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are called mean elliptical domes, and a circular dome, whose altitude 
is equal to the radius of the base, is called an hemispherical dome. 
When the base of the dome, and therefore all horizontal sections 
of it, are-circles, it is a surface of revolution, and is commonly called 
cupola. 
The lines of curvature of the domic surface are peculiarly cal- 
culated to suggest not only principles for the construction of the 
dome, but point out the most natural and elegant decorations for 
it; decorations not depending on the fancy or caprice of the archi- 
tect, but arising necessarily out of the form and properties of the 
surface itself. 
The perpendiculars to the surface passing through the several 
points of a line of curvature, form a surface perpendicular to the 
surface of the dome. There are two systems of lines of curvature 
on every surface, and the lines of each system intersect those of the 
other system at right angles. If several lines of each system be 
described upon the domic surface, they will divide the whole 
vault into regular and symmetrical compartments, included by 
curvilinear limits intersecting perpendicularly. The perpendi- 
culars to the surface through all these lines will form curved sur- 
faces, which will also intersect perpendicularly, and will divide 
a shell of the vault of any assumed thickness into voussoirs 
bounded by those rectangular curved surfaces. If, however, the 
lines of curvature be drawn sufficiently close, so as to reduce the 
magnitude of these voussoirs to a sufficiently small proportion to the 
entire magnitude of the dome, the bounding surfaces may be con- 
sidered as planes, scil. the tangent planes to the normal developable 
surfaces already mentioned. The magnitude of the voussoirs must 
be regulated by the magnitude of the whole vault, and the peculiar 
uature of the materials of which it is constructed. The decorations 
