the little tower relatively to the great one, but there
probably was some meaning in it which might appear
had we a plan of the original walls around the towers.
It is very doubtful that these walls, which now mark
off the sacred enclosure, are of the same period as the
towers. They are shaded darkly in our plan because
they are fairly well b uilt; but although they are better
built than most of the secondary walls, yet they are
not equal in point of execution to the great outer
wall and the towers, and their lines, too, are not so
regular as those of the original walls generally are.
It seems probable that they are rough copies of some
old walls which had fallen, and are wanting in some
of the essential features of their originals. We can
only say that the centre of one tower is distant 17-17
feet from the centre of the other, within a limit of
error of two inches.
The angular height of both the towers measured
from the centres of the curves which determine their
forms is the same—namely 23° 1'.
None of the angular values of the arcs seem to
have been of any special significance, except perhaps
the angle at the altar in the great temple, which is subtended
by the arc a k . The value of this angle is about
57°, and is equal to our modern unit of the circular
measure of an angle, which is the angle at the centre
of any circle that is subtended by an arc equal to the
radius. It is hardly likely that it can have had this
meaning to the builders of the temple, and the probable
cause of the coincidence is that at A they
meant to halve the angular distance between k and
the doorway. Besides, the sun’s rays, when it rises at
the summer solstice, do not fall directly on the part of
the wall beyond A, and this probably had some connection
with their reason for changing the radius of
the arc at this point.
There is no evidence th it any of the trigonometrical
functions were known to the builders of
Zimbabwe ; not even the chord, which was probably
the earliest recognised function of an angle, for the
chords of the various arcs bear no simple relation to
each other. The only interesting mathematical fact
which seems to have been embodied in the architecture
of the temples is the ratio of diameter to
circumference, and it may have % «/ had an, .o ccult siOgnificance
in the peculiar form of nature worship which
was practised there. We do not suppose that it was
intended to symbolise anything of an astronomical
nature, and it is extremely improbable that the
builders of Zimbabwe had any notion of mathematical
astronomy, for their astronomy was purely empirical,
and amounted merely to an observation of the more
obvious motions of the heavenly bodies. When the
minds of men were first interested in geometry it
would at once occur to them that there must be some
constant ratio between the circumference of a circle
and its diameter, and they would easily discover what
this ratio was, and they may have considered this discovery
so important and significant that they desired
to express it in their architecture. Analogous instances
of an embodiment of simple mathematical principles
in architectural forms will occur to every one.