This page last modified 2003 January 23

*Uriel's Machine* — a
Commentary on some of the Astronomical Assertions

* Uriel's Machine* by Christopher Knight and Robert Lomas

Arrow Books, London, 1999

ISBN 0-09-928182-1

This commentary will concentrate on the astronomical assertions used. I am not competent to comment upon the archaeological or the geological assertions.

At the end of the Prologue (p. xx), the authors state:

"...ancient
sites from northern Scotland to Brittany all exhibited the use of a standard
unit of measurement that was accurate to a fraction of a millimetre. (...) we
show beyond all reasonable doubt that this prehistoric unit was derived from
observational astronomy."

They claim that the "machine"
that they built using "instructions recorded thousands of years ago"
gives this curiously precise value.

Knight and Lomas claim that the pendulum that they produced had a length of 16.32" (41.45cm), i.e. precisely half a megalithic yard. This was truly exciting, and a quick mental calculation suggested that the value they published was realistic. However, having been caught out previously when I accepted something without checking, I decided to check. (Note: The authors have objected to my calculation. See here.)

The period of a pendulum, T, is given by: T = 2π(l/g)^{0.5}
where:

l = length of pendulum

g = acceleration due to gravity.

Knight and Lomas use a "pulse", which I shall abbreviate as "P",
of T/2, so we then have:

P =
π(l/g)^{0.5} or: l = g(P/π)^{2}

T is derived from the (sidereal) revolution of Earth, from the authors'
notion of a "megalithic degree", and the "instructions" from
the distant past.

There are 86164 seconds in a sidereal day.[1]

This is divided by 366 to give the number of seconds in a megalithic degree,
i.e. 235.42 secs.[2]

From the authors' interpretation of
the "instructions", the pendulum should give 366 "pulses"
per "megalithic degree", i.e. have a pulse of 0.643 sec.

The acceleration due to gravity in the British Isles varies from 9.8116 ms^{-2}
at latitude 51° (southern England) to 9.8183 ms^{-2}
at 59° (Orkney). (Values derived from
IGF)

Hence the length that will give this Orkney is:

l = 9.8183 (0.643/π)^{2}
m

= 0.4113 m

= 41.13 cm (= 16.19")

This decreases to 0.4110 m in southern England; i.e. the variation in
the MY over the British Isles (excluding Shetland) would, according to Uriel's
machine, be of the order of 0.3mm — to all intents and purposes, this can
be taken as being constant. At the latitude of the Algarve (38°) the length
is 0.4105m, i.e. less than 1mm different from the Orkney value.

This is close, but not equal, to the value that Knight and Lomas claim to
have attained, which is the precise value of Thom's "half megalithic yard",
i.e. 41.45 cm or 16.32". To produce this length, g would need to be 9.8946
ms^{-2}, i.e. greater than it is at Earth's poles
(9.832 ms^{-2})

Gravitational cognoscenti will have noted that I have not taken the affect
of altitude into account. At a mean value of 0.3086 mGal m^{-1}
this will not affect the calculations above at their 0.1mm precision.

If, as they assert, the precise value of the megalithic yard ("accurate
to a fraction of a millimetre") was attained through physical means,
Uriel's Machine does not do it. The frequent replication of the megalithic yard
would, if it is as precise as is asserted ("*a precise megalithic yard*"),
give it a mean value slightly (but measurably — i.e. 3.5mm or 0.14")
smaller than the value that is cited for it by Thom and by Knight and Lomas. I
can only assume that the authors inadvertently measured their pendulum or its
period inaccurately.

Also, I find it curious that the authors did not present a calculation in the book to confirm their supposition. The high school physics required should be well within the capability of Lomas, who is said (front matter of book) to have a first class honours degree in electrical engineering.

**The astronomy presented in the book certainly leaves a lot to be
desired. Some examples:**

- The authors seem unable to agree on the dates of the solstices and equinoxes, as differing ones are given [3], and they seem unaware that the calendar date of any given solstice or equinox can change by up to a day (depending upon where in the 4-yr leap-year cycle we are).
- The authors falsely assert (p299) that, in a leap year, the half-years from equinox to equinox are equal in length. The "summer half" is, in fact, approximately 6 days longer than the "winter half", owing to the ellipticity of Earth's orbit and the perihelion being less than a fortnight from the northern hemisphere winter solstice. Even using the most "favourable" (i.e. to their assertion) erroneous equinox dates given by the authors, the "halves" cannot be made equal.
- The authors assert that "
*[Venus] appears to move in the form of a five-pointed star*" (p108). I would be delighted to find out how they observed this "appearance"! This is a common misrepresentation of a phenomenon whereby the positions of five successive similar synodic events of Venus will plot the positions of the angles of an approximate regular pentagram on the celestial sphere. [4] - The authors also claim that "
*the appearances of Venus against the backdrop of fixed stars was used by astronomers to correct the civil calendar until the development of the atomic clocks...*" (p110). I find it curious that not only do they not cite a source or evidence for this claim, but also that no mention of it appears in the any standard work on time measurement or calendars. I suspect that they are somewhat confused with the use of the motion of the Moon to establish Ephemeris Time until the introduction of Dynamical Time in 1984. - The authors claim "
*Venus can be guaranteed to occupy*[my emphasis]**exactly***the same zodiac position as it does today, in 14,607 days time*" (p110). The position is close but not, as the author's assert,**exact**. (The term*zodiac position*is not used in astronomy, so it is not clear exactly which co-ordinate system the authors wish us to use, but their assertion is false for both equatorial and ecliptic co-ordinate systems.) - The authors assert "
[my emphasis]**Wherever***an observer is located, on the equinoxes (...) the rising sun*[my emphasis]**appears exactly***due east and the setting sun due west, causing the morning and evening shadows to align in a straight line*" (p178). The "wherever" condition is obviously incorrect — the azimuth of sunrise and sunset is partially determined by horizon topography. However, even given the case of a flat horizon level with the observer, the assertion is false. At a latitude of 51°N (a latitude the authors cite on the same page as being "*special*" ), for example, even if the Sun appears to rise at the exact moment of equinox, on a flat level horizon it will appear to rise and set just over 1.5° north of east and west respectively. At the nearest sunrise or sunset to the moment of equinox, the rise or set can**never**be**exactly**on the cardinal points at the latitude of the British Isles. The final clause of the assertion concerning shadow alignment is therefore entirely false. This is a consequence of atmospheric refraction, which causes the Sun to**appear**to rise before it does so geometrically; i.e. the bending of light from the Sun causes it to**appear**whilst , geometrically, it is still below the horizon. - The authors seem to believe that small astronomical telescopes are used "
*to magnify the images of stars*" (p255). This is false. Stars are essentially point objects and, as a consequence of the wave nature of light, increasing an aperture causes the**image**of a star to appear smaller [5]. Whilst it is a common misconception amongst lay-people, it is a surprising one for someone with a "*keen interest in observational astronomy*" (as one of the authors describes himself) to make.

In summary, I believe that the astronomical basis of this book is sufficiently flawed as to render any conclusions that the authors draw from it to be highly suspect.

### Endnotes

1. Tidal drag has, over five millennia, the effect on the sidereal day is a mere 0.1s, so its effect is insufficient to reconcile the "Uriel's Machine" value with Thom's value for the MY.

2. For some curious reason, the authors arrive at "just over 236", thus giving a sidereal day of "just over" 86376 seconds; perhaps they are using the solar day, 86400 s, which gives 236.07 s per megalithic degree. However, they specifically refer to using a pendulum in relation to a star (p 302), so it is the sidereal, not solar, day that is relevant.

3.E.g. dates given for the northern hemisphere Autumnal equinox include the incorrect date of 21 Sep (pp.163, 178). The only possible dates are 22 Sep and 23 Sep.

4. Five synodic revolutions of Venus take place in 8 years (to within a day). If Venus is represented by a pentagram, it most likely refers to the positions of successive similar positions of the planet's synodic revolution in relation to the stars. E.g. eastern elongations occur at intervals of approximately 19 months (actually 584 days), hence the intervals between 6 of them will take approximately 8 years, with the 6th occurring very near the position of the first. The positions of the intervening 4 eastern elongations, taken with the 1st/6th will plot an approximate pentagram on the celestial sphere. The pentagram describes the positions of the events, it does not, as Lomas and Knight assert, show how the planet "appears to move" — the apparent motion of Venus is far more complicated.

5. This is true for telescopes whose aperture is less than that necessary to resolve a star into a disc. The smallest aperture that has yet done this is 2.4m (94 inches) — the Hubble Space Telescope has resolved the disc of Betelgeuse, a nearby red-giant star. For Earth-based telescopes to do this, they need a greater aperture and adaptive optics to overcome the degrading effects of Earth's atmosphere.

**Update:2002 Jul 22**

MrKnight has emailed me and asserted that the calculation
that I had presented here (and which arrived at a smaller value for the pendulum
length) was "inaccurate" and that the mathematics was "spurious".
He did not specify why in either case, but he did, fairly, take issue with the
value for **g** that I had used (although deriving **g** from the
International
Gravity Formula does not alter the value for the length that I obtained at
the precision of 1mm). In the interests of fairness to Knight and Lomas I have
agreed to
**temporarily** withdraw my calculation whilst I await receipt of the "far
more sophisticated" calculations that Mr Knight implies will support the
claims made in the book and which he states he will send "shortly".

**Update:2003 January 23 **

It is now six months later, and Mr Knight has not yet sent me Dr Lomas's "far
more sophisticated" calculations that I was to to be sent "shortly".
I am therefore reinstating a calculation. In an email to Mr Knight on 2002 July
22, I wrote with respect to Dr Lomas's calculations:*If you would like
to send them to me, I shall be happy to check
them and if, as you imply, they produce "a precise megalithic yard" I
will be more than happy to retract and apologise*.

With respect
to Mr Knight's general objections I stated:

*If you are unable to provide me with the information for which
I have asked, I shall reinstate my calculation ... and will briefly note your
objections to it. In this eventuality I will, if you so wish, include a
hyperlink to a URL where you state your objections yourself.*

This offer still stands.