everything which could enlarge the circle of our ideas,—expresses himself in the following noteworthy sentence: "Everything that we call Invention, discovery in the higher sense, is the ultimate outcome of the original perception of some truth, which, long perfected in quiet, leads at length suddenly and unexpectedly to productive recognition." Schopenhauer too, whose thoughts not unfrequently seem to take the same direction as those of Göthe, says upon a very similar question:—"Our best, most able and deepest thoughts often seem to enter our consciousness like an inspiration,—sometimes directly in the form of a weighty sentence. Evidently, however, they are the result of long and unconscious meditation, and numberless long past and often entirely forgotten thoughts and conclusions. The whole process of thought and conclusion seldom lies on the surface,—seldom takes, that is, the form of a chain of reasoning clearly thought out, although we may endeavour to attain this in order to be able to give ourselves and others an account of what has occurred: commonly, however, the rumination by which the material received from without is converted into thoughts, occurs as it were in darkness,—taking place almost as unconsciously as the change of the nourishment into the fluid and substance of the body. Thus it comes about that we can often give no account of the origination of our deepest thoughts;—they are born from our most secret being. Out of its depths arise unexpectedly Opinions. Ideas, arid Conclusions."6
There is nothing, however, impossible in the ideas necessary for the origination of a mechanism being "clearly thought out," and they can then lead to what is sought just as in mathematics the clearly-reasoned and well-connected ideas lead up to the result. In other words, the invention of a mechanism will be to the scientific kinematist a synthetic problem,—which he can solve by the use of systematic, if also difficult, methods. The clever man, supplied with such powerful instruments, will leave the less clever behind in future as hitherto,—just as the mathematical genius leaves behind the mere algebraist who works only with operations learnt by rote.
The thorough understanding of old mechanisms, however, is even more important than the creation of new ones. It is indeed astonishing to how small a depth the methods hitherto used have penetrated into their real nature, and how incompletely known
