INTENSITY OF REFLECTED AND REFRACTED LIGHT. 406 



becomes 



^-P^^--P=0 (A) 



e ax e, ax ' 



We need hardly repeat that the latter hypothesis, by which equations (3) and (4) 

 are deduced and combined, is true only for the particular value x = Q. 



Now, even without retaining the restrictions imposed on the functions in 

 art. 2, we may shew, by the reasoning used there, that 



P P, 



— + -' = 

 e e^ 



dx d.v 



two conditions which completely satisfy the equation (A) 

 Hence the final result is, that when x = 



7=T 



dx dx 



and the general values of 7 are already determined. 



Thus the results above obtained, approximately in the case of particles whose 

 action is insensible at sensible distances, is proved true, without any approxima- 

 tions, by the reasoning we have employed. 



SECTION n. 

 ON LIGHT CONSISTING OF VIBRATIONS IN THE PLANE OF INCIDENCE. 



8. We shall assume that it has been demonstrated that light cannot consist 

 of vibrations partly transversal, partly normal, and shall consequently distinguish 

 strictly between a motion in the direction of transmission, and a vibration in that 

 direction. 



At a distance from any break in the state of the molecules, one fimction will 

 be sufficient to represent the motion of a particle, since any motion not belonging 

 to the type of that function will be transmitted independently of it, and unaffected 

 by it, on the principle of the coexistence of vibrations. When, on the other hand, 

 the state of the particles in the immediate neighbom-hood of that under conside- 

 ration is discontinuous, Ave cannot assume that a state of motion represented by 

 one type will have no influence on that which is represented by another. On the 

 contrary, we should expect, from the ordinary laws of fluids, that the particular 

 type of the wave itself should undergo a considerable change, and possibly anti- 

 cipate a reversion of some of the previous axioms by which our calculations were 

 guided. It will be necessary then to retain every term which enters into our ex- 

 pressions, except those only which disappear of themselves by the conditions of 

 symmetry. 



VOL. XIV. PART II. 3 L 



