348 REPORT — 1844. 



collisions, or any other motions which impair moving force; the particles 

 simply glide for the moment over each other into a new arrangement, and 

 retire back to their places. Thus the wave resembles that which we may 

 conceive to pass along an elastic column, each slice of which is squeezed into 

 a thinner slice, and restored by its elastic force to its original bulk, only in 

 the water wave the force which restores the force of each water column is 

 gravity, not elasticity. 



To conceive accurately of the forces which operate in wave transmission, 

 and of the modus operayidi, to understand how the primary moving force 

 acts on the column of fluid in repose, how this force is distributed among 

 the particles, to distinguish the relative and absolute motions of the particles 

 and the nature of the transmission of the form, and to understand how the 

 force operates in at once propagating itself and restoring completely to rest 

 those particles which form the vehicle of its transmission, is a study of much 

 interest to the philosopher. To show how under a given form and outline of 

 wave, in a given time, all and each of the individual particles of water obey- 

 ing every one its own impulse and that of those around it, and subject to 

 the laws of gravity and of the original impulse, shall describe its own path 

 without interfering with another's, and shall unite in the production of an ag- 

 gregate motion consistent with the continuity of the mass and with the laws of 

 fluid pressure, — this is a problem which belongs to the mathematician, which 

 has hitherto proved too arduous for the human intellect, and which we have 

 thus endeavoured to facilitate and promote by the study of the absolute forms 

 and phaenomena of the waves themselves, and by the determination of the 

 actual paths and motions of the individual particles of water. 



The Negative Wave of tlie First Order. — The negative wave is a phaeno- 

 menon whose place among waves it is somewhat difl[icult to assign. Its phae- 

 nomena partake of those of the first order. But in its genesis and propagation 

 it is always attended by a train of following phaenomena of the second order. 



The genesis of the negative wave of the first order is effected under condi- 

 tions precisely the reverse of those of the positive wave. A solid body, Qj Q3 

 (PlateLII. figs. 7, 8), is withdrawn from the water of the reservoir at one ex- 

 tremity, a cavity is created, and this cavity, W,, is propagated along the sur- 

 face of the water under a defined figure. 



The velocity of the negative wave in a shallow channel is nearly that which 

 is due to the depth calculated from the lowest part of the wave (as in the 

 positive from the highest), but in longer waves it is sensibly less than that 

 velocity. In Plate XLVIII. fig. 5 the observations are compared with this 

 formula, from which they exhibit considerable deviations. Table XI. is a 

 collection of negative waves observed in a small rectangular channel, and 

 Table XII. contains others made in a triangular channel, both being made 

 under the same conditions as the positive waves already given. 



Table XI. 



Observations on the Velocity of Negative Waves of the First Order. — //* a 

 rectangular cluinnel 12 incites toide. 



Col. A is the depth of the fluid reckoned in inches from the lowest point 

 of the wave. 



Col. B is the depth of the wave reckoned below the surface of repose. 



Col. C is the number of seconds observed while the wave described the 

 space given in column D in feet. 



Col. E is the resulting velocity. 



