Only one theory has been advanced to account for this discrepancy, and that is the Einstein theory of gravitation. This ingenious speculation was first propounded in comprehensive form nearly fifteen years ago, and its author has developed from it mathematical formulæ which appear to yield results even more precise than those based on the Newtonian theory.
In expressing the difference between the law of gravitation and his own conception, Einstein says: "Imagine the earth removed, and in its place suspended a box as big as a moon or a whole house and inside a man naturally floating in the center, there being no force whatever pulling him. Imagine, further, this box being, by a rope or other contrivance, suddenly jerked to one side, which is scientifically termed 'difform motion,' as opposed to 'uniform motion.' The person would then naturally reach bottom on the opposite side. The result would consequently be the same as if he obeyed Newton's law of gravitation, while, in fact, there is no gravitation exerted whatever, which proves that difform motion will in every case produce the same effects as gravitation…. The term relativity refers to time and space. According to Galileo and Newton, time and space were absolute entities, and the moving systems of the universe were dependent on this absolute time and space. On this conception was built the science of mechanics. The resulting formulas sufficed for all motions of a slow nature; it was found, however, that they would not conform to the rapid motions apparent in electrodynamics…. Briefly the theory of special relativity discards absolute time and space, and makes them in every instance relative to moving systems. By this theory all phenomena in electrodynamics, as well as mechanics, hitherto irreducible by the old formulæ, were satisfactorily explained."
Natural phenomena, then, involving gravitation and inertia, as in the planetary motions, and electro-magnetic phenomena, including the motion of light, are to be regarded as interrelated, and not independent of one another. And the Einstein theory would appear to have received a striking verification in both these fields. On this theory the Newtonian dynamics fails when the velocities concerned are a near approach to that of light. The Newtonian theory, then, is not to be considered as wrong, but in the light of a first approximation. Applying the new theory to the case of the motion of Mercury's perihelion, it is found to account for the excess quite exactly.
On the electro-magnetic side, including also the motion of light, a total eclipse of the sun affords an especially favorable occasion for applying the critical test, whether a huge mass like the sun would or would not deflect toward itself the rays of light from stars passing close to the edge of its disk, or limb. A total eclipse of exceptional duration occurred on May 29, 1919, and the two eclipse parties sent out by the Royal Society of London and the Royal Astronomical Society were equipped especially with apparatus for making this test. Their stations were one on the east coast of Brazil and the other on the west coast of Africa.
Accurate calculation beforehand showed just where the sun would be among the stars at the time of the eclipse; so that star plates of this region were taken in England before the expeditions went out. Then, during the total eclipse, the same regions were photographed with the eclipsed sun and the corona projected against them. To make doubly sure, the stars were a third time photographed some weeks after the eclipse, when the sun had moved away from that particular region.
Measuring up the three sets of plates, it was found that an appreciable deflection of the light of the stars nearest alongside the sun actually exists; and the amount of it is such as to afford a fair though not absolutely exact verification of the theory. The observed deflection may of course be due to other causes, but the English astronomers generally regard the near verification as a triumph for the Einstein theory. Astronomers are already beginning preparations for a repetition of the eclipse programme with all possible refinement of observation, when the next total eclipse of the sun occurs, September 20, 1922, visible in Australia and the islands of the Indian Ocean.
A third test of the theory is perhaps more critical than either of the others, and this necessitates a displacement of spectral lines in a gravitational field toward the red end of the spectrum; but the experts who have so far made measures for detecting such displacement disagree as to its actual existence. The work of St. John at Mt. Wilson is unfavorable to the theory, as is that of Evershed of Kodiakanal, who has made repeated tests on the spectrum of Venus, as well as in the cyanogen bands of the sun.
The enthusiastic advocates of the Einstein theory hold that, as Newton proved the three laws of Kepler to be special cases of his general law, so the "universal relativity theory" will enable eventually the Newtonian law to be deduced from the Einstein theory. "This is the way we go on in science, as in everything else," wrote Sir George Airy, Astronomer Royal; "we have to make out that something is true; then we find out under certain circumstances that it is not quite true; and then we have to consider and find out how the departure can be explained." Meanwhile, the prudent person keeps the open mind.