Irwin Shapiro incidentally hears "something about the speed depending
on the gravitational potential" and realizes that the speed of light
is obviously variable:

http://www.hep.yorku.ca/menary/cours...relativity.pdf
Irwin Shapiro: "...I attended an afternoon of presentations c.
1961-1962 by MIT staff on their progress on various research projects,
conducted under joint services (DOD) sponsorship. One was on speed-of-
light measurements by George Stroke who mentioned something about the
speed depending on the gravitational potential. This remark surprised
me and I pursued it via "brushing up" on my knowledge of general
relativity and realized the obvious: whereas the speed of light
measured locally in an inertial frame will have the same value
everywhere, save for measurement errors, the propagation time of light
along some path will depend on the gravitational potential along that
path."

Of course, although Shapiro and Stroke are free to discuss anything,
even the variation of the speed of light, believers are not. They
should just sing, as fiercely as possible, "Divine Einstein" and "Yes
we all believe in relativity, relativity, relativity".

Pentcho Valev