For an opposite view putting into question the decisive value of the experimentum crucis in choosing one hypothesis or theory over its rival see Pierre Duhem.
Francis Bacon in his Novum Organum first described the concept of a situation in which one theory but not others would hold true, using the name instantia crucis; the phrase experimentum crucis, denoting the deliberate creation of such a situation for the purpose of testing the rival theories, was later coined by Robert Hooke and then famously used by Isaac Newton.
The production of such an experiment is considered necessary for a particular hypothesis or theory to be considered an established part of the body of scientific knowledge. It is not unusual in the history of science for theories to be developed fully before producing a critical experiment. A given theory which is in accordance with known experiment but which has not yet produced a critical experiment is typically considered worthy of exploration in order to discover such an experimental test.
In his Philosophiæ Naturalis Principia Mathematica, Isaac Newton (1687) presents a disproof of Descartes' vortex theory of the motion of the planets. In his Opticks, Newton describes an optical experimentum crucis in the First Book, Part I, Proposition II, Theorem II, Experiment 6, to prove that sunlight consists of rays that differ in their index of refraction.
A 19th-century example was the prediction by Poisson, based on Fresnel's mathematical analysis, that the wave theory of light predicted a bright spot in the center of the shadow of a perfectly circular object, a result that could not be explained by the (then current) particle theory of light. An experiment by François Arago showed the existence of this effect, now called the Arago spot, or "Poisson's bright spot", which led to the acceptance of the wave theory.