522 PROCEEDINGS OF THE AMERICAN ACADEMY 



from which we may infer that 



(9) E + pxH + k — G (E + pxH) = 0. 



Obviously, we may derive equation (10) by an exactly similar process 

 in which the terms involving G do not enter. And if we wish to use 

 an infinitesimal charge of some other shape, we may consider it as 

 divided up into a number of cylinders, not necessarily right cylinders, 

 such as we used above. ^ 



Meanings of the Laws. — To find out what we can about the 

 properties of the ether, we may now examine carefully the meanings 

 of these five laws: 



<1) V-E = p, (2) V-E = p, 



(3) VxH = E + pi (4) VxH = E + p p, 



(11) 8 j j \{W - GK') - (E2 — GE' + 2 U)](Jrdt = 0. 



«, 00 



The first two of these laws contain no reference whatever to time, 

 and deal with quantities whose existence is in no way dependent 

 on motion or change with time. Therefore, we may infer that they 

 probably express relations between the geometrical configurations of 

 different parts of the ether, and show the dependence of these geometri- 

 cal configurations upon the presence in the ether of the peculiar mov- 

 able spots called charges, whose indestructibility and ability to be 

 located definitely at different times (specified in equations (3) and 

 (4), as well as the internal forces, suggest that they are due to the 

 presence of some substances not present in the rest of the ether but 



freely movable through it. Since these substances can be located at 



+ - 



any time if the vectors E and E are known at every point, the question 



•arises whether any more information than the value of these vectors 



needs to be given to determine completely the configuration of the 



ether. A suggestion of the answer to this question is given by the 



fact that in applying Hamilton's Principle to problems of ordinary 



dynamics, the variations must be such as to give the actual iconfigura- 



6 To be certain that no equations not derivable from equations (I)-(IO) 

 can be derived from (11) and (I)-(4), we need only to consider the facts that 

 any possible variation in equation (11) can be made up of variations of the 

 types treated above, and that the mutual energy of two independent varia- 

 tions of the first order is an infinitesimal of the second order. 



