176 THE PRINCIPLES OF SCIENCE. 



into an infinite number of rays, which form a hollow 

 cone within the crystal, and a hollow cylinder when 

 emerging from the opposite side. In another case, a 

 somewhat different, but equally strange, effect is pro- 

 duced. These phenomena are peculiarly interesting, 

 because cones and cylinders of light are not produced in 

 any other cases. They are, in fact, wholly opposed to all 

 analogy, and constitute singular, or exceptional cases, of 

 a kind which we shall afterwards have to consider more 

 fully. Their very strangeness rendered them peculiarly 

 fitted to test the truth of the theory by which they were 

 discovered ; and when Professor Lloyd, at Hamilton's 

 request, succeeded, after considerable difficulty, in wit- 

 nessing the new appearances, no further doubt could 

 remain of the validity of the great theory of waves, which 

 we owe to Huyghens, Young, and Fresnel 1 ", 



Predictions from the Theory of Undulations. 



It is curious to reflect that the undulations of light, 

 although so inconceivably rapid and small, admit of more 

 accurate observation and measurement than the waves of 

 any other medium. But so far as we can carry out exact 

 experiments on other kinds of waves, we find the phe- 

 nomena of interference repeated, and analogy gives con- 

 siderable powers of prediction. Sir John Herschel was 

 perhaps the first to suggest that two sounds might be 

 made to destroy each other by interference s . For if one- 

 half of a wave travelling through a tube could be sepa- 

 rated, and conducted by a somewhat longer passage, so as, 

 on rejoining the other half, to be one-quarter of a vibra- 



r Lloyd's 'Wave Theory,' Part ii. pp. 52-58. Babbage, 'Ninth 

 Bridgwater Treatise,' p. 104, quoting Lloyd, 'Trans, of the Royal Irish 

 Academy,' vol. xvii. Clifton, ' Quarterly Journal of Pure and Applied 

 Mathematics,' January, 1860. 



8 ' Encyclopaedia Metropolitans,' art. Sound, p. 753. 



