Eddington became interested in the theory of general relativity which provided an explanation for the previously noticed, but unexplained, advance of the perihelion of Mercury. In 1919, Eddington led an eclipse expedition to Principe Island in West Africa to verify the bending of light passing close to the sun which was predicted by relativity theory. At that time such observations of stars close to the sun in the sky could only be made during a total eclipse. Of sixteen photographs, one plate gave a result agreeing with Einstein, providing the first confirmation of Einstein's theory that gravity will bend the path of light when it passes near a massive star.

Eddington wrote, in a parody of the Rubaiyat of Omar Khayyam:

		Oh leave the Wise our measures to collate.
		One thing at least is certain, light has weight.
		One thing is certain and the rest debate
		Light rays, when near the Sun, do not go straight.

Eddington's lectures on relativity at Cambridge gave it a beautiful mathematical treatment, as basis for his 1923 book Mathematical Theory of Relativity. Einstein said this work was "the finest presentation of the subject in any language".

Besides his work in relativity theory Eddington also did important work on the internal structure of stars. He discovered the mass-luminosity relationship for stars, he calculated the abundance of hydrogen and he produced a theory to explain the pulsation of Cepheid variable stars. His early research on this is contained in the important 1926 work The Internal Constitution of Stars. Eddington had a long running argument with James Jeans over the mechanism by which energy was created in stars. He wrote, correctly of course, that as to the process of generating energy, "probably the simplest hypothesis ... is that there may be a slow process of annihilation of matter". Jeans, however, favoured the theory that the energy was the result of contraction. Of course this is not entirely wrong since a star when it forms will initially heat up under the energy generated by contraction before nuclear reactions begin and then provide the energy source for most of the star's life.

Among Eddington's many books were philosophical works such as The Nature of the Physical World (1928), New Pathways of Science (1935) and The Philosophy of Physical Science (1939).

Eddington had a fascination with the fundamental constants of nature and produced some surprising numerical coincidences most of which were published after his death in Fundamental Theory (1946), a book prepared for publication by mathematical physicist Sir James Whittaker. He writes in that book that his aim was to determine the relation between the sizes of different physical systems (a science began by Galileo, as noted elsewhere at this Website), attempting to unite quantum physics and general relativity (fields still separate in 20001). Eddington considered that epistemology ("how-we-know") is at the basis of physics; that physical laws and physical constants are the consequences of the condition of observation. His work on algebras attempted to give a symmetrical description of nature. [I first learned about Clifford algebra from Eddington.]

Eddington delighted in giving public lectures on science. At one of these, Eddington was describing stars and planets swimming in space when a woman in the back interrupted. "That's all nonsense. You know the Earth is supported on the back of a Giant Tortoise!" Eddington had heard this one before, so politely asked, "And what, Madam, supports this Tortoise?" She retorted, "Oh, you can't catch me on that one. It's tortoises all the way down!"