CONFIRMATION OF THE UNDULATORYTHEORY.487 



light, in which cases we cannot imagine any definite 

 arrangement of the particles, such as might form 

 the mechanism requisite for the purpose. Accord- 

 ingly, it does not appear that any one has been able 

 to suggest even a plausible hypothesis on the sub- 

 ject. Yet, even here, something has been done. 

 Professor Mac Cullagh, of Dublin, has discovered 

 that by slightly modifying the analytical expressions 

 resulting from the common case of the propagation 

 of light, we may obtain other expressions which 

 would give rise to such motions as produce circular 

 and elliptical polarization. And though we cannot 

 as yet assign the mechanical interpretation of the 

 language of analysis thus generalized, this gene- 

 ralization brings together and explains by one com- 

 mon numerical supposition, two distinct classes of 

 facts; a circumstance which, in all cases, entitles 

 an hypothesis to a very favourable consideration. 



Mr. Mac Cullagh's assumption consists in adding 

 to the two equations of motion which are expressed 

 by means of second differentials, two other terms 

 involving third differentials in a simple and sym- 

 metrical manner. In doing this, he introduces a 

 coefficient, of which the magnitude determines both 

 the amount of rotation of the polarization of a ray 

 passing along the axis, as observed and measured 

 by M. Biot, and the ellipticity of the polarization of 

 a ray which is oblique to the axis, according to Mr. 

 Airy's theory, of which ellipticity that philosopher 

 also had obtained certain measures. The agreement 



