The term itself originates in Bacon's _Novum Organum_. Contrary to Duhem's assumption, it does not refer to a signpost at cross-roads giving various routes, nor is it connected with _croix ou pile_, heads or tails. _Experimentum crucis_ denotes rather a divine judgment at the cross, that is a test that is absolutely decisive and beyond further appeal. But no! adds Duhem, there is no room for a third judgment in the case of two contradictory statements in geometry, but there is between two contradictory statements in physics. And, in fact, this third possibility has manifested itself in the discovery of Maxwell, who has shown that the nature of light is founded on a process of periodic electromagnetic disturbances. Hence, so concludes Duhem, experiment can never decide whether a certain theory is alone valid. The physicist is never certain that he has exhausted all conceivable possibilities, of thought. The truth of a physical statement, the validity of a discovery, cannot be confirmed by any _experimentum crucis_. According to this argument, therefore, it is also possible that the scientific grounds of spectral analysis do not conform to truth. A contradictory hypothesis may, indeed, be set up, with the result that the same experiments that had led Kirchhoff's discovery from one triumph to another would have to be interpreted in a totally different sense. I must frankly confess that I cannot subscribe to such an extreme eventuality, since, in my opinion, Duhem's analogy with mathematics excludes this possibility. For if a certain probability is expressed by a trillion to one, then I venture to state that even in the case of mathematical truths certainty reaches no higher degree of probability. From the history of mathematics we know of theorems which were enunciated and provided with complete proofs, and yet did not succeed in establishing themselves; hence we see that, however evident a mathematical theorem may be, it is still only a matter of very great probability. If, following our usual habits of thought, we take this for absolute certainty, then we may also consider the sum-total of experiments in the realm of spectral analysis to be a great _experimentum crucis_ for the correctness of the theory itself.