244 REPORTS ON THE STATE OF SCIENCE. 



It appears from these equations that there is an intimate connection 

 between the internal energy of a system and its inertia in the Newtonian 

 sense. A mass m corresponds to energy mc 1 . Even the enormous stores 

 of energy exhibited by radio-active bodies represent only a small fraction 

 of the energy suggested by this equation. 



8. 



We have seen that the principle of relativity may be used to obtain 

 from known phenomena in a given system the corresponding phenomena 

 in the same system when supposed to be as a whole in motion with a 

 uniform velocity of translation. But we cannot determine by means of 

 the principle the influence of a system A upon a system B, when B is 

 moving relative to A, from a knowledge of that influence when they are 

 relatively at rest. This fact is closely associated with the fact that events 

 which are simultaneous to one observer are not simultaneous to another. 



The following example will illustrate this : — 



Suppose two points A B to move along a straight line. When they are 

 relatively at rest let the acceleration of B towards A be f B (x B — x A ) and 

 let that of A towards B be f A (x B — x A ), as measured by an observer at 

 rest relative to them both. 



We have seen that when they are both moving with velocity v along 

 the line their accelerations will be / B //3 3 , /a//? 2 . 



Suppose, however, we seek to deduce the accelerations when A has a 

 velocity v A and B a velocity zero relative to a given observer. 



The acceleration of B must be of the form F B (x B , x A , 0, v A ), and is 

 such that 



F B (X B , X A , V B , V A )=F B (x B , * A , 0,v A )/iP . . (a) 



«A + «B 



where v A = « A t) B . 



1 + "c y ' 



If we are given the function F B (x B . x A , 0, v A ) for all values of v A then 

 we can therefore deduce the fimction for all values of v B , but if we are 

 only given F B (x B , x A , 0, 0) this is impossible. 



Suppose we could determine any one fimction satisfying («) then 

 we could determine any number of others by multiplying F by any quantity 

 which is the same function of (x B , x A , v B , v A ) as of (X B , X A , V B , V A ). Of such 

 invariants an infinite number can be found, so that the principle of 

 relativity affords only a certain means of discrimination between possible 

 and impossible forms of F A and F B , but not a means of unique deter- 

 mination. 



All that the principle can do, for instance, in respect of the law of 

 gravitation is to say that the Newtonian Law cannot be exact, and to 

 suggest an infinite number of possible ways of rendering it so. Of course, 

 if gravitation is to be included in an electromagnetic scheme of matter, 

 we must expect it to be an effect propagated through the sether with the 

 velocity of light. If, on the other hand, it has nothing to do with the 

 electromagnetic properties of matter, we shall hardlv expect it to conform 

 to the principle of relativity. Just as the Newtonian dynamics breaks 

 down in the light of the electrical theory, so the latter may become only 

 an approximation, if gravitation is concerned with more remote and yet 

 undiscovered properties. 



