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Thom's terrestrial refraction observations

Issues around transcribing

• Thom observed several target from The Hill, which is at an elevation of 148m above sea level and at 4.52727 West and 55.70659 North (WGS84).
• Thom did not observe objects at apparent altitudes due to vast level surfaces. It is expected these would have a larger influence from the temperature gradient near ground level.
• At this moment four sets of observations have been transcribed (in total 181 observations). The calculations around these transcriptions were performed using ARCHAEOCOSMO (and Excel).
  
• It might be that some 35% of the observations are in the retrieved notebooks (at Historic Environment Scotland in Edinburgh).
• It looks Thom has used two different (type of) theodolites: one which reads apparent altitude values around 0 (or 360) or 180 (Set 1 and 5) and one which reads apparent zenith angles around 90 and 270 (Set 3, 4).
  
• Thom wrote numbers in front of his theodolite apparent altitude readings (normally close to 16 or 116). See below numbers within the red outline (Thom, MS/430/27, 1954)
  Not clear yet what they mean: they could have a relation to the bubble (1958, page 249). No bubble corrections have yet been done. Thom determines a bubble correction in MS/430/64. But is a correction needed if both direct and reverse measurements are taken?
  
  It is important to understand this, as it might be able to systematically improve the results. If you have ideas how to solve this uncertainty, let me know.
  
• Thom abbreviates theodolite apparent altitude readings.
  Sometimes 89, 179, 269 and 359 are mostly written as '9'. Similar with 90, 180, 270 are 360: are written as 'nothing' or as '0''. This can be confusing. When one knows the theodolite target one can deduct how to read it!
• Thom records the follow parameters around the altitude recordings: target, date, time, temperature (F), pressure (Hg), wind direction, wind force, cloud cover, G (related to temperature gradient?), Z (zero/reference of G?) and bubble(?).
  Some of these parameters might not be recorded for an observation: between 2% (target) and 81% (Z) are seen to be omitted.
  
• The most important parameters to note for the terrestrial refraction are: time and wind force, and both are missing up to 40% of the observation (sometimes both are missing for the same observation). In most cases a reasonable inter/extrapolation could be made, so the effect of the omissions is not significant.
• G an Z parameters are not recorded for Set 1. Five observations in Set 5 have a serious error in G.
  
• It is not yet 100% sure how to interpret the G and Z parameters. Are these related to temperature gradient and if so are this numbers derived from thermocouples with a deflection meter or potentiometer method (ASTM, 1981, Chapter 6).
  Thom wrote about this (1958 page 250):
  ... two thermocouples were made and placed one 2.5 ft. above the ground and the other 25 ft. higher. [...] The thermocouples were opposed and the e.m.f. measured on a high resistance galvanometer.
  From this is has been deducted that Thom used the deflection meter method. And in his notebook (Thom, 1956, MS/430/64) the following is mentioned:
  
  
  
  

  From the above picture we can read:
• 'side by side'
  For calibrating? Did he place the two opposing thermocouples beside each other, aka at the same temperature?
  A value is mentioned for G.
  
• 'Short Circuit'
  For reference/zero? Did he short circuit the two opposing thermocouples to get a zero/reference value?
  A value is mentioned for Z.
• 'Reverse connection'
  Did he reverse the connection to the two opposing thermocouples or did he reverse each of the thermocouples?
  Values mentioned for G and Z.
  
• Another text from the notebook (MS/430/64) that could reveal something from the G and Z method:
  
  
  

  It looks to say: 'All found results ??? NBG (broken thermocouple)'.
  'NBG' is something related to type of thermocouple or type of connector head?
  The above text was written after several exceptionally low Gs (around 25) were noted. The NRI Stability Class does not reveal such a very low Temperature Gradient. 25 sounds almost to be half of the 'normal' G value (around 50): so one thermocouple 25 and two around 50: could this say something about the method?
  
• Another text that could help:
  

  
  

  So there is a difference between 'Open Zero' and 'Z' ('Short Circuit' or 'shorted').
  
• Comparing the G (blue), Z (green), DeltaGZ (G-Z: gray) and Temperature Gradient from NRI's Stability Class (yellow) is done in the below graph for Set 3:
  
  
  Remember that Z values were missing in 70% of the observations, so they were interpolated (hopefully that is no problem as they looked quiet stable (except for two major jumps; between two different days). The gray line (derived proxy DeltaGZ for the temperature gradient?) is perhaps somewhat followed by the theoretical Temperature Gradient from NRI's Stability Class (based on: Sun's altitude/insolation, day/night, cloud cover, cloud height and wind speed: the high values of Temperature Gradient are reached during the stable night NBL) periods: before '1hour after sunrise' and after '1 hour before sunset'.
  Interesting to see that the measured G does not become negative in this Set 3, while one would expect this to happen during the day times. But this happened also during the measurements of the Temperature Gradient at Skerries, Ireland (by the webmaster).
  
  For Set 4 (see below graph); G (blue) is most of the time below Z (green), so it looks G can become negative. DeltaGZ (gray) is followed somewhat by the NRI theoretical Temperature Gradient from Stability Class (yellow):
  
  
  Here is the overview from Set 5:
  
  
  It is important to fully understand the determination of the G and Z, aka Thom's Temperature Gradient. If you have ideas how to solve this uncertainty, let me know. This is another possible way to derive it!
  
• Thom measured the apparent altitude from The Hill by using the direct and reverse face of the theodolite. The average results of these two face measurements should for all observations be the same. In 95% of the observations that is true (for both [type of] theodolites), at the standard deviation is around 15" (1 sigma). In some observations there seems to be an error of 30', this could have been a scale-reading error. In others no 'obvious' error can be found, so these observations have been removed from the pool.
• For the three Mark locations (I, II, III) in Thom (1958), no coordinates and elevations have been mentioned. The distances from the Theodolite are know (Thom, 1958, 253). Was able to get an approximate location for Mark I and III using HeyWhatsThat, but not for Mark II.
  
• The location of the Theodolite has also been determine by using a Simplex optimisation for the azimuth measurements mentioned in MS/340/27. This Theodolite location is some 40m from the location provided by Thom (1958, page 249). Thom's Theodolite location has been used as the reference.
  
• The Terrestrial refraction coefficient has been determined for the targets evaluated in Thom (1958). The below graph shows these Terrestrial refraction coefficient (including their variations):
  
  Even though it looks remarkable constant, one could see ML and AC to be somewhat out-layers, but all is still not that far off when taking into account the variation.
  
• If the observations are analysed using the formula TerrRefracCoeff=A+B*Temperature Gradient+C*Beaufort.
  The is formula (1) in [Thom, 1985], furthermore the Temperature Gradient is [for now] assumed to be based on 20 DeltaGZ units = 1°F. When optimising this formula for some 120 observations, we get:
  A=10.8
  B=20 (if Temperature Gradient is in F/ft) or 0.11 (if Temperature Gradient is in K/100m)
  C=-0.25
  The B value is somewhat mapping Thom's B values (1958, Table II). Below is the mapping of the formula-results (orange) on the actual observations (blue):
  
  The inclusion of Beaufort does not contribute significantly to the match. Beaufort is also not an independent variable compared to Temperature Gradient (as can be deducted from the definition of NRI Stability Class).
  
• In the above formula it was assumed that the DeltaGZ (difference of Thom's G and Z) represents 20units/°F. The 20units/°F was derived by looking what the highest and lowest DeltaGZ were and optimally mapping them on the highest (+0.18°F/feet) and lowest (-0.12°F/feet) Temperature Gradient mentioned by Thom (Thom, 1958, page 250). Is it a coincidence that this optimally mapping becomes such a nice number '20'?
  In below graph the orange line uses for DeltaGZ this 20units/°F (or 11.1units/K).
  The blue squares represent the atmospheric conditions (Sun's altitude/insolation, day/night, cloud cover, cloud height and wind speed) mapped on Temperature Gradient determined by using NRI Stability Class:
  
  
  
• If we assume that the Temperature gradient is close to the above, the distribution of temperate gradients over the day (with sunrise is -1 and sunset is 1) can be seen for April/Aug/Sept (equinox) time (orange) and Dec (winter solstice) time (blue) in below figure for The Hill. This should map on Fig 7 in Thom (1958, page 262).
  
  
• The variability of the temperature gradient mentioned in several sources, can be seen in this link.
• Thom's evaluation (1958) is mainly around targets with a positive apparent altitude. The two lighthouses, that have negative apparent altitudes, are excluded from the main evaluation, because according to Thom these targets are "in a class by themselves" as "that the rays to the lighthouses ran low over the sea for many miles".
  And even the lighthouses (PI and HI) have relative high elevation (some 40 meter above sea level). All other targets were hill tops well above sea level (at least 340m). Ailsa Craig (AC) is a 340m high mountain in the sea (apparent altitude of around -0.065deg) which is included in most of Thom's evaluation.
  
• Anyway: Thom did not observe objects at apparent altitudes due to vast level surfaces (where the light path would pass at low heights from the ground). It is expected that observations touching a vast level surface would have a larger variation due to larger temperature gradient near ground level.
  
• The average Terrestrial refraction Coefficient is 10.5 (derived from observations in above picture), which maps on sun rise/set when using Thom's terrestrial refraction formula.
  

Conclusion

References

ASTM Committee E-20 on Temperature Measurement. Subcommittee E20.04 on Thermocouples. 1981. Manual on the use of thermocouples in temperature measurement (ASTM).
Reijs, Victor M.M., 2017a, "Geniet: Thom's terrestrial refraction observations", http://www.archaeocosmology.org/eng/Thom-refraction.htm
Reijs, Victor M.M., 2017b, "Geniet: Temperature gradients at Skerries", http://www.archaeocosmology.org/eng/TempGradientSkerries.htm
Thom, Alexander. 1954. "Notebook.", MS/430/27, Edinburgh: Historic Environment Scotland.
Thom, Alexander. 1956. "Notebook.", MS/430/64, Edinburgh: Historic Environment Scotland.
Thom, Alexander. 1958. 'An empirical investigation of atmospheric refraction', Empire Survey Review, Vol 14: pp. 248-62.
Thom, Alexander. 1971. Megalithic lunar observatories (Oxford University Press).

Acknowledgements

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