Mat 20, 1910] 



SCIENCE 



771 



and overestimating also the average veloc- 

 ity with which his signal travels through 

 his system in the ratio 1/(1-/3^),^ thus he 

 is Mwder estimating his time in the ratio 

 Vl — /3^- A certain time interval, that is, 

 appears less to him than to us and hence 

 his unit of time appears to us greater than 

 ours in the ratio 1/Vl — P"- 



This paper has become long enough 

 without an attempt to discuss the units of 

 mass and force. It has been my purpose 

 merely to answer a number of questions 

 which the experience of the Boston meet- 

 ing led me to believe were in the minds of 

 many who had not given the subject 

 enough thought to understand easily the 

 more profound discussions. 



The apparent transverse mass is, I think, 

 best derived by Lewis and Tolman* in their 

 excellent paper on the principle of rela- 

 tivity, and the relation between transverse 

 and longitudinal mass is shown in the 

 most direct and simple way by Bumstead^ 

 making use of the torsion pendulum. 

 Any one interested in the subject should 

 read these two papers. 



It is, of course, true that the principle of 

 relativity has a much deeper logical signifi- 

 cance than the simple, more or less con- 

 crete conceptions on which it is based in 

 the present paper would lead one to sup- 

 pose, but in an introduction to such a sub- 

 ject eoncreteness may not be a fault. 



It should be restated that the results of 

 the principle for uniform translation are 



^ The average velocity of a signal traveling 

 througli his system with a velocity which we 

 estimate as V — v in one direction and V -\- v 

 in the other, is of course obtained by dividing 

 the total distance by the total time. The total 

 time is obviously 

 t^i distance/ ( F — !>) -f * distance/ ( T -j- v), 

 and hence the average velocity is 



*PUl. Mag., 18, 510-523, 1909. 



= Am. Jour, of Science, 26, pp. 493-508, 1909. 



simply as true as its two postulates. If 

 either of these postulates be proved false 

 in the future, then the structure erected 

 can not be true in its present form. The 

 question is, therefore, an experimental one. 



I think it may be said with fairness, 

 however, that the principle is already in 

 harmony with so many phenomena that the 

 burden of proof lies with those who object 

 to it. Besides the negative result of ex- 

 periments to detect the earth's motion the 

 principle is supported directly by the re- 

 cent experiment of Bucherer," and by the 

 still more recent experiment of Hupka.'^ 

 Indirect support is also given by Lewis's^ 

 independently derived theory of non-New- 

 tonian mechanics, which agrees exactly 

 with relativity results, and by Comstock's^ 

 deductions from orthodox electromagnet 

 theory which lead to conclusions so nearly 

 coincident with those of relativity as to be 

 very suggestive. 



In closing, a word should be said with 

 regard to the "addition of velocities" ac- 

 cording to relativity rules. It will be evi- 

 dent on a little thought that if the moving 

 platform of Fig. 1, which is passing us 

 with velocity v, has on it a body traveling 

 over it in the direction of its motion with 

 velocity v (that is, with a velocity which the 

 observer on the moving platform calls v), 

 then our estimate of the velocity of the 

 iody will not be t; -|- v^. The reason is of 

 course that i; -|- i^i is the sum of two quan- 

 tities, one of which is estimated by us and 

 the other by the moving observer. We 

 should, therefore, be inconsistent because 

 we should have mixed view-points. Our 

 estimate of the platform's velocity plus our 

 estimate of the body's velocity with respect 

 to the platform equals our estimate of the 



'Ann. d. Phys., 28, S. 513-536, 1909. 

 'Anra. d. Phys., 31, S. 169-204, 1910. 

 'Phil. Mag., 16, pp. 705-717, 1908. 

 'Phil. Mag., 15, pp. 1-20, 1908. 



