82 Mr. R. Moon on the XJndulatory Theory of Interference. 



edge of the object the condensed portion of the wave will tend 

 to relieve itself laterally by an efflux of the particles it con- 

 tains into the geometrical shadow, where the density (that of 

 equilibrium) is less than its own, and thus we shall have within 

 the shadow a line of condensation in prolongation of the con- 

 densed portion of the wave. It is also clear that the portion 

 of aether within the geometrical shadow contiguous to the rare- 

 fied part of the wave will tend to flow into that part (where 

 the density is less than that of equilibrium), and thus we shall 

 have within the shadow a rarefaction in prolongation of the 

 rarefied part of the wave, and lying immediately behind the 

 prolonged condensation ; or, in other words, the wave will ex- 

 tend within the shadow. 



Of the form of this extended portion of the wave it is beside 

 my present purpose to speak, but it should be observed, that 

 as the wave thus prolonged must evidently be continuous, a 

 variation from the spherical form must necessarily take place 

 in that portion of the wave which remains without the shadow, 

 since otherwise, in the case of a series of concentric spherical 

 waves, it would be impossible that interference should occur ; 

 for each wave being continuous, it can only be by the inter- 

 section of two consecutive waves that interference can take 

 place. But here we are met by a great and what may appear 

 to some an insurmountable objection, for no such change of 

 form as that we have spoken of can take place, except from a 

 change of velocity in that portion of the wave; and it lias 

 never been disputed that in the free aether all waves are pro- 

 pagated with the same uniform velocity. In reference to this 

 point we would observe, that the present is a case of wave mo- 

 tion altogether peculiar, and one of which no example bearing 

 the smallest resemblance to it has been hitherto subjected to 

 investigation. All cases of wave motion hitherto investigated 

 algebraically resolve themselves into the simple case of the 

 propagation in the direction of the axis of a cylindrical tube 

 of a wave whose front is perpendicular to the edge. The 

 motion of a wave after diffraction may be assimilated to motion 

 along a tube, of which part of the side has been cut away ; this 

 peculiar kind of wave motion, as we have said, has not hitherto 

 been subjected to calculation, and in fact it seems to baffle all 

 attempts of the kind. It must therefore be by a general kind 

 of reasoning on simple mathematical principles, that any know- 

 ledge respecting this branch of dynamics can be obtained. 

 And upon such principles it would, we apprehend, be difficult 

 to prove it impossible, or in fact to make it appear very im- 

 probable, that the wave should propagate itself with a differ- 

 ent velocity after its lateral extension from what it would have 



