This ray of hope gave a glimpse of the degree of accuracy attainable. In this connexion the experiment confirmed infinitely more than the boldest imagination could ever have dreamed. A yellow line was detected in the spectrum of sodium. And it was found experimentally that the three-millionth part of a thousandth of a gramme of a sodium salt is sufficient to produce this sodium line in the spectrum of a Bunsen burner. There commenced a dizzying passage in the Calculus of Probabilities for, since it was found that in the sun's atmosphere hydrogen, carbon, iron, aluminium, calcium, sodium, nickel, chromium, zinc, and copper were present, the question arose as to how great was the possibility of an error in this observation. Kirchhoff calculated it as a chance of a trillion to one that these substances are actually present in the sun! Never before had an experiment verified to such an extreme degree a discoverer's idea. It seems appropriate at this stage to deal with a doctrine which seeks to shed light into the deepest recesses of the connexion between experiment and discovery. It teaches that an _experimentum crucis_, an experiment that verifies absolutely, is _impossible_ in physics. That is to say, every idea of a discoverer involves a hypothesis, and, however the experiment that follows may turn out, there still remains the possibility that this hypothesis was false, and may later have to make way for another essentially contradictory hypothesis which will be valid again only for a limited time. The chief exponent of this theory is the eminent scholar, Pierre Duhem, Membre de l'Institut. He draws a parallel between experiment and mathematical proof, particularly with the indirect, apagogic form which has been so successfully applied in Euclidean geometry. In this method it is assumed that a certain statement is erroneous; it is then shown that it leads to an obvious contradiction; consequently the statement was correct provided that a certain doubt be excluded. Thus in the domain of mathematics we have a real _experimentum crucis_. In accordance with this, Duhem tests the validity of two physical theories, both of which were put forward and claimed as discoveries. Newton had discovered the nature of light to consist in "emission"; to him, as well as to Laplace and Biot, light consists of projectiles that are emitted with very great velocity. The discovery of Huyghens, supported by Young and Fresnel, substitutes wave-motion in place of corpuscular emission. Hence, according to Duhem, we have, or we had, here two hypotheses which appear to be the only ones possible. Experiment was to pronounce a judgment, and at first it decided irrefutably in favour of the wave-theory. Therefore, the discovery of Huyghens is alone true, and that of Newton is shown to be an error; there is no third outlet, and so we have quite certainly an _experimentum_ crucis before us.