DOMBROWSKI, Jan Henryk (1755-1818), Polish general, was born at Pierszowice in the palatinate of Cracow, August 29, 1755. He was of noble family, and his father was an officer in the Saxon army. Brought up in Saxony, he entered and for some years served in the army; but when, in 1791, the Polish Diet recalled till Poles serving abroad, he returned to his native land. Placed then under the orders of Poniatowski, he took part in the campaign of 1792 against the Russians. In 1794 he distinguished himself in command of the right wing under Kosciusko assisted in the defence of Warsaw, and reunited the scattered Polish forces after its fall. He was compelled, however, to capitulate and to surrender himself prisoner of war at Radosayce, November 18. Suwaroff offered him a post in the Russian army, but this lie declined, and for two years he lived in retirement. In 1796 the rank of lieutenant-general in the Prussian army was offered to him by the king ; but this he likewise declined. He then went to Paris. The formation of a Polish legion was at this time in contemplation by the French authorities ; and in January 1797 Dombrowski was formally authorized by the Government of the Cisalpine Republic to organize it. This task he executed at Milan. In command of his legion he played an important part in the war in Italy, entered Rome in May 1798, and distinguished himself greatly at the battle of Trebbia (June 19, 1799). On this occasion he narrowly escaped death, being struck by a ball the force of which was broken by a volume of Schiller which he carried with him. He next served under Saint- Cyr and Massena ; but being severely wounded he was for some timo incapacitated for action. After Marengo he was intrusted by Napoleon with the organization of two new Polish legions ; and at the head of the new levies he captured, in January 1801, the fortified post of Casa Bianca, near Peschiera. After the peace of Amiens he passed, as general of division, into the service of the Italian republic. Summoned by Napoleon after the battle of Jena to promote a rising in Poland, he returned there, took command of the Polish army, and distinguished himself at the sioge of Dantzic (1807). He fought and was wounded at Friedland, and took an active part against the Austrians in the campaign of 1809. In the Russian campaign of 1812 he commanded a division of the great French army, and was wounded at the passage of the Beresina. He fought under General Marmont at the battle of Leipsic (1813), and in the following year returned to Poland. He was one of the generals entrusted by the emperor Alexander with the reorganization of the Polish army, and was named in 1815 general of cavalry and senator palatine of the new kingdom of Poland. He retired, however, in the following year to his estates in Posen, and employed himself in preparing for publication his History of the Polish Legions in Italy, which was published some years after his death. General Dombrowski died at his seat of Wina-Gora in Posen, in June or July 1818.
DOME is usually understood to mean a roof which is round or polygonal horizontally, and of which any vertical section is either a round or a pointed arch. There happen to be none of elliptical or any other section than these. But some, especially in the East, have what is called an ogival outline, convex below and concave towards the top, and these are generally called cupolas, though there is no real distinction. Most of the great European domes have an opening or eye at the top, on which stands a lan tern, except in the Pantheon at Rome, where the eye is open. Until modern times all the domes worth notice were of masonry, i.e., stone, brick, tiles, or pots, which last were used for lightness. Probably the first large wooden dome was St Paul s, of which the construction is peculiar, the inner dome visible in the church being of brick only 18 inches thick, except near the bottom where it grows out of a cone of the same thickness going up outside it and carrying the stone lantern, which looks right down into the church through an eye in the internal dome. Outside the cone is built a wooden dome covered with lead. The domes of St Peter s at Rome and Florence Cathedral are of two stone shells near together, and connected by some vertical ribs, and also carrying lanterns. But Wren s construction is infinitely stronger, since a cone sufficiently tied at the bottom cannot give way until it is ab solutely crushed, while the bursting pressure of a weight on the top of a dome increases the bursting force enormously. St Peter s dome is cracked in several places, and held to* gether by bands, and it is covered with lead, and therefore looks no better than St Paul s, and indeed on the whole not near so well, for various reasons which may be seen in archi tectural books ; and the lantern is smaller in proportion. The only full mathematical investigation of the theory of domes with practical results, that we know of, is in a paper by Sir Edmund Beckett (then Mr Denison) in the Memoirs of the Royal Institute of British Architects of February 1871, and two shorter ones by Mr E. W. Tarn, architect, in the Civil Engineer s Journal of March 1868, which sub stantially agree, so far as they deal with the same points. The investigation is long and complicated, and can only be done approximately, because the introduction of the thick ness deranges all the ordinaty trigonometrical relations, and so we only give the principal results of those calcu lations. Some more of them are given in Sir E. Beckett s Book on Buildirtrj. It is easy to prove by strict mathe matics that the upper 52 (nearly) of a hemispherical dome would be absolutely stable, or have no tendency to fall in or burst out, without any sensible thickness, if only tied strongly enough round the base, where the tension would be 3 of the weight of ths complete hemisphere, disregard ing the bonding effect of mortar and friction. The weight of a thin hemispherical shell is the same as that of a cylin der of the same height and thickness standing on the same base, and is twice that of the area which the dome covers, of the same thickness, provided that bears only a small pro portion to the diameter. The weight of any zone of the dome is proportional to its height. A hemisphere of ordi nary stone 100 feet wide at mid-thickness and 1 foot thick weighs about 1000 tons. It is also demonstrable that a dome spreading at the bottom a little more than a hemi sphere, so as not to start vertically, and rather flattened at the top, would stand without any sensible thickness; and so would sundry other curves, and especially an inverted catenary, which will stand even as an independent arch without thickness, for a dome is far more stable than an arch or a barrel vault of the same thickness.
matical element of a dome is not an arch of any uni form breadth, but one whose breadth, and therefore weight, decreases upwards to nothing, being in fact a lune enclosed between two meridians very close together. And it was shown in the R.I.B.A. paper, and also by models exhibited, that a dome is stable svith a thickness of only 023 of its diameter, while an independent round arch or a barrel vault requires three times as much thickness, or 072 of its diameter. Therefore a barrel vault 100 feet wide must be 7 feet thick to be stable, while a dome of that diameter need only be 27 inches ; besides which, the strength of the dome can be increased to almost any extent by building in iron bands in the lower courses, while a barrel vault cannot be so helped. Bands would be of no use whatever in a dome above 52 from the top, as the pressure above that point is entirely inward, assuming it to be tied there, and from thence it gradually increases towards
the bottom, where the tension is 215 of the weight of the
