342 REPORT — 1844. 



cursions are performed by each particle of fluid simultaneously with the hori- 

 zontal translation. These diminish in extent with the distance from the 

 bottom when they become zero. 



The Path of each Water Particle during Translation lies wholly in a Ver- 

 tical Plane. — It may be observed by means of the glass windows already 

 mentioned, its surface being graduated for purposes of measurement. The 

 path is so rapidly described that I do not think any measurements of time 

 which I have made, nor even of paths is minutely correct. The following 

 observations are such as a practised eye with long experience and much pains 

 has made out. 



When a wave of the first order in transmission makes a transit over float- 

 ing particles in a given transverse plane, the observations are as follows. 

 All the particles begin to rise, scarcely advancing; they next advance as 

 well as rise ; they cease to rise but continue advancing ; they are retarded 

 and come to rest, descending to their original level. The path appears to be 

 an ellipse whose major axis is horizontal and equal to the range of translation ; 

 the semi-rainor axis of the elliptic path is equal to the height of the wave near 

 the surface, and diminishes directly with the depth. 



The results of these observations are, therefore, as follows : — representing 

 by h the breadth of the channel, by h the depth of the fluid, by a the range 

 of translation, and by v the volume of water employed in forming the waves; 

 we have for every particle throughout the breadth and depth of the fluid 



»=f* (^•) 



which everywhere measures the horizontal range of translation. 



The range of vertical motion of each particle at the surface during trans- 

 lation being everywhere 



y^k (M.) 



we have for the vertical range y' of any other particle at a depth A' below 

 the surface, 



y=|.A .... (N.) 



being directly as the height of the particle in repose above the bottom of the 

 channel. 



Also throughout the whole period of translation we have the height of a 

 particle of the surface above its place of repose represented by 

 y=^\k versin (O.) 



and the height of any other particle in the same vertical plane at the same 

 place represented by 



y=i^ versing .... (P.) 

 n, 



The whole of these results are united in the following Table of wave phaeno- 

 raena. 



Table X. 



PJuBnornena of Wave of the First Order. 



Let c be the velocity of wave transmission; 

 h the depth of fluid in repose ; 

 k the height of wave-crest above surface of repose ; 

 b breadth of channel ; 



