This study demonstrates that contrary to the prevalent perception that Isaac Newton’s experimentum crucis was experimental proof of his optical theory, the typical experimental approach to prove his theory with mathematical certainty was “proof by experiments.”
The term experimentum crucis originated from Francis Bacon’s instantiae crucis and was brought into use by early members of the Royal Society, notably Robert Boyle and Robert Hooke. Boyle and Hooke used this term at the start of their arguments to characterize such experiments as showing that there is a fork in the road in the theories at issue. When Newton introduced his version of experimentum crucis in the beginning of his letter “New Theory about Light and Colours” (1672), he was using the term in the same manner as Boyle and Hooke had done. In contrast, in the latter half of the letter where Newton insisted that his theory had mathematical certainty, he did not specify an experiment with which to prove that the color of a light ray is not mutable by refractions. Thus experimentum crucis should not be deemed as an approach designed by Newton in pursuing mathematical “certainty,” but one applied by him to follow those early members of the Royal Society who attached importance to the “probability” of knowledge on nature.
In fact, I argue that Newton was well aware that the setup of his experimentum crucis was insufficient to prove the immutability of colored rays and subsequently made improvements. In the mathematically composed parts of his Lectiones opticae (c. 1670) and Opticks (1704), Newton improved every experiment so that it reached enough accuracy to prove his propositions. He presented his theory about light and colors as propositions, each followed by its “proof by experiments.” This method, rather than experimentum crucis, was Newton’s typical approach to pursue mathematical “certainty.”
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