By a strange fatality Kant, who had been so efficient as an iconoclast in metaphysics, was perhaps with his nebular hypothesis, followed later by the work of Goethe on animal and plant variations, the one most largely responsible for the new hope that in science at last was to be found an answer to the riddle of existence which had baffled the search of pure reason. The achievement of Kant both destructive and constructive is well known, if vaguely understood, by the world at large; but it is not so well known that a contemporary of Kant did precisely for science what the sage of Königsberg accomplished in metaphysics. In the very decade in which _The Critique of Pure Reason_ saw the light, Lagrange, a scholar of France, published a work which carried the analytic method, or the method of motion, to its farthest limit. In this work, the _Mécanique Analytique_, Lagrange develops an equation from which it can be proved conclusively that to explain any group of phenomena measured by energy an infinite number of hypotheses may be employed. So, for instance, if we establish any one theory which will sufficiently account for the known phenomena of light, such as reflection, refraction, polarisation, etc., there will yet remain an infinite number of other hypotheses equally capable of explaining the same group of phenomena. Or to use the words of Poincaré: "If then we can give one complete mechanical explanation of a phenomenon, there will also be possible an infinite number of others which will account equally well for all the particulars revealed by experiment." That is to say, no _experimentum crucis_ can be imagined which will reveal the truth or error of any given theory. This restriction on the finality of our knowledge is borne out in all physical reasoning,--and I venture also to say in the other sciences; thus in optics we can perform no experiment which will establish as finally true the theory that light is caused by the motion of corpuscles of matter emitted from a luminous body, or that it is due to vibrations propagated through a medium by a wave motion, or that it is generated by certain disturbances in the electrical state of bodies. Each of these hypotheses has its advantages and disadvantages; and in our choice we merely adopt that theory which explains the greater number of phenomena in the simplest way. If any one should here ask: Granted that from phenomena expressed in terms of energy no ultimate law can be educed, yet may not some other view of phenomena lead to other results? We answer that no other view is possible. Not that the system of the universe, if we may use such an expression, is necessarily constructed on what we call energy, but that our minds can conceive it only in terms of energy. An analysis of the concepts which enter into the idea of energy must make it evident that in our understanding of nature we cannot go beyond this point.