606 



DOIT. 



DOME. 



60 



there are other authorities which are acknowledged only by one com- 

 munion, and not by othera. Thus the Greek church acknowledges the 

 authority of the earlier councils only, while the Roman Catholics look 

 upon the later councils and the bulls and decretals of the popes as 

 equally positive authority in matters of faith ; and the Protestant and 

 reformed churches, rejecting the latter, recur to their respective 

 synods and confession* of faith. Melancthon wrote a concise expo- 

 sition of the dogmas of the Protestant or Lutheran church. Among 

 the numerous Roman Catholic writers on dogmatic theology, Bellarmiue 

 is one of the most distinguished. Dogmatic theology, as distinct from 

 scholastic as well as from moral theology and Biblical divinity, consti- 

 tutes a separate chair in several Roman Catholic universities in conti- 

 nental Europe, and in those of Ireland. 



In the Protestant universities of Germany there is a chair for the 

 history of dogmas. The busines"s of the professor is to examine the 

 doctrines of the various sects which have divided Christianity, their 

 sources, and the arguments by which they are supported. Such a 

 course of lectures forms an important addition to the study of Ecclesi- 

 astical History. 



DOIT or DUYT, a small Dutch copper coin, being the eighth part 

 of a stiver, in value half a farthing. Doit is also a division of the 

 English grain Troy. See Snelling's ' View of the Coins of Europe,' 

 8vo. London, 1766. The word is used by Shakspere, ' Coriolanus,' 

 Act i., sc. 5. 



DOLLAR. [MOSEY.] 



DOME. The mathematical theory of a dome, so far as considera- 

 ions requisite for security are concerned, is more simple than that of 



an arch. Imagine two vertical planes passing through the axis of a 

 dome, and making a small angle with each other. These planes inter; 

 cept (as in the cut) two symmetrically opposite slices of the dome, 

 which tend to support each other at the crown. This support might 

 be made complete and effectual upon principles explained in the 

 article ARCH ; so that in fact each small slice of the dome, with its 

 opposite, might compose a balanced arch. Any slice of such a dome in 

 supported by the opposite one only, so that all the rest might be taken 

 away. Now suppose such a dome to be constructed upon an interior 

 centering, of which however the arches are not separately balanced, in 

 consequence of the weight of A p K being so great that the resultant ol 

 this weight and the horizontal thrust at A falls obliquely, not being, as 

 in a balanced arch, perpendicular to i'K, but cutting the line K p pro- 

 duced towards the axis. Still this dome cannot fall : for since every 

 part of the horizontal course of stones has the same tendency to fall 

 inwards, these pressures inwards cannot produce any effect, except a 

 lateral pressure of each slice upon the two which are vertically con- 

 tiguous. Hence the condition of equilibrium of a dome is simply this, 

 that the weight of any portion A M p K must be too great for a 

 balanced arch. Upon the same principle a dome may even be con- 

 structed with a concave exterior : and in a dome of convex exterior a 

 portion of the crown may be removed, as is the case when the building 

 i-s surmounted by a lantern. The tendency of the upper part to 

 fall inwards being equal all round, each stone is supported by those 

 adjacent. 



From the preceding it appears that it would be (in comparison with 

 an arch) easy to construct a dome with perfectly polished stones, anc 

 without cement. The friction of the stones and the tenacity of the 

 cements are of course additional securities. The part in which the 

 construction is weakest will be near the base, more particularly if the 

 joints become nearly horizontal at the base, or if the circumference a 

 the base be very considerable. This weak point is generally secured in 

 practice by bringing strong chains or hoops round the horizontal courses 

 at the interior of the base. Dr. Robison says, " The immense addition 

 of strength which may be derived from hooping largely compensates 

 for all defects ; and there are hardly any bounds to the extent to which 

 a very thin dome vaulting may be carried when it is hooped or frame< 

 in the direction of the horizontal courses." This system of interna 

 h'Mijnng U every way preferable to reliance upon cements, and may 

 without interference with the ornamental part of the design, be carriec 

 to any length. Among other advantages, a dome may be made b; 

 mean* of it to rise vertically from the base, which cannot be the case 

 in an arch. 



The thickness of a dome should increase towards the base. A 

 >erfectly spherical dome, that is, a segment of a hollow shell cut off by 

 a plane, and therefore of uniform thickness, will stand securely if the 

 arch of the generating circle subtend at the centre less than 51 49'. 

 Phe law of the thickness necessary to secure equilibrium is as 

 "ollows : 



A 



Let the dome be formed by the revolution of A v and B w, and let 

 p K, the joint of one of the stones, be always perpendicular to the 

 interior curve ; which is usually the case in practice. Let A M = x, 

 M P = y, P K = 3, arc B p = s ; and let p be any constant greater than unity, 

 and A any constant whatever. Then there will be equilibrium, the 

 equation of B p w being given, if 



Ap I dx \P~ l d dx 



y ' \ dy / tls dy 



or e being the angle KGB, and p the radius of curvature at p 

 g _ Ap (tan e)g-' 

 py coif e 



For the demonstration of this formula, see Venturoli's 'Mechanics' 

 (Creswell's translation), or Robison's ' Mechanical Philosophy.' It is 

 not necessary that p should be a constant : a reference to the work first 

 cited will show how to proceed on the supposition that it is a function 

 of # greater than unity. 



It is to be observed, however, that the mathematical theory of dome 

 construction is utterly inapplicable to the extraordinary works of the 

 Mohammedan architects, in which the curve of the dome itself is 

 often carried considerably beyond the points of support. Evidently in 

 such buildings as the Madrissa of Sultan Hussein at Ispahan, the Taj 

 Mehal at Agra, or the tomb of Mahomet at Beejapore, given lay Mr. 

 Fergusson in his ' Handbook of Architecture,' the stability of the domes 

 depends entirely upon the adhesion of the materials themselves ; for 

 if they had been free to move under the influence of gravity the 

 domes must have fallen. 



DOME (in Architecture). A term usually applied in England 

 to express what more properly should be called a "cupola," or a 

 spherical covering of a building or hall. The confusion in the use of 

 this word seems to have arisen from the fact that the Italians and the 

 Germans call the cathedrals, or principal churches of their towns by 

 the generic name duomo, or dom, from the Greek Awuo, as being the 

 houses by way of distinction ; and from the additional fact that the 

 majority of the churches or cathedrals built in Italy since the revival 

 of literature have been built with cupola*. It would now be impos- 

 sible to bring the word back to its original signification, and it may 

 therefore be considered that the term ditme expresses generically the 

 spherical or the spherico-polygonal coverings of buildings, whether the 

 plans of those buildings be circular or not ; that is to say whether the 

 spherical coverings be raised over a rotunda, or over a drum carried 

 down by pendantives to a square base. Specifically the term dome 

 expresses the outer, or the convex, side of the covering ; whilst that 

 of cupijla expresses the inner, or the concave side. 



Neither the Assyrians, Egyptians, nor the Greeks appear to have 

 resorted to domical construction, although there were some rude 

 attempts occasionally made by the Latter nation, as in the treasure 

 chamber at Mycenae, to carry out that mode of vaulting. The Etrus- 

 cans seem to have been the first people who habitually employed the 

 dome, and they very frequently adopted it in their tombs or their 

 votive monuments. It was no doubt from them that the Romans 

 derived this style of ornamentation ; and it is certain that the most 

 numerous ancient ruins of domes are to be found in the neighbour- 

 hood of Rome and Naples. The principal of these in and near Rome 

 are the Pantheon and the temples of Bacchus, Vesta, Romulus, 

 Hercules, Cybele, Neptune, and Venus, and also some of the chambers 

 of the Thermae. 



The most magnificent dome of antiquity is unquestionably that of 

 the Pantheon, supposed to be a chamber of the great baths of Agrippa. 

 The diameter of the dome internally is 142 feet 84 inches, with a cir- 

 cular opening at the top in the centre 28 feet 6 inches in diameter. 

 The height of the dome from the top of the attic is 70 feet 8 inches. 

 Internally it is decorated with five rows of square compartments. Each 

 row is considerably larger than that immediately above it, as they 

 converge towards the top. The large squares, all of which are rather 

 more than 12 feet each way, contain four smaller squares mink one 

 within the other. It is supposed that these squares were decorated 

 with plates of silver, from some fragments of that metal having been 



