384 REPORT — 1844. 



forwards ; at the third, still less upwards and still more forwards, and so on^ 

 tile inclination of the path diminishing to the middle of the wave, where the 

 velocity is greatest and the direction quite horizontal. Behind this part of 

 the wave the particles are to be seen descending more and more with a 

 motion gradually retaz-ded, and at the hinder extremity of the wave they 

 are in repose, as at the front. These motions of the particles of water are 

 rendered visible by minute particles of any kind mixed with the water and 

 nearly of the same specific gravity. Such are the simultaneous motions of 

 the successive particles at different stations along the same wave, as ob- 

 served in a channel by glass windows placed in the sides and carefully gra- 

 duated in small squares for the purpose of observation, the side of the chan- 

 nel opposite to the window being similarly graduated. The second diagram 

 represents the paths of four particles described during the whole period of 

 transmission of a wave. The wave is transmitted from A towards X. The 

 anterior extremity of the Avave finds one particle at a and carries it for- 

 ward through an ellipse to b, where it is left by the end of the wave : the 

 same wave translates the particle c vertically below a through its elliptical 

 path and leaves it at d vertically below b, and in like manner e and g are 

 transferred to/ and h. All these paths are semi-ellipses (as nearly as it is 

 possible to observe them), and are of the same major axis : but the semi- 

 minor axis is at the surface equal to the height of the wave-crest, and di- 

 minishes with the distance from the bottom of the channel, where it is nil. 

 The third diagram exhibits the phasnomena of vertical sections during wave 

 transmission : small globules of greater specific gravity than water are sus- 

 pended at different depths by means of long slender stalks of less specific 

 gravity. These globules are arranged while the water is in repose, in ver- 

 tical planes at equal distances along the fluid. These vertical planes are, 

 by transmitting the wave, made to approach each other, but still retaining 

 their verticality without sensible disturbance. At the middle of the wave- 

 length they are brought closest, and at the hinder extremity they recede and 

 settle down at their original depth. The fourth diagram shows the change 

 of the position of points in the same horizontal planes during wave transmis- 

 sion, particles vertically equidistant in repose remaining equidistant during 

 wave transmission. 

 Fig. 6. Genesis of compound waves The first diagram represents the gene- 

 sis by a large low column of fluid of a compound or double wave of the 

 first "order, which immediately breaks down by spontaneous analysis into 

 two, the greater moving faster and altogether leaving the smaller. The 

 second diagram represents the genesis by a high small column of fluid of a 

 positive and negative wave, which soon separate, the positive wave travel- 

 ling more rapidly, leaving altogether the residuary negative wave. The 

 negative wave is further noticed in another Plate. \V, is the positive and 

 to 1 the residuary positive or negative wave as generated. W., and w., 

 represent them separated by propagation. 



Plate XLVIII. 



Discussion of Observations on the Velocity of Waves. — Order I. ' 



Fig. 1. Comparison of the observations marked by stars with the formula B, 

 indicated by the parabola A B, of which A X is the axis, parallel to which 

 are measured abscissaj I., II., III., &c., representing the depth of the 

 fluid in inches, the corresponding velocities being represented by ordinates 

 A 1, A 2, A 3, A Y, &c. at right angles to A X. The manner in which the 

 curve passes through among the stars, shows the close approximation of 



