442 THE POPULAR SCIENCE MONTHLY 



In consequence of the change in our ideas of velocity, there results 

 a change in one of the most widely employed laws of velocity, namely the 

 parallelogram law. Briefly stated, in the relativity mechanics, the com- 

 position of velocities by means of the parallelogram law is no longer 

 allowable. This follows evidently from the fact that there is an upper 

 limit for the velocity of a material body, and if the parallelogram law 

 were to hold, it would be easy to imagine two velocities which would 

 combine into a velocity greater than that of light. This failure of the 

 parallelogram law to hold is to the mathematician a very disturbing 

 conclusion, more heretical perhaps than the new doctrines regarding 

 space and time. 



Another striking consequence of the relativity theory is that the 

 hypothesis of an ether can now be abandoned. As is well known, there 

 have been two theories advanced in order to explain the phenomena 

 connected with light, the emission theory which asserts that light effect 

 is due to the impinging of particles actually sent out by the source of 

 light, and the wave theory which assumes that the sensation we call light 

 is due to a wave in a hypothetical universal medium, the ether. Needless 

 to say this latter theory is the only one which recently has received any 

 support. And now the relativists assert that the logical thing to do is 

 to abandon the hypothesis of an ether. For they reason that not only 

 has it been impossible to demonstrate the existence of an ether, but we 

 have now arrived at the point where we can safely say that at no time in 

 the future will any one be able to prove its existence. And yet the 

 abandoning of the ether hypothesis places one in a very embarrassing 

 position logically, as the three following statements would indicate: 



1. The Michelson and Morley experiment was only possible on the 

 basis of an ether hypothesis. 



2. From this experiment, follow the essential principles of the rela- 

 tivity theory. 



3. The relativity theory now denies the existence of the ether. 

 Whether there is anything more in this state of affairs than mere filial 

 ingratitude is no question for a mathematician. 



It should perhaps be pointed out somewhat more explicitly that these 

 changes in the units of time, space and mass, and in those units depend- 

 ing on them, are changes which are ordinarily looked upon as psycho- 

 logical and not physical. If we imagine that A has a clock and that 

 about him move any number of observers, B, C, D, . . . , in different 

 directions and with different velocities, each one of these observers sees 

 A's clock running at a different rate. Now the actual physical state of 

 A's clock, if there is such a state, is not affected by what each observer 

 thinks of it ; but the difficulty is that there is no way for any one except 

 A to get at the actual state of A's clock. We are then driven to one of 

 the two alternatives : Either we must give up all notion of time at all, 



