July 12, 1883] 



NA TURE 



253 



luminiferous ether and of palpable transparent substance. 

 But that the velocity of propagation in any one trans- 

 parent substance, should be different for light of different 

 colours, that is to say, of different periods of vibration, 

 is not what we should expect ; and could not possibly be 

 the fact if the medium is homogeneous, without any limit 

 as to the smallness of the parts of which the qualities 

 are compared. The fact that the velocity of propagation 

 does depend on the period, gives what I believe to be 

 irrefragable proof, that the substance of palpable trans- 

 parent matter, such as water, or glass, or the bisuiphuret 

 of carbon of this prism whose spectrum is before you, is 

 not infinitely homogeneous ; but that on the contrary, if 

 contiguous portions of any such medium, any medium 

 in fact which can give the prismatic colours, be examined 

 at intervals not incomparably small in comparison with 

 the wave-lengths, utterly heterogeneous quality will be 

 discovered ; such heterogeneousness as that which we 

 understand in palpable matter, as the difference between 

 solid and fluid ; or between substances differing enor- 

 mously in density ; or such heterogeneousness as differ- 

 ences of velocity and direction of motion, in different 

 positions of a vortex ring in an homogeneous liquid ; or 

 such differences of material occupying the space ex- 

 amined, as we find in a great mass of brick building when 

 we pass from brick to brick through mortar (or through 

 void, as we too often find in Scotch-built domestic brick 

 chimneys). 



Cauchy was I believe the first of mathematicians or 

 naturalists, to allow himself to be driven to the conclusion, 

 that the refractive dispersion of light can only be 

 accounted for, by a finite degree of molecular coarse- 

 grainedness, in the structure of the transparent refracting 

 matter ; and as, however we view the question, and how- 

 ever much we may feel compelled to differ, from the 

 details of molecular structure and molecular inter-action 

 assumed by Cauchy, we remain more and more surely 

 fortified in his conclusion, that finite grainedness of 

 transparent palpable matter, is the cause of the difference 

 of the velocity of different colours of light propagated 

 through it, we must regard Cauchy as the discoverer of 

 the dynamical theory of the prismatic colours. 



But now we come to the grand difficulty of Cauchy's 

 theory; 1 look at this little table (Table II.), and you will see 



Table II.- 



- Velocity ( V) according to Number (N) of Particles 

 in Wave Length 



in the heading, the formula which gives the velocity, in 

 terms of the number of particles to the wave-length, sup- 

 posing the medium to consist of equal particles arranged 

 in cubic order, and each particle to attract its six nearest 

 neighbours, with a force varying directly as the excess of 

 the distance between them, above a certain constant line 

 (the length of which is to be chosen, according to the 

 degree of compressibility possessed by the elastic solid, 

 which we desire to represent by a crowd of mutually 

 interacting molecules). If you suppose particles of real 

 matter arranged in the cubic order, and six steel 

 wire spiral springs or elastic indiarubber bands, to 



1 For an account of the dynamical theory of the "Dispersion of Light," 

 see "View of the Undulatory Theory as Applied to the Dispersion of Light," 

 by the Rev. Baden Powell, M.A., &c. (London : 1841 ) 



be hooked on to each particle and stretched between 

 it and its six nearest neighbours, the postulated force may 

 be produced in a model with all needful accuracy ; and if 

 we could but successfully wish the theatre of the Royal 

 Institution, conveyed to the centre of the earth, and kept 

 there for five minutes, I should have great pleasure in 

 showing you a model of an elastic solid thus constituted, 

 and showing you waves propagated through it, as are 

 waves of light in the luminiferous ether. Gravity is the 

 inconvenient accident of our actual position, which pre- 

 vents my showing it to you here just now. But instead, 

 you have these two wave-models (see Fig. 2 above), each 

 of which shows you the displacements and motions of a 



Fig. 6. Fig. 7- 



Four particles in Wave-Length. 



line of particles, in the propagation of a wave through our 

 imaginary three-dimensional solid ; the line of molecules 

 chosen being those which, in equilibrium, are in one direct 

 straight line of the cubic arrangement, and the supposed 

 wave having its wave front perpendicular to this line, and 

 the direction of its vibration, the direction of one of the 

 other two direct lines of the cubic arrangement. 



You have also before you this series of diagrams 

 (Fifs. 4 to 9) of waves in a molecularly-constituted elastic 

 solid. These two diagrams (Figs. 4 and 5) illustrate a 

 wave in which there are twelve molecules in the wave- 

 length ; this one (Fig. 4) showing (by the length and 

 position of the arrows) the magnitude and direction of 

 velocity of each molecule, at the instant when one of the 



