Prof. Cliallis on a Theory of the Dispersion ofLiyht. 271 



affected by a motion common to all the parts of the fluid, they 

 will be incident on the atom just as before, excepting that by 

 reason of this common motion a given condensation will reach a 

 given point of space a little earlier or a little later than it other- 

 wise would. As the effect of this inequality, as far as regards 

 the action on the atom, is a quantity of the second order, it may 

 be neglected in this investigation. Consequently the distribution 

 of condensation about the surface of the atom is to be determined 

 just as if the atom were fixed. 



The problem for the case of the fixed atom is discussed in the 

 Number of the Philosophical Magazine for May 1866 (pp. 353- 

 360), and in < The Principles of Mathematics' (pp. 279-287 & 

 441-446) ; and the expression obtained for the accelerative ac- 

 tion on the atom, insignificant terms being omitted, is 



3Hi dY 

 2A " dt' 



A being the ratio of the density of the atom to that of the aether, 

 and Hj a certain constant factor depending in an unknown man- 

 near on the breadth of the undulations. 



The resistance of the aether to the motion of the atom may be 

 at once inferred from the solution of the well-known problem of 

 the resistance of the air to the motion of a ball-pendulum j and 

 accordingly the part of the accelerative action due to this cause 



1S 2A ' df ' 



The molecular force of the medium called into action by the 

 relative displacement of its atoms will, when the condition of 

 transparency is satisfied, have a fixed ratio to the actual accelera- 

 tion of the atom. I have therefore given it the expression 



e a x 

 ~J¥~2 ' ~m> ^ ne cons t an t e 2 depending on the proper molecular 

 tc it tit 



elasticity of the medium. 



Prom these considerations it follows that 



d q x 3H, dV II d*x . e l d 2 x 



TTO- + 



dt 2 2A dt 2A df- ' /e'V dt 2 



dx 

 Hence, supposing V and -r- to vanish at the same time, which is 



another necessary condition of transparency, we have by inte- 

 grating, 



dx _ 3H/V 



Vdt~ (l + 2A)«'V-2Ae 2 * 

 It appears from reasoning contained in the discussions above 

 mentioned, that the constant Hj is equal to unity for an incom- 



