ON WAVES. 353 



Table XIII. 

 Ohsei'ved Heights of a Wave in Channel of variahU Breadth. — Depth 4 inches. 

 A. B. C. 



Breadth 12 in. Breadtli 6 in. Breadth 3 in. 



Height of wave. Height of wave. Heiglit of wave. 



in. in. in. 



These numbers appear to indicate that the increase of height does not widely 

 differ from the hypothesis, that the height of a given wave in a channel of 

 variable width is inversely as the square root of the breadth. 



Thus, the inverse square roots of the breadths are as 1*73, 2'45 and 3*47, 

 and the mean heights of the first five experiments are 1*8 2*45 3"39. 



In the first five experiments the velocity observed was 4*25 feet per second. 

 The velocity due by gravity to half the total depth 4 + 2'45 inches is 4'15 feet 

 per second ; and as the range of the wave was only 17 feet, and the time was 

 only observed to half-seconds, these numbers coincide well enough to bear 

 the conclusion that the velocity does not considerably differ from tliat due to 

 the wave of the same mean height in a parallel channel of the same depth. 



Table XIV. 

 Observations in a Channel of variable Depth. — Diminution of depth from 

 4 inches to 0" in a length of 17 Jeet. 

 A. B. C. D. E. 



Height of wave Height of wave Depth of water where Time of tra- Velocity in 



in a depth of 4 in. breaking in depth (C). wave (B) broke. versing 17ft. feet per sec. 



in. in. in. s. 



I. 4-0* 4-0* 4-0 5-5 3-09 



II. 3-7* 3-7* 3-7 5-5 3-09 



III. 3-4* 3-4* 3-4 5-5 3-09 



IV. 2-5 2-7 2-7 5-5 3-09 

 V. 2-0 2-4 2-4 5-5 3-09 



VI. 1-8 2-2 2-2 5-5 3-09 



VII. 1-5 2-0 2-1 



VIII. 1-3 1-9 1-9 



IX. 1-25 1-9 1-9 



X, 1-2 1-7 1-7 



XI. M 1-4 1-4 6-0 2-83 



XII. 1-0 1-2 1-2 



XIII. 0-8 0-8 M 6-5 2-6 



XIV. 0-5 0-7 0-9 7-0 2-4 

 XV. 0-2* 0-2* 0-2 7-5 2-0 

 Hence we find that the numbers representing depths in column C may be 



regarded as the limits of those in column B, that the depth of the fluid below 

 the level of repose is equal to the greatest height which a wave can attain at 

 that point, and at that height the wave breaks. 



* These numbers are interpolated ; the numbers in coUunn D are waves not observed on 

 the identical waves in the first three columns, but are others of nearly equal heights, in iden- 

 tical conditions. 



1844. 2 A 



