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THE POPULAR SCIENCE MONTHLY.
gard to the assumed luminiferous ether through which all this energy is supposed to be transmitted. Our planet is rushing in its orbit around the sun at an average rate of over 1,000 miles a minute, and makes its annual journey of some 550,000,000 miles in 365 days, 6 hours, 9 seconds, and 610 of a second. Mark the tenths; for astronomical observations are so accurate that, if the length of the year varied permanently by the tenth of a second, we should know it; and you can readily understand that, if there were a medium in space which offered as much resistance to the motion of the earth as would gossamer threads to a race-horse, the planet could never come up to time, year after year, to the tenth of a second. How, then, can we save our theory, by which we set so much, and rightly, because it has helped us so effectively in studying Nature? If we may be allowed such an extravagant solecism, let us suppose that the engineer of our previous illustration was the hero of a fairy-tale. He has built a mill, set a steam-engine in the basement, arranged his spindles above, and is connecting the pulleys by the usual belts, when some stern necessity requires him to transmit all the energy with cobwebs. Of course, a good fairy comes to his aid, and what does she do? Simply makes the cobwebs indefinitely strong. So the physicists, not to be out-done by any fairies, make their ether indefinitely elastic, and their theory lands them just here, with a medium filling all space, thousands of times more elastic than steel, and thousands on thousands of times less dense than hydrogen gas. There must be a fallacy somewhere, and I strongly suspect it is to be found in our ordinary materialistic notions of causation, which involve the old metaphysical dogma, "nulla actio in distans" and which in our day have culminated in the famous apothegm of the German materialist, "Kein Phosphor, kein Gedanke"
If my reviewer will compare this passage with what I have said on the undulatory theory, he will, perhaps, discover that my observations are at least proof against the charge of frivolity and irrelevancy. And it is not necessary to add, I hope, that it is no more my intention than that of Professor Cooke to call upon the physicist to throw away the undulatory theory as a working hypothesis before he has a better one.
I now come to Professor Newcomb's reflections on my discussion of transcendental geometry. Here are some of them:
In considering the author's work in detail, we begin with the subject of transcendental geometry, or hyper-geometry, as it is sometimes called. We do this because his criticisms are so readily disposed of. He speaks of the "new geometrical faith"; of the "dispute" between the "disciples" of the transcendental or pangeometrical school and the "adherents" of the old geometrical faith; of the "champions" of the old geometrical creed; of the "doctrine" of hyper-space. To the refutation of these supposed erroneous doctrines he devotes no less than sixty-two pages. Now, all his criticism is founded on an utter mis-apprehension of the scope and meaning of what he is criticising. We make bold to say that no mathematician has ever pretended to have the slightest evidence that space has four dimensions, or was in any way different from what is taught in our familiar system of geometry. He has not been an adherent or champion, or held any doctrine on the subject. Now and then it is barely possible that a physicist might be found—Zöllner, for instance—suggesting such a thing in a moment of aberration. But the great mass of men in their senses remain unaffected by any such idea.
