ON WAVES. 385 



the results of individual experiments to the formula B adopted to represent 

 them. These are taken from the Table V. 



Fig. 2 exhibits a similar comparison for waves of a larger size than the former. 

 See Table IV. 



Figs. 3 and 4 show a comparison with the observations, marked by stars as 

 before, with formulae proposed by Mr. Airy, shown as dots connected by 

 dotted lines, and with the formulae employed by the author, shown by a 

 continuous black line A B. The eye at once decides whether the black 

 ■line or the dots and dotted line most nearly coincides with the stars. See 

 Tables VI. and VII. 



Fig. 5 exhibits a similar comparison of the velocity of negative waves, as ob- 

 served in a rectangular channel along A B, and in a triangular channel as 

 shown along A B'. The stars show that the velocity falls below that which 

 the formulae would assign as due to the depth, especially in the triangular 

 channel. See Tables XI. and XII. 



Fig. 6 exhibits the general results of experiments on velocity ; the horizontal 

 spaces indicate depths of five inches to each, and the velocities in per 

 second are represented by the vertical spaces which represent each the ve- 

 locity of one foot per second in transmission of the wave. A B is the line 

 of the formula for a rectangular channel, see Table III. ; and A B' for a 

 triangular channel, see Table XV. 



Fig. 7. A X is the surface of water four inches deep ; B X represents the suc- 

 cessive heights of a wave as referred to in Table II. 



Plate XLIX. 

 Rediscussion of the Experiments on Velocity. — Bi/ the Method of Curves. 



Fig. 1. BC, DE, FG, &c. are lines drawn by the eye through the observa- 

 tions of heights of waves shown by the stars ; similar lines were drawn 

 through the corresponding observations of velocity. These waves were 

 taken as representing the experiments cleared of errors of observation ; 

 they were then collected and laid down in fig. 2. 



Fig. 2. A B is the line given by the formulae employed by the author to re- 

 present the velocity of the wave of the first order ; the stars are the ob- 

 servations freed in some measure from errors of observation as described 

 above. 



Plate XLIX4i(continued.) 



Effects of Form of Channel on the Wave. — Order I. 



Note. — In a rectangular channel on a level plane the crest of the wave is 

 a horizontal line, parallel to the bottom. 



Fig; 3. The section across a channel ; a w the surface of the water in repose ; 



a</=4 inches; we=l inch; A a the height of the wave-ci'est= 1| 



inch ; B w the height on the shallow side = 2^ inches. 

 Fig. 4. A B c? the cross section of a triangular channel, A B the crest of the 



wave, a to the level of the water in repose ; the angle A rf B = 90°. 

 Fig. 5. B c c? a slope of 1 in 3, being the cross section of a channel c df; 



A B the crest of the wave breaking on the sides, where the height of the 



wave becomes equal to the depth of the water. 

 Fig. 6. Cross section of another form of cHannel. 

 Fig. 7. The sea-beach near Kingstown and Dublin. Common sea waves, 



W,, W., W3, W4, W5, Wg, break on the ridge d, where their height is 



equal to the depth of the still water. They generate small waves of the 



first order, w„ vjo, w^, tv^, w^, &c., which are propagated through the still, 

 1844. > 2 c 



