**Abstract: **The theory presented in this paper puts forward the argument that Stonehenge marks an ancient local meridian and functioned as a form of proto-sundial or “earth-clock”. The paper will discuss the monument’s design focussing on the function of the Outer-Circle and the Great Horseshoe. Originally the Outer-Circle consisted of 30 upright pillars with the same number of connecting lintels, as suggested by the discovery of parch-marks in 2013. It is proposed that the 30 sections of the Outer-Circle represented the total duration of the day utilising a 30hr time-system. With north and south aligning to the centre of gaps 27+12 (lintels 127+112) and east and west aligning to the centre of pillars 4 and 19, the structure is precisely aligned to the cardinal directions. The Great Horseshoe is positioned so that its trilithons cast shadow and direct light against or toward pillars and gaps in a process that we could recognise as similar to the hand of a clock pointing to a digit on a clock-face.

**The Stonehenge Earth Clock: **The theory proposes that the cardinal directions align precisely with the intended placement of the structure, the function of which is a filtering and channelling process. Sunlight is intentionally filtered by the structure to frame a column of light or shadow against a specific lintel or pillar, which can then be read as data. The distance of a lintel/pillar from the central axes of the monument is equivalent to the apparent distance of the sun from the North-South and East-West meridians. The arrangement of light and shadow within the structure, at any given point during daylight hours and over the course of the year, can be read as data regarding the position of the sun and the structure can be used to give numeric values to this positioning. Azimuth readings commonly convey data relating to durations of time. A 30hr time-system functioning according to its division across the 360˚ azimuth would be arranged as follows:

360˚^30hr = 12˚ per hour

1440mins^30hr = 48mins per hour

12˚^48mins= 0.25˚ per min

1440mins*0.25˚= 360˚ per day

360˚ represents the total azimuth value of the spinning earth, 1440 represents the total duration of the day in minutes following a hypothetical or mean sun. The value 0.25 is the amount of movement of the mean sun per minute in degrees. The value 12 is the amount of movement of the mean sun per hour in degrees and the value 48 is the requisite number of minutes per hour for the time-system. The following table shows a comparison of the 24hr and 30hr time-systems and details where the (hypothetical) direct channel of light from the mean sun would strike the inner face of the circle. The table also indicates the monument position that is relative to the 360˚ circle beginning north and moving clockwise. The relative position can be used like a solar compass, wherever the true sun is behind a section of the monument, the shadow cast by that section will be more parallel to its pillar(s) in relation to the rest of the monument, indicating the sun is behind that position, assigning its relative position value will give the degree position of the true sun. For instance, if the sun is directly behind pillar 3, the shadow cast by pillar 3 will be the only shadow that is directly parallel to its pillar, and we could say the sun is at 78˚.

24hr 60mins p/h. | 30hr 48mins p/h. | Strike Position (NP Count) | Mean Sun Position/ Degrees | Relative Position |

00:00 | 30:00 | Gap 12 centre* | 0/360˚ | Gap 27 centre |

00:24 | 30:24 | Pillar 12 centre | 6˚ | Pillar 27 centre |

00:48 | 1:00 | Gap 13 centre | 12˚ | Gap 28 centre |

1:12 | 1:24 | Pillar 13 centre | 18˚ | Pillar 28 centre |

1:36 | 2:00 | Gap 14 centre | 24˚ | Gap 29 centre |

2:00 | 2:24 | Pillar 14 centre | 30˚ | Pillar 29 centre |

2:24 | 3:00 | Gap 15 centre | 36˚ | Gap 30 centre |

2:48 | 3:24 | Pillar 15 centre | 42˚ | Pillar 30 centre |

3.12 | 4:00 | Gap 16 centre | 48˚ | Gap 1 centre |

3:36 | 4:24 | Pillar 16 centre | 54˚ | Pillar 1 centre |

4:00 | 5:00 | Gap 17 centre | 60˚ | Gap 2 centre |

4.24 | 5:24 | Pillar 17 centre | 66˚ | Pillar 2 centre |

4:48 | 6:00 | Gap 18 centre | 72˚ | Gap 3 centre |

5:12 | 6:24 | Pillar 18 centre | 78˚ | Pillar 3 centre |

5:36 | 7:00 | Gap 19 centre | 84˚ | Gap 4 centre |

6:00 | 7:24 | Pillar 19 centre | 90˚ | Pillar 4 centre |

6:24 | 8:00 | Gap 20 centre | 96˚ | Gap 5 centre |

6:48 | 8:24 | Pillar 20 centre | 102˚ | Pillar 5 centre |

7:12 | 9:00 | Gap 21 centre | 108˚ | Gap 6 centre |

7:36 | 9:24 | Pillar 21 centre | 114˚ | Pillar 6 centre |

8:00 | 10:00 | Gap 22 centre | 120˚ | Gap 7 centre |

8:24 | 10:24 | Pillar 22 centre | 126˚ | Pillar 7 centre |

8:48 | 11:00 | Gap 23 centre | 132˚ | Gap 8 centre |

9:12 | 11:24 | Pillar 23 centre | 138˚ | Pillar 8 centre |

9:36 | 12:00 | Gap 24 centre | 144˚ | Gap 9 centre |

10:00 | 12:24 | Pillar 24 centre | 150˚ | Pillar 9 centre |

10:24 | 13:00 | Gap 25 centre | 156˚ | Gap 10 centre |

10:48 | 13:24 | Pillar 25 centre | 162˚ | Pillar 10 centre |

11:12 | 14:00 | Gap 26 centre | 168˚ | Gap 11 centre |

11:36 | 14:24 | Pillar 26 centre | 174˚ | Pillar 11 centre |

12:00 | 15:00 | Gap 27 centre | 180˚ | Gap 12 centre |

* Gap 12 is extended due to the half-width of pillar 11, the “centre” referred to in the table is not central to the extended gap but as if the gap were regular.

**Table 1 – 24hr + 30hr time-system comparison 12am-12pm**

Note: The above table cannot be used to read time using the monument as it details the NP count. To read time using Stonehenge it is necessary to use the SP Count. For a guide to reading time using Stonehenge use the following link

https://wordpress.com/post/cypherworks.wordpress.com/118

The fundamental design of the monument incorporates the underlying principles of an idealised or mean time system. If the true sun did move at 0.25˚ per minute, all of the time, then an upright pole at the centre of the Outer-Circle would suffice to achieve accurate mean time readings if using a 30hr time-system, however, it does not. The movements of the true sun are irregular, and vary over the course of the day and over the course of the year, and we will return to this point shortly considering the function of the Great Horseshoe. This fundamental arrangement of the Outer-Circle with hour positions beginning and ending at the centre of every gap can be thought of as the Normal Position Count (NP) as detailed in the above table and in diagram 1. The Outer-Circle consisted of 30 sarsen pillars with connecting lintels that formed gaps either side of every pillar. Each section equals 12 degrees arc of sky along the azimuth totalling 360 degrees. Each section had an approximate width of 10ft, with each pillar averaging 6ft width and each gap averaging 4ft width. It is important to note that although the width of pillars and gaps can vary generally by 1ft, none-the-less, from pillar centre to pillar centre is always approximately 10ft width, for example sometimes a pillar may be 7ft and a gap 3ft. However, it is well established that, taking the monument as a whole, the mean average of pillar width is 6ft and gap width 4ft. It is this mean average measurement of sections that is necessary in establishing the basic function of the monument, and defines the placement for the central points of pillars and gaps. Each of the sections starts at the centre of a gap and ends at the centre of the next gap with the pillar in the middle. The start/end of each section is 2ft from either edge of a pillar, and so the centre of any section will be the very centre of its respective pillar (see diagram 1). This arrangement can be used to give time-values to the position of the sun. For instance, where the centre of gap 27 occupies the north position corresponding to 0/360˚ its time-value would be 15:00SHT as at solar-noon it would be receiving the direct channel from the sun whose position would be 180˚ due south, we can see that 180^12= 15.

If we imagine we are stood at the centre of the original undamaged monument, start facing north and so looking at the centre of gap 27 (the region marked 15pm in diagram 1), with north as 0, if we count 7.5 places from this position in a clockwise direction we arrive at the centre of pillar 4 and will now be facing east. As 360˚^4= 90˚ and 30^4= 7.5, and east is 90˚ clockwise from north and the centre of pillar 4 is 90˚ clockwise from the centre of gap 27, this arrangement gives the monument a horological basis to its construction.

**Diagram 1 – Stonehenge with the 30hr clock-face NP count.**

We would give the centre of pillar 4 the reading value 22.5 as it would be receiving the direct channel from the sun when the azimuth position is due west at 270˚ as 270^12= 22.5 (as shown in diagram 1). These figures can then be converted into hours and minutes. The pre-decimal figure gives us the hour, and the post-decimal figure gives us the remaining percentage of the hour. The second can be calculated as a base-10 fraction of the minute, there are 48 minutes in an SH hour, and so there are 48SH seconds in an SH minute (counted at 48bpm), the calculation is 0.48*50= 24mins, giving us the time 22:24SHT. To convert this into the 24hr system we simply use the quotient between each time-system’s ‘degrees per hour’ rate 15^12= 1.25. We use this to divide the 30hr time value, 22.5^1.25= 18 giving us the time 18:00hrs or 6pm in the 24hr time-system. The same is true for pillar 19 in the west position its reading value would be 7.5 as it would be receiving the direct channel from the sun when the true solar position is 90˚az, 90^12= 7.5, 7.5^1.25= 6am. This is consistent with how we arrange and position a sundial with the 6am hour line to the west and the 6pm hour line to the east.

**The Horseshoe Alignment: **The formation and alignment of the Great Horseshoe is a design intended to channel and filter light for the purposes of establishing a form of specialised time. The horseshoe formation offsets direct light from the sun so that instead of landing at a place within the circle relative to the true solar position it lands at a position relative to the Stonehenge Time-System. The N-S meridian runs through pillar 54 in trilithon 2 and when the sun approaches azimuth 180˚ at solar noon the shadow and window cast by trilithon 2 create a channel of light (the T2 line). The line moves clockwise with the movement of the sun toward the north position. The T2Line actually closes at solar noon but a shadow cast from pillar 60 in T5 runs along the N-S meridian to the corresponding lintel 127 (gap 27) marking position 15:00SHT. Always indicating solar noon rather than midday, and functioning as such, the monument is much like a sundial.

Trilithons 1 and 4 (T1+T4) are positioned as to align with the East-West meridian that runs through pillars 51 and 57. When the sun is at 90˚ (or 270˚) each pillar obstructs the path of direct sunlight, as do pillars 4 and 19 in the Outer-Circle as the meridian line runs through their centre. T4 effectively offsets the position of the light channel coming through the circle and landing on the inner face of pillar 19 (see diagram 2).

**Diagram 2 – Offset caused by trilithon 4.**

The sun only rises prior to 90˚ in the summer half of the year from spring to autumn equinox. At this time of year and during the AM period of the day, the azimuth of the true solar position will be “behind” the mean sun. As it approaches solar noon this discrepancy decreases until reaching solar noon, where the process flips. For the PM period the true solar position will then be “ahead” of the mean sun. This process inverts for the winter half of the year, between the autumn equinox and spring equinox the AM is ahead and PM is behind. The aim of sundial design is to offset this variation to create a tool that approximates a representation of the day as equal proportions throughout the year.

The function of the Great Horseshoe begins to make sense when we consider it in terms of daily time relative to seasonal solar drift. Diagram 3 shows the sun at 90˚ due east and the displacement caused by T1 and T4. At this position T4’s displacement toward the north is a positive displacement because the light is travelling around the monument clockwise. T4 obstructs the direct channel of light running at 90˚ and displaces it further clockwise, effectively placing it ahead in time. We can also see that T1 has the opposite effect and displaces the light anti-clockwise putting it back in time.

**Diagram 3 – T1 and T4 Displacement E-W, Sun at 90˚az.**

We can begin to consider this function in relation to the overall calibration of the monument. We can think of the Outer-Circle as calibrated to the cardinal directions and therefore the equinoxes. A concept that can be best illustrated if we imagine an upright pole at the centre of the circle instead of the Great Horseshoe, when the sun is at 90˚az the shadow from the pole would strike the centre of pillar 19. The Great Horseshoe is calibrated so that the T4 line strikes the centre of pillar 19 when the sun is at 80˚ azimuth, meaning it is calibrated to a different date, a date when the sun is at 80˚az and it is 6:00am in the morning. There are two candidates: the 5^{th} of May and the 18^{th} of August. The 5^{th} of May is a quarter-date, meaning it is precisely halfway between the spring equinox and summer solstice, it is the day traditionally associated with the pagan festival of Beltane. The Great Horseshoe is calibrated so that it reads time most accurately on this date (see diagram 4).

**Diagram 4 – May 5 ^{th} SP Count, time-readings.**

Diagram 4 shows times in black as local mean time. Written in red are the digits for the Sundial Position Count (SP). The yellow lines indicate the T4Line positions and where the column of light hits the inner circle hour to hour. The black lines indicate the T1Shadow positions, instead of a strip of light through the centre of the trilithon, it is the shadow cast by T1 that points to the SP markers hour to hour. The SP count differs from the NP count in the way hour positions are assigned to the Outer-Circle. Instead of one hour represented as a complete section (i.e. a pillar with half a gap each side) hour markers are assigned to an individual pillar, then an individual gap, then an individual pillar etc. In this sense the SP count condenses the way hour times are read around the circle. Given that a section is 10ft in width, a pillar 6ft and a gap 4ft width, and if we take the 10ft of the overall section and divide it by Phi we get 6.18ft, therefore we can loosely think of the division of pillars and gaps as according to the Golden Ratio. Condensing the NP count into the SP count was utilisation of this mathematical principle, and allowed for the calibration of the monument. Using the trilithons in the Great Horseshoe as light filters, light was channelled to the relevant positions and the monument was calibrated to May 5^{th}. Why the monument was calibrated to this date becomes clear when we further consider the seasonal drift of the true solar position, a point made easier if we go back to imagining an upright pole at the monument centre instead of the horseshoe and compare the spring equinox to the summer and winter solstice.

**Diagram 5 – Spring Equinox times, upright gnomon positions.**

Diagram 5 shows the spring equinox with local mean time hour positions and the equivalent SP count. The black lines denote where the shadow from the upright pole or gnomon would be cast. It will be noted that each hour generally corresponds to a particular pillar; this is the “natural” calibration of the Outer-Circle. The reason the hour lines do not run straight along the E-W meridian is because on this date 6am and 6pm actually occur just prior to the sun reaching 90˚ and 270˚ respectively. It will also be worth noting that the hour angles are of a roughly consistent size and run consistently over the course of the day. Solar noon on this date occurs after midday local mean time. The maximum solar noon ever occurs before or after midday is 15mins, the same cannot be said for the other hours relative to the equinox. The daily variation for when local mean time hours occur in the morning and evening is much greater than the variation at solar noon and solar midnight. This is because as the sun appears to approach north or south it travels less vertically and begins to travel more horizontally and therefore covers its greatest distance across the azimuth.

**Diagram 6 – Summer Solstice times, upright gnomon positions.**

Diagram 6 shows the summer solstice and where the shadow will be cast at the same local mean time hours on this date. 6am occurs when the sun is at a much lesser azimuth position, by the time the sun reaches 90˚az it is over an hour later in the day. This shows the extent of variation for the morning period during summer. It will be noted that the sun travels its greatest distance across the azimuth at solar noon for the entire year, on this date, because the Northern Hemisphere is tilted toward the sun. This essentially compensates for the more extreme variation earlier in the day when the solar position is behind mean time, and therefore solar noon and midday actually occur closer in time than they do on the equinox. The diagrams not only illustrate the variation in when hours occur but also the difference in the perceived duration of hours throughout the year if using this kind of primitive sundial design.

**Diagram 7 – Winter Solstice times, upright gnomon positions.**

Diagram 7 shows the opposite is true for the winter solstice compared with the summer; 6am occurs when the sun is at a much greater azimuth position and so it is much earlier when the sun crosses 90˚az (of course, in the winter period the sun does not rise until much later and would still be under the horizon at this point). When the sun does rise it is closer to the region where it appears to travel more horizontally across the sky, and its position begins to get closer to mean time. Because the Northern Hemisphere is tilted away from the sun at this point in the year, the sun appears to travel at its slowest rate across the azimuth leading up to and during solar noon, and solar noon and midday occur only 2mins apart, despite the huge discrepancy in the AM and PM periods. Relating this information to the function of the Great Horseshoe it becomes obvious that its calibration to May 5^{th} gives the structure a bias toward summer. The annual variation produced by the perceived seasonal drift of the sun is greatly reduced for the summer period.

**Diagram 8 – Summer Solstice, SP Count positions and times.**

Diagram 8 shows the local mean hour times on the summer solstice that the sun reaches the same SP count positions as on May 5th. It can be seen that in any instance the discrepancy is no greater than 30mins, with an average of 28mins late. If we compare diagrams 6+8 with diagram 4, taking 6am as an example, in diagrams 8 and 4 we can see that the variation at 7.5SP is 29mins.

**Diagram 4 – May 5 ^{th} SP Count, time-readings.**

In diagram 6, at 6am the sun is at 74˚ azimuth, 16˚ away from 7.5SP (pillar 19 centre at 90˚az relative position), there are 4mins per degree and so 16*4= 64mins. The Stonehenge design with Great Horseshoe offset, has therefore, reduced the effect of seasonal solar drift by 35mins for this hour as 64–35= 29. The Great Horseshoe achieves significant reduction in the perceived variation of the time during the summer because it is calibrated to the quarter dates nearest to summer solstice giving the monument a bias in favour of the summer half of year. The winter, then of course, is negatively affected. Where in the summer seasonal solar drift (SSD) is reduced by the Stonehenge design, in winter it is increased. However, this does not necessarily mean that the Stonehenge design conveys truer time in summer. The reasoning is due to the advanced knowledge of the sun and its seasonal movements across the sky owing to the architects of the monument. As previously stated, when considering SSD and taking the year as a whole, the morning and evening periods will always be the most discrepant with solar noon and solar midnight always more uniform.

**Diagram 9 – Winter Solstice, SP Count positions and times.**

As diagram 9 emphasises, on the winter solstice the sun is not in the sky until after the SSD periods of maximum discrepancy have passed. We can see that at 7.5SP when the sun is at 80˚az it is 3:50am, the reading would be 130mins early, a huge increase on the natural discrepancy due to SSD, which is 78mins, a difference of 52mins. However, the sun would still be 37˚ below the horizon at this time, and so the increased discrepancy caused by the monument would not make a difference. When the sun does rise the monument is reading 94mins early, the natural discrepancy due to SSD is 64mins, therefore by this time the monument is only causing an increase of 30mins. For the next hour the monument is reading 64mins early and the natural discrepancy due to SSD is 48mins, the monument has caused an increase of only 16mins. By the next hour the monument is 35mins early and the natural discrepancy due to SSD is 31mins, the increase caused by the monument is only 4mins. It can be seen from these simple calculations that the bias in the calibration of the monument toward summer is mostly negligible. During the winter the sun is below the horizon when passing its maximum points of SSD, due to this, where the bias in the calibration of the monument reduces summer discrepancy by a maximum of 35mins, in winter it increases the discrepancy by an observable maximum of only 30mins. Another way to view this is that the bias in the monument toward summer involves an offset along the **azimuth**, and in the winter this is accounted for due to the natural variation in **solar altitude** (as the sun is below the horizon at the points of maximum SSD during winter). It is this fact that highlights the underlying and unprecedented genius in the design of the monument. The overbearing implication is that although the architects could not construct a technology that was able to read in mean time, they apparently must have had the intellectual capacity to calculate it, to have been able to construct the model evident at Stonehenge.

**Further reading: **the paper can be finished in part 2 found on this site. the full text can be accessed here

https://docs.google.com/document/d/1p5Sd-fIytsxQ88w5EbzHBxqZ2uyiu_NvcFdiKLLFaLM/edit?usp=sharing

and downloaded here

**Sources**

** **Banton, S. and Daw, T. (2014*)*. PARCHMARKS AT STONEHENGE JULY 2013 [online] Available at: https://www.cambridge.org/core/journals/antiquity/article/parchmarks-at-stonehenge-july-2013/69AAE39C702A5B844CFDD84EA0B3F26C

** **Abbot, M. and Anderson-Whymark, H. (2012). *STONEHENGE LASER SCAN: ARCHAEOLOGICAL ANALYSIS REPORT*. [ebook] ArcHeritage. Available at: http://discovery.ucl.ac.uk/id/eprint/1419104

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