It is often said, and not wholly without justification, that the scientist has solved a _riddle_. Every problem in geometry may be clothed in the garb of a _riddle_. Thus: "What thing is that _M_ which has the properties _A_, _B_, _C_?" "What circle is that which touches the straight lines _A_, _B_, but touches _B_ in the point _C_?" The first two conditions marshal before the imagination the group of circles whose centres lie in the line of symmetry of _A_, _B_. The third condition reminds us of all the circles having centres in the straight line that stands at right angles to _B_ in _C_. The _common_ term, or common terms, of the two groups of images solves the riddle--satisfies the problem. Puzzles dealing with things or words induce similar processes, but the memory in such cases is exerted in many directions and more varied and less clearly ordered provinces of ideas are surveyed. The difference between the situation of a geometer who has a construction to make, and that of an engineer, or a scientist, confronted with a problem, is simply this, that the first moves in a field with which he is thoroughly acquainted, whereas the two latter are obliged to familiarise themselves with this field subsequently, and in a measure far transcending what is commonly required. In this process the mechanical engineer has at least always a definite goal before him and definite means to accomplish his aim, whilst in the case of the scientist that aim is in many instances presented only in vague and general outlines. Often the very formulation of the riddle devolves on him. Frequently it is not until the aim has been reached that the broader outlook requisite for systematic procedure is obtained. By far the larger portion of his success, therefore, is contingent on luck and instinct. It is immaterial, so far as its character is concerned, whether the process in question is brought rapidly to a conclusion in the brain of one man, or whether it is spun out for centuries in the minds of a long succession of thinkers. The same relation that a word solving a riddle bears to that riddle is borne by the modern conception of light to the facts discovered by Grimaldi, Römer, Huygens, Newton, Young, Malus, and Fresnel, and only by the help of this slowly developed conception is our mental vision enabled to embrace the broad domain of facts in question.