88 THE PRINCIPLES OF SCIENCE. 



medium, the dispersion of mixed light by the prism and 

 the production of the spectrum could not take place. 

 Some of the most striking phenomena were thus in direct 

 conflict with the theory. The great French mathema- 

 tician, Cauchy, first pointed out the true explanation, 

 namely that all previous investigators had made an 

 arbitrary assumption for the sake of simplifying the 

 calculations. They had assumed that the particles of 

 the vibrating medium are so close together that the 

 intervals are quite inconsiderable compared with the 

 length of the wave, or in other terms infinitely small. 

 This hypothesis happened to be approximately true in the 

 case of air, so that no error was discovered in experiments 

 on sound. Had it not been so, the earlier analysts would 

 probably have failed to give any solution, and the pro- 

 gress of the subject might have been retarded. Cauchy 

 was able to make a new approximation to truth under 

 the more difficult supposition, that the particles of the 

 vibrating medium are situated at considerable distances, 

 and act and react upon the neighbouring particles by 

 attractive and repulsive forces. To calculate the rate of 

 propagation of a disturbance in such a medium is a work 

 of excessive difficulty. The complete solution of the 

 problem appears indeed to be beyond human power, so 

 that we must be content, as in the case of the planetary 

 motions, to look forward to successive approximations. 

 All that Cauchy could do was to show that certain mathe- 

 matical terms or quantities, neglected in previous theories, 

 became of considerable amount under the new conditions 

 of the problem, so that there will exist a relation between 

 the length of the wave, and the velocity at which it 

 travels. To remove, then, the difficulties in the way of 

 the undulatory theory of light, a new approach to pro- 

 bable conditions was needed?. 



P Lloyd's 'Lectures on the Wave Theory/ pp. 22, 23. 



