Now the ultimate effect of motion on the time-determination cannot be calculated along any such simple lines as these.  Indeed, it cannot be exactly calculated at all, for we have not all the data.  But there is certainly some effect.  Suppose one rows four miles up a river against a current of two miles per hour, at a rowing speed of four miles per hour.  This will take two hours, plainly.  The return trip with the river’s gift of two miles per hour will evidently require but forty minutes. Two hours and forty minutes for the round trip, then, of eight miles.

Now then, to row eight miles in still water, according to our supposition, would have required but two hours.  But, some one objects, the current must help the return trip as much as it hindered the outgoing!  Ah, here is the snare that catches rough-and-ready common sense!  How long would the double journey have taken if the river current had been faster than our rowing speed?  How shall we schedule our trip if we cannot learn the correct speed, or if it varies from minute to minute?

These explanations are necessarily symbolistic rather than demonstrative, but any one who will seriously follow out these lines of thought, or, still better, study the attitude of the hard-headed modern physicist towards our classical geometry and mechanics, cannot fail to realize how conventional, artificial—­even phantasmal—­are the limitations set by the primitive idea of flat space and straight time.

The inferences which we may draw from our hypothetical experiment are plain.  The settings of the two chronometers would be defective, they would not show the same time, but each of them would mark the local time, proper to its own place.  There would be no means of detecting the amount of error, since the messages were transmitted by a medium involved with them in their transportation.  If only local time can be established, the possibility of a warped time-plane—­the curvature of time—­is directly opened up.  Doubtless it is true that on so relatively minute a scale as is offered by the earth, any deviation from perfect flatness of the time-plane would be so inconsiderable and imperceptible as to make it scientifically negligible; but this by no means follows when we consider our relation to other worlds and other systems.

A similar condition holds with regard to space-distortion.  The Theory of Relativity enforces the conclusion that from the standpoint of our conventions in regard to these matters, all bodies involved in transportation undergo a contraction in the direction of that transportation, while their dimensions perpendicular to the transportation remain invariable.  This contraction is the same for all bodies.  For bodies of low velocity, like the earth, this distortion would be almost immeasurably slight; but great or little, no measuring instruments on the body transporting would ever disclose it, for a measure would undergo the same contraction as the thing measured.