52 THE ESSEX NATURALIST
If readers take a typical 20 x 341/2ft. rectangle and allow 18in. walls and 18in.
offsets, they can calculate for themselves that length-width ratios of 1.73
(which is 'root-three'), 1.83 and 1.61 respectively will result in the three
cases, and these ratios are just those we find most frequently.
As to the little group on the left-hand side of the diagram, these represent
some of the six churches in the Orkneys which Dr. Budge has considered.
It seems to me that they are grouped about the ratio 1.41 which is the square-
root of two, and would result from carrying out my simple 'cord' procedure
twice instead of three times as usual. Moreover, if the wall-thickness argument
be applied to the smaller churches in question, ratios of 1.36 and 1.54 arise
and churches of both these types are represented.
I may add that of Dr. Budge's Orkney churches, the others, having ratios
larger than 1.73, and which he uses to support his theory of variation of ratio
with latitude, fall quite naturally into the upper extension of my 1.73
distribution.
As I reported in my 1951 paper, I have found undoubtedly early churches
with ratios of 2.3, 2.43 and 2.64, which are approximately 'root five,' 'root
six' and 'root seven' respectively (one of each in Essex): these are eleventh-
century churches, probably just pre-Norman. None but Norman and later
builders seem to use a 2 to 1 ratio. If these odd roots as ratios are a reality
and not the wish-fulfilment of a theorist, then I maintain that it indicates a
perfectly understandable extension of the 'cord' method, in which the mason
carried out the steps as often as desired to give a 'shapely' nave: I feel quite
sure the rude Saxon knew nothing of 'root-three' and still less of 'root-five'
but was activated by some mystic regard for a triple and traditional trade
secret.
For my part, I reject the Budge theory, ingenious as it undoubtedly is,
chiefly because of the awkward delay required between solstice and equinox
and also because most of our Saxon churches are so late in date of foundation
(eleventh century) that the pagan element must long before have disappeared
from their ritual, at least as officially recognised by the Church. I am quite
ready to accept any of the other simple 'cord' methods put forward at the
E.F.C. meeting of November 24th, as alternatives to my own suggestion of
1951: these are all surmises. The one certain fact in all this seems to be that
Saxon churches often have a length-width ratio of about the square-root of
three, which is 1.732.