CASTLE RIGG PROJECT
PROGRESS REPORT
PASDA
Since
this work was presented Sir Maurice Kendall has written to say that
he is in agreement that a further term should be added to his formula
if there is a time trend in the length of the paces. Further
calculations on our data have established this. Combined data (KY5 +
KY4) show that the first step is significantly shorter than each
subsequent step. Also steps 2 & 3 combined are significantly
shorter than steps 4 & 5 combined. A similar trend is present in
the Keswick Pace data.
Hammersley
(1955) stated that the megalithic yard hypothesis could not be tested
by collecting new data in respect of stone circle diameters. In fact,
as has been shown here, the hypotheses can be tested by collecting
new data in respect of pace and stick measurements. Such real data
are so far different from the made up data of Porteous (1973) that
his conclusions, based on the made up data, are invalidated.
Our
data have been further examined and compared with those of Thom
(1955; 1962) in respect of circle diameters clustered round 4, 6, 8
and 10 M Y. It is obvious that stick measurements give the best
results. Natural paces are very variable. It does not require
statistical analysis to recognise that a perfectly laid out circle
may not be perfect 4,000 years later. Any probable method of laying
cut stone circles should give results better than those found 4,OOO
years later.
Even
paces made to simulate the megalithic yard do not give results which
are good enough but this is not the hypothesis under test. There
would be little point in trying to pace megalithic yards when they
could be measured so easily with a yardstick. It is, however,
noteworthy that the accuracy of pacing decreases with the number of
paces as was anticipated by Thom (1962).
The
Keswick pace data show that the natural paces are very variable, more
variable than was supposed by Porteous (1973) and more complex to
calculate than was proposed by Kendall (1955). The results are
obviously worse than the data found by Thom. This is confirmed by the
large standard deviation of natural paces. The pacing hypothesis is,
therefore, rejected.
The
Keswick stick data give results which are better than Thom's data but
allowing for the lapse of time, are not inconsistent with these data.
Accordingly the Yardstick hypothesis is preferred.
Further
data are being collected and the programme is being rewritten in
Algol for access to Lancaster University computer. It is hoped that
further results will be available for 29.1.77. Important additional
references are the papers by Kendall (1974), Freeman (1976) and
Angell (1976).
LEY
LINES
Data
checked by two observers have now been obtained for 20 circles, 7
cairn circles, l4 settlements and enclosures, 47 tumuli, 13
earthworks, 6 standing stones and cromlechs, and 3 other sites: a
total of 110 sites in all. It is hoped to analyse these new data
using the Lancaster University Computer. Corrected results already
obtained are given in the table below. Reports of unpublished work
suggest that our results are close to what would be expected by
chance on theoretical grounds.
19th
January, 1977 Peter Stewart,
Peter
Bestley,
Peter
Hodgson,
David
Wylie.
TABLE: ALIGNMENTS FOUND FOR 48 SITES: REAL AND RANDOM DATA 
Angle  Real  Random  p  χ^{2} 
1°  110  102  <0.6  0.15 
½°  58  51  <0.6  0.225 
¼°  36  24  <0.3  1.21 
ACKNOWLEDGEMENTS
Our
additional thanks are due to Lancaster University for computing
facilities. We are also grateful to Professor D. G. Kendall, F.R.S.
and to Dr. P. R. Freeman for advice in discussion with one of us.
(PAAS).
REFERENCES
ANGELL,
I.O. (1976) Mathl. Gaz., 60, 189193
KENDALL,
D.G. (1974) Phil. Trans. R. Soc. Lond., A., 273, 231266
FREEMAN,
P.R. (l976) J. Roy. Statist. Soc., A., 139, 2055
Z STATISTIC
STEP 

 (1)  (2)  (3)  (4)  (2+3) 
 (KY3 + KY4) 





 x  s 





(1)  0.787  0.065           
(2)  0.846  0.048  3.12         
(3)  0.843  0.054  .283  0.218       
(4)  0.874  0.050  4.84  2.09  2.21     
(5)  0.882  0.064  2.36  2.25  2.36  0.44   
(2+3)  0.845  0.051           
(4+5)  0.878  0.057          3.23 
 (KP1 + KP2) 





 x  s 





(1)  0.721  0.13           
(2+3)  0.775  0.121  1.98         
(4+5)  0.805  0.128  2.6        0.85 
Probably significant p < 0.05
Significant p < 0.01
