Paradoxes Resolved, Origins Illuminated
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T O P I C    R E V I E W
Samizdat Posted - 05 Dec 2005 : 16:29:49
Has any of you read, or have you preliminary thoughts on the new book by Michael Strauss, "Requiem for Relativity: the Collapse of Special Relativity?"
20   L A T E S T    R E P L I E S    (Newest First)
Larry Burford Posted - 10 Feb 2014 : 16:25:34
[Jim] "Its hard to isolate climate change from politics these days. What causes climate to change ..."

By this I presume you mean 'the ACTUAL causes (plural)' of climate change.

[Jim] "... is not even a concern."

as opposed to the various scapegoats and straw men at which politicians like to point.


It is truly unfortunate that the average voter is so poorly informed. (Otherwise, they would stop voting. 30% to 40% already understand this. But it is not enough.) Have I mentioned that we are doomed? I think I have.

Jim Posted - 10 Feb 2014 : 14:39:08
Its hard to isolate climate change from politics these days. What causes climate to change is not even a concern. In any event,the topic here is really far removed from either/or; is too, is not, of climate change.
Larry Burford Posted - 10 Feb 2014 : 08:26:44
[Jim] "Climate change is ... not relative to anything at this site."

We talk about a lot of things here that seem, at first glance, to be off topic.

This is primarily an astronomy site, but over the years I've come to realize that most other areas of scientific exploration are tied to astronomy in some way or another. Earth's climate for example, and the way it changes, is influenced by things that happen elsewhere in our planetary system. Changes in the output of our star are the most obvious, but a tiny asteroid or comet hitting us could also do the trick.

If we do begin a discussion of things related to climate and climate change I'd like to focus on the science rather than the politics. Political things (should we use force to "fix" it) can't be avoided, so I'm not suggesting a ban. I'm just saying we should focus on the scientific and the engineering things (what is actually happening, what can/might happen, can we "fix" it if it did/does happen, and how exactly would that be done).

[Jim] "... an important topic ..."


Any comments?
Jim Posted - 09 Feb 2014 : 21:34:45
Climate change is an important topic not relative to anything at this site. It might be better to do what you did with political matters and get it out of this forum that DR Joe has owned for years.
Larry Burford Posted - 09 Feb 2014 : 19:54:12
[Joe Keller] "... an epoch of climate extremes, with unusually many extremes of high and low temp, wet and dry."

Climate Change.

The (New/Next) Ice Age.

The (New/Next) Global Warming.


Democratic/Liberal pundits say "it" is a done deal, already too late to fix (but even if it isn't (a done deal), we ought to fix it anyway).

Republican/Conservative pundits say it isn't happening (and even if it is, it isn't being caused by human actions.)

    Have you ever noticed that when political factions argue with each other, they never use the same "buzz words" (never talk about the same things)? How else can they keep their idiotic followers hooting?

Roughly a quarter of the population sends regular checks to the politicians on the conservative side of this (or any) """""debate""""".

At the same time, roughly a quarter of the population (NOT the same quarter, I hope you see that) sends regular checks to the politicians on the liberal side of this (or any) """""debate""""".

The rest of us pretty much ignore the *ssh*l*s in the aforementioned groups. The problem with this tactic is that while you can ignore them, they (the libs and the cons) are NOT ignoring you. Your paycheck (if you are an employee) or your profits (if you are an employer) or your benefits (if you are a recipient) are clearly visible on their radar.

And since they are the government they have access to your money.


So, IMO climate change exists whether or not it is caused by/exacerbated by human action.

Climate change has always existed. We can clearly see it in the geological record. Why should now be any different?

Oh yeah - the contribution of human activity. (Only *NOW* has this become important.) IMO, it is not credible to claim that human activity has had NO IMPACT on climate change. But just as obviously it is not credible to claim that it is the only reason we have climate change right now.

We have been using energy at an exponentially increasing rate for thousands of years. Sooner or later this is going to tip a balance somewhere.


Is this a Bad Thing?

Or is it a Good Thing?

Or is it just a thing?

Your opinion is solicited.


Man-made or natural or some combination of the two, if our climate deviates too far off the norm we are SERIOUSLY screwed. As in the proverbial 'extinction level event'.


Should we start a new forum to talk about this? It seems a bit off topic here.
Joe Keller Posted - 09 Feb 2014 : 18:00:04
Hi all!

I'm still here and I'm OK, despite the six month silence. I've been busy planning, buying (in Oct. 2013) and caring for two Gotland ponies. Also my Samoyed dam had seven live puppies in Dec. 2013. This and other agricultural enterprises have been keeping me too busy to think about astronomy much.

I recommend the recent three-part series in Sky & Telescope, about the structure of our Milky Way. It's excellent!

A few days ago I heard the former Governor of Iowa, Governor Vilsack, now U. S. Secretary of Agriculture, being interviewed on National Public Radio. He said that while he didn't like the term "global warming" (a way of saying that he didn't believe in global warming) he was sure that we were in an epoch of climate extremes, with unusually many extremes of high and low temp, wet and dry.
Joe Keller Posted - 02 Aug 2013 : 16:20:58
Dear Pierre Fuerxer, Thomas Goodey, James DeMeo,

Yes, it is easier for me to mail you the 3.5" standard floppy disk, than it is for me to "cut and paste" the program into an email. The reason is, that I cannot find any way to "cut and paste" more than a few lines each time, so I must do more than a thousand "mouse clicks". The data are column sums, because this results in a twenty-fold saving of transcription labor for me, as opposed to entering the row of data for every turn of the interferometer.

The program has my own analysis (with corrections of my previous errors) which some people might find useful. But also, the program contains the data for all of Miller's steel interferometer experiments in Cleveland. (Before, I only had the data from 1922-1924, but now it is all of the Cleveland steel interferometer data, 1905-1929.) There were 140 data sheets also known as "sets" or "experiments"; each data sheet resulted in a DATA line with 16 data for the interferometer readings at the 16 azimuths (column sums of the 20, more or less, turns per set) and on a DATA line above that, another 8 data giving the midpoint time of the set (5 data for date and time), number of turns in the set, Goodey-Keller page reference (the standard pagination of the definitive, i.e. the Case Archives / DeMeo, version of Miller's notebooks, which some Iowa State college students made under Goodey's supervision when Thomas visited me in Ames in Feb. 2004) and number of fringes in view (important for evaluating the Hicks effect). Also, the program contains "REM" (i.e. reminder) statements explaining the many interpretations and emendations I had to make: correction of addition errors in the columns, adjustment for varying numbers of mirrors or varying labeling of North, omission of control experiments using heaters, determination of the most correct time, etc.

In sum, the program is not only the data; it is annotated with the important emendations and explanations I gleaned from what Miller wrote on these pages, and also there is my own analysis program.

As the program exists now, my detrending procedure still is erroneous. I believe I now understand how to detrend correctly, but my preliminary estimate of the effect of detrending, is that it will affect the result by less than one degree. I ran the program without detrending (coarse search grid only, on my slow "Intel 486" home computer) and found that on a 10x10 degree grid, my erroneous detrending made no difference in the grand result, vs. no detrending. So, my latest grand result, below, for the Cleveland drift vector, which I also have posted on the messageboard of, should not differ significantly, that is to say should not differ more than 10 degrees, from the properly detrended result. It is possible that some of the subgroups, say "1922" for example, might be significantly affected by correct detrending.

Latest version, posted yesterday to

The best fitting (least sum of squared differences of observed and predicted second harmonic coefficients for each set) drift directions (RA, Decl) with correlation coefficient of observed & expected, sigma, apparent drift speed, no. of sets, no. of turns, and mean Julian Date weighted by no. of turns:

1905* (one July set, four Oct-Nov sets)
RA,Decl = 210, 25

Apr 1922

Aug-Sep 1923

Jun-Jul 1924

Apr 1927
(There was a (-) correlation that was larger, -0.34.)

Aug 1927

Sep-Oct 1929

Grand result for all data, 1905-1929, for the steel interferometer at Cleveland:
RA, Decl = 196,82
corr coeff = +0.2392, sigma = +4.060, apparent drift speed = 9.945km/s
140 sets, 2602 turns, mean Julian Date 2423979.047 weighted by turns

* For the data subsets, I made only a coarse search on a 5x5deg northern hemisphere (including equator) grid with rough sec(Decl) correction in RA steps. For the grand data set, this was followed by strict 1x1deg search on the largest grid square centered on the best coarse point and not overlapping other coarse points.

I had reason to doubt the sign of the 1905 data (ambiguous notation in Miller's notes, giving me two possible interpretations) so I chose the interpretation for 1905 giving the largest positive correlation. As noted above, I could have obtained a larger positive correlation by reversing the sign of the Apr 1927 data but lacking any other reason, did not do so. Likewise although a convenient way to explain the three times greater apparent drift speed in 1922 would be to assume that Miller was recording hundredths, not tenths, of a fringe that year, I did not make this emendation either, because I find no evidence for it on that year's data sheets.

The coarse search on the grand data set found sigma = +4.032 for RA,Decl = 210,80. So, the significance, p, was almost as great, for a direction three great-circle degrees away from the best. This suggests, by extrapolation of sigma and integration weighted by 1/p, an error bar of at least 10 degrees, even for the grand result.

The Hicks first harmonic correlation was much larger, when I assumed that the Hicks effect should be 90deg out of phase with the drift azimuth, as I believe Hicks did also. If the Hicks effect leads by 90deg, then the largest correlation coefficient is +0.15, sigma = +2.55, at RA,Decl = 339,71; this is 26 deg from the best second harmonic indicated direction given above.

- Joe Keller
Joe Keller Posted - 28 Jul 2013 : 16:27:21
Regarding the difference between my analysis of Miller's Cleveland data and Miller's own analysis of his Mt. Wilson data

Both Miller and I use a bandpass filter on each set of turns: that is, we reduce each set to second harmonic coefficients, i. e. an azimuth and amplitude for the second harmonic approximant. But Miller uses another filter which I haven't: for the unevenly distributed data over one turn of the Earth (at a given epoch spanning a few days) Miller not only replaces the azimuth & amplitude data with first harmonic approximants (i.e. period one day); he also subtracts the mean from the azimuth. However, I tried this by subtracting the unweighted mean coefficient of sin(2*theta), and found about the same best-fitting drift direction, RA,Decl = 194,84, hardly any different from what I found without this reduction to mean zero.
Joe Keller Posted - 22 Jul 2013 : 14:17:57
Several errors to correct: the program as posted switches RA & Decl in the printout; that is, the order of these two numbers is switched compared to what the printout says they are. Also, yesterday's post says 1905 were included but really they weren't. I had changed them to REM statements and forgot to unchange them. More serious, though trivial errors: I discovered July 23, was that I forgot to convert degrees to radians in my precession adjustment subroutine. I discovered July 31, that I had entered grossly wrong ordinates for my reference second harmonic sine wave, and also that my detrending procedure was slightly erroneous. So, here are my corrected results as of July 31:

The best fitting (least sum of squared differences of observed and predicted second harmonic coefficients for each set) drift directions (RA, Decl) with correlation coefficient of observed & expected, sigma, apparent drift speed, no. of sets, no. of turns, and mean Julian Date weighted by no. of turns:

1905* (one July set, four Oct-Nov sets)
210, 25

Apr 1922

Aug-Sep 1923

Jun-Jul 1924

Apr 1927
(There was a (-) correlation that was larger, -0.34.)

Aug 1927

Sep-Oct 1929

All data, 1905-1929 for the steel interferometer at Cleveland:

* For the data subsets, I made only a coarse search on a 5x5deg northern hemisphere (including equator) grid with rough sec(Decl) correction in RA steps. For the whole data set, this was followed by strict 1x1deg search on the largest grid square centered on the best coarse point and not overlapping other coarse points.

I had reason to doubt the sign of the 1905 data (ambiguous notation in Miller's notes, giving me two possible interpretations) so I chose the interpretation for 1905 giving the largest positive correlation. As noted above, I could have obtained a larger positive correlation by reversing the sign of the Apr 1927 data but lacking any other reason, did not do so. Likewise although a convenient way to explain the three times greater apparent drift speed in 1922 would be to assume that Miller was recording hundredths, not tenths, of a fringe that year, I did not make this emendation either.

The coarse search on the whole data set found sigma = +4.032 for RA,Decl = 210,80. So, the significance, p, was almost as great, for a direction three degrees away from the best, suggesting by extrapolation of sigma and integration weighted by 1/p, an error bar of ~15deg.

The Hicks first harmonic correlation was much larger when I assumed that the Hicks effect should be 90deg out of phase with the drift azimuth. If the Hicks effect leads by 90deg, then the largest correlation coefficient is +0.15, sigma = +2.55, at RA,Decl = 339,71; this is 26 deg from the best second harmonic indicated direction.
Joe Keller Posted - 20 Jul 2013 : 16:29:05
Progress on Dayton Miller Cleveland Data

I've now inputted all of Dayton Miller's Cleveland data from the steel interferometer. These span the years 1905, 1922-1924, and 1927-1929. Searching the entire celestial sphere, the largest correlation coefficient between observed and expected second harmonic coefficients for the fringe shift, now is +0.39919, which is found for a drift parallel or antiparallel to the direction RA 208, Decl +71. Sigma for this correlation coefficient is approximately 6.9068 for one-tailed p = 2.5/10^12.

The negative correlation coefficient largest in magnitude occurs for a drift parallel or antiparallel to RA 49, Decl 18 (separated from the other axis by 90 deg). This correlation coefficient is -0.30903 for sigma = -5.2038, one-tailed p = 9/10^8: almost 40,000 times larger than p for the largest positive correlation. So it is the negative correlation which is the mathematical byproduct (the normal to the interferometer is limited to a cone and cannot range over the entire celestial sphere) and Miller's Mt. Wilson ether drift direction is confirmed by my analysis of Miller's Cleveland steel interferometer data.

These searches always are on a 5x5 deg coarse grid (with appropriately larger RA steps near the celestial poles) and then a 1x1 deg fine grid centered on the best coarse grid point and just small enough not to overlap the other coarse points. The number of experiments (sets of turns) is 135 (usually of 20 turns each, so the data set is almost half the size of the Mt. Wilson data set). The number of items correlated is 135*2 = 270, because there are sine and cosine harmonic terms.

All the 1927-1929 sets and some of the others, tell the number of fringes in view. So a phase and amplitude are likewise discoverable for the Hicks full-period effect. I haven't had time to program that yet, but the phase-only analysis somewhat confirms the above.
Joe Keller Posted - 18 Jul 2013 : 15:27:06
Dear Pierre, James, Thomas,

The Hicks first order effect has, of course, an amplitude and a phase. The amplitude isn't directly known for Cleveland 1922-1924 (or for Mt. Wilson) because the amplitude of the Hicks effect is proportional to the number of fringes in view (that is, the expected Hicks effect is found in units of length; Miller recorded in units of fringes, so unless fringes can be converted to length, the observed amplitude of the Hicks first order effect isn't known).

Miller did record the number of fringes (e.g. typically "6" or "10", small integers, but good enough for quantitative results) for the 1927-1929 Cleveland data. So the Hicks first order effect can be assessed for Cleveland 1927-1929 and used to corroborate the Maxwell second order effect.

I've already used the Hicks first order effect to corroborate my previous results, by considering only the observed and predicted phase of the effect, not its amplitude, for Cleveland 1922-1924 (excluding the heat lamp, etc., experiments which Miller knew would have to be discarded) plus Cleveland Apr 1927 (altogether the 84 sets I referred to previously, n=84 because only one datum, phase, arises per set). I found that the largest Hicks effect is for a drift line in space toward roughly RA 200, Decl +20 (or the opposite of this), i.e. about 30 degrees different from the second order effect (the one with large negative correlation coefficient, in line with Libra) and is significant (sum of cosines of angles between observed and expected phase) at sigma = 2.7.

Years ago I looked at the lengthy calculations in Hicks' paper, and wasn't able to digest it in the time then available. Miller says in his notes that Lorentz didn't understand the Hicks effect either, when Lorentz visited Miller and they talked about it, so I'm in good company. My best guess is that it is basically a matter of the photons hitting downstream or upstream when the telescope arm is crossways of the drift, that is, the whole shebang, fringes and all, is moved by the drift in a first order way (first order in theta, but second order in v/c) that has nothing to do with interference.

I gather that if phi is the drift azimuth and theta is the telescope azimuth, then the Hicks effect is proportional to sin(phi - theta). I find that this constant of proportionality is negative if the drift is toward Libra, and of course necessarily positive if the drift is in the opposite direction.

- Joe Keller
Joe Keller Posted - 15 Jul 2013 : 18:49:18
(continued) Here are emails three through five.

July 15, 2013:

Hi Pierre,

Each long data line has 16 entries; these are the fringe shifts (in tenths of a wavelength) recorded by Miller. Above each of these lines, is a short line giving the time of the observation. The first number is the year, the second is the month, the third is the day, the fourth is the hour Eastern Standard Time (add 5 hour to get Greenwich Mean Time) and the fifth is the minute. I think these times, for these data, refer to the beginning of the experiment, but since each turn required only about one minute, it would be good enough, to add one half as many minutes as turns (the sixth number is the number of turns of the interferometer). An error of ten minutes would be only about five arcminutes in the Lunar position. Knowing the time, you could of course then find the Lunar positions from the JPL online ephemeris, or from old almanacs.

- Joe Keller

July 15, 2013:

Hi James,

In 2004 I decided to work on Miller's Cleveland data because Miller himself had analyzed the Mt. Wilson data (Miller also made some analysis of the Cleveland data but it seems, from the notebooks, to have been very approximate, usually merely graphical, and incomplete). The Cleveland data are much shorter. If I analyzed them, then between Miller and myself, all of them would be analyzed and Cleveland could be compared to Mt. Wilson, showing that the ether drift is, at least approximately and on the average, independent of time on a scale of a few years, and independent of geographic location. Analyzing Mt. Wilson not only would have required much more data typing by me, but would have been basically a repeat of what Miller already had done by the old-fashioned but valid data processing methods of the 1920s. On the other hand, if I analyzed Cleveland and got the same result Miller did for Mt. Wilson, the statistical significance of the result would be the immediate implication. Shankland's laughable contention that the result had something to do with one corner of the room being warmer, or something to do with anything about the labs, which were totally different in Cleveland and Mt. Wilson, would be shown yet again for the absurdity that it is.

The data sheets are just tricky enough that it is impossible to have someone who does not understand the experiments, to be entering the data. Especially in these early 1922-1924 data, there are variations in format, for example which row is the non-detrended summed columns, and which are sums of + or sums of - or Miller's approximate detrended sums? There were a possibly significant number of column summation errors. One page even was missing one of its 16 columns. Many pages were inapplicable because they were Miller's side experiments designed to find out just how much an uneven heating of the room, or various schemes for shielding the interferometer, would affect the result. Some pages were cut off and I had to deduce the time and date by comparing with consecutive pages. A robot can't do it. Someone knowledgeable had to scrutinize it page by page and make every data entry judiciously. It had to be "custom made" work, not "mass production" work.

This might actually be my finished results. I've somewhat augmented the data now, by adding in the April 1927 Cleveland experiments, but adding them into the data pool didn't change the outcome much.

Over the years, I've wasted so much time submitting things to the mainstream journals only to be told by the editor or even by some anonymous office boy, that he wasn't even going to send it for peer review. So they're not really peer reviewed journals, because a few "peers" might get to see what is published, but the "peers" don't even get to see what the editor dictatorially rejects. So, since to my knowledge there are no hardcopy alternative journals to which any university library subscribes, electronic publication on alternative websites, whether or not they call themselves journals, is all there is going to be.

If you would like to publish any or all of these emails on your Orgone Research website, please be my guest! That may well be the only publication that there is, besides my posting them to the messageboard of (website of the late Dr. Van Flandern) which is the de facto journal in which I publish all my work.

- Joe Keller

July 15, 2013:

Dear Thomas, Pierre, James,

In 2004 I didn't realize that detrending was important and it was Thomas Goodey then who insisted that it was, thereby averting disaster. The importance of detrending can be seen, for example by looking up in a table of integrals, the integral of x * sin(2*x) from -pi to pi and seeing that it is nonzero (because both factors are "odd" functions). So, thanks Thomas! Another way to recognize this truth is to recall that Fourier analysis applies only to periodic functions, not linear ones.

I augmented my data by including the April 1927 Cleveland data. This comprised an additional 20 sets for a total now of 64+20=84 sets, though the increment in turns was more, because these April 1927 sets almost always had 20 turns, whereas the 1922-1924 sets averaged less than 15 turns.

Again I searched the northern hemisphere of the celestial sphere on the coarse 5x5 degree grid (with appropriately larger right ascension increments at high declinations). This time I then refined the result by searching on a 1x1 degree box centered at the best coarse value and extending to the surrounding coarse grid points. The largest positive correlation coefficient was +0.27705 for Right Ascension 208, Declination +74 (or equivalently RA 28, Decl -74). Because longitude lines are so close together at high latitude, this is only a few degrees from the direction Miller found from the Mt. Wilson data. Making the usual normal approximation, and recalling that for the correlation coefficient, n = 2*84 = 168 now, because of independent sine and cosine terms, this is significant at sigma = 3.65. Also, it implies an apparent ether drift speed of 11.82 km/sec, not much different from the speeds Miller found at Mt. Wilson, or from what he found in Cleveland using more rudimentary analyses.

However, the largest correlation coefficient in absolute value, was a negative correlation, -0.36205 for RA 47, Decl 14 (or equivalently RA 227, Decl -14). This is significant at sigma = -4.87 ( p = 5 * 10^(-7) one-tailed) which is hugely more significant than sigma = 3.65 ( p = 1.3 * 10^(-4) one-tailed) and more significant even than the largest absolute correlation found with the 1922-1924 data alone, -4.74 (on the original coarse grid, but with the augmented data I found -4.86 even on that same coarse grid). The implied apparent ether drift speed is 11.06 km/sec.

The location, RA 227, Decl -14, lies on the ecliptic near the center of the constellation Libra. In the 1990s, the Cornell Univ. astronomy group, in an article discussing what even mainstream astronomers have dubbed in journal titles to be "the other ether drift", i.e. the "Cosmic" Microwave Background dipole, published a graph showing that the redshifts of the seemingly most distant galaxies imply that relative to them we have on average almost the same speed and direction as our apparent Cosmic Microwave Background motion, which is toward a point south of Leo. The graph shows that if progressively nearer galaxies are studied, the Sun's apparent motion relative to these, smoothly changes until, for the nearest statistically meaningful subset of galaxies (the Virgo Cluster) this motion equals the well-known "Virgo Infall" [correction by JK July 16: the Sun's apparent motion equals the Virgo Infall plus the Sun's apparent galactic orbital motion; the Virgo Infall itself is a motion of the Milky Way toward Virgo at about 300 km/sec, superimposed on the uniform Hubble recession.]. It is plausible that the direction of Miller's ether drift, apparently toward Libra, is relative to the ether immediately at hand, while the Virgo Infall amounts to the direction relative to the ether of the nearest large galaxy cluster and the apparent motion implied by the CMB dipole gives the direction relative to the ether at infinity. From Libra to Virgo to Leo is a short, smooth curve.

It is suggestive, that the best positive-correlation direction, and best absolute-correlation direction, differ by 91 (or 89) degrees. One can confirm using elementary mathematics, that if the true motion is toward (using round numbers) RA 180, Decl 0, and the number of waves along the telescope arm aimed in this direction were to decrease rather than increase (i.e., negative correlation, opposite of the change assumed by Maxwell, Michelson, Miller) then there will as a byproduct be a positive (cos(theta))^2 correlation of the number of waves in the telescope arm, with the aiming of the telescope arm in the direction of the ecliptic pole. Specifically, let's consider latitude 41deg N (i.e. Cleveland) at sidereal times 0h, 6h, 12h, 18h, using 23deg as Earth's obliquity. By trigonometry (and a little spherical trigonometry) one sees that in units of (v/c)^2/2*(number of waves), the actual effect on the difference in number of waves between telescope arm and cross arm [with the telescope arm pointed north - JK] is

-0.4304, 1, -0.4304, 1

while the expected effect assuming the Maxwell theory and a drift toward the ecliptic pole, is

0.3300, 0.9045, 0.3300, 0.1922

and the correlation coefficient of these two series, is +0.5377. That is, if the experiments are evenly distributed in sidereal time, then the true, negative correlation coefficient should result in a byproduct positive correlation coefficient that is about 0.54 times as large, and somewhat reassuringly we find indeed that 0.277/0.362 = 0.765.

- Joe Keller
Joe Keller Posted - 15 Jul 2013 : 18:29:10
What follows is a sequence of five emails to fellow scientists, about my recent work analyzing Dayton Miller's ether drift data.

July 11, 2013:

Dear Thomas (Goodey)(cc: Pierre Fuerxer who also responded to my group email),

Great quote from Kipling about the unforgiving nature of machines; we see a lot of farm machinery injuries around here, not so much as in the past mainly because there is less child labor, but still a lot.

Also, I was able to download your map of the drift vectors and the possibly related astronomical vectors, no problem with either the attachment or the backup attachment. Well done map! Great to have such a clearly laid out map with the precise numerical data in an inset table. While it is eye catching that Miller's Mt. Wilson vector is so much closer to the normal to Luna's orbit normal vector than to anything else, still there was little correlation between the change in Miller's Mt. Wilson drift vector at his four epochs, and the change in Luna's orbit normal vector. And to be significant at the 1% level without any such correlation, Miller's drift vector would have to be 10x closer to Luna's orbit normal vector than to, say, the normal to the invariant plane. Of course many things are not statistically significant, yet are true.

I lost the data file part of my program (floppy disk and hard drive both went bad over the years) but I remembered enough to rewrite the whole program with convenient included DATA statements and explanatory REM statements, and just finished today. The program's mathematical analysis is much more competent than what I did in 2004. It includes Miller's Cleveland experiments (all with the steel interferometer) 1922-1924. I haven't had time to input the data from Miller's 1927-1929 Cleveland work or the small amount of somewhat difficult to redact work notes that he did with Morley with the steel interferometer in Cleveland in 1905. I hope to email the whole program to you and Pierre next time I get to the university and can get to a computer with a floppy drive & good email & document processing hookup.

One thing I am finding that I didn't quite wrap my brain around back in 2004 when I did this: it seems that the positive correlation of "longer telescope arm path" with a direction roughly toward the poles of the ecliptic, is merely a mathematical byproduct of a stronger correlation, a negative one. This negative correlation is roughly parallel to the CMB dipole, i.e. the alleged cosmic motion of the Sun. It is as if, yes, the wavetrain contracts so there are more waves per micron, but also the interferometer contracts more than the wavetrain. After all, the electron shell matter of the interferometer is essentially a wavetrain itself, though of shorter wavelength. However it is not Fitzgerald contraction in which the interferometer arm and the light wavetrain contract perfectly equally (i.e. "space contraction" relativistic baloney). It is a dispersion phenomenon in which the interferometer arm contracts slightly more, hence the correlation with the fringe shifts is negative, not positive as Maxwell, Michelson & Miller expected. I did write about this on the messageboard of (the website of the late Dr. Van Flandern) several years ago.

My results "hot off the presses" today (this email is my first announcement to anyone):

Best fitting constant space direction of ether drift:

RA 40, Decl +10 (from hemispheric search to nearest 5 degrees) (or equivalently RA 220, Decl -10)

correlation coefficient between observed and expected second harmonic coefficients is -0.4005 (yes, negative)
approximating sigma = -4.74 standard deviation units of significance

Among directions giving a positive correlation, the best is

RA 210, Decl +65

but the correlation coeff is merely +0.3435, sigma = +4.00

These data comprise 64 of what Miller called "experiments", each on one page of the notebook, typically comprising 10 to 20 turns of the interferometer (some 1923 experiments were excluded because they were Miller's test of a heat lamp effect which clearly swamped everything else). The correlation coefficient is for 64*2 = 128 items because of the cos(2*theta) and sin(2*theta) coefficients.

Sigma = 4.00 is highly significant but sigma = 4.74 is much more so.

Would you please forward this to Jim DeMeo? Without him we would be nowhere on this, but I misplaced his email address and this library is closing.

- Joe Keller

July 12, 2013:

To: Thomas Goodey, Pierre Fuerxer, James DeMeo

Dear sirs:

This is the BASIC program I spoke of yesterday. With the help of the student at the computer help center at Iowa State University (just down the hall from where Thomas and I worked together that long ago February night in 2004) I was able to cut and paste it about half a page at a time from the BASIC language command prompt window into an email to myself, then remove the myriad unwanted headers and word processing characters that had been inserted. It was almost as much work as retyping the program. I've checked it hastily but can't guarantee that there are no errors from this copying process. For that matter, I haven't had time to double check my data entry and can't guarantee that there are no errors there, either. Remarkably, in 2004 I found several column sum errors on Miller's notebook pages, almost all of them very small, marked those on my copies of the pages, rechecked those errors during these last few days and found that I had been correct in every case.

To reiterate and add to what was in my email yesterday, this program analyzes only what I analyzed in 2004, namely Miller's 1922-1924 steel interferometer experiments in Cleveland. I intend to augment the data to include the similar 1927-1929 experiments, which also were by Miller with the steel interferometer in Cleveland.

The program determined that if restricted to positive correlation coefficients (i.e. sign of fringe shift what was expected by Maxwell, Michelson & Miller) the best is

RA 210, Decl +65

and the correlation coeff is +0.3435, sigma = +4.00

but my best fitting constant space direction of ether drift is:

RA 40, Decl +10 (from hemispheric search to nearest 5 degrees) (or equivalently RA 220, Decl -10)

correlation coefficient between observed and expected second harmonic coefficients is -0.4005 (yes, negative)
approximating sigma = -4.74 standard deviation units of significance.

Sigma = 4.00 is highly significant but sigma = 4.74 is much more so.

So, the apparent ether drift in a direction approximating perpendicular to the ecliptic, seems to be merely a mathematical byproduct of the main effect, which is an ether drift roughly approximating parallel or antiparallel to the CMB dipole. This makes the ether drift much more credible.

Not only the negative sign, but also the small magnitude (I find about the same magnitudes Miller did) can be explained as a dispersion phenomenon: the speed of light at visible light frequency is higher than at frequencies comparable to the electron waves in the atoms of the steel arm. So, it amounts to an overcompensating FitzGerald contraction, not any distortion of space itself.

- Joe Keller

Subject: program pasted from commmand prompt
Date: Fri, 12 Jul 2013 15:47:44 -0500

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REM Program name "DMCLEV.BAS", by Joseph C. Keller, Roland Iowa May 2004
REM Redone by JC Keller June 30 - July 2013 because "text" data file lost.
REM The new program is much more capable than the old.
REM The program is written in BASIC, Microsoft "QBASIC" circa 1993 vintage
REM and runs on a 1993 vintage Intel 486 (pre-Pentium) IBM computer.
REM "There's never enough time to do it right, but there's always enough time
REM to do it over." - Jack Bergman writing in a book of humor
REM DATA lines are Dayton Miller's Cleveland data from 1922-1923:
REM in Goodey-Keller page numbering of Miller notebook
REM (obtained by James DeMeo from the Case Archives) pp. 0083-0135.
REM Goodey & Keller numbered the pages, working with the assistance
REM of hired students in the lobby of the
REM Iowa State Univ. Memorial Union, Feb. 2004 at Goodey's suggestion.
REM pp. 0083-0095 titled "Cleveland, Ohio April, 1922"
REM subtitled "5 sets, 71 turns"

REM & pp. 0095-0135 titled "Cleveland, Ohio Aug 23-Sep 4, 1923"
REM subtitled "39 sets, 477 turns" though I use only [18 sets, 263 turns]
REM & omit 21 of these 39 because they were tests of the
REM effect of heater(s) (or "three electric bulbs" on p=119) in the room.
REM In 1923 the 18 2nd harmonic displacements calculated by Miller for the
REM experiments without heaters were
REM 6,8,18,9,17,18,12,4,8,8,10,6,4,4,4,10,3,5
REM & the 21 with heaters were
REM 97,77,10,73,122,118,31,77,85,135,54,12,22,14,78,61,19,22,42,83,72
REM where the smaller heater effects were correlated with thermal shielding.
REM So the heater effect swamped all other effects and those experiments
REM must be omitted.

REM & pp. 0136-0179 titled "Cleveland, Ohio June 27-July 26, 1924"
REM subtitled "42 sets, 598 turns"; I use [41 seets, 587 turns] because
REM p=156 is missing a column

REM Miller's Index, p. 005, lists other epochs for which there were
REM steel interferometer data at Cleveland; I confirmed these as
REM present in the notebook, though it is mostly devoted to Mt. Wilson data
REM (not only the Mar-Apr 1925, Jul-Aug 1925, Sep 1925 & Feb 1926 epochs
REM discussed in Miller's Physical Review article, but also considerable
REM Apr 1921 & Sep 1924 epochs with the steel interferometer @ Mt. Wilson)
REM (1905 are Morley-Miller)
REM July 1905 (48 turns, p. 041)
REM Oct 1905 (127 turns, pp. 038-040)
REM Nov 1905 (55 turns, p. 042)
REM Apr 1927 (20, 400 turns)
REM Aug 1927 (41, 820 turns)
REM Sep-Oct 1929 (11 sets, 220 turns)(Cleveland 1927 & 1929 are pp. 977-1054)

REM Program finds best fit ether drift vector in space
REM A few pages are cut off, requiring a little guesswork about exact times;
REM I'll note this as arises.

REM setting constants

REM setting numerical constants
PRINT : PRINT : pi# = ATN(1) * 4: pi180# = pi# / 180
REM sum of squares of 1-9, 2-9,...,16-9
jv0# = 1496 - 2 * 9 * 136 + 16 * 9 ^ 2

REM setting astronomical constants
REM tropical yr 1960 from Newcomb linear formula cited by Clemence 1946
yr# = 365.242195#: yrinv# = 1 / yr#
REM Julian date of 0h Jan 1 1992
jd0# = 2448622.5#
REM JD of J2000.0 i.e. 12h Jan 1 2000
jd00# = 2451545

REM setting geographic constants
REM estimated geographic latitude & longitude of Miller's lab at Case
latcase# = 41.5056# * pi180#: longcase# = 81.6083# * pi180#
cscase# = COS(latcase#): sncase# = SIN(latcase#)
REM The location in Cleveland 1922-1924 was the "Physical Laboratory",
REM (presumably not the temporary building used by Morley & Miller in 1905 -
REM which was at 285 m alt in East Cleveland).
REM The "Physical Laboratory" would have been on the main campus therefore
REM about 41 deg 31' lat and 81 deg 33'30" long
REM In 1927 the interferometer was moved from Mt. Wilson to the Case campus
REM about 690 ft alt, 41 deg 30'20" lat and 81 deg 36'30" long
REM so these coordinates will be assumed for 1922-1924 & 1927-1929
REM at the risk of a 3' longitude error for 1922-1924.

REM physical and time constants
REM speed of light in km/s
clight# = 2.997925# * 10 ^ 5
REM number of lightwaves in usual interferometer path according to Miller
nwv# = 112 * 10 ^ 6
REM Greenwich sidereal time in radians
REM for 0h GMT Jan 1 1992 per 1992 World Almanac
REM given to nearest 0.1sec = 1.5"
stime0# = (1 * 15 + 6 / 4 + 39.6# / 240) * pi180#

REM dimensioning variables
DIM shift(200, 27) AS DOUBLE: DIM c(17) AS DOUBLE: DIM s(17) AS DOUBLE
DIM sh(200, 2) AS DOUBLE

REM read, standardize and Fourier analyze Miller's data
REM using Miller's column sums
GOSUB 9000
REM find correlation with Fourier components expected for each of a
REM grid of ether drift directions on the J2000 celestial sphere
GOSUB 7000
REM print results
GOSUB 5000


REM find cross product v1 cross v2 = v3
x3# = y1# * z2# - z1# * y2#
y3# = z1# * x2# - x1# * z2#
z3# = x1# * y2# - y1# * x2#

5000 PRINT "The constant ether drift directions giving the largest "
PRINT "correlation coefficients, in absolute value, between "
PRINT "the expected (Maxwell ether drift theory) and "
PRINT "observed (according to column sums of Miller Cleveland experiments) "
PRINT "second harmonic coefficients of the fringe shifts, are "
PRINT "in J2000 celestial coordinates:"
PRINT "RA, Declination, corr coeff, sigma"
PRINT : PRINT lat1; " "; lon1; " "; cc1#,
PRINT .5# * LOG((1 + cc1#) / (1 - cc1#)) * SQR(nn - 3)
PRINT : PRINT lat2; " "; lon2; " "; cc2#,
PRINT .5# * LOG((1 + cc2#) / (1 - cc2#)) * SQR(nn - 3)
PRINT : PRINT lat3; " "; lon3; " "; cc3#,
PRINT .5# * LOG((1 + cc3#) / (1 - cc3#)) * SQR(nn - 3)
PRINT "Estimated speeds 1,2,3 in ether, km/sec :"
PRINT speed1#, speed2#, speed3#
PRINT "Number of data pairs = number of experiments x 2, i.e. ";

REM search grid of ether drift directions on J2000 celestial sphere
7000 PRINT "Checking Declination ";
inc = 5: q = 0
sv# = 0: sy# = 0: cc1# = 0: cc2# = 0: cc3# = 0
lat1 = -1001: lat2 = -1002: lat3 = -1003: lon1 = 0: lon2 = 0: lon3 = 0
speed1# = 0: speed2# = 0: speed3# = 0
FOR lat = 0 TO 90 STEP 5
PRINT lat; " ";
IF lat = 60 THEN LET inc = 10
IF lat = 70 THEN LET inc = 15
IF lat = 80 THEN LET inc = 30
IF lat = 90 THEN LET inc = 360
decdrift0# = lat * pi180#
FOR lon = 0 TO 359 STEP inc
radrift0# = lon * pi180#: sw# = 0: su# = 0: sx# = 0
FOR I = 1 TO counter
IF q = 0 THEN GOSUB 7500
GOSUB 7600
x1# = shift(I, 22): y1# = shift(I, 23): z1# = shift(I, 24)
x3# = shift(I, 25): y3# = shift(I, 26): z3# = shift(I, 27)
h1# = xdrift# * x1# + ydrift# * y1# + zdrift# * z1#
h3# = xdrift# * x3# + ydrift# * y3# + zdrift# * z3#
REM expected column sum amplitude is
REM proportional to speed squared x no. of turns
magh# = (h1# ^ 2 + h3# ^ 2) * shift(I, 18)
REM ph# = arctan(h3# / h1#)
REM Use identity cos(2*(th-ph))=cos(2*th)*cos(2*ph)+sin(2*th)*sin(2*ph)
REM g1=cos(2*ph) & g3=sin(2*ph)

tn# = h3# / h1#: den# = 1 / (1 + tn# ^ 2)
g3# = 2 * tn# * den#: g1# = (1 - tn# ^ 2) * den#
REM Find quantities proportional to expected Fourier coeffs of fringe shifts
exps1# = magh# * g1#: exps3# = magh# * g3#
REM Find correlation coeff of these with actual fringe shifts
sx# = sx# + exps1# + exps3#
su# = su# + exps1# ^ 2 + exps3# ^ 2
IF q = 0 THEN GOSUB 7700
sw# = sw# + exps1# * sh(I, 0) + exps3# * sh(I, 1)
q = 1
coa# = nn * sw#: cob# = sx# * sy#
coc# = nn * su#: cod# = sx# ^ 2
coe# = nn * sv#: cof# = sy# ^ 2
corrcoeff# = (coa# - cob#) / SQR((coc# - cod#) * (coe# - cof#))
GOSUB 7800
NEXT lon: NEXT lat

REM subroutine to find vert. (unit normal to reference spheroid) at Cleveland
REM in celestial RA & Dec & xyz coords (v2 vector) of the equinox of date
REM & then north (v1) & east (v3) unit ground vectors
7500 jd# = shift(I, 17): t# = (jd# - jd0#) * (1 + yrinv#)
raclev# = t# * 2 * pi# + stime0# - longcase#
REM for those with times cut off and guessed,
REM will improve it by changing to Miller's written sidereal time
IF p = 90 THEN LET raclev# = (4 * 15 + 25 / 4) * pi180#
z2# = sncase#: x2# = COS(raclev#) * cscase#: y2# = SIN(raclev#) * cscase#
ra1# = raclev# + pi#: z1# = cscase#
x1# = COS(ra1#) * sncase#: y1# = SIN(ra1#) * sncase#
GOSUB 1000
shift(I, 22) = x1#: shift(I, 23) = y1#: shift(I, 24) = z1#
shift(I, 25) = x3#: shift(I, 26) = y3#: shift(I, 27) = z3#

REM subroutine to find trial ether drift vector in coords of equinox of date

REM per "rigorous" formula in 1990 Astronomical Almanac
7600 jd# = shift(I, 17): t# = (jd# - jd00#) / 36525
zetaa# = .64062# * t# + 8 / 10 ^ 5 * t# ^ 2
za# = zetaa# + 22 / 10 ^ 5# * t# ^ 2
tha# = .55675# * t# - 12 / 10 ^ 5 * t# ^ 2 - 1 / 10 ^ 5 * t# ^ 3
sn# = COS(radrift0# + zetaa#) * SIN(tha#) * COS(decdrift0#)
sn# = sn# + COS(tha#) * SIN(decdrift0#)
cs# = SQR(1 - sn# ^ 2): decdrift# = ATN(sn# / cs#)
sn# = SIN(radrift0# + zetaa#) * COS(decdrift0#) / COS(decdrift#)
cs# = COS(radrift0# + zetaa#) * COS(tha#) * COS(decdrift0#)
cs# = (cs# - SIN(tha#) * SIN(decdrift0#)) / COS(decdrift#)
radrift# = ATN(sn# / cs#)
IF radrift# < 0 THEN LET radrift# = radrift# + pi#
IF radrift0# - radrift# > .1 THEN LET radrift# = radrift# + pi#
zdrift# = SIN(decdrift#): cs# = COS(decdrift#)
xdrift# = COS(radrift#) * cs#
ydrift# = SIN(radrift#) * cs#

REM For first drift vector only, find actual shift sums for corr coeff calc
7700 sy# = sy# + sh(I, 0) + sh(I, 1)
sv# = sv# + sh(I, 0) ^ 2 + sh(I, 1) ^ 2

REM save largest, or most positive, three correlation coeffs
7800 cc# = corrcoeff#
REM find largest correlation coeff of either sign
IF ABS(cc#) > ABS(cc1#) THEN GOTO 7810
IF ABS(cc#) > ABS(cc2#) THEN GOTO 7820
IF ABS(cc#) > ABS(cc3#) THEN GOTO 7830

REM find most positive correlation coeff
7806 IF cc# > cc1# THEN GOTO 7810
IF cc# > cc2# THEN GOTO 7820

IF cc# > cc3# THEN GOTO 7830

7810 cc3# = cc2#: cc2# = cc1#: cc1# = cc#
lat3 = lat2: lon3 = lon2: lat2 = lat1: lon2 = lon1: lat1 = lat: lon1 = lon
GOSUB 7850
speed3# = speed2#: speed2# = speed1#: speed1# = speed#
GOTO 7808

7820 cc3# = cc2: cc2# = cc#
lat3 = lat2: lon3 = lon2: lat2 = lat: lon2 = lon
GOSUB 7850
speed3# = speed2#: speed2# = speed#
GOTO 7808

7830 cc3# = cc#
lat3 = lat: lon3 = lon
GOSUB 7850

speed3# = speed#
GOTO 7808

REM The best-fit slope is the best-fit 2nd harmonic amplitude
REM that would occur if the
REM velocity vector were such that Maxwell would predict amplitude = 1
REM ("1" = 0.1 wavelength in Miller's data recording shorthand)
REM so the equation is
REM 1/4*(v/c)^2*nwv*10 = slope
speed# = clight# * SQR(ABS((coa# - cob#) / (coc# - cod#)) * 4 / nwv# / 10)

REM Read, standardize, and Fourier analyze data
REM c(j) & s(j) are coeffs to convolve fringe shifts
REM with cos & sin(2*azimuth), resp.
9000 rt2inv# = 1 / SQR(2): c(1) = 1: c(9) = 1: s(3) = 1: s(11) = 1
c(5) = -1: c(13) = -1: s(9) = -1: s(1) = -1

c(3) = 0: c(11) = 0: c(7) = 0: c(15) = 0
s(7) = 0: s(15) = 0: s(11) = 0: s(3) = 0: c(17) = c(1): s(17) = s(1)
FOR I = 2 TO 16 STEP 2
c(I) = (c(I - 1) + c(I + 1)) * rt2inv#
s(I) = (s(I - 1) + s(I + 1)) * rt2inv#
counter = 0
FOR I = 1 TO 200
READ y, mo, d, hr, min, n, p
IF n = 0 THEN GOTO 9090
IF y < 1922 OR y > 1924 THEN PRINT "?! data error"
counter = counter + 1
IF y = 1922 THEN LET jd# = jd0# - 70 * 365 - 17
IF y = 1923 THEN LET jd# = jd0# - 69 * 365 - 17
IF y = 1924 THEN LET jd# = jd0# - 68 * 365 - 17
IF mo = 4 THEN LET jd# = jd# + 90
IF mo = 6 THEN LET jd# = jd# + 151
IF mo = 7 THEN LET jd# = jd# + 181
IF mo = 8 THEN LET jd# = jd# + 212
IF mo = 9 THEN LET jd# = jd# + 243
IF y = 1924 AND mo > 2 THEN LET jd# = jd# + 1
REM p=89 & p=91 reveal that turn rate was about 40 turns/35 min
REM so if one time is given it likely was the start rather than midpoint
IF p = 89 OR p = 91 OR p = 177 THEN GOTO 9010
jd# = jd# + n / 2 * 35 / 40 / 1440
GOTO 9020
9010 IF p = 89 THEN LET jd# = jd# + 25 / 2 / 1440
IF p = 91 THEN LET jd# = jd# + 10 / 2 / 1440
IF p = 177 THEN LET jd# = jd# + 45 / 2 / 1440
9020 shift(I, 17) = jd# + d - 1 + hr / 24 + min / 1440
shift(I, 18) = n: shift(I, 19) = p: js = 0
FOR j = 1 TO 16
REM (+) fringe shift is that which would occur with longer telescope arm.
REM Use of only half the mirrors reverses the sign of the expected shift??
REM IF p < 91 THEN LET jx = -jx
REM p=86,88 explicitly & p=89,90 implicitly used only half usual pathlength;
REM will correct for this:
IF p < 91 THEN LET jx = jx * 2
REM p=90 has top of copy cut off; p=89 or p=90 might need doubling.
REM p=91 explicitly used usual ("16 reflections") pathlength.
js = js + jx: shift(I, j) = jx
jm = js / 16
REM reduce to zero mean
FOR j = 1 TO 16
shift(I, j) = shift(I, j) - jm
REM detrend using best fit line
REM ju = 0
jw = 0
FOR j = 1 TO 16
REM ju = ju + shift(i, j) ^ 2
jw = jw + shift(I, j) * (j - 9)
REM Best fit line is through (0,0) & has slope equal to
REM correlation coefficient * std deviation of ordinate / std dev abscissa
REM slope# = jw / SQR(ju * jv0#) * SQR(ju / jv0#)
slope# = jw / jv0#
FOR j = 1 TO 16
shift(I, j) = shift(I, j) - slope# * (j - 9)
9090 nn = counter * 2
PRINT "Miller's column sum data have been read and standardized."
PRINT "nn = "; nn
GOSUB 9100

REM Fourier analyze data
9100 FOR I = 1 TO counter
sc# = 0: ss# = 0
FOR j = 1 TO 16
sc# = sc# + shift(I, j) * c(j)
ss# = ss# + shift(I, j) * s(j)
shift(I, 20) = sc# / 16 / (1 / 2): shift(I, 21) = ss# / 8
REM redundant variable below is to enhance array access speed
sh(I, 0) = shift(I, 20): sh(I, 1) = shift(I, 21)
PRINT "Miller's data have been Fourier analyzed."

REM Format of data:
REM time of each turning session in yr,mo,d,hr,min (Eastern Std. Time)
REM n = number of turns of interferometer
REM p = experiment's Goodey-Keller pagination number in Miller's notebook
REM I use Miller's non-detrended column sums,
REM omitting the last column
REM which is redundant except for its bottom entry.
REM Rather than use Miller's detrending, I'll detrend using a best-fit line
REM for each experiment page.

REM 1922 data
DATA 1922,4,14,14,45,10,86
DATA 100,74,56,49,63,90,112,129,119,107,107,106,105,100,98,97
DATA 1922,4,17,14,25,6,88
DATA 42,38,38,42,44,48,60,69,70,63,56,50,52,61,62,64
DATA 1922,4,17,17,0,28,89
DATA 12,10,4,15,26,46,72,92,90,79,64,44,28,15,16,21
DATA 1922,4,18,16,30,25,90
REM for p=90, must guess civil time (page cut off) but will
REM replace with Miller's sidereal time
REM in subroutine getting sidereal times from JD's
DATA -243,-258,-302,-338,-367,-369,-333,-309,-305,-323,-323,-320,-296,-284,-265,-258
DATA 1922,4,19,15,50,12,91
DATA -9,-15,-8,12,42,52,47,52,52,75,112,136,132,107,60,20

REM 1923 data
DATA 1923,8,23,13,30,11,97
REM minor addition error in col. 11 corrected
DATA -31,-31,-28,-23,-22,-20,-22,-24,-30,-27,-24,-21,-17,-9,4,12
DATA 1923,8,24,16,45,12,98
DATA 42,47,52,56,56,58,52,47,47,48,55,51,48,45,47,48
DATA 1923,8,25,9,40,18,99
REM Miller notes "Increasing telescope arm increases reading."
REM This sentence also appears for p=100,101,103,104,106,108-112,118
REM & of 1923 experiments, only p=126 has (ambiguously) contrary statement.
DATA 4,18,40,55,59,56,39,20,12,10,18,26,28,21,14,12
DATA 1923,8,25,12,0,13,100
DATA 3,7,13,-18,20,20,10,3,6,5,9,16,14,19,21,23
DATA 1923,8,27,11,20,9,101
DATA -53,-47,-42,-30,-43,-54,-63,-71,-73,-73,-76,-78,-82,-91,-97,-90
REM on p=102, Miller notes "Heater placed at azimuth 4"
REM so this experiment is omitted
DATA 1923,8,27,15,10,6,103
DATA 19,24,28,31,30,21,19,18,20,22,20,18,13,11,11,17
DATA 1923,8,27,15,30,24,104
REM "Light shielded by cardboard"
REM Many experiments in this part say they had a little shielding of some sort
REM but only the most thoroughly shielded will be quoted.
DATA -215,-193,-176,-167,-168,-182,-198,-209,-214,-213,-212,-222,-235,-240,-238,-226
REM on p=105, Miller notes "Heater placed at Az. 2."
REM so this experiment is omitted also
DATA 1923,8,28,11,45,12,106
DATA -13,-10,-8,-6,0,-1,-4,-6,-8,-12,-10,-10,-12,-12,-11,-14
DATA 1923,8,28,14,20,16,107
REM "...interferometer shielded from heat by cardboard"
DATA -196,-192,-189,-191,-197,-206,-212,-212,-217,-214,-223,-212,-215,-215,-217,-212
DATA 1923,8,28,15,30,12,108
DATA 56,60,62,60,58,56,56,57,58,60,60,60,60,59,59,63
DATA 1923,8,29,9,0,11,109
DATA -39,-35,-37,-39,-37,-45,-45,-50,-49,-47,-44,-42,-39,-43,-46,-49
DATA 1923,8,30,9,30,22,110
DATA 69,77,82,80,82,83,82,77,81,84,88,86,84,83,84,93
DATA 1923,8,30,10,0,11,111
DATA 69,74,75,79,80,81,78,75,78,78,78,79,80,79,81,87
DATA 1923,8,30,10,30,22,112
DATA 17,24,24,24,21,23,19,17,18,21,18,15,14,15,17,20
DATA 1923,8,30,15,40,22,113
DATA 64,67,67,65,66,65,66,66,69,73,76,75,70,69,70,72
REM p=114-117 have "Heater"(s) & are omitted
DATA 1923,8,31,9,0,8,118
REM minor addition error in 4th col. corrected
DATA -29,-28,-30,-36,-38,-43,-44,-44,-40,-38,-38,-37,-34,-39,-41,-38
REM on p=119 Miller notes "3 electric bulbs at Az 4"
REM so though less powerful than a "heater", this experiment also omitted.
REM p=120-123 have "Heater"; will be omitted.
DATA 1923,9,1,9,30,20,124
REM Miller notes "Glass and steel of all arms covered."
REM minor sum error col. 1 corrected
DATA 214,214,214,213,213,211,208,208,213,215,216,214,211,207,207,209
REM p=125 has "Heater" and though "Glass and steel of all arms covered"
REM will be omitted.
REM p=126-134 have "Heater" & are omitted
DATA 1923,9,4,16,30,14,135
REM minor errors summing cols. 2-4 corrected
DATA 82,85,86,85,85,83,82,84,88,89,89,87,84,81,82,84

REM 1924 Cleveland data
DATA 1924,6,27,14,5,8,138
REM Miller notes "Increasing readings, +, always means
REM increased length of telescope arm"
REM sign of column 7 corrected
DATA 3,8,0,-2,6,10,14,9,-4,-8,-4,-15,-21,-27,-17,-23
DATA 1924,6,27,15,0,10,139
DATA -119,-117,-125,-126,-127,-129,-131,-131,-132,-129,-133,-135,-141,-147,-146,-139
DATA 1924,6,28,10,45,14,140
DATA -40,-42,-50,-54,-54,-54,-55,-56,-53,-58,-66,-75,-77,-76,-73,-69

DATA 1924,6,30,10,0,19,141
DATA -31,-26,-38,-47,-66,-68,-56,-58,-59,-64,-75,-93,-101,-92,-71,-57
DATA 1924,7,1,11,40,10,142
DATA -117,-109,-100,-111,-118,-120,-103,-108,-105,-115,-139,-150,-154,-155,-144,-134
DATA 1924,7,1,16,45,9,143
REM Miller's #46
DATA -2,-10,-14,-20,-22,-22,-21,-19,-14,-12,-14,-18,-20,-21,-14,-12
DATA 1924,7,1,12,0,10,144
REM Miller's #45
DATA 35,48,52,51,37,40,48,55,55,45,24,8,2,3,8,19
DATA 1924,7,5,8,40,12,145
REM top of page cut off; time deduced by comparing with other sidereal times
DATA 104,99,86,74,64,88,117,125,117,111,101,98,95,106,121,137
DATA 1924,7,5,9,39,11,146
REM as for p=145
DATA 86,85,77,67,72,72,84,99,108,102,89,80,70,74,79,88
DATA 1924,7,5,10,10,12,147
DATA -132,-128,-121,-125,-136,-138,-126,-127,-118,-123,-138,-140,-151,-148,-149,-150
DATA 1924,7,5,11,45,10,148
DATA -94,-96,-99,-102,-107,-108,-105,-96,-96,-98,-105,-111,-116,-120,-116,-111
DATA 1924,7,7,10,45,10,149
DATA 18,19,19,17,17,16,17,20,17,17,14,11,10,10,13,19
DATA 1924,7,7,11,40,20,150
DATA -151,-149,-145,-143,-142,-142,-140,-137,-142,-146,-157,-167,-195,-180,-173
DATA 1924,7,7,14,30,20,151
DATA 18,25,32,38,37,34,33,31,29,23,19,11,4,0,14,27
DATA 1924,7,7,14,45,20,152
DATA -109,-105,-103,-103,-105,-107,-102,-100,-99,-104,-112,-12,-127,-129,-121,-112
REM minor addition error 1st col. corrected
DATA 61,55,48,40,40,37,44,47,52,50,50,39,36,35,55,76
DATA 1924,7,8,22,30,14,158
DATA 27,22,19,15,12,11,9,13,17,19,16,9,9,10,18,32
DATA 1924,7,9,9,0,20,159
DATA 168,170,173,167,162,155,156,161,165,167,174,178,172,174,175,189
DATA 1924,7,9,14,25,10,160
DATA -55,-57,-56,-55,-54,-58,-57,-59,-60,-61,-63,-67,-69,-71,-68,-64
DATA 1924,7,9,14,35,10,161
DATA 3,3,-1,-2,-3,-2,-2,0,6,7,8,5,3,1,5,8
DATA 1924,7,9,14,55,20,162
DATA 16,15,13,11,9,12,14,19,19,18,17,14,12,12,15,23
DATA 1924,7,10,10,5,11,163
DATA 143,143,147,150,152,150,153,158,159,161,162,162,160,162,166,172
DATA 1924,7,10,11,20,10,164
DATA -8,-6,-7,-7,-10,-12,-10,-11,-11,-6,-6,-10,-13,-14,-13,-7
DATA 1924,7,10,20,16,30,165
DATA -160,-166,-170,-178,-180,-182,-183,-181,-178,-184,-195,-203,-209,-211,-203,-191
DATA 1924,7,10,17,40,9,166
REM minor addition errors cols. 1-4,8,9 corrected
DATA -27,-26,-28,-29,-33,-32,-36,-33,-32,-35,-37,-41,-47,-49,-47,-40
DATA 1924,7,22,17,0,20,167
DATA 60,69,70,68,65,63,63,64,63,66,65,64,64,64,64,70
DATA 1924,7,23,9,40,10,168
DATA 6,4,-5,-11,-18,-23,-22,-20,-19,-17,-17,-16,-1,3,4,7
DATA 1924,7,23,14,25,10,169
DATA 25,23,17,14,9,8,12,16,22,26,33,38,39,36,34,32
DATA 1924,7,23,17,10,11,170
DATA 10,10,11,11,11,10,11,12,17,22,23,23,24,24,26,27
DATA 1924,7,24,9,0,10,171
DATA -14,-15,-21,-22,-22,-19,-16,-13,-15,-15,-17,-18,-18,-18,-14,-13
DATA 1924,7,24,14,35,10,172
DATA 7,8,8,8,10,10,13,16,17,17,18,19,21,22,25,29
DATA 1924,7,24,15,40,20,173
DATA 30,30,31,31,31,33,33,35,34,35,35,35,33,33,35,45
DATA 1924,7,24,17,0,20,174
DATA 1924,7,24,17,0,20,174
DATA 96,96,90,81,75,70,68,68,75,82,81,80,81,86,94,106
DATA 1924,7,24,23,40,10,175
DATA 3,8,10,10,9,8,8,8,8,8,8,7,7,7,7,9
DATA 1924,7,25,10,0,10,176
DATA 54,54,54,55,56,56,57,58,58,58,58,60,60,60,60,64
DATA 1924,7,26,3,40,27,177
REM addition errors cols. 2,4,7 corrected

DATA 142,149,151,152,151,155,169,176,181,185,189,189,190,198,212,222
DATA 1924,7,26,4,30,29,178
DATA 71,73,73,70,69,74,80,90,102,104,106,107,110,114,130,146
DATA 1924,7,26,9,30,12,179
REM minor addition errors cols. 1,3,14 corrected
DATA 72,71,65,62,60,55,58,65,68,72,71,69,64,64,67,76

DATA 0,0,0,0,0,0,0
Larry Burford Posted - 25 Jun 2013 : 13:39:39

Models are obviously not perfect. And that lack of perfection can lead to frustration. But the real world is very big and complicated and in order to think about it and talk about it we we have to break it down into 'bite sized' chunks that are intended to be less complex. We call them models. Or theories. Or guesses. Or ideas. (If our frustration becomes large enough, we have more names for them ...)

And then we live with them and their imperfections. Until we can come up with something better.

Of course, sometimes the new better thing is not really better.


Larry Burford Posted - 24 Jun 2013 : 18:10:07
By the way, we do not make up things like the electron and the proton. There really is something there. We can actually touch them. And when we do it HURTS! Sometimes enough to kill.

But we do make up the models we use to think about them and talk about them. I suspect that it is these models, and in particular our models of the electron rather than the electron itself, that you are complaining about.

Larry Burford Posted - 24 Jun 2013 : 18:09:07
The proton is only a vehicle to carry the protonic charge much like several made up items in common use these days. And proton charge doesn't obey thermal laws for very simple reasons - mainly charge is energy and thermodynamics is a study of the interplay of energy and matter (aka ATOMS, lots of them, big wads of them).

If you try to apply the laws of thermodynamics to a small wad of atoms or to individual sub-atomic particles then you are using the thermodynamic models incorrectly.

Jim Posted - 24 Jun 2013 : 13:23:20
Dr Joe, Chemistry uses moles of molecules as a base and the gas constant in SI units. Boltzmann divided the gas constant by the mole number. So, using the Boltzmann Constant should allow your equation. My issue is not that at all-I am saying the electron is only a vehicle to carry the electronic charge much like several made up items in common use these days. And electric charge doesn't obey thermal laws for very simple reasons-mainly charge is energy and thermodynamics is a study of the interplay of energy and matter(AKA protons)
Joe Keller Posted - 20 Jun 2013 : 21:43:06
Originally posted by Larry Burford

[Joe Keller] "... an electron at this radius r from the Sun, would have, if heated to the CMB temperature, ..."

[Jim] "... So then the issue is does the electron obey thermal laws? ..."

...For individual particles, temperature and especially heat are not well defined properties. ...


Yes, what you say is true and I stand corrected here. I recall now that in my undergrad Harvard course in chemical thermodynamics, Prof. Leonard Nash, then head of the chemistry dept., always was careful to speak of "ensembles" rather than individual particles, when discussing temperature.
Larry Burford Posted - 20 Jun 2013 : 20:42:46
[Joe Keller] "... an electron at this radius r from the Sun, would have, if heated to the CMB temperature, ..."

[Jim] "... So then the issue is does the electron obey thermal laws? In my world the electron is not real and does not obey any laws(why should it?). It is a sc-fi idea that is deeply embedded in physical theory and the cause of much confusion ..."

For individual atoms and molecules the propety of temperature does not have the same meaning as it has for larger accumulations of mass. For the latter it is a measure of how fast and hard the particles are vibrating and banging into each other. For the former it is essentially an alternate measure of velocity.

This is even more so for individual sub atomic particles. Jim is right to question whether electrons "obey thermal laws" (not in the way we normally interpret them) but for the wrong reason (electrons are as real as protons - we can weigh them both, and make them do things according to any number of laws).

For individual partcles, temperature and especially heat are not well defined properties.


As long as Joe understands this distinction, he is not in trouble theory-wise when he talks of 'heating' an electron to some 'temperature'. It is fairly common usage in some parts of particle physics, because it can make solving some problems easier.

But because of the potential for confusion, he should be careful to mention this when talking to a lay audience. It is kind of like when relativists divide time by the speed of light, call it a 'space-like' dimension and then create a 4D space-time model of the universe. It works mathematically, and some problems can be solved with less effort - even if you count the work needed to translate the answer into a useful format (3D space plus 1D time) for building something based on your results.

But they ought to be more careful about explaining things to lay audiences. And in this context a 'lay audience' can be anyone not working in their specific sub-speciality.

Joe Keller Posted - 13 Jun 2013 : 16:54:23
Seven crop circles in Italy, one in France, three in England, imply Aug 9, 2013

1. A crop formation was reported at Modena (Finale Emilia) in Italy on June 9, 2013. Near a paved highway, it is thought to have appeared during the previous night of June 8-9. The New Moon occurred June 8 at 16h GMT.

This was one of several crop circles that already this spring have been reported in Italy. Maybe the circlemakers cannot wait for sufficiently tall crops to appear in England.

The five disks inside the large circle, signify the first five Full Moons Feb '13 through Jun '13, which occur between Luna's most southerly and most northerly ecliptic latitudes. Luna's maximum northerly ecliptic latitude, geocentric, of date, for the month, occurs at Feb 10, 06:48 GMT whereas Luna's minimum illuminated fraction (i.e. New Moon) occurs at almost exactly the same time, at 07:20 GMT. Thus the first Full Moon occurring after, rather than before, the maximum southerly latitude, is the Full Moon of 21h GMT Feb 25. The rightmost disk of the crop formation (as the formation is shown in most of the drawings and aerial photos online) is the disk just inside the large circle at the end where there are no disks outside the circle. This disk signifies the Full Moon of Feb 25.

The outermost disk, of the three outside the large circle on the left, would signify the Full Moon of September 2013. That is the last Full Moon before the equinox.

If a New Moon could occur 5 1/2 draconic months = 5.5*27.2122 = 149.67d after the Feb 10 New Moon, it would occur at the most southerly latitude for the month. Instead, five synodic months = 5*29.5306 = 147.65d. That is, the time period between the New Moons of Feb and July, symbolized by the string of five Full Moons within the large circle, is two days too short. Maybe it would have been more obvious to put six disks inside the large circle, but six synodic months = 6*29.5306 = 177.18d slightly exceeds 6.5 draconic months = 6.5*27.2122 = 176.88d. It was perhaps decisive, that the circlemakers wished to emphasize not the position of Luna's orbit six months after the Feb New Moon, but rather a position of Luna's node when the Sun lay near the node.

The April 25 20:07 GMT Full Moon in the center, occurs at a small southern latitude -1.008deg & longitude 215.87. The May 25 04:10 Full Moon to its left, is next nearest the ecliptic, at a slightly larger northern latitude, +1.555deg & longitude 243.98. Within the large circle, the sizes of the disks signify the closeness of the Full Moons to the ecliptic, with their diameters roughly inversely proportional to their latitudes. The latitude ratio is 1.555/1.008 = 1.543. Using Luna's orbital inclination 5.145deg, the ratio of their longitude distances from the node would be arcsin(1.555/5.145)/arcsin(1.0008/5.145) = 1.557.

The diameter ratio (according to my screen measurements from the 1st, 4th & 5th aerial photos at on Aug 8, both major and minor apparent axes, giving six estimates 1.54,1.625,1.57,1.56,1.61,1.55) is 1.576 +/- 0.009 SEM. This is confirmed by the measurements printed on the map on the "ground shots" page for this crop circle at 8.70/5.50 = 1.582 +/- 0.010 rms implied rounding error. Combining mine and his with equal weight gives 1.579 +/- 0.008, differing from the foregoing theory by about 3 sigma at least. So possibly the circle designers were encoding the interpolated time ((May 25 04:10)*1 + (Apr 25 20:07)*1.579) / (1+1.579) = May 7 05:07. Luna lies on its ascending node Apr 26 14:06.5 at longitude 226.8344 and its descending node May 9 19:12.6 at longitude 46.8668 = 226.8668 - 180. Interpolation gives the ascending node at May 7 05:07, as 226.8605. The sun lies at longitude 226.8605 - 90 = 136.8605, at Aug 9 06:54. Remarkably, another interpolation scheme, interpolation in longitude according to the longitude distance of the April & May Full Moons from the node, give the same result to the nearest minute.

At this time, Mars is at long 107.8154, lat +0.7825, and Jupiter is at long 99.7007, lat -0.1533. For reference in part 2, this difference in longitude of Mars & Jupiter is 8.115deg.

2. The difference in longitude, 8.115deg, is shown on a previous crop formation reported June 6 at Barbiano Lugo near Ravenna. The diameters of the three circles given by online sources amount to 9m, 16m, and 300/pi = 95.5 m (i.e. circumference 300m). I confirmed this: despite the oblique view, one can measure the circles' diameters assuming that the farm vehicle tram tracks are equally spaced. I use the ninth photo from the top at; this is the only aerial photo on that page which appears on my browser. I find that the small circle is about 6/15 of one tram space, the midsize circle about 10/15, and the big circle about 4 + 5/10 + 6/15 = 4.90 tram spaces; the ratio of these diameters is


which, considering the crudity of the measurement, is as close as can be expected to


which is the ratio of the sidereal orbital periods


and it is these periods by which these planets seem to be identified in the crop formation. Likewise the diameters prominent on the Italian website give 9:16:95.5 which is


also a good match. A diagram on the Italian page gives more precise diameters 8.70:14.30:87.90 which is


a good match yet again.

With my protractor on the circle diagram on that page, measuring by eye from the centers of the circles, I find that the angle Mars-Earth-Jupiter is about 9deg. The most magnified aerial photo on gives a break angle for the centers of the small & midsize circles and the junction of the midsize and large circles, uncorrected, of

arctan(9.3/72.9) = 7.3deg

but the axis ratio of the midsize circle in this photo is 54/76, with the ellipse axes rotated about 13 & 6deg from the broken line, so an approximate correction for the oblique view gives break angle

arctan(9.3/72.9*(1 + 22/54*(1 - 2*sin(6)))) = 9.575deg

from which the Jupiter-Earth-Mars angle is found by the Law of Sines to be

arcsin(sin(9.575)*(11.862+1.881)/(11.862+2*1.881+1)) = 7.90deg

near the theoretical 8.115deg. The angle 7.90deg occurs Aug 8.8130.

3. A third crop formation was reported June 8 near Cava Manara in Italy. New Moons occur at about 15.5h GMT June 8 and about 22h Aug 6; the latter date is 2.37d prior to the date indicated by the other two crop formations above. The two central disks of the Cava Manara formation, signify the June & July New Moons, or the July & August New Moons, or in any case, two synodic Lunar months. The two pairs of arcs between these New Moons signify the extra two days. For more precision, let us consider the large crescent. Its sagittal depths from the tips of its horns, are 52 & 75mm on my screen. This signifies a time of (75-52)/75 / 4 synodic months = 2.19d, only 0.18d different from the date indicated by the other two formations.

4. On June 20, fifty days before Aug 9, a crop formation was reported at Cisterna di Latina, Italy. This crop formation signifies the number 50, three different ways:

#1: On the aerial photo at (same as the Earthfiles photo) I measured the diameters of the inner rim of the inner and the outer rim of the outer circles, along the long axis of the apparent ellipse due to the oblique view. One must take care to measure to the top of the crop, that is, to the line between standing crop and shade at the shady side, and to the line between the standing crop and the sun at the sunny side. The ratio fo these diameters, on two measurements, I found to be 49.45:60 and 50:60. I also found that the spaces between the small half-disks on the outer rim, are, approximately if not exactly, twice the diameters of those small half-disks. Thus assuming that the circumference of the outer rim is 20*(1+2) = 60 units, the circumference of the inner rim is 60*49.7/60 = 49.7 units +/- 0.3 SEM, where presumably each unit (diameter of a small half-disk) represents one day.

#2: If the large rings represent one synodic month and the small half-disks represent one day, then the formation represents 29.53 + 20 = 49.53d.

#3: The Platonic solid with the most faces is the icosahedron, with 20. The number of faces + edges for this solid, is 20 + 20*3/2 = 50.

5. A "vesica piscis" (pair of congruent circles each with its center on the circumference of the other) crop formation was reported at Enna, Sicily, June 16. June 16 is 54 days before Aug 9. Two sidereal months is

27.3217 * 2 = 54.6434 d

but the actual result is closer to 54 than to 55. My most precise determination of the "doomsday" time, is 06:54 GMT Aug 9, from formation (1) above. Luna's longitude (geocentric, with equinox of date) then, is the same as Jun 15 19:24, for a difference of 54.4792d. The apparent Right Ascension is the same Jun 15 19:41, for a difference 54.4674d.

The "vesica piscis" arrangement emphasizes the congruence of the circles, therefore suggesting sidereal months. Sidereal months are more equal than synodic months, because of Luna's eccentricity. Furthermore, Aug 9 is a date at which the sidereal month is especially constant. Let's measure the sidereal month as the time from August back to July when Luna's apparent Declination (geocentric, equinox of date, per JPL online ephemeris) was the same. By this definition, the sidereal month lengthens by 35 minutes between 0h Aug 8 & 0h Aug 11. Interpolating with a cubic curve through 0h Aug 8, 9, 10 & 11, I find that the rate of increase almost becomes zero (i.e., the length of the sidereal month almost becomes constant, increasing at only 0.304 seconds/hour) at the inflection point Aug 9 18:04 GMT. This may be the equality to which the vesica piscis refers.

6. The crop formation reported July 1 in Cavallo Grigio, Italy (east of Turin) amounts to a sequence of binary numbers equal to 11, 4, 11, 12, 10, 11, 11, 7. Not only is there a narrow line of demarcation between each four-digit binary number, the (two sets of) eight large triangles around the perimeter also emphasize that there are eight numbers. Naturally the small line segments would signify 0 and the much more prominent disks signify 1. The special triangle marked with six seemingly random small triangles, signifies the starting point. We shall see that these six triangles symbolize the six visible planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus. The single triangle near the third number and the double triangle near the sixth number mark for us the direction of increasing time and also the direction of increasing value to the places of these base-2 numbers. We also shall see that another purpose of these marks is to give extra value to those two numbers.

There are six visible planets and the sidereal month is about 27 days. So, Luna is in conjunction with a visible planet on average about once every 27/6 = 4.5 days. The sum of the eight binary numbers is 77; if they signify half-days, then they average 77/2/8 = 4.8 days, so maybe they signify conjunctions of Luna with a planet. Let's check this, because July 1.0 + 77/2 days = August 8.5.

According to a webpage of the TAU Astronomy Club ( ) the interval 0h GMT Jun 20 2013 to 0h GMT Aug 13 2013 contains ten conjunctions of Luna with the six visible planets Mercury through Uranus:

1) Mars Jul 6 11:56 GMT
2) Jupiter Jul 7 02:55
3) Mercury Jul 8 11:45
4) Venus Jul 10 18:21
5) Saturn Jul 16 23:31
6) Uranus Jul 27 19:16
7) Jupiter Aug 3 21:32
8) Mars Aug 4 09:37
9) Mercury Aug 5 06:20
10) Venus Aug 9 22:46

Indeed Jul 1.0 + 11/2 d = Jul 6.5 is conjunction (1). Conjunction (1) + 4/2 d = Jul 8.5 is conjunction (3). Like conjunction (3), conjunction (9) is with Mercury. Conjunction (9) is 7/2 days before Aug (5.3 + 3.5) = Aug 8.8, almost Aug 9.

The third number is 11, but the prominent small single triangle near it, perhaps increases its value, signifying a unit in the next place, 16, giving 27. Conjunction (3) + 27/2d = Jul 22.0, near the only planet-planet conjunction in the relevant interval:

A) Mars-Jupiter Jul 22 06:49 = Jul 22.284

Using the next binary number of the formation, Jul 22.0 + 12/2 = Jul 28.0 is near conjunction (6) which is at Jul 27.803. The next numbers, 10,11,11, summed give Jul 28.0 + (10+11+11)/2d = Aug 13.0. If the prominent small double triangle signifies -16, the net result is Aug 13.0 - 16/2d = Aug 5.0 which is near conjunction (9), Aug 5.264.

7. Finally there is the Jul 4 crop formation near Sarrebourg in Moselle, France. The large disk within a concentric ring, signifies not the 7h GMT Jul 8 New Moon, but rather the next New Moon, that of 22h Aug 6. That is, the next New Moon after the upcoming one.

The four smaller disks to one side, signify days after the Aug 6 New Moon. The three small disks to the other side, signify a gap of three intervening days Jul 5,6,7 between the crop formation's appearance Jul 4 and the Jul 8 New Moon. The break angle between the two opposing rows of disks might signify the 29.5/365*360 = 29deg traveled in one synodic month.

The arc implies that something will happen almost two days after the New Moon of (minimum Moon-Sun-geocentric Earth angle) Aug 6 21:53. The one aerial photo on is quite oblique but I estimate roughly that the arc touches the small disk 30 degrees from its end, i.e. (1-cos(30))/2 = 0.067d before the end of that second day. So the implied time is about

Aug 6.912 + 2 - 0.067 = Aug 8.845

which agrees with the Aug 8.8 deduced in section 6 above.

8. The crop formation reported July 6 near Avebury, England, depicts level curves of the logarithm. The rings become unusually narrow to tell us we should measure to the centers of the ring boundaries, then wide so we cannot fail to notice the rings. Measuring on the screen to the centers of the ring boundaries, along the major axis of the moderately oblique aerial photo on, I find that the largest ring is almost exactly 4x the diameter of the smallest, which in turn is almost exactly 4x the diameter of the central button. So the inner ring signifies the number 1, the outer ring the number 4. The distance between rings is proportional to the diameter of the ring, so if the rings are "level curves" of a surface, then 1 / (dy/dr) is proportional to r, that is dy/dr = a/r, so y is a logarithm function. The abscissas of the rings are 1 = 4^(0/8), 4^(1/8), 4^(2/8),...,4^(8/8). Regardless of the base of the logarithms, the ratio of the last ordinate to the next to last, is 8/7, and this number is the message of the formation.

One mean synodic month * 8/7, is

29.5306 * 8/7 = 33.7493d

Local midnight (minimum solar elevation) occurs July 6 00:12 GMT; this time + 33.7493d = Aug 8.7576. However, the New Moon to New Moon geocentric synodic month July 08 06:48 -Aug 06 2013 21:54 is 29.6292d, which gives Aug. 8.8702.

There is a double entendre in this crop formation. What about sidereal months instead of synodic, and from sunrise July 6 rather than midnight? For this option, consider the convexity of the logarithm, specifically the ratio of its integral from 1 to 4, to the area under the line from (1,0) to (4,ln(4)). Again, this ratio is independent of the base of the logarithms, and equals

(4*ln(4)-4 + 1)/(0.5 * ln(4) * (4-1)) = 1.22397

Using the mean sidereal month 27.3217d, and sunrise 04:06 GMT Jul 6 gives

Jul 6.1708 + 27.3217*1.22397 = Aug 8.6117.

9. The crop circle reported at Bienate, near Milan, Italy July 3. I use the "outstretched" photo version on The axis ratio of the large disk, I measure as 2.53; this is used as a multiplier for the tangents, to estimate the actual angles.

The large disk represents the Sun, the middle disk Venus, and the small disk Luna. The point at the head of the flag-like hook at lower right, is the geocentric observer. Measuring from the centers of the ellipses, the angle between the observer-Luna-Venus line and the Venus-Sun line, I find as 63deg, correcting for obliqueness to 36.3deg. This isn't too different from the Sun-Earth-Venus angle Aug 10.0: 34.6deg.

More precisely, the diagram signifies the conjunction of Luna & Venus; their longitudes are equal Aug 9 22:04 GMT. The flag-like hook represents a change in Luna's angle relative to Venus, measured on the screen as 24deg and corrected for obliquity to 18.9deg. This is the Luna-Venus longitude difference at Aug 8.255, or, if Luna's & Venus' position at the time of conjunction is used as the reference, then it is the longitude difference at Aug 8.405.

10. The crop formation reported Aug 1 at Milk Hill in Wiltshire, England, amounts to a direction marker. Its cross formation suggests that it is a direction relative to one of the cardinal directions NSEW. The axis ratio of the aerial photo on is 3.148 as I measure on my screen. With straightedge and protractor I find that the arrow is 10deg clockwise from the major axis of the large circle's apparent ellipsoid, and that the tramlines (tractor tracks) are 10deg counterclockwise from it. Multiplying the tangents of these angles by the correction factor 3.148 gives 40 & 29deg, resp.

So, according to my measurement on my screen and a rough correction for the obliqueness of the photo, the arrow is 90-40-29 = 21deg from perpendicular to the tramlines. Measuring degrees in an average sidereal Lunar orbit, this angle past the August New Moon corresponds to

Aug 6.9125 + 27.3217 * 21/360 = Aug 8.506

and for a synodic Lunar orbit

Aug 6.9125 + 29.5306 * 21/360 = Aug 8.635.

11. The formation reported July 15 at All Cannings, Wiltshire, England can be analyzed just as #10, and gives the same angle, 69 deg, by my measurement, thus the same predicted times. This formation has threefold symmetry and hence three times as many interpretations, however. On the other hand, its aerial photo on is less oblique so perhaps my angle estimates are more accurate.

Relationship to other dates. Aug 9, 2013 is 305 days after Oct 8, 2012. The numbers 305 & 365 have a special quadratic relationship:

305 = 5*61 in prime factors
365 = 5*73 in prime factors and

61^2 = -2 modulo 73

Besides Oct 8, 2012, the other "doomsday" date I had identified from crop circles, was Feb 17, 2013, 173 days before Aug 9. Note the similar quadratic relationship (173 is prime):

173^2 = -1 modulo 73

Oct 8 is 132 days before Feb 17 and

132 = 12 * 11
11^2 = -1 modulo 61

Organizing this, let's say that Oct 8 is A, Feb 17 is B, Aug 9 is C. Let's define the distance AB as the largest prime factor of the difference in days B-A, etc. Let's define one year as 73, the largest prime factor of 365. Then

AB^2 = -1 mod AC i.e. mod 61
BC^2 = -1 mod 73
AC^2 = -2 mod 73

To complete the pattern, I need a date "O" such that

OB^2 = -1 or -2, mod AC i.e. mod 61

Let O = the beginning of the Mayan Long Count:

B - O = 5200*360 + (Feb 17 - Dec 23) = 1872056
= 8*234007

where I use the alternative Dec 23 end for the Long Count. The prime number 234007 = 61*3836 + 11 so

OB^2 = 234007^2 = 11^2 = -1 mod 61

This is evidence not only for the coherent planning of crop formations to indicate the dates Oct 8, 2012, and Feb 17 & Aug 9, 2013, but also to indicate Dec 23, 2012 as the correct end of the Long Count.

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