"And Coleridge, too, has lately taken wing.
But like a hawk encumbered with his hood,—
Explaining Metaphysics to the nation—
I wish he would explain his Explanation."
(Dedication to "Don Juan.")
he had still a sure footing in intelligibility, compared with the non-mathematician, who demands an explanation for such a construction. And what a complex of mathematical dangers must be overcome even before the question of the meaning of this integral is crystallized out!
But now the explanation had arrived and could be evaluated, if only approximately. Before we give the result, let us just describe at least one technical term, namely, "Perihelion." It is that point of a planetary orbit which lies nearest the sun. This orbit is an ellipse, that is, an elongated curved fine in the interior of which one distinguishes a major axis in the direction of elongation, and a minor axis perpendicular to the former at its middle point. The perihelion of a planetary orbit is at one of the end points of the major axis.
In time the perihelion alters its position in space, advancing in the same sense as the orbit is traversed. It would naturally be assumed that the amount of this advance as measured astronomically would agree with the calculation resulting from Newton's theory. But this was not the case. An unaccountable remainder was left over, which astronomers ascertained to be 45 seconds (of arc) per 100 years, with a possible fluctuation of plus or minus 5 seconds. Thus, if the new result were found to be between 40 and 50 seconds, the new theory would henceforth have to be regarded as the only valid one.
It happened just as Einstein predicted: calculation according to his theory shows that for the planet Mercury the perihelion should advance 43 seconds per 100 years. This signifies full agreement with observation and fully removes the former apparent difficulty. Whereas Leverrier in his time had pointed out a new planet, Einstein brought to view something far more important: a new truth.
It was a test of accuracy so dazzling that it alone would have sufficed to prove the correctness of Einstein's Principles. Yet, a second test, fraught with graver and more far-reaching consequences, presented itself—a test which could be applied only several years later, and which developed into a scientific event of the highest importance.
For at the same time that Einstein solved the problem of Mercury, he had investigated the path of light-rays according to his revolutionary method, and had arrived at the conclusion that every ray under the influence of a gravitational field, as, for example, in the neighbourhood of the sun, must become curved. This daring announcement gave a new possibility of putting the theory to a practical test during the total eclipse of the sun on 29th May 1919. For, when the disc of the sun is obscured, the stars that are closest to it become visible (even to the naked eye). They may be photographed, and the distances of the points of light on the negative allow us to detect whether the rays from the stars in passing the massive body of the sun have actually been deflected by the amount prophesied by Einstein.
Once again current thought encountered a sharp corner, and "common sense," which furnishes its own certificate of merit, threatened to become rebellious. How now? A ray from a star could be curved? Does not this contradict the elementary conception of the straight lines, that is, the shortest lines, for which we have no better picture than just these rays? Did not Leonardo da Vinci define the straight line by means of the term linea radiosa.
But such supposedly self-evident facts have no longer a place in the space-time world. The point was to test whether a physical anomaly which had been predicted actually existed. If the deflection of the rays really happened, it should manifest itself in the distances between the stars on the photographic plate being greater than one would expect from their actual position.