When the top of a tower of height h emits light with frequency f and
speed c (relative to the emitter), a receiver on the ground measures
the frequency to be f'=f(1+gh/c^2), a result confirmed by the Pound-
Rebka experiment, and the speed to be c'=c(1+gh/c^2). In the period
1907-1914 Einstein had to put up with this conclusion of Newton's
emission theory of light and even used it explicitly. Still, in 1911,
he advanced a fundamental camouflage nowadays called gravitational
time dilation:

http://www.relativitybook.com/resour...n_gravity.html
Albert Einstein 1911: "Therefore the two clocks in S1 and S2 do not
both give the "time" correctly. If we measure time in S1 with the
clock U, then we must measure time in S2 with a clock which goes 1+phi/
c^2 times more slowly than the clock U when compared with U at one and
the same place. (...) For if we measure the velocity of light at
different places in the accelerated, gravitation-free system K',
employing clocks U of identical constitution we obtain the same
magnitude at all these places. The same holds good, by our fundamental
assumption, for the system K as well. But from what has just been said
we must use clocks of unlike constitution for measuring time at places
with differing gravitation potential. For measuring time at a place
which, relatively to the origin of the co-ordinates, has the
gravitation potential phi, we must employ a clock which - when removed
to the origin of co-ordinates - goes (1+phi/c²) times more slowly than
the clock used for measuring time at the origin of co-ordinates. If we
call the velocity of light at the origin of co-ordinates c0, then the
velocity of light c at a place with the gravitation potential phi will
be given by the relation c=c0(1+phi/c^2)."

So in 1911 the gravitational time dilation becomes the real effect
while the variable speed of light turns out to be an artefact - one
can only obtain it with the help of nonidentical clocks. However in
the subsequent development of Divine Albert's Divine Theory the speed
of light did remain variable, even more variable than in Newton's
emission theory of light:

http://www.physlink.com/Education/AskExperts/ae13.cfm
"So, it is absolutely true that the speed of light is not constant in
a gravitational field [which, by the equivalence principle, applies as
well to accelerating (non-inertial) frames of reference]. If this were
not so, there would be no bending of light by the gravitational field
of stars....Indeed, this is exactly how Einstein did the calculation
in: 'On the Influence of Gravitation on the Propagation of Light,'
Annalen der Physik, 35, 1911. which predated the full formal
development of general relativity by about four years. This paper is
widely available in English. You can find a copy beginning on page 99
of the Dover book 'The Principle of Relativity.' You will find in
section 3 of that paper, Einstein's derivation of the (variable) speed
of light in a gravitational potential, eqn (3). The result is,
c' = c0 ( 1 + V / c^2 )
where V is the gravitational potential relative to the point where the
speed of light c0 is measured."

http://www.d1heidorn.homepage.t-onli...k/VSL/VSL.html
"In two works from 1907 and 1911 Einstein introduces a variable speed
of light. Sometimes this is taken as a contradiction to the constancy
of the speed of light, which was postulated in the foundation of
Special Relativity in 1905. However there is no contradiction at all -
even if in the fully developed GR from 1916 there is a variable speed
of light."

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. It predated the full
formal development of general relativity by about four years. You can
find an English translation of this paper in the Dover book 'The
Principle of Relativity' beginning on page 99; you will find in
section 3 of that paper Einstein's derivation of the variable speed of
light in a gravitational potential, eqn (3). The result is:
c'=c0(1+phi/c^2) where phi is the gravitational potential relative to
the point where the speed of light co is measured......You can find a
more sophisticated derivation later by Einstein (1955) from the full
theory of general relativity in the weak field approximation....For
the 1955 results but not in coordinates see page 93, eqn (6.28):
c(r)=[1+2phi(r)/c^2]c. Namely the 1955 approximation shows a variation
in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm
"In geometrical units we define c_0 = 1, so Einstein's 1911 formula
can be written simply as c=1+phi. However, this formula for the speed
of light (not to mention this whole approach to gravity) turned out to
be incorrect, as Einstein realized during the years leading up to 1915
and the completion of the general theory. In fact, the general theory
of relativity doesn't give any equation for the speed of light at a
particular location, because the effect of gravity cannot be
represented by a simple scalar field of c values. Instead, the "speed
of light" at a each point depends on the direction of the light ray
through that point, as well as on the choice of coordinate systems, so
we can't generally talk about the value of c at a given point in a non-
vanishing gravitational field. However, if we consider just radial
light rays near a spherically symmetrical (and non- rotating) mass,
and if we agree to use a specific set of coordinates, namely those in
which the metric coefficients are independent of t, then we can read a
formula analogous to Einstein's 1911 formula directly from the
Schwarzschild metric. (...) In the Newtonian limit the classical
gravitational potential at a distance r from mass m is phi=-m/r, so if
we let c_r = dr/dt denote the radial speed of light in Schwarzschild
coordinates, we have c_r =1+2phi, which corresponds to Einstein's 1911
equation, except that we have a factor of 2 instead of 1 on the
potential term."

Apart from being variable in a gravitational field (more variable than
in Newton's emission theory of light), the speed of light is also
constant in Divine Albert's Divine Theory (due to gravitational time
dilation). Steve Carlip would say that the speed of light is both
variable and constant:

http://www.amazon.com/Brief-History-.../dp/0553380168
Stephen Hawking, "A Brief History of Time", Chapter 6:
"Under the theory that light is made up of waves, it was not clear how
it would respond to gravity. But if light is composed of particles,
one might expect them to be affected by gravity in the same way that
cannonballs, rockets, and planets are.....In fact, it is not really
consistent to treat light like cannonballs in Newton's theory of
gravity because the speed of light is fixed. (A cannonball fired
upward from the earth will be slowed down by gravity and will
eventually stop and fall back; a photon, however, must continue upward
at a constant speed...)"

http://www.amazon.co.uk/Plus-vite-lu.../dp/2100072471
Joao Magueijo, PLUS VITE QUE LA LUMIÈRE, Dunod, 2003, pp. 50-51:
"En cours de route, en 1911, Einstein proposa même une théorie où la
vitesse de la lumière variait! Aujourd'hui, les scientifiques sont
soit horrifiés par cette article écrit par le grand Albert Einstein,
alors professeur à Prague, soit tout simplement ignorants de son
existence. Banesh Hoffmann, collègue et biographe d'Einstein, décrit
ce texte de la manière suivante: "Et cela signifie... Quoi! Que la
vitesse de la lumière n'est pas constante, que la gravitation la
ralentit. Hérésie! Et de la part d'Einstein lui-même."

http://www.amazon.fr/gp/product/2738...668551-5396107
Alexandre Moatti (p. 140): "La théorie corpusculaire se heurtait
toutefois à une contradiction expérimentale de taille : elle
impliquait que la lumière fût non seulement déviée mais aussi ralentie
par un champ de gravitation (comme le serait un faisceau de
corpuscules), alors que toutes les mesures donnaient une constance de
la vitesse de la lumière, indépendante de la vitesse de la source, et
indépendante de toute masse gravitationnelle à côté de laquelle elle
passerait !"

http://www.hawking.org.uk/index.php?...64&It emid=66
Stephen Hawking: "Interestingly enough, Laplace himself wrote a paper
in 1799 on how some stars could have a gravitational field so strong
that light could not escape, but would be dragged back onto the star.
He even calculated that a star of the same density as the Sun, but two
hundred and fifty times the size, would have this property. But
although Laplace may not have realised it, the same idea had been put
forward 16 years earlier by a Cambridge man, John Mitchell, in a paper
in the Philosophical Transactions of the Royal Society. Both Mitchell
and Laplace thought of light as consisting of particles, rather like
cannon balls, that could be slowed down by gravity, and made to fall
back on the star. But a famous experiment, carried out by two
Americans, Michelson and Morley in 1887, showed that light always
travelled at a speed of one hundred and eighty six thousand miles a
second, no matter where it came from. How then could gravity slow down
light, and make it fall back."

http://helios.gsfc.nasa.gov/qa_sp_gr.html
"Is light affected by gravity? If so, how can the speed of light be
constant? Wouldn't the light coming off of the Sun be slower than the
light we make here? If not, why doesn't light escape a black hole?
Yes, light is affected by gravity, but not in its speed. General
Relativity (our best guess as to how the Universe works) gives two
effects of gravity on light. It can bend light (which includes effects
such as gravitational lensing), and it can change the energy of light.
But it changes the energy by shifting the frequency of the light
(gravitational redshift) not by changing light speed. Gravity bends
light by warping space so that what the light beam sees as "straight"
is not straight to an outside observer. The speed of light is still
constant." Dr. Eric Christian

http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Einstein went on to discover a more general theory of
relativity which explained gravity in terms of curved spacetime, and
he talked about the speed of light changing in this new theory. In the
1920 book "Relativity: the special and general theory" he wrote:
". . . according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. THIS INTERPRETATION
IS PERFECTLY VALID AND MAKES GOOD PHYSICAL SENSE, BUT A MORE MODERN
INTERPRETATION IS THAT THE SPEED OF LIGHT IS CONSTANT in general
relativity."

Pentcho Valev