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, 14 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. (1976) 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
