i 5 8 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 aver- 

 age 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 -^ 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 metaphys- 

 ical dogma, "nulla actio in distans" and which in our day have culminated in 

 the famous apothegm of the German materialist, " Kein Phosphor, Icein 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 NTewcomb'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 tran- 

 scendental 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 geo- 

 metrical 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 Zollner, for instance suggesting such a thing in a 

 moment of aberration. But the great mass of men in their senses remain unaf- 

 fected by any such idea. 



