Royal Irish Academy. 133 



present continuation, confining himself to the comparatively simple 

 case in which the molecules of the aether and of the body are uniformly 

 diffused. 



The differential equations of motion inferred from these considera- 

 tions contain, each, the displacements of the molecules of the aether 

 and of the body, with coefficients depending on the masses and di- 

 stances of the molecules, the law of force to which they are sub- 

 jected, and the length of the wave. By a particular method of elimi- 

 nation, these pairs of simultaneous equations may be reduced each to 

 a single one, of the simple form which occurs in the case of a single 

 vibrating medium, the new coefficient being connected with those of 

 the original equations by an equation of the second degree. The ex- 

 pression for the displacement, then, is of the same form as in the case 

 of a single vibrating medium j but the relation between the coeffi- 

 cients of the time and of the distance, and consequently the velocity 

 of propagation, will be very different. 



The quadratic equation above alluded to expresses the relation of 

 these coefficients, or, in other words, the relation between the period 

 of vibration and the length of the wave. When the action of the 

 molecules of the aether and of the body, inter se, and on one another, 

 is governed by the same law, this equation is resolvable into simple 

 factors, one of which only seems to belong to the problem, the other 

 giving an expression for the velocity of propagation independent of 

 the length of the wave. The author accordingly proceeds to develop 

 the former of these formulae, converting the triple sums which it con- 

 tains into triple integrals, according to the method of ML Cauchy. 



Among the consequences deducible from this development is the 

 following : In the expanded expression for the velocity of propaga- 

 tion, each term consists of two parts, one of which is due to the 

 action of the aether, and the other to that of the body. It is not im- 

 probable that there may be bodies for which the first or principal term 

 is nearly nothing, the two parts of which it is composed being of op- 

 posite signs, and nearly equal. In this case the principal part of the 

 expression for the velocity will be that derived from the second term ; 

 and, if that term be taken as an approximate value, it will follow that 

 the refractive index of the substance must be in the sub-duplicate 

 ratio of the length of the wave nearly. Now, it is remarkable that 

 this law of dispersion, so unlike anything observed in transparent 

 media, agrees pretty closely with the results obtained by Sir David 

 Brewster in some of the metals. In all these bodies the refractive 

 index (inferred from the angle of maximum polarization) increases 

 with the length of the wave. Its values for the red, mean, and blue 

 ray, in silver, are 3866, 3*271, 2*824 j the ratios of the second and 

 third to the first being *85 and '73. According to the law above 

 given, these ratios should be *88 and '79. 



Professor MacCullagh made a verbal communication on the pro- 

 bable nature of the light transmitted by the diamond and b}' gold leaf. 

 He conceives that as there is a change of phase caused by reflexion 

 from these bodies, so there is also a change of phase produced by re- 

 fraction ; the change being different according as the incident light 



