PRE-CONQUEST CHURCHES OF ESSEX 277
Then he would mark off the proposed width of the nave, from one end
of this line, usually the south end.
Thirdly, he would lay out another straight line at right angles to the first
at its south end ; the trick of doing this with a "3-4-5" triangle was certainly
known to him and need not be explained here, as it is not relevant to my
argument.
Then comes the crux of the supposed method.
With an assistant to hold one end of a long cord, he marks off along the
east-west line, from the starting-point, a distance equal to the proposed width
of the nave. The assistant then walks to the north end of the first line,
paying out more cord to stretch across to the mason, who stands still. The
assistant (who does most of the walking) then goes back to the starting-point,
while the mason moves farther along his line until the cord is taut once more;
he is then √2 widths from the starting-point, as elementary geometry will
show.
The assistant and mason repeat the procedure, the mason ending up
√3 widths from the starting-point. This, I maintain, is how the length of
the Saxon church nave was determined, probably as a well-kept guild secret
of the Saxon builders. The rectangle of the nave could be completed by
using the cord to check the equality of diagonals, or in some other simple
way, such as might be used even today. But so many Saxon church naves
have sides that are not quite parallel, and in some are not even straight,
that I feel sure that only one end and side were set out carefully, the chancel-
arch and north wall being often put in "by eye".
You will notice that my list shows every well-known pre-Conquest
church in Essex, and includes for comparison a few known to be early, but
not pre-Conquest. In this list there are a few churches having nave propor-
tions which are neither √3 (the usual Saxon shape) nor 2.0 (the usual
Norman shape). It may seem an extravagant claim to make, but I believe
that where √3 gave too short a nave for their purpose, the builders went
on with their strangely simple method, through √4 (which is the Norman
value 2.0) to √5, √6, and even to √7, of each of which there is one example,
the two latter, both pre-Conquest, being so extraordinarily near to the
mathematical values that I cannot see any other explanation for their origin.
One final point.
On looking closely at the proportions of the eight examples having √3,
or thereabouts, as the ratio of their present internal dimensions, we find two
distinct groups, one very near to √3 (Inworth, Strethall, Hadstock, Little
Bardfield, White Roding), the other distinctly greater (Chickney, Fobbing,
Corringham), although the mean of the eight ratios is only 1 per cent less
than the value of √3.
If we add two feet to each of the two internal dimensions of those in the
latter group, we find that they now conform very nearly indeed with the
√3 relation, and I suggest that sometimes the lines laid out were used as
the inner lines of the foundation trenches (as in the first five), while in other
cases they were taken as the centre-lines (or even the outer lines), thereby
reducing the internal dimensions of the finished church by a wall-thickness
from the width and length as laid out. But I do not insist on this explanation;
it may simply be one more result of the lack of dimensional precision before
the Normans introduced their more disciplined techniques.
Therefore, if the hypothesis put forward in this note be acceptable, the
fact of nave dimensions being exactly, or almost exactly, equal to √3, √5,
√6, or √7 may be an additional criterion of pre-Conquest date for the ground-
plan, or at least of such a plan having been laid out by masons unused to
making direct dimensional measurements, such as the Norman builders
employed, and which came into general use after the thirteenth century.