Apart from these cases, there are achievements by men who may be called _lucky_ discoverers, although they displayed no genius for finding nor for creating. The philosopher-physicist, Ernst Mach, has devoted a lecture to such intellects, which seems to me very valuable, if only for the reason that he traces back the conceptions of discovery and invention to one common root of knowledge, and explains their difference as being due only to a difference in the application of this discovery. But when Ernst Mach in this lecture, "On the Influence of Accidental Circumstances on the Development of Inventions and Discoveries," extends the influence of chance to include accidental circumstances that can only enter when the discoverer is closely attentive, it seems to me that certain limitations are advisable. Otherwise, if we pursue Mach's line of thought to its extreme, we could declare every discovery to be due to chance, and this would be the end of the intuitive-creative idea. This assertion would ultimately mean that genius owes its achievements to the accidental arrangement of the molecules in the brain-cells of its associated body. This would be just as wrong as saying that chess is a game of chance because we lose a game when, by chance, we come up against a better player. Huyghens, the great discoverer and inventor, says, in his _Dioptrica_, that he would have to consider anyone who invented the telescope without the favourable intervention of chance to be a superhuman genius. Why should he choose just the telescope? To many the invention of the Differential Calculus will appear grander and due to a higher degree of ingenuity. And since it was produced quite methodically, and since chance was excluded, we may follow Huyghens and with good reason proclaim its authors superhuman geniuses. * * * * * * * *