Light and the Theory of a Quasi-labile Ether. 133 



phase of the two reflected and the two refracted rays in the 

 most general case. It is easy, however, to deduce from these 

 four complex conditions, two others, which are interesting and , 

 sometimes convenient. It is evident from the definitions of 

 w' and w" that if u, v, u\ and v' are continuous at the inter- 

 face w' and w" will also be continuous. Now — w" is equal to 



the component of ¥(§. normal to the interface. The follow- 

 ing quantities are therefore continuous at the interface : 



the components parallel to the interface of (g, ) 



the component normal to the interface of W&, > (7) 



all components of curl (g. ) 



To compare these results with those derived from the elec- 

 trical theory, we may take the general equation of monochro- 

 matic light on the electrical hypothesis from a paper in a 

 former volume of this Journal. This equation, which with an 

 unessential difference of notation may be written* 



-Pot § - F Q = 47T<2>& (8) 



was established by a method and considerations similar to those 

 which have been used to establish equation (6), except that the 

 ordinary law of electro-dynamic induction had the place of the 

 new law of elasticity, g 1S a complex vector representing the 

 electrical displacement as a harmonic function of the time ; 

 is a complex linear vector operator, such that 4:7i@?$ represents 

 the electromotive force necessary to keep up the vibration g. 

 Q is a complex scalar representing the electrostatic potential, 

 pQ the vector of which the three components are 



dQ dQ dQ 



dx ' dy ' dz ' 



Pot denotes the operation by which in the theory of gravita- 

 tion the potential is calculated from the density of matter. f 

 When it is applied as here to a vector, the three components 

 of the result are to be calculated separately from the three 

 components of the operand. — p Q is therefore the electrostatic 



force, and —Pot g the electrodynamic force. In establishing 

 the equation, it was not assumed that the electrical motions 

 are solenoidal, or such as to satisfy the so-called " equation of 

 continuity." We may now, however, make this assumption, 



* See this Journal, vol. xxv, p. 114, equation (12). 



f The symbol —Pot is therefore equivalent to 4 -Try -2 , as used by Sir William 

 Thomson (with a happy economy of symbols) at the last meeting of British Asso- 

 ciation to express the same law of electrodynamic induction, except that the sym- 

 bol is here used as a vector operator. See Nature, vol. xxxviii, p. 571, sub. init. 



