 \), hence

\[ \frac{3 \tan \epsilon}{2} = 0-27 \text{ and its square } = 0-0729. \text{ Also } f = 5000, \text{ and } w = 100, \text{ consequently, } d = \frac{h^2}{50 - h} \]

\[ \left( -0-27 + \sqrt{\frac{2Rh(5 - 0-18h)}{h^2}} + 0-0729 \right) \]

For sandy earth \( R = 4-84 \), therefore \( d = \frac{h^2}{50 - h} \)

\[ \left( -0-27 + \sqrt{\frac{4-8}{h} - 0-113} \right) \text{ and making } h \text{ successively 10, 20, etc., feet, the numbers obtained will be the same within one-tenth of a foot, as those in the following Table, column fifth, in which the thickness of leaning and curved walls for supporting dry sand is shown, at an inclination of 10 degrees.} \] 63. **Table V.—A Table of the Thicknesses for Retaining Walls, Revetments, Dock-walls, etc.**

| Height of Wall | Thickness of Rectangular Walls to support | |---------------|------------------------------------------| | | Water | Dry Sand | Mloat Sand | | 10 feet | 4'0 feet | 2'7 feet | 3'1 feet | 1'1 feet | | 20 | 12'9 | 8'6 | 9'8 | 2'8 | | 30 | 29'2 | 19'4 | 22'2 | 5'2 | | 40 | 62'5 | 41'7 | 47'5 | 9'2 |

Our investigation informs us that the mortar of high walls must be of a superior strength; indeed, we know that when its consolidation takes place, under considerable pressure, it is of much greater strength. According to what function of the pressure the strength increases, we have not experiments to determine, and we therefore point out the circumstance to the notice of experimental inquirers.

For further particulars as to construction of walls, particularly of railway embankments, see article Construction.

64. The proper quantity of mortar to be employed in stone-work is another point to which it will be useful to direct the mason's attention. A stone cannot be very firmly bedded upon a very thin layer of mortar; and if the stone be of an absorbent nature, the mortar will dry too rapidly to acquire any tolerable degree of hardness (Vitruvius, lib. ii., cap. viii.), however well it may have been prepared. On the other hand, if the bed of mortar be thicker than is necessary to bed the stone firmly, the work will be a long time in settling, and will never be perfectly stable.

When the internal part of a wall is built with fragments of stone, they should be closely packed together, so as to require as little mortar as possible. Walls are often bulged by the hydrostatic pressure of mortar, when it is too plentifully thrown into the interior, to save the labour of filling the spaces with stones.

The walls of houses are frequently built with hewn stone on the outside, and rubble stone on the inside. The settlement of these two kinds of stone-work during the setting of the mortar are so different, that the walls often separate; or where this separation is prevented by bond stones, the wall bulges outwards, and bears unequally on its base. These evils are best prevented by using as little mortar as possible in the joints of the interior part of the wall, and not raising the wall to a great height at one time.

III.—OF FOUNDATIONS.

On Land.

65. Having considered the nature of the materials to be used, and the scientific principles on which we should proceed in their disposition, we must turn to practical results, and first consider the foundations, or the base, upon which these superstructures are to be placed, so as to stand safely. When a good hard soil is easily accessible, as solid gravel, chalk, or rock, we have nothing to do but to excavate the surface mould to the sound bottom, and to build at once, first putting in the footings, which are one or more courses, forming a sort of steps, each a little wider than the other, and the wall that stands on them (see Building, Pl. 147, fig. 5), according to the judgment of the architect. On hard ground one course of masonry, about half as wide again as the superincumbent wall, is ample. On softer ground it was usual to employ footings at least double the width of the wall, and frequently more; but since the invention, or rather revival, of the use of concrete, this is seldom or never done. In this case, or when the ground is a deep clay, be the material used what it may, it should at least go so deep as not to be affected by change of temperature, or the rising and falling of springs, as the alternate shrinking and swelling of the ground must affect the building. As has been shown (article Climate, p. 768), frost seldom penetrates a foot into the ground in this country; but in clay soils, fissures, the consequences of drought, are found three feet and more in depth. The basis should, therefore, be below this point in such a stratum. If the ground be springy, it should be drained, if possible; if not, a foundation should be made with concrete as low as the lowest level of the water; or if very deep or boggy, piles must be used. The plan of building on sleepers and planking, so common a few years ago, is very bad, as they soon rot, and the building settles in all directions, as the greater weights crush the decayed timbers sooner than the lighter portions of the building. Where ground is alternately wet and dry, the best timber soon decays; even piles should always be wholly below the water.

66. The use of concrete, except in very peculiar occasions, has entirely superseded every other artificial foundation. It may be defined as a sort of rough masonry, concre-posed of broken pieces of stone or gravel, not laid by hand, but thrown at random into the trenches, cemented together with lime prepared in various ways, and thoroughly mixed with it before it is so thrown in. In this country, the lime is generally ground and mixed, when hot, with the stones; in France, the lime is first made into a paste, and the mixture is then called béton, not concrete.

67. The use of this material is of very remote antiquity. History of It is no doubt the signum opus of Vitruvius, and is de- concrete. scribed by Alberti. It is very common in medieval buildings, walls and even arches frequently being made of it. In Rochester castle the staircases are composed of it; the undersides, or soffits, show to this day the marks of the boards which sustained it till it was set. Smeaton states that he was induced to employ it from the observation of the ruins of Corfe castle. Dance employed a sort of concrete in rebuilding Newgate, 1770–1778. The foundation of part of the new structure was a deep bog, and it was rendered available by shooting a quantity of broken bricks into the holes, mixed with occasional loads of mortar, in the proportions of four to one, and suffering them to find their bed.

68. Any hard substance, broken into small pieces, will make good concrete. That most used is gravel, or ballast, of course. This should not be sifted too fine, as the sand which is left crete, will mix with the lime, and form a sort of mortar, and assist to cement the stones together (see I., sec. 29). If broken stones, or masons' chips, are used, it is well to mix some sharp sand with them. The general rule is, that no piece should exceed a hen's egg in size. In this country the lime is generally ground, and used hot. It is mixed with the ballast by scattering it among the stones, and turning them over with a shovel, water being at the same time thrown upon the mass. It is then immediately filled into the Laying trenches, sometimes by shooting from stages erected for the concrete purpose, six or eight feet above the work. But this process has been very justly censured as uncertain by eminent engineers, who prefer to put it in layers of not more than 1 foot in thickness, and to level each course, and ram it down thoroughly. About one-sixth part of lime is generally used. When too hastily put into the trenches, the lime, Swelling of which has not had time thoroughly to be slackened, will con-crete. tinue to do so, and the mass will puff or swell, and sometimes cause considerable mischief. The author has seen the wing walls of bridges thrust out by this means. From some experiments made by the Architectural Publication Society, where the materials were carefully mixed, no change took place in the bulk. The lime, if it can be procured, should be hydraulic; and concrete is much improved by the addition of the volcanic sands. The French authors recommend, as good proportions, one-fifth hydraulic lime, one-fourth pozzolano, one-eighth sharp sand, and the rest broken stone or gravel; or 20 per cent. hydraulic lime, the same of terrass, the same of sharp sand, 15 per cent. of gravel, and 25 per cent. of broken stone. Perhaps, after all, the very best concrete is made of a simple mixture of gravel with Portland cement.

Foundations in Water—Ancient Systems.

69. These are often made by shooting quantities of loose rough stones, &c., into water, at hazard, till the mass finds its own bottom, and becomes solid by degrees. When a sufficient quantity has been shot, so as to appear above the surface, the material is levelled, and the superstructure erected upon it. Most of the break-waters (see Art.) have been thus constructed. This method is called by the French, foundations à pierre perdue (see Breakwater, Harbour, &c.). Concrete has been used in the same way with great success. Where it is practicable, it is very desirable first to bring the bottom to a level by dredging. (See Navigation, Inland, p. 68.)

70. Another method is to drive a number of piles, side by side, through the mud or other soft soil till they reach a sound bottom, the heads are then cut off to a level, and a platform of timber, or better still, of flat stones, is laid on them, and the superstructure erected. The heads of the piles should always be under water. For small operations they may be driven without dams; but for larger a more elaborate system must be pursued, the most effectual of which are coffer-dams.

71. These are of as great antiquity as the time of Vitruvius, and most probably much older. That author, however (lib.5, cap. iii.), describes the method of forming them, and calls them areae. Like those of later times, they were composed of two parallel rows of piles driven into the water, and kept together by strong horizontal timbers, and continued around the place where the proposed work is to be erected, so as to form a sort of box or coffer entirely round it. The two rows are kept in their places by other timbers, and the vacant space between such double row stuffed full of clay and weeds, till the whole is quite tight, the water is then pumped out by proper engines till the ground appears, which is then levelled and excavated to a solid stratum, if such is readily accessible. The foundations of the pier, &c., are then laid, and the superstructure carried up to above the water-level, when the dam is removed. If solid ground is not easily accessible, structural piling is resorted to. In large works these are of whole timber, pointed at the end, and shod with iron, to facilitate their penetrating the earth. They are driven by a weight called a monkey, which is raised by a machine called a pile-engine, worked by horse or other power, now frequently by steam. When the monkey is raised to a sufficient height, it is suddenly liberated by a contrivance much like a double pair of scissors, and falls with great impetus on the head of the pile, and of course forces it downward into the bed of the stream. When driven to a proper depth, the heads are cut off to a level line, cross timbers are bolted on these, and the superstructure erected, as shown in Bridge (Plate CXLV.fig.3.) The piles of the dam should not be drawn, as that would allow the water to form holes, and to work under the foundations, but they should be cut off close to the bottom of the stream. Fig. 11 shows a plan of the coffer-dam and pier of a bridge erected by Rennie on the Thames. The outer lines are the parallel piles which keep out the water, and form the coffer; these, as will be seen, are strongly bolted together, both across and lengthwise, and also braced diagonally. The general plan is elliptical, the better to resist the pressure of the water,—a course afterwards adopted in the coffer-dams of London Bridge. The plan of the pier is within this, and is shown in four quarters:—A shows the plan of the great piles, driven down to the solid; B shows the heads of the same piles, when cut off and tied together by strong cross timbers; C shows the planking laid thereon; and D the first courses of the masonry.

72. As the system above described is extremely expensive, especially before the introduction of steam-power for pumping, &c., a very ingenious method was introduced into this country by a Swiss named Labeye, and first used at Westminster Bridge. The bed of the stream was first carefully levelled by dredging. (See Navigation, Inland, page 68.) Strong frames of timber were then constructed, having upright sides like those of a box, and being about the same area as a coffer-dam. These were floated over the place where the piers were to be built, and the masonry of each pier commenced inside these large cases (the word caisson meaning a large box or caisse). It was, in fact, like building in the bottom of a large flat-bottomed barge. Of course, as the weight increased this barge or caisson would gradually sink. The sides were somewhat deeper than the river, and well caulked and pitched to keep the water out and enable the men to work. When the first course of stone was laid and cramped together, the water was let into the caisson by sluices, and the whole sunk to the bottom. It being found this was not sufficiently level, the sluices were closed, the water pumped out, when the whole floated again, and the bottom was again dredged and levelled. This operation was performed three times before the work settled to a level bed. The pier was then built up to a height above water-level, when the sides of the caisson were removed, and used again for the next pier. Blackfriars Bridge was afterwards built on the same plan, but in consequence of the removal of old London Bridge, the scour of the river increased so much as to work under the piers; these directly began to settle in all ways, and the bridges must both be rebuilt. The system of caissons might, perhaps, nevertheless, be used in still waters, but it is manifestly improper for a sharp current, and still worse for a tidal river. Foundations in Water—Modern Systems.

73. The great advance in all objects of engineering, and the desire to avoid expense, has led to some very ingenious and novel systems of laying foundations in water.

74. The first of these is chiefly owing to the invention of the diving dress. (See Diving, vol. viii., Plate CCV.) This has now been brought to such perfection, that excavating, levelling the bottom, setting large blocks of stones, cutting off the heads of piles, in fact, all engineering operations are effected under water almost as easily as on land; the men, in fact, working in a large bag filled with air. The most extraordinary work of this kind is now being carried on at Dover, where a huge mole projects into the ocean, of an extent and construction that exceeds any thing yet achieved. Our limits prevent our giving a full account of this work. It must suffice to say, that the outside of the pier are composed of two parallel walls, built with large blocks of granite, which are sunk into the solid chalk partly by dredging and partly by excavation. A number of piles are driven into the sea, on the tops of which are strong cross-sleepers, each traversed by a series of iron rails, on which a number of travelling cranes move in all directions. These convey the stones exactly over their intended beds, on to which they are lowered, according to signals given by the divers below, who then cramp them together as well as they can. Between these two outer walls is a filling-in, composed of immense blocks of concrete, made of the ballast from the beach and Portland cement. These blocks are cast, as it were, in wooden boxes, the sides of which are removed when the concrete is set. Pieces of rope or chain are cast within the body of the block, and by them they are raised and lowered just as if they were masses of stone. The pier, therefore, is composed of concrete faced with granite; and the work stands extremely well.

75. The next important change in building in the water is the substitution of iron piles for those of timber. Their success emboldened engineers, and from small piles, driven in the usual way, large cast-iron cylinders came into use. These vary, according to the nature of the work, from 3 or 4, to 6 or 7 feet in diameter. They are first lowered into the water in a vertical position, and driven down as far as they will go without much difficulty. A quantity of clay is then thrown in round the outside of each, to keep the water from coming in under the bottom as little as possible. That inside is then pumped out, and workmen descend and excavate the bottom, sending up the stuff in buckets, just as a well is excavated. The cylinder then sinks partly by its own weight, and partly from weights above, as the earth is excavated beneath to the depths required; each cylinder has a series of flanges, on which another is screwed from time to time as the former sinks into the bottom. When the cylinders are sunk to a proper depth, they are brought to a level at the top, and a platform of girders and planking is fixed for permanent use. In many instances the cylinders have been filled in solid with concrete after they have been thus submerged.

76. The most extraordinary operation of this kind has, however, just been executed in the piers of the new bridge at Rochester. The ground here was very difficult to work, being composed partly of rag rock and partly of very hard chalk, and it was found almost impracticable to sink the piles in the manner last described, which is successful enough in clay. To overcome this difficulty the following plan was devised—a proper stage of piles, sleepers, &c., was first erected, and a number of cast-iron cylinders, each 9 feet long and 7 feet in diameter were bolted together in proper lengths. As it was necessary to employ diving-bells to dredge the bottom, it was considered that each cylinder might easily be converted into a sort of bell by putting on it an air-tight cap. This was done, and an ingenious method contrived by which the men could pass in and out of the cylinder without admitting the air. It would exceed our limits to go into all the details of this invention, which was called an air-lock, probably from its permitting or hindering the passage of air, much as the lock-gates on a canal do with that of water. But there was this great difference between the method described in [sec. 75] and this new method. In the former the water was pumped out of the cylinder, but in this air was forced into the cylinder below the air-tight cap and locks, and the water driven out by its pressure. The men then entered through the air-locks, and excavated the ground under the cylinder, which descended by its being heavily weighted above. As each cylinder sunk, the cap was removed and another cylinder screwed on, so that some of the piles (as in fact they may be called), consisted of seven pieces, and measured over 60 feet in length, one half of which was buried in the bed of the river. The girders, tying the heads together on the top, as well as the skew-backs, &c., from whence the arches spring, were then fixed in the usual way. (See Iron Bridges.)

77. A still more curious method of employing iron screw-piles is the invention of Mr Mitchell, and succeeds admirably in soft ground and even in sands. These are hollow, and of wrought-iron, varying in diameter from 5 or 6 inches to about a foot. They terminate at the end with screws of various shapes (see figs. 12, 13, and 14), and are screwed into the bed of the river or the bottom of the sea, as the case may be, to such a depth as to hold the pile firm, their heads are then connected together with sleepers, &c., and the intended superstructure erected. The lighthouse on the Chapman Sand, in the mouth of the River Thames, is built on piles 7 inches in diameter and about 40 feet long, the screw part is of cast-iron, about 4 feet in diameter. They are screwed down till only 2 or 3 feet remain above the sand; on their heads are cast-iron cylinders, braces, &c., which support the lighthouse, which is entirely of wrought-iron. The piles are only seven in number; one driven in the centre, and the others at equal distances around it.

78. Several very ingenious adaptations of iron for coffer-dams have been tried with success in various places; they are all, however, more or less expensive, not only in construction and removal, but because they entail constant expenses in pumping.

79. The method lately invented by Mr Page for getting in the piers of the new bridge now in course of erection at Westminster is, however, so novel and so important, we feel our work would not be complete without a short description of it. Figs. 15, 16, and 17 show the plan, the long and cross-sections of half each pier. Rows of

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1 These piles form a scaffold, and are removed when the work is done. strong elm piles, AA, about 30 feet long, are driven into the bed of the river, as shown in the plan, passing first through the gravel, which is about 4 or 5 feet thick, and then going about 20 feet into the London clay. There are about 140 or 150 piles to each pier, ranged alternately in threes and fives, around these a range of cast-iron piles BB, are driven about 4 feet apart, as shown in the figure. These are round, 15 inches in diameter, and have strong grooves cast on each side of them. They, however, go into the clay only 10 or 12 feet. Into these grooves large plates of iron, which the engineer calls "plate-piles," are fitted and driven down between the piles, BB. They are marked CC on the cross-section (fig. 16), and, as will be seen, go about 10 feet into the blue clay, and extend to about a foot or two above the natural bed of gravel. Upon these are a series of slabs of granite, DD, placed edgewise, retained in their places thus,—The bottom rests on the "plate-pile" CC, the edges are secured to the round iron-pile A, and the tops to the other masonry. The plate-piles are secured together by two sets of ranges of iron-rods passing through the pier and tying them together. These are all fixed by the divers. It will be seen, therefore, a sort of case or box is made which surrounds the wooden piles AA on all sides. The loose sand and mud

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1 The same letters apply to all three figures. is then dredged out, and the case filled up solid with hydraulic concrete, in which, of course, the piles are embedded, and the whole forms one solid mass to about a foot above low water-mark. At this level the tops of the piles are cut off, and on each top a stone 2 feet square and 1 ft thick is bedded, the spaces between which are again filled in solid with concrete. The gravel is then dredged out around the pier on the outside of the case, and the space also filled with concrete, as shown at EE. It has been urged that the steamers will come into collision with the round piles, BB, and break them, so that the granite slabs, DD, will escape, as it were, and fall into the river. This, however, cannot be as long as the concrete E remains in its place, as the top of the slab D is secured by the masonry, and the bottom would not be accessible. It is, however, intended to protect the piles by floating booms, which would prevent the chance of collision, and would act as safeguards for the steamers as well as the bridge.

For the action of waves, running water, &c., on walls, piers, &c., see Harbour.

IV.—STONE-CUTTING.

80. The different methods of reducing stones to shape by the axe or scabbling-hammer, the saw, or the tool; of dressing by the chisel or point; the nature and value of plain work, sunk work, moulded work, and beds and joints; the various sorts of bond, and of rubble, coursed, or ashlar, with their proper backings and quoin-stones; the mortar, and such methods of working and setting the beds of stones, that the faces may not chip or flush; the mode of securing and strengthening work, by discharging and relieving arches; by hoop-iron bond, cramps, dowels, joggles, plugs, &c.; the descriptions of copings, cornices, string-courses, blocking-courses, sills, landings, balconies, paving, curbs, steps, hearths, chimney-pieces, &c.; and of columns, with their beds, joggles, flutes, &c.; in short, all that relates to the mechanical part of stone-cutting, has been already given, article Building, pages 737 to 741, to which we refer our readers.

81. Before working the various pieces of stone, it is necessary to prepare certain moulds, which are generally of thin metal, wood, mill-board, or some similar substances, of the exact form with which each face of the stone is to be worked; and which are applied to the sides of the stone, and their shapes marked or "scribed" thereon. They serve the double purpose of guiding the workmen, and of enabling him to select pieces of stones of convenient sizes, so that there should be as little waste and labour thereon as may be. We shall now proceed to show how to find these lines, the most important thing a mason can learn.

82. The general principles of the making working drawings; the projection of lines, of planes, and of curved surfaces; the finding the angles of planes inclined to one another; the describing mouldings, and the methods of finding the lines where they mitre, on the level or on the rake; in short, all the general principles of projection are given in Joinery, sect. I., 1 to 20.

Arches, to Describe.

83. But as arches form no part of joiners' work, and as our articles Arch, Architecture, Bridge, &c., though containing full scientific developments on the subject, necessarily involve the highest branches of pure mathematics, we shall refer the readers of abstract science to these articles, and shall proceed to give a few problems in descriptive geometry for the use of masons, as we have done before for joiners.

84. First, of circular arches. These, if of moderate size, may be set out by a long lath, one brad awl as a centre, and another to trace, or by beam compasses; but if they are flat, the centre is frequently at such a distance as to render this inconvenient, if not impossible. The best way Circular arches, to draw.

Flat arches.

to proceed, far better than most of the cyclographs, is thus:

Let AB (fig. 18), be the width of the arch, and CD its height; set out their width and height on a floor, or on some boards joined together for the purpose; drive pins at A and B. Take two straight rods AD, DB, place them so that their sides may touch A and B, and their intersection coincide with D. Tack them together, and also a third lath across, to keep them at the same angle; place a pencil at D, which will trace the curve if the rods are moved to the right and left, and are kept pressed against the pins A and B.

85. Another way (fig. 19), let the letters represent the same): join AD, draw DE parallel to AB, and make DE equal to AD, then cut out a triangle in wood, or form one as above with three laths; put a pin into the board at D, and a pencil at the same point of the triangle, and it will trace half the curve AD; reverse it, and it will trace the other half DB.

86. Next to circular forms, the most common are those from the sections of a cone, of which the most usual is the ellipse; the parabola is sometimes used, and so is the hyperbola, but very seldom. As these forms are necessary in sections setting out Grecian mouldings, as well as in almost all problems in masonry, it is proposed to treat of all three as shortly as possible.

87. Let ABC (fig. 20) be the section of a cone, or one cut through its axis downwards to its base, and ABD be half the plan of its base. If the cone be cut by a plane passing through EF, in other words, if it was cut into two parts by a large flat knife passing in that direction, but wholly above the base, its section would be an ellipse. Then EF would be its length, or axis-major. To find its height or axis-minor, bisect EF in G, through G draw a line parallel to AB, touching the sides of the cone; bisect this in O, and on it describe the semicircle as shown; then draw GH parallel to the axis of the cone CD, and this line GH will be the half the height, or the semi axis-minor, and the ellipse will be described within the parallelogram EF, HH' (fig. 21). 88. This may be done, first, by finding the foci, and describing the ellipse by a cord or string, thus:

Take the distance FG (fig. 22) in your compasses, and from H as a centre strike the portion of a circle 1, 2, 3, then 1 and 3, where it cuts EF, are the foci. Stick two pins, or brad awls, in their points, and strain a string round H, 1 and 3; place a pencil at H, and move it round, keeping the string tight. The pencil will draw the ellipse.

Or it may be done by a trammel. (See vol. viii., Plate CCXXXI., fig. 1; and see article ELLIPTOGRAPH.)

89. Let the parallelogram be, as before (fig. 23). Divide EG, E4, each into any number of equal parts; here they are divided into 4; from HH' draw lines through 1, 2, 3, as shown, and where they intersect are points in an ellipse; mark these points, bend a thin lath round them, and strike the curve. The same repeated for the other quarters will complete the ellipse. These methods are mathematically true; but as it is difficult to get laths to bend round a large curve, and very difficult to tie a string exactly to the proper length; and also to prevent its stretching when tied, other means have been taken as approximations.

90. It is of the utmost importance to the mason, whether in Gothic or other work, to remember, that in all cases where two circles touch each other, the two centres from which they each are struck, and the point in which they touch, must lie in the same straight line; in other words, a line drawn from one centre to the other must pass through the point of contact, a point where they each touch without cutting each other. If this rule be not strictly attended to, any curve coming out of another will not flow freely, but must be crippled. If we attempt to draw an ellipse with the compasses, we must strictly attend to that rule. Now, if we take a diagram similar to fig. 23, but instead of four parts, we suppose the diameter EG and the side E divided into two parts, as fig. 24.

Now, joining the lines H1, H'1, we get at their intersection, a point K, which, as has been shown before, is a point within the true curve of the ellipse. To prevent the confusion of so many lines, we will now suppose a similar point found in the right hand quarter, and will call it L. Now, we have to draw two portions of circles, one through L and F, the other through LH and K, and they are, of course, to touch each other in L; then this point of contact L and the centres of the circles must be all in the same straight line. To do this we have to join HL by a straight line, and bisect it by a perpendicular line. This is done by taking any convenient opening of the compasses, and from the points H and L cross two small segments, as shown, and draw a line through them on till they meet HG produced to M. Join ML, cutting EF in N. From N as a centre strike the segment of a circle LF; and as LN and M are in the same straight line from the centre M, strike the segment KHL, which will pass through H, and touch LF at L. We have, therefore, a curved line passing through the points KHLF, all of which points are in the curve of a true ellipse, though the curve itself is not so, but parts of circular arcs. Proceed in the same way for the other side of the parallelogram, and the ellipse is complete. If greater accuracy is required, divide EG, E2, each into three or four or even more points, instead of two, and proceed on the same principle given above, viz., join the first pair of points so formed (beginning at the top) by a straight line, bisect this by a perpendicular projected till it cuts the line HG, and then join the next pair of points, and bisect again as before.

91. Let ABC (fig. 25) be the section of a cone as before, and ABD half the plan of its base; if the cone be cut through by a flat straight cut or plane in the direction EF, but it always must be parallel to one of the sides (as it is here to the side CB), the section of the cone thus cut will be a parabola, and its height or axis will be EF. From F draw FG at right angles to the base AB, and FG is half the base of the same.

92. Draw a parallelogram (fig. 26) of which the height shall be equal to FE, and the base equal to twice FG. Divide the height and each half the base into any number of equal parts (in this case they are divided into 4), draw co-ordinates crossing each other as shown, and abc will be points in the curve; bend a lath round, and strike the curve, which will be a parabola. In a similar way a parabola may be drawn, any height and width being given.

93. Let ABC, &c. (fig. 27), be the cone and its plan as before, and let it be cut by a plane at EF, falling within the base, but not parallel to the side. The curve of the section is a hyperbola, and FE is its height. From F draw FG at right angles to AB; then twice FG is the base of a parallelogram, within which the hyperbola lies.

94. Construct a parallelogram (fig. 28) of the height EF, and width twice FG; then in fig. 27 produce the side AC and the line EF till they meet in H, and make EH (fig. 28) equal EH (fig. 27), divide the sides as shown into any number of equal parts, cross the co-ordinates as before, and through their intersections draw the curve.

95. It is now necessary to say a few words on the regular solid figures with which the mason has most to do. These are the cone, the cylinder, the globe, and the spheroid. The cone may be considered to be formed

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1 For the definitions of the words foci, ordinate, axis, &c., see CONIC SECTIONS, pp. 252, 258, and 260. by taking a right angle triangle (ABC, fig. 29), holding it upright, and turning it round as if the perpendicular side AB was an axis. The surface traced by the hypotenuse AC as it turns, would be the surface of a cone, and that

and the cone divided in a similar way by lines drawn to the apex A; suppose these lines drawn in wet ink, or paint, and the cone then rolled on its side along a flat surface, A1, A2, A3, &c., would mark the different portions of the cone; and C1 2 3–6 will be the stretch out of half its base, and AC 6 the development of half its surface. The other half will be merely a continuation of the same. To draw this development from the centre A with the radius AC, describe the segment of a circle, and set off upon it the openings 0, 1–6, equal to the circumference of the half-circle O–6 on the plan, and join A1, &c. Each division will be the development of a portion of the cone—thus, AC3 will be a quarter of the cone, AC4 one third, &c.

98. If a cylinder be cut parallel to its axis, the section is a parallelogram; if the plane be inclined from the axis so as not to pass outside the ends or bases (fig. 33), a trapezium, ABCD; if at right angles to the axis, a circle; and if cut obliquely to its axis, the plane not cutting into the ends, the section is an ellipsis (fig. 34), of which AB is the larger and CD the lesser axis.

99. Let ABCD (fig. 35) be the elevation of a cylinder, and its plan be below it; and suppose it divided as directed for the cone, and then rolled along a plain surface from Eo to F6. O–6 is the stretch out of half its base, and Eo–F6 is the development of half its surface. To draw this proceed as directed for the cone.

100. Let ABCD (fig. 36) be a cylinder cut square at the base BC (of which the plan is below), but obliquely at the top, as AD.

The upper section (sec. 98), will be an ellipse, of which AD will be the length, and the radius of the circle (or the most of an plan) equal to half the height EF. This may be described by any of the foregoing methods. Divide the circle at the base as before, and draw lines on to the surface of the cylinder; set out the stretch out from 0 to 6 as before directed, and draw the perpendiculars—as 0'0', 1'1', 2'2', Again, draw perpendiculars from O12, &c., on the stretch out, and cross them by horizontal lines drawn from similar points in the elevation, cutting the lines on the development at 1'2'3', &c., the surface between the curved and the straight line is its development. In like manner the other half may be drawn.

If a globe be cut through by any plane, the section is a circle. If the plane passes through the centre of the globe it is called a great circle, being the largest that can be cut out of that solid. For the development of a globe see 117, 118.

If a spheroid be cut by a plane at right angles to its larger axis, the section is a circle; all other sections are oval, of which all parallel sections are similar.

These foregoing problems are indispensable to a mason, and should be carefully studied and gone over till they are thoroughly understood. Several other mathematical curves have been used for arches, as cycloidal, catenary, cassinoidal, &c.; but the trouble of setting them out, and the difficulty and confusion the workmen often get into has led engineers and architects to the use of circular and elliptical arches almost exclusively. Indeed, in many cases where the latter were formerly used, it has been found better and cheaper practically to substitute segments of circles.

To find the Joints of Arches.

In all cases the joints of all arches should be at right angles to the tangents of the curve. For this reason those of circular arches should simply be drawn to the centre of the circle of which they form a part. If that be very distant, as is frequently the case with very flat arches (fig. 37), divide the arc into as many equal parts as may be convenient, having relation to the size of the arch-stones or voussoirs, and taking care that the middle of the key-stone A shall be exactly in the centre of the curve. Then, from every alternate centre as B and C, with any convenient opening of the compasses, strike two small arcs, as at D, crossing each other; these will give the angles for the joints. In fact, this way is very nearly true for all flat arches, whether circular or elliptical.

Let EHF be an ellipse, and a the point from which the arch-joint should be struck; find the foci 13 (sec. 88, fig. 29), and draw lines from each through the point a, as shown towards b and c. Bisect the angle b a c, by the segments as shown; draw b a, which is the arch-joint. In cases of arches drawn by segments of circles, as fig. 39, the arch-joints are simply parts of radii from the respective centres ABC. This figure shows the case of an arch drawn from three centres in each quadrant instead of two. The arch-joints from D to E are to be ruled from C, from E to F they are to be drawn from B, and F to G from A. The method of finding these points is shown on the other half of the diagram. (See also sec. 90.)

The same rule holds good with parabolic arches as joints to with others, that the arch-joint shall be at right angles to a parabolic tangent, passing through the point whence it rises. Then arches let ABC be a parabola, drawn as shown, sec. 92, figs. 25 and 26. It is required to find the arch-joint at D, draw DE parallel to AB, and make CF equal to CE; through D, draw FD a as shown; take a, b equal distances from D, and raise the perpendicular D e, which is the arch-joint.

To find the Arch-Stones or Voussoirs.

Let fig. 41 be the elevation of the arch, below which Voussoir is its plan. Then, as the stones are generally longer than of right they are high, the workman will take a block of about of right size required, and will work any long side, say the bed a b c f (see plan). He will then work the ends square, and of course they will be parallel with the face of the wall; he will then, by means of bevels, set off the angles a b c, b a d, b c d, and work these sides; he will then apply a mould the exact shape of the arch-stone, as shown by the shaded lines, to each end of the stone he is working, and describe its exact shape, taking care to keep the moulds out of winding, and work off the waste between the dotted lines a d, b c, reducing them to the curve shewn by the mould, and the work is complete.

If the arch be splayed inside, as on the right hand side of the plan, fig. 41, and \( l \) be the half of the width of the square part, and \( l \) that of the splayed, then the line marked \( r, s, n' \), is an ellipsis. Draw this by any of the methods given above, taking \( l \) as the length and \( l \) as the height. Then the plan of the bed (No. 1) at the springing will be \( mnoq \) (see plan, fig. 41). The next bed \( ss', fig. 42, No. 2; \) the third, \( r, r_p, r_p, \&c., \&c. \)—the depth of the square part, and the entire thickness of the arch being always the same.

108. Let \( AB \) represent the plan of an opening (as a door or window) which cuts obliquely into a wall. If the face of the arch be a circle, proceed as in 41; but instead of working the stones square at the end, they must be worked according to the bevel 1 2 3. The face bevels are obtained as shown before. But if the section of the arch be an ellipse, as \( CED \) (fig. 43), and the depth of the voussoir \( EF \), the delineation of the face will be found by drawing \( HI \) at right angles to and bisecting \( AB \), and making \( HI \) equal to \( GE \) as the height, and \( AB \) the length, and describing an ellipse; also make \( IK \) equal to \( EF \), and describe a second ellipse through \( K \) as shown; \( AKB \) will be the face of the arch. If these arches are of great length, or skew very oblique, another method has been lately used, which is given in the separate article Skew Arches.

109. The soffit of an arch may always be found by considering it to touch a cylinder placed as a centre under soffits, it, and by finding the development of such cylinder by the methods given in Joinery, and in the sections 99, 100.

110. Let \( ABC \ldots F, abcf \) (fig. 44) be the section of the arch of a tunnel, or of one in a terrace wall, the face of oblique walls, which also batter.

which is not square with the section, but inclined on the plan at the angle \( NAF \), and which also batters or falls back out of the perpendicular at the angle \( UST \) on the longitudinal section, \( SU \) being perpendicular to the springing line. From the intrados \( def, \&c., \) draw the taint lines to \( ST, \) as \( 1e, 2d, \&c., \) and from the extrados draw the dotted lines \( 3E, 4D, \&c.; \) also let fall the perpendicular \( bb', cc', dd', \) on \( AF'. \) Then take the several divisions intercepted between \( ST \) and the perpendicular \( US, \) and transfer them to the line \( AF', \) and set them off at right angles to it as shown; then \( a'b'd', \&c., \) will be the line of the intrados on plan, and \( A', B', \&c., \) that of the extrados; and the portion between those lines will represent the battering face of the arch. From \( B'b', Cc', \&c., \) let fall perpendiculars as shown, and the shaded portions will represent the places of the arch-joints on the plan.

111. Take any line \( OP \) equal to the stretch out of the inner circle of the arch \( ab \ldots f, \) and divide it into as many parts as there are arch-stones. Draw perpendiculars from fits and these points as shown in the figure, and set out on them \( gb', hc', \&c., \) equal to the same on the plan. Then \( a'b', c', \&c., \) is the development of the line of the intrados; and each portion, as \( cd'op, dp're, \) is the mould for the soffit of each respective stone. Next make \( lm, no, \&c., \) equal to \( Aa, \) or \( Dd, \) in the section which will represent the depth of each arch-joint, and make \( B'l', C'n, \&c., \) in the development equal to \( B'l', \&c., \) on the plan. \( B'b'lm, \) dDpq, &c., are the moulds for the arch-joints, as shown by the shaded surfaces.

112. Let Aa b c, &c. (fig. 45), be a circular-headed arch over a door or window, in the wall of a circular bow or tower; the plan of which is LMNOPQ. Draw the arch-joints dB, eC, &c., in the section, and let them fall on the plan in bB', cC', then the shaded part will represent the lines of the arch-joints on the plan.

113. Draw any line in the plan RS perpendicular to the lines let fall. Also draw GH in the development, and make it equal to the stretch out a b . f, and divide it into as many parts as there are arch-stones at 1, 2, 3, &c.; draw the perpendiculars, and set down 1, b', 2, e', on the development equal to 1b', 2e', &c., on the plan. Do the same with 1m, 2n, 3o, &c., and the line a' b' c', &c., is the front line of the soffit, and l m, q, the inner line of the same; also e'd' n o, b' c' m n, will represent the soffit of each arch-stone.

114. From the lines b m, c n, &c., set out the depth of the arch-stone equal to Bb, &c., on the cross section, and on the line GH set down 6B', 7C', &c., equal to the same on the plan. The shaded portions will then be the moulds for the arch-joints.

115. The above problem may be used for any sort of arch, or any form of wall, whether cylindrical or conical, care being taken that all section lines be first carefully transferred to the plan and then to the development. Perhaps the method of finding the arch-joints will be better understood if the reader will suppose the stones of an arch to be transparent or made of glass; and the joints or surfaces where they touch to be blackened. If the eye were placed exactly above such an arch, it would present the appearance as shown in our plans.

Spherical Vaults, Domes, Niche Heads, &c.

116. Spheres or globes may be developed in two ways,—first, in horizontal sections or zones; and, second, in vertical sections or gores.

117. Let Ao, 1, 4 (fig. 46) be the section of a dome, and 1, 2, 3, 4 the places of the arch-joints; AB 4, the springing line; B, o, the line through the vertex; produce this line towards C, and through 2 1, 3 2, 4 3; draw chords to the vertical line, cutting it in a, b, C. Then o is the centre of the eye of the globe, or the key-stone of the dome; a the centre of the development of the first zone, 1, 2; b, the centre of the second 2, 3, C, of the third 3, 4; and so on for as many divisions as you may think proper to divide the globe into.

118. Let xy, in fig. 46, be a gore or section of globe, made by two vertical planes passing through its centre. Then those planes are portions of great circles 101, and their sections are quadrants. Let ADB (fig. 47) be one of these quadrants, draw DC parallel to AB, and make it equal to half the gore required. Draw CF parallel to DB; produce AB to F, and CF to E, and join DF. Divide AD into any number of parts, as 0, 1, 2, 3, &c., and draw ordinates parallel to AB, cutting DF and CF. On CE set out 0, 1, 2, &c., so that CE will be the stretch out of AD. Draw ordinates through these points, and make 1, a; 2, b; &c., in CE, equal to the same lines intercepted between DF and CF. The curved line which passes through Da b c, &c., will be the development of half the gore. Transfer these points to the other side, and the whole is completed.

By these two methods any portion of the surface of a globe may be drawn, and if cut out of any thin material will form a mould for any of the curved surfaces.

119. Let fig. 48 be the section, and fig. 49 the plan of a semi-circular dome, or a niche head. For greater clearness this is drawn with only two ranges of arch-stones besides the key, but the theory is the same for any number. Then a b e d upon the plan will be the bed; a b e f on section, the end mould of the first voussoir; the face moulds will be found by the preceding problems. It remains to find the upper bed at ef. With the radius Of strike part of a circle (fig. 50), and set out on it the line fp g, equal to fg stretched out on the plan. If the thickness of the dome be parallel, as on the left side of the diagram, set out such thickness ef (fig. 48), and then describe the circle e h, and efgh is the mould. The bevels can easily be set from the plan and section. If the arch-stones are intended to bond in with the level masonry, as shown on the right side of the section (fig. 48), make pq (fig. 50), equal to pq in the section, and proceed as before. In this latter case it will be better to work the arch-stones thus: from the point 1 on section let fall (through p) the perpendicular 1 p 2, and draw 4, 3, parallel thereto; then 2, r, 3, 5, 6, on the plan. will be the mould of the bed: 1, 4, 2, 3, on the section, fig. 50, of the end; and the plane 1, 2, 3, a square angle No. 1. Join AB on plan No. 3, and draw OC perpendicular to AB, and equal to OC, Nos. 1 and 2. Then the line of intersection will be an ellipse, the length of which is AB, and the height OC. The section, No. 2, will be an upright ellipse, the greater axis of which is OC and the less DE, all which may be drawn as before. If the cross vault be a semicircle, the main vault will be a flat ellipse, and the groins found as before.

122. These are either from the same springing, in which case the crowns of the intersecting arches are not level; or the crowns are level, in which case the springing of the lesser arch is higher than that of the greater. In fig. 55, No. 1 is the section of the main arch, No. 2 of the cross arch, No. 3 is the plan of a groin in which both arches are semicircular, but No. 2 is less than No. 1, and of course of different heights. In the smaller arch, No. 2, take any number of points, 0, 1, 2, 3, 4, and draw horizontal lines from them to the perpendicular O, 1, 2, 3, transfer them to No. 1, return them to the curve, and draw co-ordinates from these points, meeting in the line a b c d, which is the curve of intersection. These are called under-pitch groins, and sometimes Welsh arches. In the same way the lines may be formed where one arch intersects another obliquely (fig. 56), where the respective numbers and letters refer to the same things.

123. In this case the springing of the smaller arch must be higher than the other. This often occurs in Roman work, and almost always in Norman groining. No. 2 (fig. 57) is the smaller semicircle, the springing line of which is AB, the crown. Make OC in No. 2 equal to OC in No. 1, which is the height from the crown to the springing of the main arch. Take any points in the curve 0, 1, 2, 3, &c., of No. 2, draw them to the perpendicular A 4, and transfer them to No. 1, and cross the co-ordinates as before, and the line of intersection will be found. But it must be noticed this is a curved line, and not a straight groin point, as will be the case in the next problem.

124. This is often the case at the end of a building with a canted bow, or a church that ends with a hexagonal apsis. Let ABCD (fig. 58, No. 3), be the plan of a cylindrical vault, the section of which is DEF, No. 1, and let it be sealed by a pierced by the portion of a conical vault GHIK. Produce portion of GH, IK, O, till they meet in O the vertex of the cone, and till \(d_e\) in No. 2 is made equal to DE in No. 1;—\(d_e\), of course, being parallel to GI. Draw the semicircle \(d_e f\) in No. 2 equal to DEF in No. 1, and divide each into the same number of equal parts. In No. 2, draw ordinates, first perpendicular to \(d_e\), and thence radiating to the point O; cross these by the co-ordinates from No. 1, all as shown in the diagram, and the curved lines GK, HI, will show the intersections.

125. The lines for these may be formed on exactly the same principles, viz., from a plan, two sections, and a double set of ordinates. In descending vaults, however, we have to remark, if it is intended the cross arches should be cylindrical, the groined points will be curved, as in 123 and 124. If it be intended that the groined points shall be straight, and should intersect in the middle of each bay, then the section of the cross arch will be an oblique oval.

If a mason will carefully master these problems, he will find very little difficulty in any methods of stone-cutting.

The same problems give the lines for centering, the practical method of executing which is found in Carpentry, Centering, &c., &c.

Mouldings.

126. All the sections for Roman mouldings are given in Joinery, p. 807, but as those used in stone work, particularly in Grecian architecture, are parts of Conic Sections, and not struck by compasses, we give a short problem by which they may all be easily set out.

127. Let (fig. 59) the moulding required, be an ovolo, the height of which (to the point where the moulding curves backward) is AC or BD, and the greatest projection AB or CD; and let CE be a tangent line, or line which the curve must touch but not cut. Produce CA to F, and make AF equal to AC, and AG to ED. Divide GB BE each into the same number of equal parts as 5. Draw the co-ordinates from F and C to the respective numbers, their intersections will trace the curve. If BE be more than half the whole height, the curve is an ellipsis; if exactly half the height, it is a parabola; and if BE be less than half BD, the curve will be a hyperbola. All other moulding can be drawn by this method, remembering that cymas, ogees, and all reflex curves, must be divided and drawn in two separate portions.

Staircases.

128. The general principle of designing staircases, as regards the rise and tread of steps, setting out curves, curtains, landings, &c., are given in the article Joinery (35, &c.). The chief difference between these and other staircases consists in the fixing, the one being framed with wooden strings, while the other have no strings, but are supported entirely by the walls. If there be a wall at each end, they are simply built in at the time the work goes up; but if they are supported at one end only, they are called geometrical stairs, and depend entirely on their being securely wedged into the wall; on which, and on the support each derives at one edge from the step below, they wholly rest. If they are square in section, they are called solid steps; but as the under side or soffit, then, is irregular, it is usual to make the steps of somewhat a triangular shape, so as to present a regular soffit. In this case they are called arris, or feather edge steps. Care should be taken that there are no sudden or irregular changes in the curves. These may be easily avoided by the method shown for the easing of the curves and ramps in handrails. (See Joinery.)

129. Landings should also be very carefully pinned into the walls. Fig. 60 will show the danger, should they not be so, through the full length of their insertion. If the front edge be pinned up, as at A, but a vacancy be left, as at B, the point C will become the fulcrum of a lever, and the landing have a tendency to turn at that point, and to break at the edge C. Every step and landing should have 8 inches hold in a brick wall. (130.) All landings should be well joggled; the joint Joggles... made as at \(a\) (fig. 61) is called by workmen a he, and that at \(b\) a she, joggle.

The late accident at the Polytechnic Institution in London arose no doubt from the carelessness of the workmen, who put two landings together, on which two she joggles were worked (fig. 62), and filled the open space with plaster. There happened to be a large fossil in the stone close to the wall in the landing \(b\), which having no support from the other landing \(a\), gave way, and caused the destruction of the staircase below, upon which it fell.

V.—STONE-MASONRY—MEDIEVAL.

131. It has already been stated (secs. 67, 68) that many of the early buildings of the middle ages were entirely constructed of masses of concrete, often faced with a species of rough cast. This early masonry seems to have been for the most part worked with the axe and not with the chisel. A very excellent example of the contrast between the earlier and later Norman masonry may be seen in the choir of Canterbury cathedral. In those times the groining was frequently filled-in with a light tufa stone, said by some to have been brought from Italy, but more probably from the Rhine. The Normans imported a great quantity of stone from Caen, it being easily worked, and particularly fit for carving. The freestones of England were also much used; and in the first pointed period, Purbeck and Betherden marbles were employed for column shafts, &c. As time went on the art of masonry advanced with us, till in point of execution it at length rivaled that of any country. The methods of working and setting stone were much the same as at present, except that, as the roads were then in a very bad state, and in many places the only means of conveyance was by pack-horses, the stones were used in much smaller sizes than at present. The methods of setting out work were, however, different from those of other styles, as might be expected from the difference of forms.

132. The earliest arches were circular (see Architecture, page 480, and figs. 1 to 9, Plate LXVII.), and of course easily set out. But as the pointed styles came in, several methods were used for describing them. Pointed arches may be classed as—1st, lancet; 2d, equilateral; 3d, depressed; and 4th, four-centred or Tudor. In the first the centres \((1, 2, fig.\) 63) are without the arch \(ab\). At Westminster Abbey the arches of the choir are so acutely pointed, that the distance from \(1a-2b\) is nearly two-thirds of the entire opening \(ab\). In the nave at York the points are without the arch at a distance of about one-fifth the opening \(ab\). In equilateral arches the centres are exactly on the points \(ab\) (fig. 64), so that the apex \(e\), joined to \(a\) and \(b\), will form an equilateral triangle. The nave arches at Wells are of this description, and also those at Lincoln (Plate LXIX., fig. 1). In later times the arches were of lower pitch, and then of course the centres \(1, 2\) (fig. 65), were within the arch \(ab\). At Salisbury Cathedral (Plate LXVII., fig. 14), the distance \(a1\) is one-sixth of \(ab\), while in the choir at Lincoln (fig. 2, Plate LXIX.) it is as much as two-fifths.

133. To describe arches which shall be similar to one another throughout a building, however the openings may differ, this principle must always be borne in mind: that the centres shall always be distant from the points \(ab\) by some aliquot portion of the whole opening. This is the more important, as the lines of tracery will not fall into their proper places except the arches are set out upon some regular principle (sec. 136). If the arches are not equilateral, some distance from each point, \(ab\) should be first determined on (say one-third the opening \(ab\)), and after this, whatever the span of the other arches may be, one-third its own opening is to be taken from the points \(ab\), as the centres from which to strike its curves. The only exception is, that in medieval buildings, the arches to the doorways are frequently somewhat flatter than those of the windows.

134. In the Tudor period the arches are very frequently four-centred from four centres instead of two. It must be remembered that it has already been stated (sec. 90) the point where two circles touch each other must always be in the same straight line that is drawn through both their centres. As there has been great misapprehension as to four-centred arches, some persons treating them as parts of conic sections, whereas they are really parts of segments of circles, it is thought well to give two methods of describing these arches. First, when the width \(AB\), and the apex height \(OC\), are given, and a tangent to the upper circle \(CD\). In this case draw \(AD\) perpendicular to \(AB\), and set out \(A1\) equal to \(AD\); draw \(C3\) perpendicular to \(CD\), and make \(CE\) equal to \(AD\) or \(A1\); join \(1E\) and bisect the same as shown by a perpendicular meeting \(CE\) produced in \(3\); join \(31\) and produce towards \(F\); then \(1\) and \(3\) will be the centres for half the arch; and, transferring the points across, \(2\) and \(4\) will be the centres for the other half. In the second case, when the width \(AB\) and the height \(OC\), and the centres of the small circles \(1, 2\), are given. Make \(AD\) equal to \(A1\), join \(CD\) (which will be a tangent to the upper curve), draw \(C3\) at right angles thereto, make \(CE\) equal to A1, join I E, bisect the same, and proceed as before. The points FG, as has before been explained, are the points where the circles will touch each other. The joints to these arches will all radiate to their respective centres, as has before been explained in secs. 103, 104.

Mouldings.

135. The mouldings of medieval architecture are almost infinite in variety, and even a short description of those used in each style would exceed our limits. They are sometimes set out with the compasses, and many often appear to have been drawn by eye. We must refer our readers to the works of Willis, Paley, and particularly of J. H. Parker, for their description. A very curious treatise was published by the former gentleman called the Architectural Nomenclature of the Middle Ages, which goes at great length into the subject. A beak or astragal seems to have been called a bowtelle; a torus, a grave bowtelle; a hollow or scotia, a casement; an ogive, a ressante, &c., &c.; but the subject is too long to be discussed in our pages.

136. The various sorts of tracery which adorn the windows of the medieval periods, and are in fact their greatest glory, are treated of in the art. Architecture, and specimens given in the different plates, particularly Plate LXVIII., figs. 4 to 8. The designs for these are almost infinite, and the various methods of setting them out would fill a volume. But although they display such ingenuity and fancy that one would think the design to be quite arbitrary, it is a curious fact they are all, or very nearly all, set out on the principle of geometrical intersections. An example, therefore, is given (fig. 67) to show the principles on which the medieval architects proceeded to describe the tracery, and also the method of finding the joints of the various pieces of stone. Let ab be the opening of the arch; as there are to be two mullions, divide the same into three equal parts, as ac, cd, db; then determine the points from which to strike the arch. In this instance, for the sake of simplicity, we make it equilateral (sec. 132 and fig. 64); a and b then are the centres for striking the main arch ag, bg, and the height og is that of an equilateral triangle. Produce the springing line, and the same opening of the compasses through c, and d will give the principal inner branches of the tracery ce, df. From the centre o, with an opening extending to the middle of the lights ac, db, strike a semicircle, raise perpendiculars from e and d to 1 and 2; draw a line through 1 and 2; on this and the springing line will be found the centres of the lower ogges; bisect the line from the intersection 1, 2, in h, which is in fact the same thing as dividing the whole height og into three; divide hg into three parts, as 3, 4; through 3 draw a horizontal line, and set off from 3 equal to one-third of the width od, or draw the perpendicular lines as shown, which is better; then 5, 6, will be the centres of the upper quatre-foil. From the line 1, 2, on the same perpendicular as last, set down similar points as at 7. These will be the centres for the lower sub-division as shown. Next draw ef and sub-divide by similar perpendiculars, and where the lines intersect, as at 8, 9, will be the centres for the upper sub-divisions. The lines thus drawn will form a species of skeleton diagram, as shown on the right side of fig. 67, which is called the element of the Element of the tracery, and is in fact the centre line of the mullion, as tracery, shown by a, fig. 68. On each side of this, using always the same centres for the same branches, draw lines, showing the face (or what the workmen call the nose) of the mullion, and answering to bc; and then others answering to the sides of the mullion as de. Any other mouldings upon their sides or faces may be drawn in like manner. Put in the cusplings as shown, and the tracery is complete. The practical stone-mason will take care never to make a joint where there is an angle of any sort, as the point of a cusp. In all cases the joints must tend to the centres of the circles from which they are struck, and where the lines branch off in two directions, the joints must not be in one line, but must tend in two, or as many directions as there are branches, and each to the centres of such respective branch. When the lines are perpendicular, as at ed, and at the joint below h, the joints are horizontal. A close inspection of fig. 67, where they are carefully drawn, will elucidate the matter more than any number of words can do. Our readers would scarcely believe that the elaborate west window at York is entirely set out on this principle; and so is the still more remarkable instance, the eastern window at Carlisle, which is composed of 86 pieces of stone, and the design for which is drawn from 263 centres. On no account should Cramps, iron be used as cramps or dowels in Gothic work, as it rusts dowels, &c., and breaks pieces out of the stone. The best material is slate run with the Portland cement. Lead is often used; but any metal will expand and contract with heat and cold, and its use is much better avoided altogether. All the upper construction of windows and doors, and of aisle relieving arches, should be protected from superincumbent pressure arches by strong relieving arches above the labels (see fig. 67), which should be worked in with the ordinary masonry of the walls, and so set that the weight above should not press on the fair work, in which case the joints of the tracery, &c., will sometimes flush or break out.

137. Medieval vaults differ much from those before vaulting, described, principally that the crowns ab, cd, are not level, as shown in fig. 52, but all have a slight curve or spring, and the filling-in between them also is slightly curved, so as to partake in some degree of the character of the dome as well as of the groined arch. Bearing this carefully in mind, and setting the lines out thus on the sections, the rules we have given for finding the various lines for groins (120–125) will apply as well to Gothic groins as to those of ordinary character; the principle of working from plan, section, and stretch-out being the same, though for the most part the ribs in early vaulting are not true segments of ellipses, but approximations drawn by the compasses. The triumph of medieval stone-masonry, however, is that species of... Artificial groin known as fan vaulting. This is unlike that of any other age or time. The roofs of King's College Chapel, Cambridge, and of Henry VII's Chapel at Westminster, are eminent examples. It is impossible in our limited space to give demonstrations of them, and we must refer our readers to the admirable treatises on the subject by Professor Willis, published in the first volume of the Transactions of the Institute of British Architects. The filling-in between the ribs of mediæval groins is generally of clunch or some soft stone, over which some concrete is placed in such manner as to bind all together, and to resist the thrust.

138. The bold and beautiful termination to mediæval towers, which the French call flèches and we call spires, is another proof of the skill of the mediæval masons. These are generally octagonal, and rise partly from the walls of the tower and partly from arches thrown anglewise from wall to wall, to cut off the corners, as it were, and afford a springing to the spire. The wonder of these constructions is their extreme thinness and lightness. The top of the spire at Salisbury is 411 feet from the ground, of which 207 is taken up by the tower, leaving, of course, 204 feet for the height of the spire itself; this is only 9 inches thick at the bottom, diminishing to 7 inches, or on an average only about the three-hundredth part of its height. It has been attempted to show mathematically that the joints of a spire would be stronger if at right angles to its face; but they would then slope inwards and hold the wet, which in sudden frosts would do most serious injury; practically, therefore, it is found best to lay the courses on a level bed. They should, however, be frequently dowelled and cramped together, but not with metal, as above stated.

VI.—ON ARTIFICIAL STONES, AND ON THE INDURATION OF SOFT STONES.

139. The great expense of obtaining and working Portland has driven our masons into the use of the softer freestones. These (as has before been described, sec. 19, &c.), are liable to rapid decay from the action of frost and wet, and in towns from the action of the sulphurous acid in the coal-smoke. To avoid these inconveniences several contrivances have been resorted to within the last century to obtain a cheap and durable material in which to execute external architectural ornament; or to invent some process by which soft stones may be so protected by an outer coat of impervious matter as to throw off the wet; or may be so indurated as to resist the ordinary wear to which Portland or the harder stones may be subjected. The earliest attempts were to manufacture a hard hydraulic cement, which might be modelled with the tool, or cast into moulds. The earliest use of this is said to have been by the Adam's, it suiting very well with the low relief of their style of ornamentation. (For an account of cements, see this article, sec. 22, ut supra.) Another method, which has been frequently tried with success, but seems too expensive to come into general use, was to model the ornaments in good plastic clay, as colourless as possible, and burn them in kilns. The best known of these systems was that called Coade's artificial stone, the manufactory of which, however, is now discontinued. (For an account of this species of manufacture, see POTTERY, TERRA COTTA, &c.) A method, however, which seems to bid fair to excel them all in beauty, cheapness, and durability is that patented by Mr Ransome of Ipswich. It appears, the idea suggested itself to him as long back as 1844, that if he could mix sand, or pounded flint with anything that would make a sort of fluid glass, and stick it together, as it were, in a pasty state, it might be pressed into moulds, and when dry it would form a sort of strong glass. After a variety of experiments, and trying to accomplish his object through a number of changing theories, he at length succeeded in the following process. He first obtains a strong caustic alkali, which is purified by a most ingenious process. This is made, by the assistance of steam and heat, to act upon some broken flints, which it does, and the alkaline solution is then drawn off and evaporated till it becomes the thickness of treacle. One part of this is mixed with ten parts of sand, one of flint, and one of clay. The whole is kneaded up till like putty, so as to be readily pressed into moulds, and so as to take the sharpest forms. Our space will not permit us to give the full details; but it may suffice to say that the objects, after being dried in close stoves, are then submitted to a strong red-heat in a kiln like that of a potter, which drives off all the alkaline and other chemical agents in the process, and leaves the granules of the sand and flint enveloped in, and, as it were, stuck together by a sort of glass. Time alone, however, can only ultimately show the results. At present the material seems of beautiful colour, texture, and sharpness; and unless some unknown or unforeseen chemical agent should act upon it, Ransome's stone appears to be indestructible.

140. The rendering soft stones hard, and the protecting Induration the surfaces from the weather when worked and set, has of stone, been the subject of great investigation lately. The idea of the latter seems to have originated with the late well-known John Sylvester, who tried the method of washing Sylvester's over the faces of stone walls with first a solution of soap and then of alum. Another method was that of washing with what was called water-glass, or silicate of potash, both Water-of which are said to have failed. The next idea was to glass, soak the stone, or in some way to cause the surface to imbibé a quantity of oily or fatty matters to throw off the Oleaginous wet, as well as to harden the stone itself. The first patent processes, was taken out by Mr Hutchison, at Tunbridge Wells, in Hutchi-1847, and was applied to the new sandstone there. The son's, stones, when worked, were boiled in a solution of resin, turpentine, wax, oil, &c., and sometimes, we believe, pitch, till they were impregnated a sufficient depth from the surface. In 1851 Mr Barrett took out a patent something Barrett's, like the preceding, but far more elaborate; in fact, too long to be described in our pages. The main elements, however, were resins, fats, and tallows, some of which were mixed with gutta-percha, unsacked lime, copperas, and a number of other ingredients. In April 1856 Mr Daines took Daines's, out a patent, not so much to indurate stone, but to preserve stone, or cement walls from damp and efflorescence. His process was to apply, first, a solution of sulphate of zinc, or solution of alum, to the wall, and then a composition of sulphur dissolved in oil. In the same year, and in the next month, Mr Page took out a patent for a similar pur-Pages's, pose; his material was wax dissolved in coal-tar, naphtha, or, for more delicate work, in camphine. We are informed the manufacture of the first of these patents is discontinued, but not from any failure of process. Of the others it is impossible to say much, as so little time has elapsed since they commenced, and as early experiments in all manufactures often fail; judging, however, on the grounds expressed as to mastic (37, supra), we should fear they would fail from a like cause, especially as such very volatile media as naphtha, camphine, &c., are used. Mr Ransome's, Ransome's, however, seems to promise better. His is deduced from his experiments on the artificial stone. It consists of treating the surface of the stone first with a solution of silicate of potash or soda, and then with a solution of the chloride of barium, or chloride of calcium, by which means an insoluble silicate, either of barium or lime, is deposited in the pores of the stone. The most extraordinary results, however, are promised by Mr Szerelmey's process. The author Szerel- of this article has been informed by that gentleman that it may's, will not only entirely protect the surface of stone or brick, or cement, but of iron; as a proof, he states that an anchor coated with it was sunk in the sea many months, and raised