944 



SCIENCE 



[N. a. Vol. XXXVII. No. 964 



ment, it is doubtful if many persons actually 

 construct their idea of the universe so as to 

 make this motion of the earth a reality. It 

 is not many years since the assertion of Poin- 

 care that the rotation of the earth is a hy- 

 pothesis, met with as much glee in some quar- 

 ters as it did astonishment in others. When 

 the average man says that so far as he is con- 

 cerned, the earth is stationary, he means prac- 

 tically that none of the experiences he has 

 had lead him to think of the earth as in mo- 

 tion. When, hovpever, he becomes a physicist, 

 and tries to harmonize the motion of Fou- 

 cault's pendulum with his ideas of mechanics, 

 or the deviation of a falling body from the 

 vertical, or the motion of storms across the 

 surface of the earth, he is led to assert as the 

 simplest explanation that the earth must ro- 

 tate. When he becomes an astronomer and 

 endeavors to reduce the varying configura- 

 tions of the heavens to some kind of sim- 

 plicity, he is ultimately led to assert that the 

 earth is moving in space. He is thus brought 

 to consider the question, is the whole universe 

 in motion? and how can its motion be de- 

 tected? At once he remembers Archimedes's 

 remark: Give me a fulcrum and I will move 

 the world. What is the fulcrum? Here is 

 the trouble. If the earth may be thought of 

 as moving around the sun, the sun may be 

 thought of as moving around the earth. If 

 the mountains and oceans of the earth can 

 turn smoothly around once every twenty-four 

 hours why can not the heavens turn? The 

 problem comes home and must be phrased 

 thus: How can the absolute motion of the 

 earth be proved? Was Galileo right when he 

 said: E pur si muove. 



We turn first to dynamics for help, but we 

 find that its laws will not avail. The funda- 

 mental law is that the rate of change of the 

 momentum of a moving body is proportional 

 to the force acting, where force and momen- 

 tum are taken as directed quantities. But if 

 we locate the moving particle with respect to 

 an origin which itself is moving uniformly in 

 a straight line we can not detect the fact that 

 the origin is in motion, for the law holds 

 equally well in either case; that is to say. 



change in momentum is measured by a differ- 

 ence of velocities and can never give us the 

 absolute value of velocity itself. This is the 

 relativity principle of ordinary mechanics. 

 Conversely, if we agree that all we know of 

 the kinetic energy of a particle is that the 

 increment of the energy is measured by the 

 work done by the external force in moving the 

 particle an infinitesimal distance, and that 

 this is invariant for a system whether it is at 

 rest or in motion, with a uniform rectilinear 

 velocity, then all the equations of dynamics 

 are dedueible from this basis. 



Since dynamics gives us no help, we turn 

 to electrodynamics. There is here a constant 

 which seems to be an absolute constant, the 

 velocity of light. It would seem that if light 

 is a movement or a disturbance in a stationary 

 ether, then we should be able to detect the 

 motion of the earth against this ether. Aber- 

 ration indeed seems to indicate that we have 

 found our fulcrum. But other experiments 

 seem to show that if there is an ether, it 

 moves with the earth. And the only apparent 

 way to reconcile all the experiments seems to 

 be the assumption of certain laws which make 

 the hypothesis of an ether superfluous. The 

 physicist is here hard pressed for a satisfac- 

 tory substitute. When the fundamental equa- 

 tions of electrodjmamics are examined mathe- 

 matically, it is found that certain changes 

 can be made in the variables of these equa- 

 tions without affecting the form of the equa- 

 tions. In the new variables the equations 

 read just the same as in the old. That is to 

 say, for certain moving systems the equations 

 are of the same form as for a stationary sys- 

 tem. Consequently the quantities involved 

 can only be determined relatively. 



The specific statement of the case is this: 

 Let one end of our laboratory table be our 

 origin, and we will suppose that with respect 

 to an omnipresent stationary observer who 

 appreciates distance and time directly, the 

 origin is in motion in a straight line with 

 uniform velocity, v. The velocity of light we 

 will represent by c, and we will suppose that 

 any velocity can be measured absolutely. 

 This is our first assumption. Then if the fol- 



