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 ether 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 formulas, converting the triple 

 sums which it contains into triple integrals, according to the 

 method of M. Cauchy. 



Among the consequences deducible from this development 

 is the following: — In the expanded expression for the velocity 

 of propagation, each term consists of two parts, one of which 

 is due to the action of the ether, and the other to that of the 

 body. It is not improbable 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 opposite signs, and 

 nearly equal. In this case the principal part of the expres- 

 sion 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 3.866, 3.271, 2.824; 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. 



