The Plates That Were Set Aside

I · The claim at full strength

Two telescopes, one answer, in their words

Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighbourhood of the sun and that it is of the amount demanded by Einstein’s generalised theory of relativity, as attributable to the sun’s gravitational field.

Dyson, Eddington and Davidson 1920, p.332

The report set up three possibilities in its first paragraph: no deflection at all, the Newtonian one, and Einstein’s.

If the law of gravitation is strictly the Newtonian law, this leads to an apparent displacement of a star close to the sun’s limb amounting to 0″.87 outwards.

Dyson, Eddington and Davidson 1920, p.291

This leads to an apparent displacement of a star at the limb amounting to 1″.75 outwards.

Dyson, Eddington and Davidson 1920, p.291

Its headline came from seven photographs taken through a 4-inch lens at Sobral during totality and seven taken of the same stars at night in July, when the Sun was elsewhere (two of the July seven are exposures on one plate). The report printed, for every one of those fourteen photographs, how far each of seven stars sat from its place on an intermediary “scale plate” (Table II, 196 numbers in micrometer turns), the form it fitted to them, and the normal equations it solved. Each plate gets its own fit: a shift, a rotation, a change of scale, and the deflection coefficient α. Subtracting the night plates’ mean α from the eclipse plates’ removes the scale plate. The page does the same 28 fits, here, now.

The result from declinations is about twice the weight of that from right ascensions, so that the mean result is 1″.98 with a probable error of about ±0″.12.

Dyson, Eddington and Davidson 1920, p.331

Two cells the report’s own arithmetic disagrees with

The report printed its normal equations two pages after Table II, and every right-hand side in them is a sum over the stars that can be rebuilt from the table. The page rebuilds all 112 of them. In 22 of the 28 plate-and-coordinate sets every row agrees with print to within 0.004. For each set that does not, the engine asks whether changing one printed number by a whole number of thousandths brings all four rows back to within 0.0025, and three times closer than before. At that tolerance it finds exactly three such numbers:

Three more sets (eclipse I in declination, comparison 15₁ in declination, comparison 17₂ in declination) disagree only in their last row, by at most 0.009, and no single number explains them; they are reported, not repaired. The count depends on the tolerance; the result does not. The two table cells are found at every tolerance from 0.001 to 0.006 that the page tried, in steps of 0.0005, and forcing the best single number onto the three unexplained sets anyway would move the headline by only 0.002″. The offset below the line does not change α at all. So the two table cells are the only repairs that move the result: with them the fits return 1.980″, the value the authors computed; with the table as printed they return 2.012″. The page opens on the first, because that is the arithmetic the authors actually did, and keeps the second one click away. Solving the authors’ own printed normal equations returns their printed α on all 28 sets to within 0.0011 r, so the tables were read with the right structure.

What “about ±0.12″” meant

The probable error of the result judging from the accordance of the separate determinations is about 6 per cent.

Dyson, Eddington and Davidson 1920, p.306

A probable error is the half-width that contains half the outcomes: 0.6745 standard errors. So the report’s ±0.12″ is a standard error of 0.178″, and Principe’s ±0.30″ is 0.445″; this is the 1.98 ± 0.18″ that Harvey printed for the report in 1979. The page’s own estimate from the scatter of the fourteen plates is a standard error of 0.140″ (probable error 0.094″, 4.8 per cent of the result), beside the report’s “about 6 per cent”. The page never adds a probable error to a standard error; the engine refuses to.

Reference to the normal equations shows that the declination result is of double the weight of that from the right ascensions.

Dyson, Eddington and Davidson 1920, p.306

The weight is in the design: on every plate the declination fit pins α with inverse variance 2.229 and the right-ascension fit with 1.242 (the report printed 2.224 and 1.242), a ratio of 1.79, which the report rounded to two. That moves the headline by 0.003″. The report’s own intermediate numbers do not quite agree with each other either: its right-ascension α of 0.105 r converts to 2.08″, not the 2.06″ it printed in its conclusions.

Principe, reproduced the same way

At Principe cloud spoiled most of the eclipse plates. The report kept two, each compared with two plates of the same field taken at Oxford:

Accordingly plates W and X are the only ones likely to give a trustworthy result.

Dyson, Eddington and Davidson 1920, p.321

The report printed the last stage of each comparison in full: the residual displacement of each star in declination after scale, orientation and a provisional Einstein shift were removed, beside the star’s predicted displacement coefficient. The correction to the deflection is the least-squares slope of one on the other. The earlier stages (the scale from the check plates, the orientation) are taken as printed.

The mean of the four is 1.648″ (printed 1.65″), and with the report’s correction of −0.04″ for the orientation, 1.608″, printed 1.61″. A fifth plate, U, gave 2.90″ with a probable error of ±0.87″ and was, in the report’s words, “ignored in the subsequent discussion”. The Principe plates themselves have since been lost, so nobody can remeasure them.

The deflection obtained was 1″.61. The probable error is about ±0″.30, so that the result has much less weight than the preceding.

Dyson, Eddington and Davidson 1920, p.331

Both of these point to the full deflection 1″.75 of Einstein’s generalised relativity theory, the Sobral results definitely, and the Principe results perhaps with some uncertainty.

Dyson, Eddington and Davidson 1920, p.331

II · The plates that were set aside

One assumed number decides where they land

The second Sobral telescope was the Greenwich astrographic object glass, stopped down to 8 inches and fed by a 16-inch cœlostat mirror in the tropical sun. It took 16 usable eclipse plates with up to 12 stars each, far more material than the 4-inch. It also went wrong the day it was used.

May 30, 3 a.m., four of the astrographic plates were developed, and when dry examined. It was found that there had been a serious change of focus, so that, while the stars were shown, the definition was spoilt. This change of focus can only be attributed to the unequal expansion of the mirror through the sun’s heat. The readings of the focussing scale were checked next day, but were found unaltered at 11.0 mm. It seems doubtful whether much can be got from these plates.

Dyson, Eddington and Davidson 1920, p.309, footnote, quoting a note made at the time

These changes must be attributed to the effect of the sun’s heat on the mirror, but it is difficult to say whether this caused a real change of scale in the resulting photographs or merely blurred the images.

Dyson, Eddington and Davidson 1920, p.309

That second sentence is the whole problem. An outward deflection grows toward the Sun; a change of scale grows away from the plate’s centre. Across a field of a dozen stars the two patterns overlap, so a plate cannot measure both freely. The report’s Principe section put the cost in numbers:

Knowing the scale, the greatest relative deflection to be measured amounts to 1″.2 on Einstein’s theory; but if the scale is unknown and must be eliminated, this is reduced to 0″.67.

Dyson, Eddington and Davidson 1920, p.329

For the set-aside plates the report printed the measured declination shifts of the five bright stars on all 16 plates (p.311), combined them so that the deflection α enters strongly and the scale difference e weakly, and printed one value of “α + 0.240e” per plate. Everything then depends on what you take e to be. The page recomputes those sixteen values from the measures, and gives you e.

With the scale the plates’ own fits returned, 0.082 r, the recomputed line gives 0.913″. The report printed 0.93″. Its own printed mean and coefficient give 0.918″, and it rounded α to 0.024 r before converting, which alone is worth 0.017″; the other 0.005″ is the gap between the report’s printed mean and this page’s recomputation of it from the measures. Then it printed the alternative:

It may be noticed that the change of scale arising from differences of refraction and aberration is 0r.020. If this value of e be taken instead of 0r.082 we obtain α = +0r.039 = +1″.52 at the sun’s limb.

Dyson, Eddington and Davidson 1920, p.312

The recomputed line gives 1.498″ there. The report’s two other routes, both printed, give 0.860″ (Table IX, printed 0.86″) and 0.974″ (each plate’s own least squares, printed 0.99″). And its verdict on the lot:

There remain the Sobral astrographic plates which gave the deflection 0″.93 discordant by an amount much beyond the limits of its accidental error. For the reasons already described at length not much weight is attached to this determination.

Dyson, Eddington and Davidson 1920, p.331

The set-aside number is a line

The result the page can state, and that anyone can check from p.311 of the report: the set-aside deflection at the limb is 1.687″ − 9.43″ × e, where e is the assumed scale difference in micrometer turns. Each 0.01 r of assumed scale moves it by 0.094″. Einstein’s value needs a scale difference of −0.007 r, essentially none. Newton’s needs 0.087 r, almost exactly what the blurred plates’ own fits returned (0.082 r). The whole distance between the two theories on these plates is a scale difference of 0.093 r: 1.15″ at 50′ from the Sun, or 3.8 parts in 10,000 of the plate scale.

This is not a new observation. Daniel Kennefick made it in 2009: he set Harvey’s remeasurement beside the report’s alternative, and his article illustrates the two displacement patterns, deflection and change of scale, side by side (p.39):

What is most striking is the close agreement between the result for the astrographic lens and the alternative value given by Dyson and Crommelin in 1919.

Kennefick 2009, p.42

Although it could be coincidence, the reanalysis provides after-the-fact justification for the view that the real problem with the Sobral astrographic data was the difficulty, with the limited means available in 1919, of separating the scale change from the light deflection.

Kennefick 2009, p.42

What the page adds is the recomputation from the printed measures, the size of the scale difference in question, and your hand on it.

III · The deciding control

The same glass, remeasured in 1979

Most of the Sobral plates stayed in the Royal Greenwich Observatory’s archive. For the centenary of Einstein’s birth the plates were measured again, on a Zeiss Ascorecord, by E. D. Clements, and reduced with existing computer programmes, as G. M. Harvey reported in 1979: star positions against a reference catalogue averaged from the comparison plates, fitting six plate constants and one coefficient λ that multiplies the report’s own predicted Einstein displacements. λ = 1 is Einstein; λ = 0.497 is Newton.

Five eclipse and five comparison plates taken with the 4-inch, and 16 eclipse and 12 comparison plates taken with the Astrographic, were selected.

Harvey 1979, p.196

All ten of the 4-inch plates were reduced, but of the Astrographic plates only nine eclipse and nine comparison plates were selected, these having at least the ten images most commonly appearing.

Harvey 1979, p.196

On three of the Astrographic plates (numbers 2, 6 and 11) the measured displacements of the image nearest to the Sun were clearly in error, reflecting the difficulty in identifying and measuring a faint image within the corona. This star was excluded from the solutions for those three plates.

Harvey 1979, p.197

So the remeasurement of the set-aside plates rests on 9 of the 16 eclipse plates, with a star dropped on three of them, and one comparison plate excluded after a first solution. His Table II prints λ and its standard error for every plate he reduced, and states the rule for combining them:

Each value was assigned a weight equal to the reciprocal of the square of its standard error

Harvey 1979, p.197

Both of Harvey’s results reproduce from his own table: 1.908 ± 0.104″ against his 1.90 ± 0.11″, and 1.540 ± 0.334″ against his 1.55 ± 0.34″. His conclusion:

For the Astrographic plates, however, a significant improvement has been achieved by the new measurements. Where the previous reduction yielded a value of 0″.93 with an unspecified, large error, the new determination is 1″.55 ±0″.34. This is still a weak result, but does provide support for that from the 4-inch plates.

Harvey 1979, p.198

Combining the two fresh determinations, weighted according to their standard errors, gives 1″.87±0″.13, a result which is just within one standard error of the predicted value.

Harvey 1979, p.198

That combination does not follow from his stated rule. Weighting 1.90 ± 0.11″ and 1.55 ± 0.34″ by their inverse squared standard errors gives 1.867 ± 0.105″; the centre reproduces, the error does not, and no rounding of his printed values reaches 0.13″ (the widest the page can make it is 0.109″). With the rule’s error, the combined value sits 1.12 standard errors from Einstein’s, not “just within one”. One arithmetic route does return his number: averaging the two standard errors themselves, with the same weights as the values, gives 0.132″. The paper does not say how 0.13″ was reached, and the page draws no conclusion from the coincidence; 1.1 against 0.9 standard errors is no difference worth having.

Harvey had not reduced every plate. Ask for any Sobral astrographic plate and the page shows what each reduction printed for it:

IV · The control on the control

Could the 1979 remeasurement have decided?

A test that fails to tell two hypotheses apart has not chosen between them. So before reading Harvey’s astrographic value as support for anything, ask how far apart Einstein and Newton sit in units of that control’s own standard error. In λ they are 0.503 apart; the astrographic control’s standard error, from his printed per-plate errors by his own rule, is 0.191.

The rule, fixed and not offered as a choice: a control can decide between the two if, whichever were true, it would land at least two of its standard errors away from the other at least 97.7 per cent of the time. That needs the two hypotheses to sit at least 4 of its standard errors apart.

The page labels this grade B: Harvey printed no star positions, so it cannot plant a deflection in his measurements and rerun his plate solutions. It trusts his per-plate standard errors, his exclusions and his choice of plates, and computes what they imply. One check on that trust is possible from his own table: his plates scatter about his weighted means about as his errors say they should (chi-square 7.4 on 8 degrees of freedom for the astrographic plates, probability 0.49; 1.5 on 4 for the 4-inch, probability 0.83). On those terms the 4-inch remeasurement could decide, 8.47 standard errors between the hypotheses. The astrographic remeasurement, the only fresh look at the set-aside plates, could not: 2.64. If Einstein were true it would land two standard errors clear of Newton only 74 per cent of the time. Its value, 1.540″, sits 2.01 standard errors above Newton and 0.63 below Einstein. For the set-aside plates taken alone the page therefore says INCONCLUSIVE, which is close to what Harvey said himself: “still a weak result”. Dropping plate 12, the one negative value, moves the astrographic result to 1.908 ± 0.370″ and makes the control weaker, not stronger (2.38 standard errors between the hypotheses).

The 4-inch remeasurement is decisive, but it re-reads the plates the report already relied on. It checks the measuring and the reduction. It cannot check the decision to set the other plates aside.

V · The claimants’ method on nothing

Could their reduction manufacture Einstein from Newton?

Plant a known deflection in synthetic plates built like theirs and run the report’s procedure, the same function that reproduced 1.98″ above. The synthetic plates keep the seven stars’ geometry, each real plate’s fitted shift, rotation and scale, the scale-plate term the night plates share, and independent errors on every star with the spread of the real residuals, 0.0238 r, 0.149″ at 50′.

With Newton’s deflection planted, the report’s method returns 0.869″ on average with a spread of 0.136″, and reaches Einstein’s value in 0 of 10,000 runs. What this covers is accidental error at the level the plates themselves show. A systematic difference common to every eclipse plate, such as the daytime-against-night difference in the images that worried the observers, is outside it; that is why the report’s own discussion of systematic error, and the later independent measurements, matter.

VI · The second layer

Can the three 1919 results be averaged?

In 1980 the philosophers of science John Earman and Clark Glymour argued that the 1919 data selection was not justified. Gilmore and Tausch-Pebody, replying in 2022, quote them:

If one kept the data from all three instruments, the best estimate of the deflection would have to be somewhere between the Newtonian value and the Einstein value

Earman and Glymour 1980, as quoted by Gilmore and Tausch-Pebody 2022, p.164

We have carried out the missing calculations (detail in appendix A, table A4), and show Earman and Glymour’s guess is incorrect.

Gilmore and Tausch-Pebody 2022, p.164

Their calculation assigns the set-aside plates an error, and so must anyone’s, because the report printed none. Earman and Glymour gave the set 0.48″, and the reply explains where that number came from:

…the value they quote, 0.48 arcsec, is the internal dispersion of the 18 results of the 16 measured Sobral astrograph plates, provided one naively treats the dispersion as representing an underlying normal distribution. Earman and Glymour then consider this internal dispersion as equivalent to a standard deviation-like uncertainty on the mean, which would include a contribution from systematic errors.

Gilmore and Tausch-Pebody 2022, p.163

The reply’s own figure is the dispersion about the mean of its own least-squares fit, 0.9″ about 0.95″, which its Table A2 enters as the error on the mean. This page adds a third: the standard error of the mean that the plates’ own scatter gives. The error, and the scale assumed for the plates, decide the argument. Choose both:

With this page’s error, 0.127″ (each plate’s α from its own row of p.311 and its own Table IX scale; accidental error only, with the assumed scale taken as exact), and at the scale the blurred plates’ own fits returned, where the line gives 0.913″, the three results disagree at chi-square 24.4 on 2 degrees of freedom, a probability of 5.1 × 10⁻⁶, and the two Sobral instruments disagree with each other by 4.9 standard errors. The engine refuses to print an average of sets that disagree like that. An average exists, and it does land between Newton and Einstein, as the 1980 critique expected; but a number between two theories that three instruments do not agree on is a symptom, not a measurement.

That refusal belongs to the scale as much as to the error. With the same error, any set-aside value from 1.23″ to 2.63″ would pass, and the line leaves that range only for an assumed scale above 0.048 r. At the refraction scale the sets pass (chi-square 4.9, probability 0.087) and combine to 1.658 ± 0.101″, with the two Sobral instruments 2.2 standard errors apart.

The critique’s own error does not give the critique’s expectation. With the reply’s inputs and Earman and Glymour’s 0.48″ the sets are consistent and combine to 1.823 ± 0.158″, 0.46 standard errors from Einstein’s value; with the reply’s 0.9″, to 1.896 ± 0.164″. Gilmore and Tausch-Pebody’s rows reproduce here (the check lists them). Under those two errors the test can hardly fail: the set-aside plates carry 10.8 per cent and 3.3 per cent of the weight, and would pass with any value from 0.22″ to 3.63″, or from −1.14″ to 5.00″. With the reply’s inputs the combination falls below Einstein’s value only if the set-aside plates are given an error below 0.35″, 0.74 of the critique’s own figure. This page’s error is a dispersion divided by the square root of the number of plates, and the reply holds that for these plates no such error can be derived without a model:

Given the non-Gaussian error distribution and unknown systematics noted above, there is no model-independent way to use this dispersion to derive a standard error on the mean.

Gilmore and Tausch-Pebody 2022, p.175

So the argument turns on two numbers the report never printed: the error of the set-aside result, and the scale assumed for it.

The same test on the 1979 numbers: the 4-inch and astrographic remeasurements disagree by 1.0 standard errors, against 4.9 in the 1919 numbers at the plates’ own scale. The conflict is gone for two reasons, and the page can separate them. Moving only the astrographic value to 1979’s, with the 1919 errors, would leave 2.0 standard errors; widening only its error to 1979’s, 2.7 times this page’s, would leave 2.8. The remeasurement removed the conflict partly by moving the value and partly by being less precise, and by its own errors it could not decide between the theories (section IV).

VII · A fallback worth keeping

Same glass, sixty years apart

Harvey’s astrographic 1.540″ sits well above the report’s 0.86″ from Table IX, the report’s reduction most like his (every star, each plate its own scale). The rise, 0.680″, splits exactly into four steps. Counting plates 7 and 12 once each, instead of once per row, moves the mean of Table IX’s 18 rows from 0.860″ to 0.885″ (+0.025″). Keeping only the nine plates Harvey reduced moves it to 0.951″ (+0.066″): that is his choice of plates. His own values for the same nine plates average, unweighted, 1.686″ (+0.735″): that is the new measurement and reduction, which also used both coordinates and dropped a star on three plates, and the page cannot separate those. Weighting them by his rule brings the mean to 1.540″ (−0.146″).

Plate by plate, the two reductions do not track each other: the correlation over the nine is −0.30, consistent with no relation at all, which is what independent errors this size would give: with nine plates and no shared signal, a correlation scatters by about 0.35 either way. The page shows it rather than hides it. For the 4-inch, if Harvey’s plates 1, 4, 5, 7 and 8 are the report’s I, IV, V, VII and VIII (an inference: he says one of the seven is missing and one broken, and does not map the numbers), those five plates gave 2.01″ in the report’s reduction and 1.91″ in his.

VIII · The check

Every number, printed against recomputed

Tolerances were set from the sources’ own rounding before the comparison was made. “Printed” is the number as the source prints it; “recomputed” is this page’s engine on the transcribed tables.

Every free choice

• Table II cells. As the normal equations imply (default) or as printed: 1.980″ or 2.012″.
• Declination weight. 2 (default), the design ratio 1.79, or 1: 1.980″, 1.983″, 2.003″.
• Astrographic scale difference. Any value from −0.020 r to 0.170 r; outside that range the engine refuses, because no plate in Table IX and no printed calculation supports it. The range is padded beyond Table IX’s own 0.000 r to 0.166 r at both ends so that both crossings can be drawn; Einstein’s, at −0.007 r, lies in that padding, where the same objection applies.
• Astrographic route. Table IX (0.860″), five stars with a common scale (follows e), five stars per plate (0.974″).
• Orientation for plates 7 and 12. Mean of the two Table IX rows (default), first, second: at e = 0.082 r the line gives 0.913″, 0.906″, 0.920″.
• Control instrument. Astrographic, 4-inch or both, chosen separately for the recombination (section III) and for the power (section IV); and, for the astrographic power, leaving out any one of Harvey’s nine plates.
• Error assigned to the set-aside plates. This page’s 0.127″, with the set-aside value at the assumed scale; Earman and Glymour’s 0.48″, as Gilmore and Tausch-Pebody tested it; or Gilmore and Tausch-Pebody’s own 0.9″; the last two with the reply’s inputs; or none.
• Planted deflection in the null runs. Newton’s or none; any seed.

Fixed, not offered: the decision rule for the control (at least 4 standard errors between the hypotheses), the refusal level for averaging (a chi-square probability below 0.0027), and the conversion of probable to standard error (divide by 0.6745). There is no free “exclude a plate” menu on the 1919 data.

What remains uncertain

• Every table here is a transcription by eye from page scans, checked against the arithmetic the sources printed beside it. It is not a measurement of the plates. Where a printed number disagrees with that arithmetic the page says so and shows both.
• The Principe result is reproduced from its last stage only; the earlier steps are taken as printed.
• The set-aside 0.93″ has no printed error. Every statement about its significance, including this page’s accordance estimate, rests on an assigned error, and on the scale assumed for the plates.
• Harvey printed per-plate results, not star positions, so the control is recombined, not rerun, and its power is grade B. His plate numbers are read as the report’s.
• The null runs cover accidental error only, with Gaussian errors of the spread the plates show.
• The Will 2014 quotations were read in the arXiv text (arXiv:1403.7377v1) and checked against the published text as Europe PMC serves it: the four passages read the same, except that the published text sets the years without spaces around the dash.

The frozen files

data/sobral-4inch.json sha256 4fdab471f0ed634ac0635613a8b71ecc69afe717ef954ebd0148323198015bc4
data/sobral-astrographic.json sha256 88d6d751150cac067318ae776b328c096b90f0c287c4df6d1015f8faa94ffe3c
data/principe.json sha256 4a65cc1163cbd71b9413d964c2a033485cccc5f4bf7ca0aedd29e369c8ff2944
data/harvey1979.json sha256 30072e3d009c367e9dd307f75ec06260e1a8c91ec38693a72eb30f184759d27d
data/published.json sha256 f01a5ce56be49120a6b1b5050bb215c0d56397b7c985aeef41a37328f74ba449

IX · What the record decided

The verdict, dated

What decided it was not the 1919 plates, and not their 1979 remeasurement. Optical eclipse measurements after 1919 were not much better; radio interferometry, which does not need an eclipse, did it.

…the experiments of Eddington and his co-workers had only 30 percent accuracy… Succeeding experiments were not much better: the results were scattered between one half and twice the Einstein value…

Will 2014, section 4.1.1

A number of measurements of this kind over the period 1969 – 1975 yielded an accurate determination…

Will 2014, section 4.1.1

A 2004 analysis of almost 2 million VLBI observations of 541 radio sources, made by 87 VLBI sites yielded (1 + γ)/2 = 0.99992 ± 0.00023

Will 2014, section 4.1.1

In Harvey’s terms that last number is λ = 0.99992 ± 0.00023 (on that scale a deflection of exactly half Einstein’s is 0.5, and the report’s printed Newtonian value is 0.497), against the 0.191 standard error of the 1979 astrographic control: a sensitivity about 830 times finer. It is quoted, not recomputed. The current review of the field:

All currently performed gravitational experiments in the solar system, including perihelion advances of planetary orbits, the bending and delay of electromagnetic signals passing near the Sun, and very accurate ranging data to the Moon obtained by laser echoes, are compatible with the post-Newtonian results of Eq. (21.15), Eq. (21.13), and Eq. (21.14).

Damour, PDG 2026, section 21.5

What would change the verdict: A reproducible measurement of the Sun’s deflection of light, radio or optical, departing from the relativistic value by much more than its stated errors with its systematic errors controlled, would change this verdict. What would reopen only the narrower question of the set-aside plates, without touching the physics: a complete modern digitisation and scale-free reduction of the surviving Sobral astrographic plates returning a deflection near 0.87″ with an error well below 0.3″.

The narrower question, the set-aside plates: INCONCLUSIVE on the remeasurement alone. The 1979 values remove the conflict between the two Sobral instruments, partly by being less precise, and lean toward Einstein on those plates, but by their own printed errors they cannot decide between Einstein and Newton. The physics did not need them to.

Who decided what, and the replies

The Sobral reductions, and the decision to give the astrographic plates little weight, were the Greenwich team’s, under the Astronomer Royal, F. W. Dyson; the Sobral observers were A. C. D. Crommelin and C. Davidson. The Principe observations were A. S. Eddington’s and E. T. Cottingham’s. The report flagged the astrographic trouble before any reduction, in the note of 30 May, printed the 1.52″ alternative beside the 0.93″, and weighed Principe well below Sobral’s 4-inch:

The photographs taken with the astrographic telescope support those obtained by the “4-inch” to the extent that they show considerable outward deflection, but for the reasons already given are of much less weight.

Dyson, Eddington and Davidson 1920, p.312

In summarising the results of the two expeditions, the greatest weight must be attached to those obtained with the 4-inch lens at Sobral.

Dyson, Eddington and Davidson 1920, p.330

The authors could not answer the 1979 control; Dyson died in 1939 and Eddington in 1944. Earman and Glymour’s 1980 paper is an argument about data selection and about the errors assigned to each set. Gilmore and Tausch-Pebody’s 2022 reply recomputes the combinations with the errors they assign, and adds a caution about Harvey:

Harvey does not re-analyse the exact same set of stars and plates used by the 1919 report, so his conclusions in detail are not exactly comparable.

Gilmore and Tausch-Pebody 2022, p.161

…the Sobral astrograph results do not allow any distinction between any of the three hypotheses…

Gilmore and Tausch-Pebody 2022, p.175

Kennefick, in 2009, gave the historical judgment and the reading of the remeasurement that this page tests:

…there are good grounds for believing that Dyson made the scientifically correct decision in choosing to ignore the astrographic data.

Kennefick 2009, p.41

Indeed, their treatment of the data appears to be vindicated by a subsequent 1979 reanalysis of their plates using modern astrometric data-reduction methods.

Kennefick 2009, p.38

This page agrees with the first sentence and narrows the second, as Kennefick’s own hedge on p.42, quoted in section II, already does. The 1979 reanalysis vindicates the report’s 4-inch result decisively. On the set-aside plates it is consistent with the decision and cannot, by its own errors, confirm it.

The page’s own result

Recomputed from the numbers the 1920 report printed, the Sobral 4-inch plates give 1.980″ and Principe 1.608″, both near Einstein’s 1.75″ and far from Newton’s 0.87″; the set-aside plates give 0.913″ or 1.498″ depending on one assumed plate scale, the two theories lying 0.093 r of scale apart; and the 1979 remeasurement of those plates, 1.540 ± 0.334″, separates Newton from Einstein by only 2.64 of its own standard errors, too few to decide on its own.

We searched the Artificial Wasteland index and the open web on 2026-09-22 and did not find an interactive page that recomputes the 1919 Sobral astrographic result from the five-star measures printed in the 1920 report as a function of the assumed plate scale, beside the 1979 plate-by-plate remeasurement. Closest precedents: Kennefick 2009 (the observation, and an illustration of the two displacement patterns), Gilmore and Tausch-Pebody 2022 (a static reanalysis of the printed data), and Goldoni and Stefanini, arXiv:2002.01179 (a century of light-bending measurements, brought into the classroom).

Sources

1. F. W. Dyson, A. S. Eddington and C. Davidson, “A determination of the deflection of light by the sun’s gravitational field, from observations made at the total eclipse of May 29, 1919”, Philosophical Transactions of the Royal Society of London, Series A, 220, 291 to 333. Received 30 October 1919, read 6 November 1919, published 27 April 1920. DOI 10.1098/rsta.1920.0009. Read from a full scan at astronomyforchange.org (the publisher’s PDF answered scripts with a challenge page). doi.org/10.1098/rsta.1920.0009
2. G. M. Harvey, “Gravitational Deflection of Light: A re-examination of the observations of the solar eclipse of 1919”, The Observatory 99, 195 to 198 (December 1979). ADS 1979Obs....99..195H. Plates measured by E. D. Clements; the author thanks C. A. Murray for guidance throughout the work. ADS scan.
3. Gerard Gilmore and Gudrun Tausch-Pebody, “The 1919 eclipse results that verified general relativity and their later detractors: a story re-told”, Notes and Records: the Royal Society Journal of the History of Science 76, 155 to 180 (2022; published online 21 October 2020). DOI 10.1098/rsnr.2020.0040. CC BY 4.0. doi.org/10.1098/rsnr.2020.0040
4. Daniel Kennefick, Physics Today 62(3), 37 to 42 (March 2009). DOI 10.1063/1.3099578. Title as printed: “Testing relativity from the 1919 eclipse—a question of bias”. doi.org/10.1063/1.3099578
5. John Earman and Clark Glymour, “Relativity and Eclipses: The British Eclipse Expeditions of 1919 and Their Predecessors”, Historical Studies in the Physical Sciences 11(1), 49 to 85 (1980). DOI 10.2307/27757471. Quoted here only as quoted by Gilmore and Tausch-Pebody.
6. Clifford M. Will, “The Confrontation between General Relativity and Experiment”, Living Reviews in Relativity 17, 4 (published 11 June 2014). DOI 10.12942/lrr-2014-4. CC BY 4.0. Quoted from the arXiv text, arXiv:1403.7377v1, and checked against the published text (Europe PMC, PMC5255900), where the four passages quoted here read the same except that the years are set as 1969–1975, without spaces. arXiv:1403.7377v1
7. T. Damour, “21. Experimental Tests of Gravitational Theory”, revised August 2025, in Review of Particle Physics (Particle Data Group), 2026 web edition, pages dated 1 June 2026. pdg.lbl.gov
8. S. S. Shapiro, J. L. Davis, D. E. Lebach and J. S. Gregory, Physical Review Letters 92, 121101 (26 March 2004). DOI 10.1103/PhysRevLett.92.121101. The 2004 VLBI analysis Will quotes; its value is taken from Will, not from the paper.

Only transcribed numbers and short attributed quotations are used; no scan or page image is reproduced. Sources and terms · machine-readable claim record · frozen transcriptions: 4-inch, astrographic, Principe, Harvey 1979, later papers.