﻿The Propagation of Periodic JEther Disturbance. 809 



regards the differentiating action of D. In (28) the force- 

 quaternion P e is immediately expressed by the electro- 

 magnetic bivector F and its complementary Gr. Thus, the 

 formula (28) is adapted for showing the properties of the 

 Maxwellian stress and of the electromagnetic momentum 

 along with the flux and the density of energy, in corre- 

 spondence to the equivalent formula of Minkowski's four- 

 dimensional system. 



But, since we already know everything about the be- 

 haviour of each constituent of P. i. e. of P e , P m , we may 

 dismiss them altogether and use more conveniently the full 

 dynamical biquaternion P, as defined by (24). Thus, using 

 again the equation fVI.), we shall have, more simply, 



P = D[F.F], .... (XIV.) 



where the purpose of the brackets is only to emphasize the 

 circumstance that F . F plays the part of a dyad. This will 

 lead us to the quaternionic treatment of questions regarding 

 stress, and localization and flux of energy- 



But these fundamental dynamical questions will best be 

 postponed and reserved for a future publication, in which 

 also the quaternionic treatment of the electrodynamics of 

 ponderable bodies and of some other relativistic subjects will 

 be given. 



November, 1911. 



LXXVII. On the Propagation of Periodic JEther 

 . Disturbance. By Andrew Stephenson*. 



1. OLNCE the Rontgen rays do not exhibit refraction, the 

 k5 velocity of transmission of gether disturbance through 

 a medium depends only upon forced oscillations set up within 

 the molecule, the aether being otherwise unaffected by the 

 presence of the material particles t. 



2. If the aether is treated as an elastic solid the presence 

 of resonators in the case of periodic disturbance is equi- 

 valent to a change in the density, so that a material non- 

 crystalline medium and the sether differ optically only in 

 density. 



* Communicated by the Author. 



t As a deduction it may be noted that any deviation from the 

 (fi 2 — 1)/D formula for the refraction of a compound or mixture, derived 

 from the atomic refraction equivalents, is the result of deformation of 

 the atoms, or of interatomic vibration, and cannot be subject to any 

 g-eneral 'law.' 



