358 REPORT— 1844. 



motion. This process may be repeated any number of times without affect- 

 ing any of the wave phaenomena excepting the direction of motion. 



When the angle which the ridge of the incident wave makes with the solid 

 plane is small, that is, when the direction of propagation does not deviate 

 much from the perpendicular to the plane, the wave undergoes total re- 

 flextion, and the angles of reflexion and of incidence are equal, as in the case 

 oflight. 



When the deviation of the direction of propagation from the perpendicular 

 is considerable, the reflexion ceases to be total. At 45° the reflected wave 

 is sensibly less than the incident wave. 



When the ridge of the wave is incident at about 60° from the plane sur- 

 face, and the direction of the ridge only diverges about 30° from a perpendi- 

 cular to the plane, reflexion ceases to be possible. A remarkable phaenomenon 

 is exhibited which I may be allowed to designate the Lateral Acciiinulation 

 and Non-Reflexion of the wave. It is to be understood by considering the 

 eflPect of supposed reflexion ; this would be to double over upon itself a part 

 of the wave moving in nearly the same direction ; the motions of translation 

 of the particles being compounded will give a resultant at right angles to the 

 plane, and will also give a wave of greater magnitude and a translation of 

 greater velocity. By these means accumulation of volume and advancement 

 of the ridge in the vicinity of the obstacle take place ; as represented in the 

 diagram. 



These phtenomena are accurately represented in Plate LIIL, as observed 

 in a large shallow reservoir of water. 



On the Lateral Diffusion and the Lateral Accumulation of the Wave of 

 the First Order. — When a wave of the first order has been generated in a 

 narrow channel, and is propagated into a wider one, it becomes of some im- 

 portance to know whether and how this wave will affect the surface of the 

 larger basin into which it is admitted. It is known that common surface 

 waves of the second order diffuse themselves equably in concentric circles 

 round the point of disturbance. How is the great primary wave diffused ? 



Table XVI. 



Observations on the Lateral Diffusion of the Wave of the First Order, generated 

 in a narroio Channel and transmitted into a wide Reservoir. 



The apparatus employed for this purpose is exhibited in Plate LIV. 

 figs. 1 and 2. T was a tank 20 feet square, filled to the depth of 4 inches ; the 

 chamber C, fig. 2, was 12 inches square, in which the wave was generated by 

 impulse for the first five experiments, in all subsequent to which C was en- 

 larged in width to 2 feet, as shown in fig. I . The line marked A, figs. 1 and 

 2, was a wooden bar, in which were inserted at intervals of 6 inches, sharp 

 pieces of pencil, projecting downwards to the surface of the water ; the num- 

 bers of which, reckoning from the side of the tank outwards, are contained in 

 the first vertical column of numerals, the Roman numerals in this table de- 

 noting the number of the experiment. The bar being placed parallel to the 

 side of the tank at C, and distant from it 12 feet, consequently distant 9 feet 

 from the mouth of the channel, whose length is 3 feet; the distance from its 

 under edge to the surface of the still water was carefully measured, and when 

 the wave had passed, and before its reflexion, the bar was removed, the 

 distances from its under edge to the highest marks on the pencils were put 

 down in column A of the table, and the absolute height of the wave itself, 

 obtained by subtracting these figures from the statical level, was put down in 

 column B. 



J 



