17 
of the internal concave surface of the dome, as well as the 
external convex surface, should be all regulated by the directions 
of the lines of curvature, and by the compartments into which they 
resolve the surface. The position, directions, and general figure of 
these lines should be also attended to in the decoration and structure 
of the hall over which the dome is suspended. The columns, 
cornices, and the other ornamental parts of the building, both in- 
ternal, and internal should harmonize with these lines. 
There are in some surfaces points called umbilical points, which 
are so surrounded by the lines of curvature that they all turn their 
concavities towards them. On different sides of these points, there- 
fore, the lines of both systems have their curvatures turned in op- 
posite directions. In the decorations of domes having such points 
they should therefore be attended to, as they must immediately at- 
tract the eye from the peculiar disposition of the compartments of 
the dome which surround them. When such points occur in either 
of the principal vertical sections of the dome, and at any consider- 
able elevation from its base, they would be adapted to receive any 
suspended ornament, such as lamps, lustres, chandeliers, &c. If 
these points, as is the casein the mean ellipsoidal dome, are placed 
upon the base, they suggest a peculiar disposition in the architectu- 
ral decorations of the lower part of the hall. 
The projections of the lines of curvature upon the floor of the 
hall point out the proper method of disposing its flagging, so as to 
correspond with the decorations already suggested for the other parts 
of the building. The methods of ornamenting an edifice, thus de- 
duced necessarily from the very nature of the structure, while they 
set no limit either to the richness or the quantity of ornament, 
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