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SCIENCE 



[N. S. Vol. LI. No. 1315 



lis would be glad to welcome for personal 

 reasons in our international meetings of the 

 future. He protested against the famous 

 manifesto of the German professors in 1914 

 and was one of the eager supporters of the 

 German Eepublic when it arose from the 

 wreck of the Empire. 



But, in presenting the subject of Einstein's 

 study of the law of gravitation, I must begin 

 many years ago. In the treatment of Max- 

 well's equations of the electromagnetic field, 

 several investigators realized the importance 

 of deducing the form of the equations when 

 applied to a system moving with a uniform 

 velocity. One object of such an investiga- 

 tion would be to determine such a set of 

 transformation formulse as would leave the 

 mathematical form of the equations unaltered. 

 The necessary relations between the new 

 space-coordinates, those applying to the mov- 

 ing system, and the original set were of 

 course obvious; and elementary methods led 

 to the deduction of a new variable which 

 should replace the time coordinate. This 

 step was taken by Lorentz and also, I believe, 

 by Larmor and by Voigt. The mathematical 

 deductions and applications in the hands of 

 these men were extremely beautiful, and are 

 probably well known to you all. 



Lorentz' paper on this subject appeared in 

 the Proceedings of the Amsterdam Academy 

 in 1904. In the following year there was 

 published in the Annalen der Physik a paper 

 by Einstein, written without any knowledge 

 of the work of Lorentz, in which he arrived 

 at the same transformation equations as did 

 the latter, but with an entirely different and 

 fundamentally new interpretation. Einstein 

 called attention in his paper to the lack of 

 definiteness in the concepts of time and space, 

 as ordinarily stated and used. He analyzed 

 clearly the definitions and postulates which 

 were necessary before one could speak with 

 exactness of a length or of an interval of 

 time. He disposed forever of the propriety 

 of speaking of the " true " length of a rod or 

 of the "true" duration of time, showing, in 

 fact, that the numerical values which we 

 attach to lengths or intervals of time depend 



upon the definitions and postulates which we 

 adopt. The words " absolute " space or time 

 intervals are devoid of meaning. As an 

 illustration of what is meant Einstein dis- 

 cussed two possible ways of measuring the 

 length of a rod when it is moving in the 

 direction of its own length with a uniform 

 velocity, that is, after having adopted a scale 

 of length, two ways of assigning a number 

 to the length of the rod concerned. One 

 method is to imagine the observer moving 

 with the rod, applying along its length the 

 measuring scale, and reading off the positions 

 of the ends of the rod. Another method 

 would be to have two observers at rest on the 

 body with reference to which the rod has the 

 uniform velocity, so stationed along the line 

 of motion of the rod that as the rod moves 

 past them they can note simultaneously on a 

 stationary measuring scale the positions of 

 the two ends of the rod. Einstein showed 

 that, accepting two postulates which need no 

 defense at this time, the two methods of 

 measurements would lead to different ntmier- 

 ical values, and, further, that the divergence 

 of the two results would increase as the 

 velocity of the rod was increased. In assign- 

 ing a number, therefore, to the length of a 

 moving rod, one must make a choice of the 

 method to be used in measuring it. Ob- 

 viously the preferable method is to agree that 

 the observer shall move with the rod, carrying 

 his measuring instrimient with him. This 

 disposes of the problem of measuring space 

 relations. The observed fact that, if we 

 measure the length of the rod on different 

 days, or when the rod is lying in different 

 positions, we always obtain the same value 

 offers no information concerning the " real " 

 length of the rod. It may have changed, or 

 it may not. It must always be remembered 

 that measurement of the length of a rod is 

 simply a process of comparison between it 

 and an arbitrary standard, e. jr., a meter-rod 

 or yard-stick. In regard to the problem of 

 assigning nmnbers to intervals of time, it 

 must be borne in mind that, strictly speaking, 

 we do not " measure " such intervals, i. e., 

 that we do not select a unit interval of time 



