Mr. A. J. Robertson on the Positive Wave of Translation . 519 



Since the water in the channel remains at the same level as 

 before the passage of the wave, the volume of the generator is 

 contained in the swell of the water above the level of repose; 

 and calling the width of the channel unity, the number of 

 units in the area of the curve ARETB above AB equals the 

 number of units in the volume of the generator. The column 

 DH, at rest at the commencement of the wave, has been 

 moved forward by the time that D has risen to E, or when the 

 crest of the wave has come over the column DH, a certain di- 

 stance DC, which is the sum of the contractions of all the 

 columns in front; and since the water formerly contained in 



DAGH is now contained in ERAGS, DC= — . 



a 



2V 



The total horizontal motion is therefore — . 



a 



Both vertical and horizontal motions now described as the 

 result of existing forces, are precisely those observed by Mr. 

 Scott Russell in his experiments on the wave of translation. 



From the nature of the case, the motion of the wave must 

 be uniform. If then T be the half-period of the wave, and t 

 an intermediate time, the distance passed through in t is 



-t(^). 



point; and, moreover, as the horizontal and vertical motions cross one 

 another, and the particles do not come to rest after the passage of one 

 wave, there must be a succession of waves. The following figures show 

 the difference between the motions on this supposition. 



Wave of Translation. 



Path of particle. 



Wave of Oscillation. 



Path of particle. 



|l 



The law of the diminution of horizontal motion, according to the depth 

 of the particle below the surface in an oscillating wave, the author is unable 

 to determine. 



