A Determination of the Deflection of Light by the Sun’s Gravitational Field,from Observations Made at the Total Eclipse of May 29, 1919

Frank Watson Dyson, Arthur Stanley Eddington and Charles Davidson

PURPOSE OF THE EXPEDITIONS

1. The purpose of the expeditions was to determine what effect, if any, is produced by a gravitational field on the path of a ray of light traversing it. Apart from possible surprises, there appeared to be three alternatives, which it was especially desired to discriminate between—

   (1) The path is uninfluenced by gravitation.

   (2) The energy or mass of light is subject to gravitation in the same way as ordinary matter. 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.

   (3) The course of a ray of light is in accordance with Einstein’s generalized relativity theory. This leads to an apparent displacement of a star at the limb amounting to 1".75 outwards.

In either of the last two cases the displacement is inversely proportional to the distance of the star from the surfs centre, the displacement under (3) being just double the displacement under (2).

It may be noted that both (2) and (3) agree in supposing that light is subject to gravitation in precisely the same way aa ordinary matter. The difference is that, whereas (2) assumes the Newtonian law, (3) assumes Einstein’s new law of gravitation. The slight deviation from the Newtonian law which on Einstein’s theory causes an excess motion of perihelion of Mercury, becomes magnified as the speed increases, until for the limiting velocity of light it doubles the curvature of the path.

2. The displacement (2) was first suggested by Prof. Einstein in 1911, his argument being based on the Principle of Equivalence, viz., that a gravitational field is indistinguishable from a spurious field of force produced by an acceleration of the axes of reference. But apart from the validity of the general Principle of Equivalence there were reasons for expecting that the electrornagnetic energy of a beam of light would be subject to gravitation, especially when it was proved that the energy of radio-activity contained in uranium was subject to gravitation. In 1915, however, Einstein found that the general Principle of Equivalence necessitates a modification of the Newtonian law of gravitation, and that the new law leads to the displacement (3).

3. The only opportunity of observing these possible deflections is afforded by a ray of light from a star passing near the sun. (The maximum deflection by Jupiter is only 0".017.) Evidently, the observation must be made during a total eclipse of the sun.

Immediately after Einstein’s first suggestion, the matter was taken up by Dr. E. Freundlich, who attempted to collect information from eclipse plates already taken; but he did not secure sufficient material At ensuing eclipses plans were made by various observers for testing the effect, but they failed through cloud or other causes. After Einstein’s second suggestion had appeared, the Lick Observatory expedition attempted to observe the effect at the eclipse of 1918. The final results are not yet published. Some account of a preliminary discussion his been given, but the eclipse was an unfavorable one, and from the information published the probable accidental error is large, so that the accuracy is insufficient to discriminate between the three alternatives.

4. The results of the observations here described appear to point quite definitely to the third alternative, and confirm Einstein’s generalised relativity theory. As is well-known the theory is also confirmed by the motion of the perihelion of Mercury, which exceeds the Newtonian value by 43" per century—an amount practically identical with that deduced from Einstein’s theory. On the other hand, his theory predicts a displacement to the red of the Fraunhofer lines on the sun amounting to about 0.008 Å in the violet. According to Dr. St. John this displacement is not confirmed. If this disagreement is to be taken as final it necessitates considerable modifications of Einstein’s theory, which it is outside our province to discuss. But, whether or not changes are needed in other parts of the theory, it appears now to be established that Einstein’s law of gravitation gives the true deviations from the Newtonian law both for the relatively slow-moving planet Mercury and for the fast moving waves of light.

The spatial positions of the stars near the sun during the solar eclipse of May 29, 1919. The sun moved from S to P in the interval between totality at Sobral, Brazil, and at the Island of Principe. The angular scale of the diagram can be inferred from the disk of the sun, which is 31.6 min of arc in angular diameter.

Table 123.1 Expected gravitational displacements of star positions

			Coordinates (unit=50’)		Gravitational displacement
					Sobral		Principe
No.	Names	Photog. mag.	x	y	x	y	x	y
		m.			"	"	"	"
1	B.D., 21°, 641	7.0	+0.026	-0.200	-1.31	+0.20	-1.04	+0.09
2	Piazzi, IV, 82	5.8	+1.079	-0.328	+0.85	-.09	+1.02	-.16
3	K2 Tauri	5.5	+0.348	+0.360	-0.12	+.87	-0.28	+.81
4	K1 Tauri	4.5	+0.334	+0.472	-0.10	+.73	-0.21	+.70
5	Piazzi, IV, 61	6.0	-0.160	-1.107	-0.31	-.43	-0.31	-.38
6	v Tauri	4.5	+0.587	+1.099	+0.04	+.40	+0.01	+.41
7	B.D., 20°, 741	7.0	-0.707	-0.864	-0.38	-.20	-0.35	-.17
8	B.D., 20°, 740	7.0	-0.727	-1.040	-0.33	-.22	-0.29	-.20
9	Piazzi, IV, 53	7.0	-0.483	-1.303	-0.26	-.30	-0.26	-.27
10	72 Tauri	5.5	+0.860	+1.321	+0.09	+.32	+0.07	+.34
11	66 Tauri	5.5	-1.261	-0.160	-0.32	+.02	-0.30	+.01
12	53 Tauri	5.5	-1.311	-0.918	-0.28	-.10	-0.26	-.09
13	B.D., 22°, 688	8.0	+0.089	+1.007	-0.17	+.40	-0.14	+.39

It seems clear that the effect here found must be attributed to the sun’s gravitational field and not, for example, to refraction by coronal matter. In order to produce the observed effect by refraction, the sun must be surrounded by material of refractive index 1 qqq .00000414/r. where r is the distance from the centre m terms of the sun’s radius. At a height of one radius above the surface the necessary refractive index 1.00000212 corresponds to that of air at 1/140 atmosphere, hydrogen at 1/60 atmosphere, or helium at 1/20 atmospheric pressure. Clearly a density of this order is out of the question.

PREPARATIONS FOR THE EXPEDITIONS

In late 1917 it was noted that the eclipse of May 29, 1919, was especially favorable for testing Einstein’s theory because of the unusual number of bright stars in the field of stars surrounding the sun. As the eclipse track ran from North Brazil across the Atlantic Ocean through the Island of Principe and then across Africa, an application was made to the English government for a grant of 1,100 pounds to cover expenses for expeditions to Sobral, North Brazil, and to the Island of Principe. The photographic magnitudes, standard coordinates, and expected gravitational displacements for the stars visible at the two sights are given in table 123.1. Here the gravitational displacements are calculated on the assumption of a radial displacement of 1.75 ro/r sec of arc, where r is the distance from the sun’s center and r0 is the radius of the sun.

Figure 123.1 shows the relative positions of the stars given in table 123.1. The square shows the limits of the plates used at Principe and the oblique rectangle the limits with the 4-in lens at Sobral. The sun moved from S to P m the 2.25-h interval between totality at the two stations, and the sun is here represented as midway between them.

THE EXPEDITION TO SOBRAL

For the expedition to Sobral, the Greenwich astrographic telescope of 3.43-m focal length was stopped to 8 in, mounted in a steel tube, and fed with a 16-in coelstat. An auxilliary 4-in lens was mounted in a 19-ft-long square wooden tube in conjunction with an 8-in coelstat. A description of the moment of eclipse follows. [p.830]

The morning of the eclipse day was rather more cloudy than the average, and the proportion of cloud was estimated at 9/10 at the time of first contact, when the sun was invisible: it appeared a few seconds later showing a very small encroachment of the moon, and there were various short intervals of sunshine during the partial phase which enabled us to place the sun’s image at its assigned position on the ground glass, and to give a final adjustment to the rates of the driving clocks. As totality approached, the proportion of cloud diminished, and a large clear space reached the sun about one minute before second contact. Warnings were given 58s., 22s. and 12s. before second contact by observing the length of the disappearing crescent on the ground glass. When the crescent disappeared the word "go" was called and a metronome was started by Dr. Leocadino, who called out every tenth beat during totality, and the exposure times were recorded in terms of these beats. It beat 320 times in 310 seconds: allowance has been made for this rate in the recorded times. The programme arranged was carried out successfully, 19 plates being exposed in the astrographic telescope with alternate exposures of 5 and 10 seconds, and eight in the 4-inch camera with a uniform exposure of 28 seconds. The region round the sun was flee from cloud, except for an interval of about a minute near the middle of totality when it was veiled by thin cloud, which prevented the photography of stars, though the inner corona remained visible to the eye and the plates exposed at this time show it and the large prominence excellently defined. The plates remained in their holders until development, which was carried out in convenient batches during the night hours of the following days, being completed by June 5.

Reference photographs of the eclipse field were made on July 11 from the same station with the same instruments as those used to photograph the eclipse. The positions of the stars on the reference and eclipse photographs were then compared to obtain a mean displacement of 0.625 sec of arc at a distance of 50 min of arc from the sun center for the photographs taken with the 4-in object glass. Because the radius of the sun at the time of the eclipse was 15.8 min of arc, the observed displacement is equivalent to a 1.98 sec of arc deflection at the limb. After making corrections for differential refraction, aberration, plate orientation, and changes of scale, the displacements of the different stars given in table 123.2 were established. In this table the calculated values are those given by Einstein’s theory with the value of 1.75 sec of arc at the sun’s limb.

Table 123.2 Displacements of star positions

	Displacement in right ascension		Displacement in declination
	Observed	Calculated	Observed	Calculated
No. of star	(")	(")	(")	(")
11	-0.19	-0.32	+0.16	+0.02
5	-.29	-.31	-0.46	-.43
4	-.11	-.10	+0.83	+.74
3	-.20	-.12	+1.00	+.87
6	+.10	+.04	+0.57	+.40
10	-.08	+.09	+0.35	+.32
2	+.95	+.85	-0.27	-.09

The photographs taken with the astrographic object glass had diffuse images caused by focusing changes induced by the sun’s heat. The results were of poorer quality than those taken with the 4-in refractor: they conflicted with the latter results, in that a mean deflection of 0.93 sec of arc was obtained when the observations were referred to the sun’s limb.

THE EXPEDITION TO PRINCIPE

For the expedition to Principe, the Oxford astrographic telescope was stopped to 8 in and fed with a 16-in coelstat. A description of the moment of eclipse follows.

The days preceding the eclipse were very cloudy On the morning of May 29 there was a very heavy thunderstorm from about 10 a.m. to 11:30 a.m. a remarkable occurrence at that time of year. The sun then appeared for a few minutes, but the clouds gathered again. About half-an-hour before totality, the crescent sun was glimpsed occasionally and by 1.55 it could be seen continuously through drifting cloud. The calculated time of totality was from 2h. 13m. 5s. to 2h. 18m. 7s. G.M.T. Exposures were made according to the prepared programme, and 16 plates were obtained. Mr. Cottingham gave the exposures and attended to the driving mechanism and Prof. Eddington changed the dark slides. It appears from the results that the cloud must have thinned considerably during the last third of totality, and some star images were shown on the later plates. The cloudier plates give very fine photographs of a remarkable prominence which was on the limb of the sun.

A few minutes after totality the sun was in a perfectly clear sky, but the clearance did not last long. It seems likely the break up of the clouds was due to the eclipse itself, as it was noticed that the sky usually cleared at sunset.

In addition to the eclipse plates, a check field including Arcturus was photographed at Oxford and at Principe. Comparison photographs of the eclipse field could not be made at nighttime for several months. The check plates were used to show that none of the displacements exhibited on the eclipse plates were present on the plates of the held containing Arcturus. The inference is that the displacements in the former case could only be attributed to the presence of the eclipsed sun in the field.

lf X and W denote the eclipse plates and G, H, D, and I denote comparison plates taken at Oxford, the following results are obtained for the equivalent limb deflection.

The four determinations from the two eclipse plates are

giving a mean of 1.65 sec of arc, with a probable error of 0.30 sec of arc. They evidently agree with Einstein’s predicted value 1".75.

GENERAL CONCLUSIONS

In summarising the results of the two expeditions, the greatest weight must be attached to those obtained with the 4-inch lens at Sobral. From the superiority of the images and the larger scale of the photographs it was recognised that these would prove to be much the most trustworthy. Further, the agreement of the results derived independently from the right ascensions and declinations, and the accordance of the residuals of the individual stars provides a more satisfactory check on the results than was possible for the other instruments. These plates gave

The result from declinations is about twice the weight of that from right ascensions, so that the mean result is

with a probable error of about qqq 0".12.

The Principe observations were generally interfered with by cloud. The unfavorable circumstances were perhaps partly compensated by the advantage of the extremely uniform temperature of the island. The deflection obtained was

The probable error is about qqq 0".30, so that the result has much less weight than the preceding.

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 There remain the Sobral astrographic plates which gave the deflection

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.

It has been assumed that the displacement is inversely proportional to the distance from the sun’s centre, since all theories agree on this, and indeed it seems clear from considerations of dimensions that a displacement if due to gravitation, must follow this law. From the results with the 4-inch lens, some kind of test of the law is possible though it is necessarily only rough. The evidence is summarised in figure 123.2, which shows the radial displacement of the individual

The mean radial displacement of the positions of stars near the sun during the solar eclipse of May 29, 1919, plotted against the angular distance of each star from the center of the sun in minutes of arc. The displacement according to Einstein’s theory is indicated by the middle line, that according to the Newtonian law by the dashed line, and that from these observations by the top line.

stars (mean from all the plates) plotted against the reciprocal of the distance from the centre.

Thus the results of the expeditions to Sobral and Principe can leave little doubt that a deflection of light takes place in the neighborhood 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. But the observation is of such interest that it will probably be considered desirable to repeat it at future eclipses. The unusually favorable conditions of the 1919 eclipse will not recur, and it will be necessary to photograph fainter stars, and these will probably be at a greater distance from the sun. This can be done with such telescopes as the astrographic with the object-glass stopped down to 8 inches, if photographs of the same high quality are obtained as in regular stellar work. It will probably be best to discard the use of coelostat mirrors. These are of great convenience for photographs of the coronal and spectroscopic observations, but for work of precision of the high order required, it is undesirable to introduce complications, which call be avoided, into the optical train. It would seem that some form of eq uatorial mounting (such as that employed in the Eclipse Expeditions of the Lick Observatory) is desirable.

1. Annalen der Physik 35, 898.

2. Observatory 42, 298.

3. Astrophysical Journa1 46, 249.