386 REPORT — 1844. 



shallow water to great distances, and the intervals between them are left 

 level and in repose. 



Plate L. 

 Waves of the First Order — Drawn by themselves. 

 These eight waves are of the natural size, being mere transcripts of the out- 

 line of a wave left on a dry surface. The four lower outlines in the Plate 

 were obtained by inserting a dry surface, moved horizontally with a uni- 

 form velocity equal to that of the wave, and instantly removing it. The 

 moist outline lei't by the wave was copied on tracing paper, and transferred 

 without change to the copper-plate. Another method produced the four 

 upper outlines, which were obtained by passing under the wave to be ob- 

 served another wave transmitted in the opposite direction. These outlines 

 are not therefore to be regarded as copies of a wave, but as transcripts of 

 the outline left by the passage of one wave over another ; the crests of both 

 describe horizontal straight lines on the side of the channel, but as every 

 point of one may be regarded as passing over the crest of the other, there 

 is a moist outline left on the side of the channel at the crossing, which 

 outline is simply transferred to the copper, as in the four upper waves. 

 Where a dotted line occurs a blank was left in the outline, which is filled 

 up by, the eye. The depth of the water was 2 inches, and the parallel 

 lines in the figure are at 1 inch apart and serve as a scale. 



Plate LI. 



These waves are taken in the same manner, but have been reduced from the 

 original outlines to a smaller scale — smaller than the original in the ratio 

 of 2 to 3. The horizontal lines are frds of an inch apart, which represents 

 an inch on the full size. The four lowest are taken from waves in water 

 2 inches deep on a sloping beach, parallel to ^ X, A X, /X and m X, with 

 an inclination of 1 in 12. The four next are imperfect or compound waves, 

 taken from the outline left by passing another in the opposite direction. 

 The two highest are taken in the same way, one of them in the act of 

 breaking. 



Plate LII. 

 The Wave of the First Order. 



Fig. 1 represents the genesis of a compound wave by impulsion of the plate 

 with a variable force and velocity, which variations have produced corre- 

 sponding variations on the wave form. After propagation tiie wave breaks 

 down by spontaneous analysis ; the higher part moves forward, as shown 

 by the dotted line, and ultimately leaves the rest behind, so that after the 

 lapse of a considerable period the compound wave is resolved into sirtgle 

 separate waves, each moving with the velocity due to the depth. 



Fig. 2 represents the phaenomena resulting from genesis by a long, low co- 

 lunm of water. Instead of genesis of a compound wave, as in the former 

 case of impulsion, the added mass sends off a series of single waves, the first 

 being the greatest : these however do not remain together, but speedily 

 separate, as shown in the dotted lines, and become the further apart the 

 longer they travel. 



Figs. 3, 4, 5 and 6 give geometrical approximations to the representation of 

 the wave form and phasnomena. In fig. S, dY) d is the length of a small 

 wave divided into ten equal parts; erf is equal to the height of the wave, 

 on which a circle is described, and of which the circumference is also di- 

 vided into ten equal parts. Through these equal divisions of the circle are 



