388 REPORT — 1844. 



if it encounter a positive wave of the first order, of equal volume, does 

 not pass over it, but they neutralize each other and are annihilated. If 

 unequal, their difference, positive or negative, alone remains, and is pro- 

 ])agated as a wave of the fii'st order. 

 Figs. 9 and 10 record observations, showing that although the negative 

 wave is in its own order solitary, yet that its existence is the cause of ge- 

 nesis of a group of gregarious waves, or waves of oscillation of the second 

 order ; W 1 is a negative wave of the first order : W 1 , W 2, W 3, &c., 

 are all waves of the second order. The curved arrows in fig. 9 show the 

 semi-elliptical path of the particles during the transmission of the negative 

 wave. After which, during the transmission of the waves of the second 

 order, the particles describe circles, continually diminishing in diameter as 

 the waves gradually subside. 



Plate LIII. 

 Waves of the First Order. — Reflexion, Non-reflexion and Lateral 

 Accumulation. 

 In this Plate a wave of the first order, W, R, is represented as incident upon 

 a vertical plane surface immovable at II ; i. e. the ridge of the wave forms 

 a given angle RiW A. After impact at R the wave is reflected, so that 

 the angle of reflexion is equal to the angle of incidence ; and when the 

 angle of direction of transmission is great (i. e. when the angle of the ridge 

 with the surface is small, not greater than 30°), the reflexion is complete 

 in angle and in quantity. When the angle of direction of transmission 

 diminishes (i. e. when the ridge of the wave makes an angle gi-eater than 

 30°), the angle of reflexion is still equal to the angle of incidence, but tlie 

 reflected wave is less in quantity than the incident wave. The magnitude 

 of the reflected wave diminishes as the angle of incidence diminishes, until 

 at length, when the angle of the ridge of the wave is within 15° or 20° of 

 being perpendicular to the plane, reflexion ceases, the size of the wave near 

 the point of incidence and its velocity rapidly increases, and it moves for- 

 ward rapidly with a high crest at right angles to the resisting surface. 

 Thus at diflerent angles we have the phsenomena of total reflexion, partial 

 reflexion, and non-reflexion and lateral accumulation ; phainomena analo- 

 gous in name, but dissimilar in condition from the reflexion of heights, &c. 



Plate LIV. 

 Lateral Diffusion of the Wave of Translation round an Axis. 



Figs. 1, 2, 3 and 4 represent a large rectangular reservoir of water filled to 

 an uniform depth with water. It is 20 feet square. From a chamber C 

 in one corner a wave of the first order was transmitted in the direction 

 W 1, W2 ; and the observations made which appear in the figures. 



In fig. 4 the aspect of the phsenomenon is represented. The wave is propa- 

 gated in the direction of original propagation, which we shall call its axis, 

 with a gradual diminution of its height according to the length of its path 

 along the axis. The observations are probably not yet sufficiently nume- 

 rous to determine accurately the law of diminution. From this axis the 

 wave spreads on every side. At right angles to the axis of propagation the 

 height of the wave is scarcely sensible, and the diminution of magnitude is 

 very rapid as the line of direction diverges from the axis. The wave is 

 also propagated faster in the direction of the primary axis than in any other 

 direction, so that the wave-crest is elliptic and elongated in that direction. 



In fig. 3 the heights of a wave are marked by lines. Each line along W w 



