No one will question that mathematicians have a way of thinking all their own; but even this is too general. The arithmetician, the algebraist, and more generally the analyst, in whom invention obtains in the most abstract form of discontinuous functions--symbols and their relations--cannot imagine like the geometrician. One may well speak of the ideal figures of geometry--the empirical origin of which is no longer anywhere contested--but we cannot escape from representing them as somehow in space. Does anyone think that Monge, the creator of descriptive geometry, who by his work has aided builders, architects, mechanics, stone cutters in their labors, could have the same type of imagination as the mathematician who has been given up all his life to the theory of number? Here, then, are at least two well-marked varieties, to say nothing of mixed forms. The physicist's imagination is necessarily more concrete; since he is incessantly obliged to refer to the data of sense or to that totality of visual, tactile, motor, acoustic, thermic, etc., representations that we term the "properties of matter." Our eye, says Tyndall, cannot see sound waves contract and dilate, but we construct them in thought--i.e., by means of visual images. The same remarks are true of chemists. The founders of the atomic theory certainly _saw_ atoms, and pictured them in the mind's eye, and their arrangement in compound bodies. The complexity of the imagination increases still more in the geologist, the botanist, the zoologist; it approaches more and more, with its increasing details, to the level of perception. The physician, in whom science becomes also an art, has need of visual representations of the exterior and interior, microscopic and macroscopic, of the various forms of diseased conditions; auditory representations (auscultation); tactile representations (touch, reverberation, etc.); and let us also add that we are not speaking merely of diagnosis of diseases, which is a matter of reproductive imagination, but of the discovery of a new pathologic "entity," proven and made certain from the symptoms. Lastly, if we do not hesitate to give a very broad extension to the term "scientific," and apply it also to invention in social matters, we shall see that the latter is still more exacting, for one must represent to oneself not only the elements of the past and of the present, but in addition construct a picture of the future according to probable inductions and deductions.