288 The Rev. Prof. O'Brien on the Laws 



The quantities cr, ^, P and 9 in these expressions are to he 

 obtained by equaling the possible and impossible parts of the 

 following equations, viz. 



Vl-P^-^^^^/ ^ B'V « / 



where B, B' and C are certain constants which occur in the 

 equations of motion of the aether. B is the same for all colours, 

 but B' and C are different for different colours, being given 

 by the equations 



B' = ? 



1+C2-C47Z2+C6«4 ' 



_ C,~C^n^+C,n'^ 



^ - l^C^-C^n^+CQii^ ' 



where B, C^, Cg, Cgj&c. are certain constants depending simply 

 upon the constitution of the aether and of the transparent body. 

 3. The following are the laws of reflexion and refraction for 

 vibrations 7;«rc7//^/ to the plane of incidence. 



Let the general expression for the incident disturbance be 

 h cos \n t — k [p X -\- s z) }, 

 then the expression for the reflected disturbance will be 



P QZ»cos {nt — k {p x-Vsz) — Q — »}; 

 and the expression for the refracted disturbance will be 

 Kbe-''^''{cos{nt—k{pA' + (rz) +x} 



+ PQcos {nt—k{px + (Tz) + X — 9 — <} j, 



where P, 9, <r and x ^^'^ the same quantities as before, and Q, 

 I, K and x are to be obtained by equating the possible and 

 impossible parts of the following equations, viz. 



1 B / _C \ 



^i^^T^-B'V^ ;z^-V' 



where for brevity we have put U^ to represent the expres- 

 sion 



A^B Qe-'^^-e^^^^ 



A and A' being certain constants which occur in the equations 

 of motion for normal waves, occupying the same places re- 



