reverting, in the concentric circles of their ramparts, to the round raths and hill-forts of our remote predecessors in the British isles, or to the form which Herodotus ascribes to the sevenfold enceinte of Ecbatana; our Browns and Telfords, in their suspension-bridges, perfecting with all the appliances of modern art the rude swings of grass-rope or rattan, which for unknown ages have spanned the mountain rivers of northeastern India; and, last of all, Stephenson and Fairbairn, carrying our thoughts back to the world's youth, when a pine falling over a stream gave man his first bridge, direct all the plenitude of English gold and iron, all the resources of calculation, experiment, and practised skill, to span the Menai with a single beam.

NOTE J.-TARTAGLIA.

Nicholas, surnamed Tartaglia, (the Stutterer,) a celebrated mathematician and speculative philosopher, was born at Brescia about 1500. He has told us his early history, and how he got his nickname, in one of the dialogues contained in his book called Diverse Questions and Discoveries. His father filled the humble office of letter-carrier to their honours the magistrates of Brescia, and was generally known as "Little Mike the Postboy," (Micheletto Cavallaro.) If he was entitled to any other name his son was not acquainted with it, the father having died when the latter was six years old, leaving his family in poverty. When the French sacked Brescia in 1512,* their house was plundered of what little it held, whilst the widow, with her children, took refuge in the cathedral. This did not save them from the violence of the troopers, and little Nicholas got five severe wounds in the head and face, one of which broke his jaws and disfigured him for life. It was long before he could speak plainly again, and hence he acquired from his playmates the soubriquet which he afterwards adopted as a surname. Before his father's death, the child had a few months' schooling; and, when fourteen years old, he went of his own accord to a writing-master. The fees being payable by instalments according to progress, when Michael had achieved the A, B, C, as far as K, his funds were expended, and he could pay for no further tuition. "After that," he says, "I had never another master, but ever worked in company with that daughter of Poverty whose name is INDUSTRIA."

In that good company Tartaglia studied to such good purpose as to reach the highest rank among the mathematicians of his time. After teaching at Verona and Vicenza, he became professor of mathematics in his native city, and afterwards at Venice, where he died in 1557. His fame mainly rests on his discoveries in algebra. In the solution of cubic equations he was the real inventor of the method known as Cardan's rule. It was communicated to the latter under a solemn promise of secresy, but published by him in a work of his own notwithstanding.

*Under Gaston de Foix. "And as the miseries that war draweth with it are infinite, so the whole citie for vii dayes together was exposed to the covetousnesse, to the lust, and to the crueltie of souldiers; things sacred as well as prophane being parcel of the praie and no lesse the lives than the goods of men committed to the discretion of spoylers."-Fenton's Guicciardini, book x.

The Essay on Fortification forms one of the books of the collection of questions above mentioned, and consists of two series of dialogues. In the first, held with His Reverence Gabriel Tadino, Knight of Rhodes and Prior of Barletta, the latter questions Tartaglia as to the possibility of the art of fortifying reaching a higher pitch of perfection than it had then attained, as exemplified in the defences of Turin. Of these he exhibits a plan, showing the place as a square bastioned fort, with cavaliers in the middle of the curtains.

Tartaglia gives the knight to understand that he sees very little merit in this trace, and that it is deficient in six properties which he considers essential to good fortification. These are: 1st, That the curtains should be so traced that they can only be battered obliquely. 2d, The contour should be such that any possible site of an enemy's battery must always be nearer to some one of the bastions than to the curtain which it is intended to breach. 3d, That an assailant at any point should be exposed to an artillery fire from at least four distinct works. 4th, That the curtain should be so constructed that, if breached, in ruins it will be a greater obstacle to the enemy than before. 5th, That the place should be secured by some contrivance for enabling a very moderate guard on the curtain to baffle any attempt at escalade with heavy loss and disgrace to the assailants. 6th, That to supply the garrison with food there should be such an arrangement of works as shall allow of ground being cultivated under the guns of the place, and protected from annoyance by the enemy. The series concludes with pledges on Nicholas's part to produce plans and models showing how all these desirable objects can be attained.

In the second set of dialogues, Dr Marc Antonio Morosini expresses natural curiosity to learn how the conditions are to be fulfilled. Tartaglia proceeds to explain one of his projects meeting the first three conditions the poorest of all his designs, he says, since he would follow the shopkeepers' practice in showing his worst wares first. The trace is en tenaille, having bastions at both salient and re-entering angles, with cavaliers in the middle of the curtains; and on each side of the inner bastions along the curtains are thrown up a number of small oblique traverses, each armed with a falconet bearing on the space between the salients. There is a covered-way, wide enough for two carriages to pass each other, and a glacis with its crest only two feet lower than the curtain. He enlarges on the covered-way as a novelty. Though not found in Albert Durer, it is in Francesco di Giorgio's designs. Signor Morosini commends the plan as ingenious but odd-looking. "Illustrious sir," replies Tartaglia, "had Nature from the beginning made men without nose or ears, till by chance one was turned out in the possession of both, assuredly he would be considered by the rest as a very odd fellow. And so with my system. But be it as you will; in fortification we want strength, not symmetry."

The fulfilment of the paradoxical 4th condition is to be sought for in breaking the height of the escarp into two by a sort of berm wide enough to receive the ruins of the upper half of the wall when it is breached,* The escarps of Fort-William, at Calcutta, are constructed somewhat after this fashion.

which he considers will render ascent more difficult instead of facilitating it; whilst the loose stones struck by the shot from the flanks will fly about, dealing destruction among the assailants. How No. 6 is to be accomplished is not explained, and there appears nothing else in the tract worth mentioning.

Tartaglia does not appear to have professed fortification as an engineer, but merely to have taken up the subject speculatively, as he did many others. Many of the articles in his Quesiti are devoted to the theory of gunnery, though, as he says, he had never fired gun, bombard, musket, or arquebus; others are on the composition of gunpowder, on tactics, on surveying, and on mixed mathematical subjects. He also published the first Italian translation of Euclid, and many other mathematical works.

One of his books treats of the method of raising sunken ships, and in it he gives one of the earliest descriptions of a diving-bell. He does not appear to provide any means for replenishing the bell with fresh air.

NOTE K.-MARCHI.

Francesco de' Marchi, one of the most eminent Italian engineers of the sixteenth century, was born of a noble family at Bologna. He served Alexander de' Medici, first Duke of Florence, his widow Margaret, Duchess of Parma, and Pope Paul III. successively. In 1547 he constructed the fortress of Placentia, and for two-and-thirty years afterwards appears to have acted as engineer to the King of Spain in the Low Countries.

His work on fortification first appeared in 1546, but was published after his death in a more complete form at Brescia, in 1599.* It is entitled, Della Architettura Militare libri tre, nelli quali si descrivono li veri modi del fortificare che si usa a tempi moderni." The work contains one hundred and sixty-one systems of fortification which Marchi declares to be of his own invention, and in which are to be found traces of most of the methods designed or executed by the ablest succeeding engineers. The work is now excessively rare and expensive. A copy containing some additional plates is stated to have been sold for about £55. The Italians allege that foreign engineers destroyed the copies of Marchi's work to conceal their own plagiarisms, including in this charge even Vauban, whose three systems, it has been pretended, were borrowed from Marchi.

The work was republished magnificently by Luigi Marini, at Rome, in 1810, in five folio volumes, which cost £20 to the subscribers.— (Biographie Universelle.)

Several of Marchi's systems are given in the Travaux de Mars, by A. Manesson Mallet. Amsterdam, 1684.

1597, according to Colonel Portlock's list of Italian military writers in the R. E. Corps Papers, i. 65.

I

NOTE L.-MAGGI AND CASTRIOTTO.

Girolamo (or Jerome) Maggi was born at Anghiari, in Tuscany, in the sixteenth century. He was by profession a student of law, but devoted his leisure to military architecture and antiquities. Having settled at Venice, after holding various political and judicial posts in different parts of Italy, he was appointed by the Venetian government Judge of the island of Cyprus, and so was present in Famagosta (1571) when it was besieged by the army of Selim II. Maggi lent all his abilities and energy to the defence; and by his skill in the management of artillery and mines, as well as by the engines which he devised, greatly contributed to retard the capture of the city.

The Turkish trenches, hewn in some places through the rock, were carried on by 40,000 pioneers; their huge cavalier batteries mounted 80 pieces of artillery; and the army was so numerous that their leader boasted that, were each of his men to cast a slipper into the ditch, it would suffice to form a causeway to the rampart.

"Such forces met not, nor so wide a camp,

When Agrican, with all his northern powers,
Besieged Albracca."

The garrison consisted of 7000 men, half Italians, half Greeks.

After a siege of four months, but not till after the magazines were empty and the ramparts a continuous mass of ruins, the gallant commandant, Marc Antonio Bragadino, consented to surrender. Most honourable terms were granted; but these were violated with ferocious treachery by the Turkish general Mustapha Pasha. Bragadino was mutilated and horribly tortured to death. Maggi, a prisoner with the rest, was sold to a shipmaster who took him to Constantinople. Whilst languishing in captivity there, from the resources of his powerful and well-stored memory alone, he composed two Latin treatises abounding in curious learning: one, De Tintinnabulis, suggested by the prohibition of bells in Turkey; the other, De Equuleo, (on the Wooden Horse,) by the instruments of torture in daily exercise before his eyes. He dedicated these to the ambassadors of France and the Empire, then at Constantinople, and they endeavoured to negotiate his deliverance. But in the meantime Maggi, in an attempt to escape, was recaptured; and by order of the Vizier was strangled in prison, May 1572. He left works, published and unpublished, on a vast variety of subjects. His treatise on fortification was printed at Venice as a commentary on that of Castriotto in 1564, and again in 1583–4. In it he frequently refers to a work of his own on "Ingegni Militari;" but this does not appear to have been printed. (Sketches of Venetian History-Biographie Universelle.)

Of Captain Jacomo Fusto Castriotto I can find no particulars, save what are afforded by incidental allusions in his book. From these it appears that he was a native of Urbino, and that he was an engineer in the service of Pope Julius III., by whom he was employed in 1548 on the fortification of the Borgo at Rome, in 1552 to design the works of attack on the strong fortress of Mirandola, (though his cattivo sorte did not allow of his being present to execute them,) and to fortify Sermo

neta, Palliano, Anagni, and other places in the Papal territory. Afterwards he attached himself to Henry II. of France, and was in the army of the Constable Montmorenci when he was defeated and taken by the Spaniards at St Quentin, was present at the capture of Calais, (1558,) and at the sieges of Don Carico and Borgo in Flanders, (which I presume to represent Dunkirk and Bergues,) under the Maréchal de Termes, as well as at the ensuing defeat and capture of this general by the Spanish King. The last service which he mentions himself to have been present at was the capture of Thionville in Burgundy. He states that he had held various conversations with the great soldiers of the time-the Constable Montmorenci, the Duke de Guise, and the Admiral Chatillon (Coligny)—on the defects of existing fortresses, and had been employed to design new works in all parts of France.

The work called Della Fortificatione delle Città, (on the Fortification of Cities,) consisting of Castriotto's Memoranda, and designs, with comments by Maggi, is very sensible, and free from the geometrical pedantry of many of the old engineers. That there is nothing new under the sun is, in no branch of art, more true than in Fortification. There are probably few remarks or projects in modern essays on this subject of which an indication is not to be found in those of the sixteenth century.

The following are a few points selected from the book. The various features of a Fortress, besides the curtain, are the Bastions or Bulwarks, (Balluardi); the Platforms, which are small intermediate works either square or bastion shaped, in the middle of the curtain; the cavaliers, generally over the platform, sometimes in the bastion or on the flank produced inwards; the ditch; the casemates, in the flanks; the covert way (via coperta, via delle sortite); and the glacis (spalto or argine.)

The length of a front is laid down at about 400 yards, of the face of the bastion 73 yards, of the flanks 37. In Vauban's first system, with the same exterior side, the two last dimensions would be 114 and 60.

The square is not approved of on account of the acuteness of its angles. The salients of bastions should always be right angles or more. In laying out a work always mark out the interior area first, otherwise your eye will probably deceive you, and your outline will be much too contracted.

In designing new fortifications be not contented with accurate plans; always make a model also.

It is recommended to plant poplar trees along the ramparts. This binds the soil well, and the trunks are most useful for retrenchments, &c. Embrasures appear always to have been made narrow towards the middle, and widening both inwards and outwards.

Various patterns are given of escarp revetments, all well backed with counterforts. In one, Castriotto anticipates great benefit from throwing several tiers of brick arches between the counterforts. The latter always rise to the superior surface of the parapet. One of his designs on which he strongly insists is an anticipation of Cormontaingne's demi-revetment, a narrow berm intervening between the cordon and the parapet.

Against mining, Maggi recommends a cunette filled with water in the middle of the ditch. It is a good plan, he remarks, to make the bottom