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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 electromagnetic
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 has been given, but the eclipse was
an unfavourable one, and from the information published the probable accidental
error is large, so that the accuracy is insufficient to discriminate between
the three alternatives. » |
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« 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.
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+0.00000414/r, where
r is the distance from the centre in 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 a 1/20 atmospheric pressure. Clearly
a density of this order is out of the question.
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| Preparations
for the expedition |
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« 5.
In March, 1917, it was pointed out, as a result of
an examination of the photographs taken with the Greenwich
Astrographic Telescope at the eclipse
of 1905, that this instrument was suitable
for the photography of the field of stars surrounding the Sun in a total
eclipse.
Attention was also drawn to the importance of
observing the eclipse of May 29, 1919,
as this afforded a specially favourable
opportunity owing to the unusual
number of bright stars in the field, such
as would not occur again for many years.
With weather conditions as good as those at Sfax
in the 1905 eclipse – and these were by no means perfect – it
was anticipated that twelve stars would be shown.
Their positions are indicated in the diagram
on next page, on which is also marked
on the same scale the outline of a 16 x 16 cm plate (used with the astrographic
telescopes of 3.43 metres focal length) and a 10 x 8-inch plate (used with
a 4 –inch lens of 19 feet focal length).
It may be noted that No.1 is lost in the corona
on the photographs taken at Sobral. The
star, No. 13, of magnitude 8•0, is shown on some of the astrographic plates
at Sobral. »
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« 6.
The track of the eclipse
runs from North Brazil across the Atlantic, skirting the African coast
near Cape Palmas, passing through the
Island of Principe, then across Africa to the western shores of Lake Tanganyika.
Enquiry as to the suitable sights and probable
weather conditions was kindly made by Mr. Hinks.
It appeared that a station in North
Brazil,
the Island of Principe in Africa,
and a station on the west of Lake Tanganyika
were possible.
A station near Cape Palmas did not seem desirable
from the meteorological reports though, as the event proved, the eclipse
was observed in a cloudless sky by Prof. Bauer, who was there on an expedition
to observe magnetic effects.
At the station at Tanganyika it was thought
the Sun was at too low an altitude for observations of this character ,
owing to the large displacements which would be caused by refraction.
A circular received from Dr. Morizethe Director
of the Observatory at Rio, stated that Sobral
was the most suitable station in North Brazil
and gave copious information on the meteorological conditions, mode of
access &c ...
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Preparations and the many
necessary precautions ...
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| « 7.
Acting on this information, the Joint Permanent Eclipse
Committee at a meeting on November 10, 1917, decided, if possible, to send
expeditions to Sobral in North Brazil and
to the Island of Principe. Application
was made to the Government Grant Committee for £ 100
for instruments and £ 1000 for the expedition,
and a sub-committee consisting of Sir F. W. Dyson, Prof. Eddington, Prof.
Fowler and Prof. Turner was appointed to make arrangements for the expeditions.
This sub-committee met in May and June 1918, and
made provisional arrangements for Prof. Eddington and Mr. Cottingham to
take the object glass of the Oxford astrographic
telescope to Principe, and Mr. Davidson
and Father Cortie to take the object glass
of the Greenwich astrographic telescope to Sobral.
It was arranged for the clocks and mechanism
of the cœlostats to be overhauled by Mr.
Cottingham.
Preliminary inquiries were also set on foot as
to the shipping facilities, from which it appeared very doubtful whether
the expeditions could be carried through.
Conditions had changed materially in Novemeber,1918,
and at a meeting of the sub-committee on November 8 it
was arranged to assemble the instruments at Greenwich,
and make necessary arrangements with all speed, for the observers to leave
England by the end of February 1919. In addition to the astrographic object
glasses fed by 16-inch cœlostats,
Father Cortie suggested to the sub-committee
the use of the 4-inch telescope of 19-feet focus, which he had used at
Hernosand, Sweden, in 1914, in conjunction with an 8-inch cœlostat, the
property of the Royal Irish Academy. It
was arranged to ask for the loan of these instruments. As Father Cortie
found it impossible to spare the necessary time for the expedition, his
place was taken by Dr. Crommelin of the Royal Observatory.
8. In
November, 1918 the only workman available at the Royal Observatory was
the mechanic, the carpenter not having
been released for military service. In these circumstances Mr. Bowen, the
civil engineer at the Royal Naval College, was consulted. He kindly undertook
the construction of frame huts covered with canvas, which could be easily
packed and readily put together. These were generally similar to those
used in previous expeditions from the Royal Observatory (see "Monthly Notices",
vol. LVII, p.101). He also lent the services of a joiner who worked at
the Observatory on the woodwork of the instruments.
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Preparations and the many
necessary precautions ...
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| « It
was found possible to obtain steel tubes for the astrographic objectives.
These were, for convenience of carriage, made in two sections which could
be bolted together. The tubes were provided with flanges at each end, the
objective being attached to one of these, and a wooden breech piece to
the other. In the breech piece suitable provision was made for the focusing
and squaring of the plates. The plate holders were of simple construction,
permitting the plate to be pushed into contact with three metal tilting
screws on the breech piece thus ensuring a constancy of focal plane. Eighteen
plate-carriers were obtained for each of the astrographic telescopes, made
according to a pattern supplied.
With the 4–inch lens Father Cortie, lent the
square wooden tube used by him in 1914.
This was modified at the breech end to secure greater
rigidity and constancy of focus.
It was designed for dark slides carrying 10
x 8 inch plates, and four of these, carrying
eight plates, were lent with the telescope. The desirability of using larger
plates was considered, but the time at disposal to make the necessary alterations
was insufficient.
The 16-inch cœlostats,
which had been overhauled by Mr. Cottingham, were mounted and tested as
far as the unfavourable weather conditions of February, 1919, would permit.
The 8- inch cœlostat
was constructed for these latitudes. To make it serviceable near the equator
a strong wooden wedge was made on which the cœlostat
was bolted. The 8-inch mirror was silvered
at the observatory, but owing to lack
of facilities for maintaining a uniform temperature approaching 60°
F in the wintry weather of February, the larger mirrors were sent away
to be silvered.
Photographic plates, suitably packed in hermetically
sealed tin boxes, were obtained from the Ilford and Imperial Companies.
The Ilford plates employed were "Special Rapid & Empress", and those
of the Imperial Company "Special Sensitive, Sovereign & Ordinary".
The instruments were carefully packed and sent
to Liverpool a week in advance, with the exception of the objectives.
These were packed in cases inside hampers and
remained under the personal care of the observers, who embarked on the
"Anselm" on March 8. » |
The set up and the run in
...
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| « 10.
... the race course of the Jockey Club was provided with a covered grand
stand, which we found most convenient for unpacking and storage and in
the preparatory work. We laid down a meridian
line, after which brick piers were constructed
for the cœlostats
and for the steel tube of the astrographic telescope. Whilst this was in
progress, the huts were being erected.
The pier of the small cœlostat
was constructed so as to leave a clear space in the middle of one end for
the fall of the weight, which was thus
below the driving barrel of the clock.
By continuing the hole below the foundations of the pier, space was provided
for a fall of the weight permitting a run
of 25 minutes. In the case of the 16-inch
cœlostat, the clock was mounted on
the top of a long wooden trunk, nearly 4 feet in length, which was placed
on end, and sunk in the earth to a depth of about 2 feet. The weight descended
inside the trunk directly from the driving barrel, and had space for a
continuous run of over half-an-hour.
The 16-inch cœlostat had free adjustment for
all latitudes; but the
8-inch one, constructed for European latitudes, was mounted on a wooden
base, inclined at an angle of about 40 degrees, constructed before leaving
Greenwich. The clock had to be separated
from the cœlostat,
mounted on a wooden base and reversed, to adjust to the Southern Hemisphere.
It performed very satisfactorily and no elongation of the star images is
shown with 28 seconds’ exposure.
To provide for the changing declination of the
Sun, the piers of the astrographic telescope were made with groves in the
top in which the wooden V-supports of the
tube could slide, thus allowing for the change of azimuth.
The tube of the astrographic telescope was circular
in section, and could rest in any position in the Vs; for convenience it
was adjusted so that the directions of R.A. and declination were parallel
to the sides of the plate; this involved a tilt of the plate holders of
about 4 degrees to the horizontal. »
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The
set up and the run in ...
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| « The
4-inch lens was taken as an auxiliary; we used the square
wooden tube, 19 –feet in length, originally
used by Father Cortie at Hernosand in 1914, together
with the 10 x 8-inch plate carriers. Study
of the star-diagram showed that seven stars
could be photographed by turning the plate through 45 degrees.
The tube was therefore placed on its angle, large wooden V-supports being
prepared to fit the tube; these rested on strong wooden trestles.
The focusing was at first done visually on
Arcturus, using an eyepiece fitted with
a cobalt glass (after the plate supports and the object-glass had been
adjusted for perpendicularity to the axis).
A series of exposures was then made, the focus
being varied slightly so as to cover a sufficient range.
Examination of these photographs showed at once that there was serious
astigmatism due to the figure of the mirror
of the 16 –inch cœlostat. By inserting
an 8-inch stop this was reduced to a large extent, and this stop was henceforth
used though-out; but the defect was of such a character that it was clear
that it would be necessary to stay at Sobral and obtain comparison plates
of the eclipse field in July when the Sun had moved away.
The focus of the 4–inch was determined in a
similar manner. The images, though superior
to those of the astrographic, were not quite perfect, and here again comparison
plates in July were necessary. Once the
focus had been decided on, the breech end was securely screwed up to avoid
any changes of subsequent movement.
A few check plates of the field near Arcturus
were taken, but have not been used. » |
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The set up and the run in
...
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| « 12.
Although water was generally scarce, we were very fortunately situated,
as we enjoyed, an unlimited supply of good water laid on at the house.
This was of great benefit in the photographic operations. Ice was unobtainable,
but by the use of earthen-ware water coolers it was possible to reduce
the temperature to about 75° F, and, by working only at night, or before
dawn, development of the plates was fairly easy.
Formalin was used in every case to harden the
films, and thereby minimise the chance of distortion due to the softening
of the films by the warm solutions. We
had provided ourselves with two brands
of plates, but it had become apparent
from photographs taken and developed before the eclipse that one
of these brands was unsuitable in the hot climate, and it was decided to
use practically only one brand of plates.
In taking the experimental photographs it was
noticed that the clocks and cœlostats were
very sensitive to wind. We had reason
to fear strong gusts about the time of totality, such as had occurred in
other eclipses; and as the conditions of our locality seemed to render
them specially probable, protective wind
screens were erected round the hut openings at
every point where it was possible without interfering with the field of
view. Happily dead calm prevailed at the critical time. Screens also protected
all projecting parts of the telescopes tubes from direct Sun-light.
The performance of the 16 –inch cœlostat was
unsatisfactory in respect of driving.
There was a clearly marked oscillation of the images on the screen in a
period of about 30 seconds. For this reason exposure
time was shortened, so as to multiply the number of exposures in the hope
that some would be near the stationary points.
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"D" day ...
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| « 13.
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. Leocadio, 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 a uniform exposure of 28 seconds.
The region round the Sun was free 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. » |
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The great result !!! ...
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Eddington’s
photograph showing the “deviation”
of two stars due to the Sun’s
deflection of the space ... |
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Dismounting: departure and
return to secure the comparison plates ...
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| « 15.
On June 7, having completed the development,
we left Sobral for Fortaleza, returning on July 9 for the purpose of securing
comparison plates of the eclipse field.
Before our departure we dismounted the mirrors
and driving clocks which were brought into the house to avoid the exposure
to dust. The
telescopes and cœlostats were left "in situ".
Before removing the mirrors we marked their
positions in their cells so that they
could be replaced in exactly the same position.
After our return to Sobral the mirrors and
clocks were remounted.
The photography of the eclipse field was commenced
on the morning of July 11 (civil).
The difficulty of finding the field with the
cœlostats was overcome by making a rough hour circle on the heads of the
cœlostats out of millimetre paper.
17. The
micrometer at the Royal Observatory is not suitable for the direct comparison
of plates of this size.
It was therefore decided to
measure each plate by placing, film to film upon it, another photograph
of the same region reversed by being taken through the glass.
A photograph for this purpose was taken on July 18.
This plate is regarded merely as an intermediary
between the eclipse plates and comparison plates and is referred to as
the scale plate, being used simply as a scale providing points of reference.
In all cases measurement was made through
the glass of the scale plate.
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General conclusions
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| « 39.
In summarizing 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 recognized 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:
from declinations
1".94
from right ascensions
2".06
the result from declinations is about twice the
weight of that from right ascensions, so
that the mean result is 1".98 ±
0".12.
The Principe observations were generally interfered
with by cloud. The unfavourable circumstances
were perhaps partly compensated by the advantage of the extremely uniform
temperature of the island.
The deflection obtained was 1".61 ±
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 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.
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| Eddington’s
diagram ... |
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« The
evidence is summarised in the following table and diagram,
which show the radial displacement of the individual stars (mean from all
the plates) plotted against the reciprocal of the distance from the centre.
The displacement according to Einstein’s
theory is indicated by a heavy blue line;
according to the Newtonian law by the dotted
line, and from these
Observations by the thin line.
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Are Eddington’s measurements
reliable ? ....
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| The original precision seemed, however, poor.
Dyson & others,
optimistically, underlined the measurements could be slightly inaccurate.
Others asserted, due to systematic errors, but also to prejudice. Modern
re-visitations of the data proved that Eddington’s analysis was accurate
(*).
The quality of the measurement was doubted for
about fifty years, until observations could be carried out with the use
of radio frequencies.
Only in 1960 it was finally proved the amount
of deflection was exactly that foreseen by Einstein’s generalised theory
of relativity, and not its half.
(*) a simple
study I made, on the displacements declared and the physical dimension
of the image, shows that Eddingnton, in
order to measure about 1 arc-second deflection
(star n°2 and star n°3), should
have measured on a plate 0.02 mm over a distance of many centimetres.
The precision of a hundredth of a millimetre
is requested. "A
star distant twice its radius from the centre of the Solar disc, for example,
considering that the principal telescopes had a focal length of about 3.5
m., due to deflection would have varied its position on the plate by 0.01
mm. only! "
(l'Astronomia - n° 296)
Experts said that with a microscope and micrometric
slides such measurement is possible. Modern scanners have no difficulty
to distinguish microns. |
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