The rules which hold good in prehistoric times also hold good in historical times, and the remarks made on invention may be applied almost without modification to discovery; for the two are distinguished solely by the use to which the new knowledge is put. In both cases the investigator is concerned with some _newly observed_ relation of new or old properties, abstract or concrete. It is observed, for example, that a substance which gives a chemical reaction _A_ is also the cause of a chemical reaction _B_. If this observation fulfils no purpose but that of furthering the scientist's insight, or of removing a source of intellectual discomfort, we have a discovery; but an invention, if in using the substance giving the reaction _A_ to produce the desired reaction _B_, we have a practical end in view, and seek to remove a source of material discomfort. The phrase, _disclosure of the connexion of reactions_, is broad enough to cover discoveries and inventions in all departments. It embraces the Pythagorean proposition, which is a combination of a geometrical and an arithmetical reaction, Newton's discovery of the connexion of Kepler's motions with the law of the inverse squares, as perfectly as it does the detection of some minute but appropriate alteration in the construction of a tool, or of some appropriate change in the methods of a dyeing establishment. The disclosure of new provinces of facts before unknown can only be brought about by accidental circumstances, under which are _remarked_ facts that commonly go unnoticed. The achievement of the discoverer here consists in his _sharpened attention_, which detects the uncommon features of an occurrence and their determining conditions from their most evanescent marks,[88] and discovers means of submitting them to exact and full observation. Under this head belong the first disclosures of electrical and magnetic phenomena, Grimaldi's observation of interference, Arago's discovery of the increased check suffered by a magnetic needle vibrating in a copper envelope as compared with that observed in a bandbox, Foucault's observation of the stability of the plane of vibration of a rod accidentally struck while rotating in a turning-lathe, Mayer's observation of the increased redness of venous blood in the tropics, Kirchhoff's observation of the augmentation of the _D_-line in the solar spectrum by the interposition of a sodium lamp, Schönbein's discovery of ozone from the phosphoric smell emitted on the disruption of air by electric sparks, and a host of others. All these facts, of which unquestionably many were _seen_ numbers of times before they were _noticed_, are examples of the inauguration of momentous discoveries by accidental circumstances, and place the importance of strained attention in a brilliant light.