I'm not sure this is entirely accurate. I believe there was one experimental observation that could not be explained by Newtonian gravity: Le Verrier in 1859 saw that the perihelion of Mercury advanced by 38" / century more than Newtonian gravitation would predict. Later they discovered that it was really 43" per century, but the point is that it could not be explained by Newton's law and was widely known. It is not what led Einstein to develop GR, but it was one of the more influential pieces of his puzzle and when an early paper he wrote predicted this effect (based on incorrect field equations, but in such a way that they did not come into play in this particular calculation) I'm sure he felt more confident in his progress.
From: firstname.lastname@example.org [mailto:email@example.com] Sent: Friday, August 06, 1999 8:12 AM To: firstname.lastname@example.org Subject: Re: Psi and Science Fiction
Bryan Moss, <email@example.com>, writes:
> Eliezer S. Yudkowsky wrote:
> > Actually, from what I've read, Einstein came up with the General Theory
> > of Relativity completely out of the blue, based on no experimental
> > evidence whatsoever. I find this to be the single most impressive
> > mental feat of all time.
> Previous to Relativity there had been experiments to show that the speed
> light could be absolute and that time dilation could be necessary to
> some inconsistencies in electromagnetism. In fact Relativity was
> answer to the apparent time dilation necessary in electromagnetism (there
> had been papers on the concept of relativity but apparently Einstein
> read them). Later Minkowski created the concept of spacetime. Einstein
> came up with the idea of spacetine curvature while investigating tidal
> gravity. Not exactly 'out of the blue' but still very impressive.
I think what Eliezer means is that there was no experimental evidence showing any problems with Newtonian gravitation. However it is clear that Newtonian gravity is incompatible with special relativity, since it requires instantaneous action at a distance. If you try to patch it up with "lagged gravity" (where you are attracted to where the object was at the speed-of-light time in the past) you get unstable orbits. It was an attempt to come up with a theory of gravity that is consistent with special relativity that led, after enormous difficulty, to general relativity. This then turned out to make some predictions that were slightly different from Newtonian gravity, and to everyone's amazement they were confirmed, turning Einstein into a superstar.