148 THIRD REPORT — 1833. 



there are waves of much more sensible magnitude than the pre- 

 ceding. Their summits are propagated with a uniform velocity, 

 which varies as the square root of the breadth a fleur deau of 

 the fluid originally disturbed. Yet the different waves which 

 are formed in succession are propagated with different veloci- 

 ties : the foremost travels swiftest. The amplitude of oscilla- 

 tions of equal duration are reciprocally proportional to the 

 square root of the distances from the point of disturbance. 



(4.) The vertical excursions of the particles situated directly 

 below the primitive impulse, vary according to the inverse ratio 

 of the depth below the surface. This law of decrease is not so 

 I'apid but that the motion will be very sensible at very consider- 

 able depths : it will not be the true law, as the theory proves, 

 when the original disturbance extends over the whole surface 

 of the water, for the decrease of motion in this case will be 

 much more rapid. 



The results of the theory, when the three dimensions of the 

 fluid are considered, are analogous to the preceding, (1), (2), (3), 

 (4), and may be stated in the same terms, excepting that the am- 

 plitudes of the oscillations are inversely as the distances from 

 the origin of disturbance, and the vertical excursions of the par- 

 ticles situated directly below the disturbance vary inversely as 

 the square of the depth. 



There is a good analysis of M. Poisson's theory, and a com- 

 parison of many of the results with experiments, in a Treatise 

 by M. Weber, entitled Wellenlehre aiif Experimente gegrim- 

 det*. The experiments of M. Weber were made in a manner 

 not sufficiently agreeing with the conditions supposed in the 

 theoi'y to be a correct test of it. They, however, manifest a 

 general accordance with it, and confii'm the existence of the 

 small accelerated waves near the place of distui'bance, and of a 

 sensible motion of the fluid particles at considerable depths 

 below the surface. In one particular, in which the theory ad- 

 mits of easy comparison with experiment, it is not found to 

 agree. When the body employed to cause the initial agitation 

 of the water is an elliptic paraboloid, with its vertex downwards 

 and axis vertical, and consequently the section in the plane of 

 the surface of the water an ellipse, theory determines the velo- 

 city of propagation to be greater in the direction of the major 

 axis than in that of the minor in the proportion of the square 

 root of the one to the square root of the other. This result, 

 which it must be confessed has not an appearance of probabi' 

 lity, is not borne out by experience. 



* Leipzig, 182,5. 



