512 PROCEEDINGS OF THE AMERICAN ACADEMY. 



But acceleration means rate of change of velocity, and therefore 

 absolute acceleration means rate of change of absolute velocity, and, 

 if there is no such thing as absolute velocity, how can there be such 

 a thing as rate of change of it? We must, therefore, redefine the 

 absolute acceleration of any system to mean the acceleration relative 

 to another system moving in such a way that the simple electromag- 

 netic equations hold on it, and on which the velocity of the first system 

 is zero at the instant in question. 



Even now, however, there is difficulty, because in place of our set 

 of systems with the constant relative velocities, for which the equations 

 hold, we might equally well imagine any other exactly similar set of 

 systems each of which has a certain given acceleration relative to the 

 corresponding one of the first set. And, disregarding the rather 

 arbitrary definition of absolute acceleration given above, it is evident 

 that, if space had no properties other than those of geometry and time, 

 any difference between the laws of nature as observed from two of 

 these relatively accelerated systems would be impossible. But 

 since the observed laws are simpler in one of the first set than in one 

 accelerated relative to it, the space must have other properties than 

 the above mentioned ones ; and, because of these properties, it appears 

 highly probable that there must be some sort of a substance, or me- 

 dium, filling all space, having no acceleration relative to any of the 

 systems for which the simple electromagnetic equations hold, not 

 directly affecting our senses, but having properties which account 

 for all the laws of the phenomena that are directly observable, includ- 

 ing the exact mathematical similarity of the expressions for these 

 laws in terms of quantities measured on any system moving with 

 uniform velocity, less than that of light, through it. This is the 

 medium to which we give the name of "ether." 



The Ether. — To obtain any knowledge of the properties of this 

 medium, that enable it to show the phenomena of electricity, mag- 

 netism, and gravitation, and to account for the laws of motion of 

 matter, the principal of relativity, and the permanent existence of 

 positive and negative electrons in spite of the possibility of collisions 

 between them, it will be necessary to obtain the simplest possible 

 form of the set of laws which govern these phenomena. 



Since many of the quantities that we deal with are vectors, we shall 

 find it convenient to use some simple vector analysis, with the follow- 

 ing notation, that of Gibbs, in which all vectors will be printed in 

 Clarendon type while scalars are in italic type. The scalar product, 



(axbx + a,yhy -\-&zhz), 



