The simple observation by Huygens that disproved Newton's rule for the extraordinary refraction of calcite
Huygens (1629–1695), in his Treatise on Light (1690), explained the double refraction of calcite on the correct hypothesis that the secondary waves for the “extraordinary” refraction are spheroidal rather than spherical. His theory explained, inter alia, his simple observation that when a calcite crystal is placed on a horizontal page of text, the ordinary image appears higher than the extraordinary image (Ch.V, Art. 39).
Newton, in Qu. 17 of the Latin edition of his Opticks (1706), or Qu. 25 (in Bk. 3) of later English editions, gave his own ‘rule’ for double refraction. Let a ray from an external point L strike one face of a calcite crystal at point P, and be refracted to point O on the opposite face by the Ordinary refraction, and to point E on the opposite face by the Extraordinary refraction. According to Newton's rule, the displacement vector OE does not vary with the direction of the incident ray.
It is easily shown that if this rule were true, the two text images reported by Huygens would have been at the same height.
Newton's rule was disproven in 1788. That it had already been disproven by a single qualitative observation, before it was published, seems to have escaped notice.