of Physical Quantities to Directions in Space. 263 



cluced for to must obviously hold for the other quantities. 

 Thus :— 



1. Let /J contain X~*Y~*Z~*. Then [m] contains 



(X-iY-^Z" 1 ) R (X*5r*Z*) rrRlT 1 . 

 This becomes scalar only when R coincides with Y. 



2. Let //,* contain X*Y*Z~*. Then [to] contains 



(X*Y § Z"*) R (X*Y~ I Z*) = RX. 

 This becomes scalar only when R coincides with X. 



3. Let fJ contain X*5T~*Z~"*. Then [to] contains 



(X*Y~ I Z-*) R (X^Z 1 ) =R x Y" 1 . 

 This becomes scalar when R coincides with Z. 



4. Let fj? contain X~*Y*Z~*. Then [to] contains 



(X-^rtZT 1 ) R (X*Y~*Z*) =R. 



This cannot become scalar. 



Thus, in order to render the scalar quantities scalar, R 

 must ultimately coincide with X, Y, or Z. There are thus 

 three cases to be considered : — 



1. When R coincides with Y, /-t contains (XYZ) -1 * 



2. „ „ „ X, „ (XYZ- 1 ). 



3. „ „ „ Z, „ (XY-'Z- 1 ). 



But, according to the electromagnetic theory of light, R cannot 

 coincide with Z, for XY is the wave-front of an instan- 

 taneous plane-polarized disturbance at a point in the medium— 

 the disturbance ultimately originating in the displacement R, 

 and since the medium is isotropic, the linear displacement 

 specified by R can have no components along Z. We are 

 thus restricted to the two cases where R coincides with Y, 

 and the dimensions of /j, involve (XYZ) _1 , or where R coin- 

 cides with X, and the dimensions of ja involve XYZ -1 . In 

 the former case, the instantaneous linear displacement R of 

 the medium at any point is in the plane of polarization (the 

 plane of magnetic displacement), magnetic energy is kinetic, 

 and electrical energy potential. In the latter case, the dis- 

 placement R is at right angles to the plane of polarization, 

 magnetic energy is potential, and electrical energy kinetic. 

 Physicists are not yet agreed as to the interpretation of 

 Weiner's results, so that no arguments as to the direction of the 

 instantaneous displacement of the medium at a point can be 

 based upon his experiments. We have, therefore, to suppose 



