5 1 2 Mr. A. J. Robertson on the Positive Wave of Translation, 



tricity left in the atmosphere after the positive had been dis- 

 charged in the shape of lightning. Mr. Joule appears to 

 take this view of the case*. The account of these discharges 

 is also especially interesting, as they seem to have been in 

 many respects a near approach to an aurora. It is a pity no 

 experiments could be made to ascertain the state of the air. 



I would say, in conclusion, I should like to see brought 

 forward in this Journal any fair objection to my explanation 

 of the cause of lightning and the aurora. 

 I am, Gentlemen, 



Your very obedient Servant, 

 7 Prospect Place, Ball's Pond Road, REUBEN PHILLIPS. 



November Q, 1850. 



LXX I. On the Positive Wave of Translation. 

 By A. J. Robertson, Civil Engineer.^ 



[With a Plate.] 



IN the following pages is discussed, not the theory of waves 

 under its most general form, but merely one of the sim- 

 plest cases — the Wave of Translation or Wave of the First 

 Order. To determine from the general laws of fluids what 

 must be the effect of the protrusion of a solid into a given 

 body of water, and to give an equation which shall be an 

 expression of all possible cases of wave motion, would be un- 

 doubtedly far more useful and far more satisfactory. But in 

 the absence of the capability of attaining so high an object, it 

 is hoped that, although far from perfect, the following investi- 

 gation may not be wholly in vain. In order that the reader 

 may be in possession of those experimental results upon 

 which it is founded, the following passage is extracted from 

 Mr. Scott Russell's first report on waves to the British Asso- 

 ciation J. 



" This wave has been found to differ from every other 

 species of wave in the motion which is given to the individual 

 particles of the fluid through which the wave is propagated. 

 By the transit of the wave the particles of the fluid are raised 

 from their places, transferred forwards in the direction of the 

 motion of the wave, and permanently deposited at rest in a 

 new place at a considerable distance from their original posi- 

 tion. There is no retrogradation, no oscillation ; the motion is 



* Phil. Mag. vol. xxxvii. p. 128. 



f Communicated by the Author. 



X Seventh Report of the British Association, 1837, p. 423. For further 

 particulars of the wave of translation see Mr. S. Russell's Second Report on 

 Waves contained in the Report of the British Association for 1844. 



