24 Mr. O'BRIEN ON THE REFLEXION AND REFRACTION OF LIGHT 



SECTION VII. 



Hoiv ice must proceed when the Equations of Connection are taken in their most 



general Form. 



(28.) The equations (5), (8), and (9), Article (19), are still true, being deduced from 



the equations (D), Section 11., without making any hypothesis respecting the constants. But 



instead of (6) and (7), we shall arrive at two equations, somewhat more complicated in form, 

 as follows. 



The equations (E) and {F), Section 11., may, in virtue of the equations — — = —— , _Z = _Z_ 



dx ax dx dx 



be put in the forms 



yda: dx! \dz dx I dx 



\dz dx) \dis dx j dx 



Now, in these equations, as in Article (19), we shall put a + Oj + Ou, 7 + 71 + 7^, a + a", 

 7' +7", for a, 7, a, y, respectively, and then, as in Article (19), and by the equations 

 (A), (B), (C), Section i., we obtain immediately the following equations, 



V + V V r V V"\ 



(C + D) — !— ' = (C + i)') - - 2 {D' - D) (s'p - + s" - ] 



V V" I V' V"\ 



(C + £) ^ = (C + E')~ +(D'-E'-D + E)( s'p' ~ - p'" — ) . 



From these equations, and the equations (8) and (9) Article (19), we may find F,, V", 

 V2, and V" in terms of V. We shall not calculate these values, as they are rather complicated, 

 and not necessary to the object of the present paper. The last of the equations just obtained 

 considerably simplifies when we suppose the ether to obey the common law of elasticity, in which 

 case we have D' - E' - D + E = 0. (See Article 12.) 



It is easy to see that Fresnel's formulas cannot be deduced from these equations, unless D = D', 

 and E^E, and therefore it will be useless to employ the equations of connection in their 

 most general form, as it is highly probable that Fresnel's formulae are experimentally true for 

 a great number of substances. 



SECTION VIII. 

 Intensity and Phase of the Reflected Ray, in the case of highly Refractive Substances. 



(29.) There are some substances, such as the diamond and other bodies of high refractive 

 power, for which Fresnel's formula do not appear to be accurately true. It is easy to account 

 for this in the following manner. 



When we do not assume that v^ = v", we have, by Article (22), 



V = ^iiZil^V V, where , = (.= - 1) (,^ _ ,) - P'P" 



flS + S + ,, ' ^ ' S - 1/S2 



