*THE POPULAR SCIENCE MONTHLY.*

soon as its work has been accomplished. And, if the scientific architects are so captivated with the scaffolding that they insist upon maintaining it intact, its eventual demolition is none the less sure in the progress of observation and experiment. Facts supply the *ictus calcis* which the theorist refuses to administer.

Du Bois-Reymond's proposition is nothing less than this, that natural science is constrained, by the law of all its methods, to exhibit the arbitrary scaffolding of the intellect as the real nature of the universe. He not only confounds the scaffolding of his intellect with its own structure, but he confounds this scaffolding with the structure of Nature. He mistakes the beams of his temporary platform for the rafters of the permanent edifice; the arbitrary masses of his mathematical calculations (the "atoms") for bricks of Nature's building; and the ropes of his scientific tackling (the "forces") for the ingenerate energy of the Universe. There are, it is true, passages in Du Bois-Reymond's lecture which may be construed as a virtual disclaimer of this, but his assumption that the limits of mathematical reasoning about atoms and their constant central forces are the irremovable bounds of all possible knowledge respecting physical phenomena, and the emphatic "*Ignoramusâ€”Ignorabimus*" with which he concludes his lecture, utterly invalidate the disclaimer. He forgets that the framework on which he and his compeers have thus far been stationed is by no means the only scaffolding that can be devised. The spectroscope has convinced the chemist that a chemical analysis can be effected otherwise than by mixing substances in a testing-tube, and that he can react upon the gas of a distant comet as well as upon the hydrogen in the water which flows from a stop-cock in his laboratory. Modern analysis has shown that the limits of mathematical insight, which the synthetical geometrician supposed to be absolute, may be transcended indefinitely; and Gauss's and Hamilton's new conception which is now expanding into the calculus of operations, or calculus of quaternions, is opening theoretical vistas which, even to the analyst of modern times, seem next to illimitable. It is true that no mathematical wings will ever carry us into the regions of the "Absolute," and no spectroscopic vision will discern the indelible spectral bands of the "thing *per se;*" but, before we indulge in any lamentations over this fact, it may be well to examine the livery of the messenger who brings us the wonderful intelligence of the existence of these entities without all possible relation to the intellect, and to inquire of him how he became possessed of his message.

I must not be understood as asserting or intimating that our knowledge can ever be other than asymptotic to the endless and boundless fact of the universe. But there is a dogmatism of ignorance which is no less audacious than the dogmatism of sciolistic knowledge. The "*Ignoramusâ€”Ignorabimus*" at the close of Du Bois-Reymond's lecture is at least as presumptuous as the pretended omnis-