An investigation of the Lines of Curvature of Ellipsoids, Hyper- 
boloids and Paraboloids, with a view to the improvement of the 
Theory of the structure and decoration of Domes. By the Rev. 
Dionysius Lardner, 4. M. M.R.I. A. 
Read June 14, 1824, 
'THERE is no department of architecture in which the principles 
of geometry are more usefully or elegantly applied than in the the- 
ory of the structure and decoration of domes. A dome isa vault 
or roof, forming a segment of a curved surface, the concavity of 
which is turned inwards. All horizontal sections should be similar 
figures, and it should be supported by a base of the same figure. 
It is however by no means necessary that the edifice over which the 
dome is to be thrown should be of this figure, for there are 
methods well known to architects, but which would be foreign to 
my present object to enter upon, by which any polygonal base may 
be made to terminate in acircle, or in such other curve as may be 
required. From this curve a cylindrical wall may be erected, on 
which the dome is to be raised. Domes are denominated circular 
or elliptical, according to the base on which they are constructed, 
which is usually one of these figures. Domes, which rise higher 
than the semitransverse axis of the base, if they be elliptical, or 
than the radius of the base, if they be circular, are called sur- 
mounted domes ; those whose altitude is less than the semiconjugate 
axis of the elliptic base, or than the radius of the circular base, are 
called surbased domes, Elliptical domes of an intermediate altitude 
VOL. XIV. ty) 
