purpose, ultimately to embody the results of his investigation in a_
"Trattato delle Cupole." _The amount of materials is remarkably
extensive. MS. B is particularly rich in plans and elevations of
churches with one or more domes--from the simplest form to the most
complicated that can be imagined. Considering the evident connexion
between a great number of these sketches, as well as the
impossibility of seeing in them designs or preparatory sketches for
any building intended to be erected, the conclusion is obvious that
they were not designed for any particular monument, but were
theoretical and ideal researches, made in order to obtain a clear
understanding of the laws which must govern the construction of a
great central dome, with smaller ones grouped round it; and with or
without the addition of spires, so that each of these parts by
itself and in its juxtaposition to the other parts should produce
the grandest possible effect.

In these sketches Leonardo seems to have exhausted every imaginable
combination. [Footnote 1: In MS. B, 32b (see Pl. C III, No. 2) we
find eight geometrical patterns, each drawn in a square; and in MS.
C.A., fol. 87 to 98 form a whole series of patterns done with the
same intention.] The results of some of these problems are perhaps
not quite satisfactory; still they cannot be considered to give
evidence of a want of taste or of any other defect in Leonardo s
architectural capacity. They were no doubt intended exclusively for
his own instruction, and, before all, as it seems, to illustrate the
features or consequences resulting from a given principle._

_I have already, in another place,_ [Footnote 1: Les Projets
Primitifs pour la Basilique de St. Pierre de Rome, par Bramante,
Raphael etc.,Vol. I, p. 2.] _pointed out the law of construction for