78 Dr. C. Y. Burton on a 



harmonic train of plane-waves, propagated with velocity 17 

 in the direction of ^-increasing. It will be convenient to 

 define the waves in terms of the variations of pressure taking- 

 place in the sether ; thus 



p =TJ + Bsm 2 -^(x-Yrt + e); . . . (4) 

 A, 



so ihat B is the semi-amplitude of pressure-variation, 17 the 

 velocity of the disturbance, X the wave-length, and X/17 the 

 period ; while e is a linear magnitude serving to fix 

 the otherwise undefined question of phase. 



12. As a particular case, suppose that F, the extrusion of 

 a3ther per unit-mass of atomic matter (§ 7), is zero, any given 

 volume of space thus containing precisely the same amount 

 of aetherial substance, whether atomic matter is present in 

 that space or not. It is then evident from general con- 

 siderations that the sether affected by the wave-motion, in 

 surging to and fro, will merely carry with it whatever atomic 

 matter may be present ; no tendency arising for those strain- 

 distributions which constitute matter to lag behind or to 

 outrun the bodily excursions of the setherial plenum. The 

 same conclusion is reached when we put F = in (3) ; there 

 are then no forces belonging to the class there concerned, or, 

 in other words, the wave-motion has no tendency to accelerate 

 the motion of atomic matter with respect to the aether; so 

 that every portion of atomic matter will continue in its state 

 of rest, or of uniform or accelerated motion toitli respect to the 

 cether, precisely as if no wave-motion were taking place. 

 Under this particular assumption that F = 0, the wave- 

 motion (at least in the case of sufficiently great wave-lengths) 

 would appear to be without influence on any of the pheno- 

 mena which come within the range of our observation, and 

 to belong to that class of activities for which the name 

 aphenomenal has been suggested *. Apart from any question 

 as to the correspondence between our special assumptions 

 and the conditions obtaining in the physical universe, it is 

 instructive to realize that the picture here presented — of 

 vibratory motions affecting all matter without influencing 

 the phenomena of ordinary dynamics — is in no way in- 

 compatible with the fundamental concepts of dynamical 

 science. 



13. If, instead of F = 0, as in § 12, we suppose F to be 

 finite, so that the mean density of setherial substance in a 

 region containing atomic matter is different from the density 

 in free sether, it is evident that a general bodily acceleration 



* But see also Appendix B. 



