LEWIS AND TOLMAN. — THE PRINCIPLE OF RELATIVITY. 723 



Combining this equation with III gives 



E 1 



E Q Vi - W 



We thus see that energy changes with the velocity in the same way 

 that mass does, and that the so-called kinetic energy is a " second 

 order effect " of the same character as the change of length and the 

 change of mass. The only reason that this effect is easily measured 

 and has become a familiar conception in mechanics, while the others 

 are obtainable only by the most precise measurements, is that we are 

 in the habit of measuring quantities of energy which are extremely 

 minute in comparison with the total energy of the systems investigated. 



Conclusion. 



We have shown how observers stationed on systems in motion rela- 

 tive to one another have been able to preserve their fundamental prin- 

 ciples of mechanics only by adopting certain novel conclusions. These 

 conclusions are self-consistent ; in the one case where they have been 

 tested they are in accord with experiment ; and they enable us to save 

 all the fundamental physical concepts which have been found useful in 

 the past. We have, however, considered primarily only systems which 

 are initially in uniform relative motion. Whether our conclusions can 

 be retained when we consider processes in which the relative motion is 

 being established, in other words, processes in which acceleration takes 

 place, it is not our present purpose to determine. 



The ideas here presented appear somewhat artificial in character, and 

 we cannot but suspect that this is due to the arbitrary way in which 

 we have assumed this point or that point to be at rest, while at the 

 same time we have asserted that a condition of rest in the absolute 

 sense possesses no significance. 



If our ideas possess a certain degree of artificiality, this is also true 

 of others which have long since been adopted into mechanics. The 

 apparent change in rate of a moving clock, and the apparent change in 

 length and mass of a moving body, are completely analogous to that 

 apparent change in energy of a body in motion, which we have long 

 been accustomed to call its kinetic energy. We may with equal reason 

 speak of the kinetic mass found by Kaufmann and Bucherer, or the 

 kinetic length assumed by Lorentz. We say that the heat evolved 

 when a moving body is brought to rest comes from the kinetic energy 

 which it possessed. We thus preserve the law of conservation of 

 energy. It is in order to maintain such fundamental conservation 



