AS EXPLAINED BY THE HYPOTHESIS OF FINITE INTERVALS. 155 



for dispersion, at the same time I think that simple as they may ap- 

 pear at a first glance, and satisfactory as they undoubtedly are to a 

 certain extent, it will be found a difficult task to pursue them into 

 detail, even in the case of sound. We know little or nothing of the 

 laws which regulate the developement of heat, which affect the velocity 

 of light, at least if we adopt the hypothesis of molecular radiation, and 

 have thus only shifted our difficulty without removing it. If on the 

 other hand, we choose to regard heat as an effect consequent on the 

 alteration of the positions of the attractive or repulsive particles within 

 a medium (which seems reasonable from some recent experiments on 

 the Polarization, &c. of Heat), then, by analogy, Mr Airy's hypothesis 

 amounts in fact to supposing the particles endued with attractive or 

 repulsive energies, influenced by the particular positions into which they 

 are thrown, and varying with the change of these positions, to the 

 action of which all the effects are assigned. 



The great obstacle to a simple explanation of this subject appears 

 to have arisen from the fact, that theorists generally have not divested 

 themselves of the idea of motion directly : velocity has been substituted 

 for force, and tvave for change of force. 



It occurred to me about two years since, that if we could deduce 

 a simple equation of motion on the supposition that the particles of 

 a medium are at a finite distance from each other, we might arrive at 

 results very different in form from those usually adopted. In fact it 

 appeared probable that the velocity might depend on the positions into 

 which the particles should arrange themselves, and thus might be 

 affected by the length of a wave. 



Such a formula I actually obtained, and deduced from it the ne- 

 cessary result, that the square of the velocity is represented by a series 



of terms of which c (^j is a type. There was, however, one point 



in my analysis which I regarded as fatal to the whole; namely, that 

 having a function involving the distance between two consecutive par- 

 ticles, and the space through which a particle is disturbed, I had ex- 

 panded it in terms of the ratio of the latter quantity to the former. 



U2 



