'H- Mr. MacCullagh on the Laws ()f Crystalline Reflexion. 



r' /• . /\ * fl/ . / « 7o.sin\l;'cos\|;'sin^i ,, . 



-tau^ =cos(^ + ?)cotan(l +(a'-i')^^,-^._^ ^._^,^ (J.) 



These equations (a.) and {b.) are to be substituted for 

 equations (2.) and (3.), which are the equations that M. See- 

 beck found to be at variance with his experiments. 



By means of formula (5.), e(|uation (a.) becomes 



/3 = -g- sin 2 gr sin {p-<^), (c.) 



from which the deviation in any azimuth may be readily cal- 

 culated. The azimuth (as M. Seebeck reckons it) begins 

 when, 5 = 0, and p is then positive. This formula (c.) perfectly 

 represents the experiments of M. Seebeck on Iceland spar. 

 The corresponding expressions for biaxal crystals may be 

 easily deduced, and will be given in a paper which I am pre- 

 paring to lay before the Royal Irish Academy. 



At the time of my last communication 1 was not aware that 

 the case in which the plane of incidence is a principal section 

 of the crystal (or the azimuth = 0,) had been solved by 

 M. Seebeck, and that formula (T.)? which I regarded as my 

 own, had been obtained by him long before. 



It remains to say a word respecting the new principle of 

 equivalent vibrations, the most important, perhaps, of all, as 

 it is certainly the simplest that can be imagined. If we con- 

 ceive an ajthereal molecule situated at the common surface of 

 two media, it would seem that its motion ought to be the same, 

 whether we regard the molecule as belonging to the first me- 

 dium or to the second. Now the incident and reflected vibra- 

 tions are superposed in the first medium, and the refracted 

 vibrations in the second ; and therefore we may infer (when 

 the phase is not changed by reflexion or refraction), that if the 

 incident and reflected vibrations be compounded, like farces 

 acting at a point, their residtant will be the same, both in length 

 and direction, as the resultant of' the refracted vibrations simi- 

 larly compounded. This is the law of equivalent vibrations, 

 and it gives, at once, three equations. A fourth e(juation is 

 aftbrded by Fresnel's law of the vis viva ; and thus we have 

 the four conditions necessary for a general solution of the 

 problem. From the principle of equivalent vibrations, as we 

 have stated it, it follows that the vibrations resolved parallel 

 to the separating surface are e(juivalent in the two media; and 

 in fact, this part of the general principle was assumed by 

 Fresnel ; but the other part, namely, that the vibrations per- 

 pendicular to the separating surface are equivalent, was not 

 assumed by him, nor is it by any means true in his theory. 

 It appears then that three conditions only are afforded by the 



