The following tables show the expected number of alignments according to the Furness formula, and the average number of alignments actually found in computer simulations. It can be seen that the Furness formula, which was used in the original Linear Dream, tends to underestimate the number of alignments. Thus the computer simulations confirm, or indeed somewhat strengthen, the negative results found by Bob Forrest.
Case 1.Relevant to Paul Screeton’s Quicksilver Heritage, p. 43, on the South Durham leys.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 1926 | 2378.85 | 2379.50 | 89.95 |
| 4-pointers | — | 4059.71 | 4060.00 | 238.58 |
| 5-pointers | 222 | 271.35 | 271.07 | 25.69 |
| 5-pointers | — | 442.91 | 443.14 | 65.99 |
| 6-pointers | 19 | 23.08 | 23.07 | 6.16 |
| 6-pointers | — | 36.70 | 36.87 | 17.74 |
| 7-pointers | 1 | 1.57 | 1.58 | 1.46 |
| 7-pointers | — | 2.46 | 2.51 | 4.82 |
Case 1: Map 40 × 45 km; ley width 0.02 mile; 400 sites; 20,000 simulations
Case 2.Salisbury Plain.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 25426 | 45794.8 | 45868.7 | 356.5 |
| 4-pointers | — | 183119.2 | 183154.1 | 4913.1 |
| 5-pointers | 7132 | 14869.1 | 14834.2 | 331.3 |
| 5-pointers | — | 53311.1 | 53294.9 | 2612.9 |
| 6-pointers | 1499 | 3487.6 | 3487.4 | 153.2 |
| 6-pointers | — | 11793.4 | 11760.3 | 1037.8 |
| 7-pointers | 252 | 649.5 | 648.3 | 50.4 |
| 7-pointers | — | 2111.9 | 2089.3 | 374.5 |
| 8-pointers | 35.2 | 100.6 | 100.6 | 15.5 |
| 8-pointers | — | 318.7 | 307.2 | 130.8 |
| 9-pointers | 4.2 | 13.4 | 13.3 | 5.1 |
| 9-pointers | — | 41.7 | 37.4 | 40.9 |
Case 2: Map 40 × 40 km; ley width 0.02 mile; 1006 sites; 500 simulations
Case 3.Relevant to Janet and Colin Bord Mysterious Britain, p. 200, leys in the Bedford and Luton area.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 6622 | 9305.13 | 9315.02 | 197.67 |
| 4-pointers | — | 20655.79 | 20665.77 | 835.24 |
| 5-pointers | 1144 | 1630.23 | 1629.56 | 80.60 |
| 5-pointers | — | 3391.64 | 3396.58 | 293.63 |
| 6-pointers | 148 | 211.15 | 211.16 | 22.83 |
| 6-pointers | — | 423.36 | 425.76 | 94.41 |
| 7-pointers | 15 | 21.85 | 21.98 | 6.27 |
| 7-pointers | — | 42.79 | 43.82 | 34.16 |
| 8-pointers | 1 | 1.89 | 1.90 | 1.71 |
| 8-pointers | — | 3.64 | 4.02 | 14.27 |
| 9-pointers | 0.1 | 0.14 | 0.15 | 0.45 |
| 9-pointers | — | 0.27 | 0.39 | 5.45 |
Case 3: Map 40 × 45 km; ley width 0.02 mile; 600 sites; 2,000 simulations
Case 4.Relevant to John Michell’s The View Over Atlantis, p. 40, concerning Dorchester and Weymouth 1:50,000 OS sheet 194.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 402 | 541.08 | 541.16 | 36.67 |
| 4-pointers | — | 778.52 | 778.49 | 73.41 |
| 5-pointers | 29 | 41.21 | 41.17 | 8.35 |
| 5-pointers | — | 57.45 | 57.40 | 16.85 |
| 6-pointers | 1.6 | 2.35 | 2.34 | 1.75 |
| 6-pointers | — | 3.21 | 3.20 | 3.81 |
| 7-pointers | 0.07 | 0.11 | 0.11 | 0.36 |
| 7-pointers | — | 0.14 | 0.14 | 0.87 |
Case 4: Map 40 × 40 km; ley width 0.02 mile; 250 sites; 50,000 simulations
Case 5.Again relevant to John Michell’s The View Over Atlantis, from the notes and illustrations p. xx, concerning alignments of moats in East Anglia.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 3-pointers | 92 | *** TO DO *** | 109.57 | 10.70 |
| 3-pointers | — | 182.88 | 182.90 | 27.33 |
| 4-pointers | 12.5 | *** TO DO *** | 15.62 | 5.19 |
| 4-pointers | — | 24.15 | 24.16 | 11.87 |
| 5-pointers | 1.1 | *** TO DO *** | 1.44 | 1.50 |
| 5-pointers | — | 2.14 | 2.14 | 3.41 |
| 6-pointers | 0.08 | *** TO DO *** | 0.10 | 0.36 |
| 6-pointers | — | 0.14 | 0.14 | 0.83 |
Case 5: Region 9 × 14 km; ley width 0.075 km; 38 sites; 200,000 simulations
Case 6.Also from notes and illustrations p. xx of John Michell’s book, being the small map there presented showing an alignment of 5 moats between Athelington and Laxfield.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 191 | 217.322 | 217.292 | 21.728 |
| 4-pointers | — | 306.077 | 306.102 | 42.063 |
| 5-pointers | 14 | 15.549 | 15.533 | 4.938 |
| 5-pointers | — | 21.249 | 21.258 | 9.733 |
| 6-pointers | 0.8 | 0.832 | 0.831 | 1.031 |
| 6-pointers | — | 1.117 | 1.123 | 2.136 |
| 7-pointers | 0.03 | 0.036 | 0.037 | 0.207 |
| 7-pointers | — | 0.047 | 0.048 | 0.398 |
Case 6: Map 40 × 45 km; ley width 0.03 mile; 172 sites; 100,000 simulations
Case 7.Relevant to John Michell The View Over Atlantis, Notes and illustrations p. xvi: Alignments of Norfolk Castles and Mounts.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 5 | 4.2602 | 4.2606 | 2.2981 |
| 4-pointers | — | 4.6961 | 4.6988 | 2.8609 |
| 5-pointers | 0.1 | 0.0841 | 0.0846 | 0.3046 |
| 5-pointers | — | 0.0919 | 0.0922 | 0.3864 |
| 6-pointers | 0.002 | 0.0012 | 0.0012 | 0.0364 |
| 6-pointers | — | 0.0013 | 0.0013 | 0.0480 |
Case 7(a): Map 40 × 45 km; ley width 0.02 mile; 75 sites; 200,000 simulations
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 6-pointers | 19 | 23.077 | 23.065 | 6.123 |
| 6-pointers | — | 36.702 | 35.899 | 18.017 |
Case 7(b): Map 40 × 45 km; ley width 0.02 mile; 400 sites; 15,000 simulations
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 5-pointers | 65 | 72.189 | 72.133 | 11.529 |
| 5-pointers | — | 104.224 | 104.137 | 24.802 |
| 6-pointers | 4.2 | 4.558 | 4.543 | 2.508 |
| 6-pointers | — | 6.450 | 6.449 | 5.943 |
| 7-pointers | 0.22 | 0.231 | 0.232 | 0.531 |
| 7-pointers | — | 0.323 | 0.325 | 1.387 |
| 8-pointers | 0.01 | 0.010 | 0.010 | 0.112 |
| 8-pointers | — | 0.014 | 0.014 | 0.291 |
Case 7(c): Map 40 × 45 km; ley width 0.02 mile; 300 sites; 50,000 simulations
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 5-pointers | 181 | 203.373 | 203.267 | 22.523 |
| 5-pointers | — | 351.755 | 351.318 | 63.586 |
| 6-pointers | 16 | 19.440 | 19.377 | 5.746 |
| 6-pointers | — | 32.654 | 32.570 | 18.162 |
| 7-pointers | 1.2 | 1.487 | 1.473 | 1.429 |
| 7-pointers | — | 2.450 | 2.459 | 5.008 |
| 8-pointers | 0.08 | 0.095 | 0.096 | 0.353 |
| 8-pointers | — | 0.155 | 0.160 | 1.177 |
Case 7(c): Map 40 × 45 km; ley width 0.03 mile; 300 sites; 15,000 simulations
Case 8.Relevant to John Michell, The View Over Atlantis, pl. xxix, facing p. 45: leys through Gare Hill, Wiltshire.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 3867 | 5503.0 | 5508.0 | 148.9 |
| 4-pointers | — | 11106.9 | 11115.0 | 524.2 |
| 5-pointers | 556 | 840.5 | 841.0 | 53.5 |
| 5-pointers | — | 1600.6 | 1602.4 | 166.8 |
| 6-pointers | 60 | 95.1 | 95.1 | 14.2 |
| 6-pointers | — | 175.1 | 175.2 | 47.7 |
| 7-pointers | 5 | 8.6 | 8.7 | 3.7 |
| 7-pointers | — | 15.5 | 15.4 | 13.4 |
Case 8: Map 40 × 40 km; ley width 0.02 mile; 500 sites; 5,000 simulations
Case 9.Relevant to Alfred Watkins, The Old Straight Track, Fig. 6, of South Radnor Leys.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 219 | *** TO DO *** | 288.06 | 26.35 |
| 4-pointers | — | 436.34 | 436.34 | 58.15 |
| 5-pointers | 16.5 | *** TO DO *** | 25.09 | 6.70 |
| 5-pointers | — | 36.98 | 36.98 | 15.02 |
| 6-pointers | 0.925 | *** TO DO *** | 1.67 | 1.52 |
| 6-pointers | — | 2.42 | 2.42 | 3.74 |
| 7-pointers | 0.041 | *** TO DO *** | 0.091 | 0.339 |
| 7-pointers | — | 0.129 | 0.129 | 0.897 |
| 8-pointers | 0.0015 | *** TO DO *** | 0.0041 | 0.070 |
| 8-pointers | — | 0.0058 | 0.0057 | 0.200 |
Case 9: Region 20 × 40 km; ley width 0.02 mile; 178 sites; 100,000 simulations
Case 10.Relevant to Major F. C. Tyler’s The Geometrical Arrangement of Ancient Sites, Fig. 2, of leys in the region of Tiverton, Devon.
| Expected by Furness formula |
Expected by strip formula |
Mean of simulations |
St. dev. of simulations |
|
|---|---|---|---|---|
| 4-pointers | 227 | *** TO DO *** | 264.3379 | 24.2871 |
| 4-pointers | — | 369.2372 | 369.0922 | 46.5233 |
| 5-pointers | 15 | *** TO DO *** | 18.3656 | 5.3925 |
| 5-pointers | — | 25.0197 | 24.9930 | 10.5007 |
| 6-pointers | 0.75 | *** TO DO *** | 0.9715 | 1.1134 |
| 6-pointers | — | 1.2969 | 1.2870 | 2.2308 |
| 7-pointers | 0.03 | *** TO DO *** | 0.0410 | 0.2236 |
| 7-pointers | — | 0.0546 | 0.0505 | 0.3942 |
| 8-pointers | 0.001 | *** TO DO *** | 0.0011 | 0.0349 |
| 8-pointers | — | 0.0019 | 0.0013 | 0.0533 |
Case 10: Map 27 × 18 miles; ley width 0.02 mile; 200 sites; 50,000 simulations