modify the laws of optics and suppose that light does not travel rigorously in a straight line.
It is needless to add that all the world would regard the latter solution as the more advantageous.
The Euclidean geometry has, therefore, nothing to fear from fresh experiments.
- Is the position tenable, that certain phenomena, possible in Euclidean space, would be impossible in non-Euclidean space, so that experience, in establishing these phenomena, would directly contradict the non-Euclidean hypothesis? For my part I think no such question can be put. To my mind it is precisely equivalent to the following, whose absurdity is patent to all eyes: are there lengths expressible in meters and centimeters, but which can not be measured in fathoms, feet and inches, so that experience, in ascertaining the existence of these lengths, would directly contradict the hypothesis that there are fathoms divided into six feet?
Examine the question more closely. I suppose that the straight line possesses in Euclidean space any two properties which I shall call A and B; that in non-Euclidean space it still possesses the property A, but no longer has the property B; finally I suppose that in both Euclidean and non-Euclidean space the straight line is the only line having the property A.
If this were so, experience would be capable of deciding between the hypothesis of Euclid and that of Lobachevski. It would be ascertained that a definite concrete object, accessible to experiment, for example, a pencil of rays of light, possesses the property A; we should