404^ The Astronomer Royal on a difficulty 



November Number of your Journal, with the diagrams drawn 

 by me in the Eiicyclopcedia Metropolitana. But I have pre- 

 ferred to show, step by step, that there is strong analogy in 

 every part of the mathematical process in the two cases. 



The rapid change of velocity implies in both cases very 

 violent forces of compression among the particles ; and very 

 sudden alterations of the surface for the water, and very rapid 

 expansions for the air. 



Now in the case of waves of water we cannot by mathema- 

 tical process (so far as I know) pursue the investigation of the 

 condition of the particles to its limit, but we can in some 

 measure observe it experimentally. And the fact which we 

 observe is this, that in a long river, where the magnitude of 

 the tide is considerable, the tide in the upper parts of the river 

 presents the phsenomenon of a bore. The surf formed upon 

 extensive flat sands is probably a phsenomenon of the same 

 class. Physically considered, the expression of this fact is, 

 that the continuity of the particles is interrupted. 



Now I imagine that in the critical state of the waves of air 

 the same thing occurs, namely that the continuity of the par- 

 ticles is interrupted ; and that with it the laws of motion of 

 the air, depending essentially as they do upon the existence 

 of that continuity, are interrupted. I imagine that the air is 

 in a state exactly analogous to that of a bore or a surf. Adopt- 

 ing this analogy, I do not think that there is anything of the 

 nature of reflexion of the wave (for I have never been able to 

 observe the smallest trace of reflected wave from a surf), 

 although at the same time I am utterly unable to account for 

 the disposal of the vis viva. 



Taking this view of the matter, it appears to me that the 

 expression " a plane wave of air is impossible " stands on pre- 

 cisely the same footing as the expression " a tide in the Severn 

 is impossible." In both cases, if the assumption is made 

 *'that the waves are to preserve the same character through 

 infinite space and infinite time," the wave is impossible. In 

 both cases, the ordinary understandings on the theory of waves 

 will apply for a considerable distance. 



I believe also that in both cases, if by friction or other causes 

 the coefficient of vibration be materially diminished, the waves 

 may travel to a very great distance without any aquatic or 

 aerial bore. 



The second subject of my communication is the probable 

 sensational indication of the physical phaenomenon, " inter- 

 ruption of continuity of particles of air." And it is my belief 

 that it produces that sound which, according as it is in a high 

 key, or is in a low key, or is articulately interrupted, is called 



