TRANSACTIONS OF THE SECTIONS. 19 



regarded ns distinct and independent phenomena, referable to different causes ; in 

 evidence of which it is remarked that a low refractive power may consist with a high 

 dispersive and extrusive power, or vice versa. To arrive with accuracy at the expo- 

 nent of the normals for any medium and temperature, it is advisable to know, from 

 observations on all the seven lines, made with an approximate degree of correctness, 

 the refraction, the dispersion, and the irrationality ; seeing the exponent depends on 

 the relation of the irrationality to the dispersion. 



A pretty close approximation to the value of the exponent and the two relative 

 constants may be made, from having given only the indices of the two extreme, and 

 one of the central lines ; and from these the other four indices might thus be found. 

 But there is no advantage in proceeding in this imperfect manner. Observations on 

 the whole seven lines can never be dispensed with in practice ; and as these tend 

 mutually to check. one another, it will always be found more expedient to take the 

 whole seven into account in the determination of the exponent and the constants. 

 The exponential law should therefore be regarded less as a substitute for observation, 

 than as a method of reducing the observations, when made within certain limits of 

 accuracy, under the dominion of law, and of thus rendering their accuracy more 

 perfect. The essential difference between the law of M. Cauchy and the exponen- 

 tial law,, then, is, that the latter substitutes a variable exponent, capable of determi- 

 nation, for the squares of the normals employed in the former. 



The constant e represents the effects of the refractive power alone, such a6 they 

 would appear in achromatic combinations of prisms. It shows how much the waves 

 are shortened by the mere increased proximity of the ethereal particles, or centres of 

 elasticity, within the medium ; and as it affects all the waves rateably, it may sub- 

 sist without either dispersion or irrationality. In so far as this property is concerned, 

 the waves, on entering the medium, embrace, in their length, the same number of 

 ethereal particles as they did in the free ether. 



The constant cc represents the effects of the dispersive power alone, which is 

 attributed to the medium increasing the persistence of the ethereal particles in their 

 normal positions, beyond that degree in which it would be augmented by their mere 

 mutual approximation. It is supposed that, by this action, a certain definite num- 

 ber of ethereal particles are excluded from the length of each wave, so as to cause all 

 of them to be shortened by the same definite amount. Thus the shorter waves are 

 more shortened, in proportion to their primary length, than are the longer waves. 

 These consequently exhibit unequal degrees of refrangibility, and are accordingly, on 

 issuing from the medium, dispersed. 



In explanation of the extrusive property, to which the irrationality is attributed, 

 two views are suggested. Evidencing, as they do, an apparent transfer of motive 

 energy from the extreme to the central parts of the spectrum, so that the central 

 waves are less refracted, and the extreme waves more refracted, than they would 

 otherwise be, the effects of the extrusive power present, as respects distribution, a 

 conformity with the degrees of brightness of the spectrum; for all spectra are brighter 

 towards the centre, and fade off on either side. This circumstance indicates that, 

 at the recipient surface, the amplitudes of the individual vibrations embraced in the 

 waves are greatest towards the centre. Now the action of the medium may be such 

 as to lessen the amplitude of the vibrations, in all the waves, by a certain definite 

 amount — the rapidity of vibration (consequently the refrangibility of the wave) being 

 increased in the same proportion. But the waves whose individual vibrations have 

 the greatest amplitude will, by such a constant force, be less affected, in proportion 

 to the primary amplitude, than are the waves whose individual vibrations are of 

 smaller amplitude. The consequence will be, that the latter will appear to have 

 their refrangibility increased in a slightly greater degree than the former ; so that 

 the waves corresponding to the lines B, C, G, and H will be further removed towards 

 the violet extremity of the spectrum, and those corresponding to the lines D, E, and 

 F less removed towards that extremity, than they would be in the absence of the 

 extrusive property.' 



As an alternative to this view, it is suggested that these slight alterations in the 

 rapidity of the individual vibrations may be due to a sympathetic action between 

 the vibrations of the ponderable atoms of the medium and those of the ethereal par- 

 ticles, resembling the sympathy of pendulums, in virtue of which some of the latter 



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