474 Prof. Challis on the Theory of Double Refraction 



Having arrived at this expression for the relative velocity of the 

 sether and an atom, we have next to investigate the retarding 

 effect of the atoms taken collectively on the undulations of the 

 sether. As already explained, the retardation is due to the 

 reflexions of velocity from the surfaces of the atoms, the reflexion 

 from each atom depending only on the relative velocity of the 

 atom and the sether. The total reflected velocity consists of two 

 parts, of which one depends on the new condensation to which 

 the reaction of the surface of the atom gives rise, while the other 

 is unaccompanied by condensation, being a velocity of the kind 

 by which the fluid moves so as to fill space continuously without 

 change of density. The latter part, inasmuch as it fulfils that 

 coodition and is due to the reaction of a spherical surface, takes 

 place in the directions of the radii produced, and varies with the 

 distance according to the law of the inverse square. Also the 

 mathematical theory of motion in an elastic fluid tending to or 

 from a centre, shows that for all distances from the centre very 

 small compared with the breadth of the waves, or the value of X, 

 the part of the velocity unaccompanied by condensation is very 

 much larger than the other part. If, therefore, the velocity V 

 be incident on the atom at a point the radius to which makes an 

 angle 6 with the direction of incidence, and c be the radius of the 

 atom, the velocity at the distance r from the centre reckoned on 



Yc 2 



the produced radius of the point is —$- cos 6, r being very small 



compared with X. Now it is this reflected velocity which gives 

 rise to a retarding force acting always counter to the accelera- 

 tive force due to the elasticity of the aether. The mode of action 

 will be such as follows. Since it is an experimental fact that 

 parallel lines, engraven on glass, and separated by intervals less 

 than X, can be seen with a microscope without the least appear- 

 ance of discontinuity of the surface of the glass, it follows that 

 the mean interval between the atoms must be almost an infinite- 

 simal quantity compared with X. Consequently, if we conceive 

 a plane to be drawn in the medium parallel to the front of the 

 waves, the retarding force at any point of the plane will be due 

 not alone to the reflexion of velocity from atoms situated in the 

 plane, but also from simultaneous reflexions from atoms situated 

 within a certain small distance beyond it in the direction towards 

 which the waves are propagated. The limiting distance the 

 reflexions beyond which have no sensible effect at the plane, while 

 it is small compared with X, must at the same time be supposed 

 to contain many multiples of the mean interval between the 

 atoms. Eor, considering that in fluids and solids the atoms 

 occupy spaces very small in comparison with the intervening 

 spaces, unless the reflexions take place from a vast number of 



