368 REPORT — 1844. 



As these waves appear in groups, their velocity and lengths are easily ob- 

 served and measured. I have reckoned as many as a dozen such waves in a 

 group all about the same magnitude, so that the aggregate length of the first 

 six was sensibly equal to the length of the second group of six. The method 

 of observation was this : a given distance was marked off along one side of 

 the channel ; an observer marked the instant at which the first of a group of 

 secondary waves arrived at a given point, while another observer at the fur- 

 ther end of the given distance counted the number of waves as they passed, 

 and marked the point at which the last had arrived when the signal was 

 given that the first wave had reached the other station ; thus it was observed 

 that in a group of waves moving over 100 feet in 28 seconds, there were 

 seven comprehended in a distance of 25 feet, whence 



j:_=3'57 feet per second for the velocity of the Avave, and 



25 



— =3*57 feet as the length of the wave. 



Also, since the wave passes along 3*57 feet its own length in one second, 

 its length divided by the velocity gives 1 second as the period of one com- 

 plete oscillation. 



The velocity of the wave of the second order, the lenyfh from the crest of 

 one wave to the crest of the next, or from hollow to hollow, and the time of 

 passing from one crest to another, called the period of the wave ; these are 

 the principal elements for observation. 



These elements are calculated for the convenience of observers in the 

 Table XXI. It will also be observed that the circles which represent the 

 oscillatory motion of the water particles (Plate LVI.), showing the Wave 

 Motion of the Second Order, diminisli very rapidly Avith the increasing depth 

 of the particles below the surface of the water at tiie lowest part of the wave. 

 By my observations I found that in high waves at a depth = ^rd of a wave 

 length, the range of oscillation of the particles is only about j'jth of that of 

 particles on the surface*. 



* I have here to express the favourable opinion which I have formed of a wave tlieory given 

 to the world by M. Franz Gerstner, so early as 1804*, and reprinted in the work of the MM. 

 Weber, to whom I am indebted for my acquaintance with this theory. Gerstner's theory is 

 characterized by simplicity of hypothesis, precision of application, its conformity with the 

 phajnomena, and the elegance of its results. It is not without faults, yet I cannot agree with 

 the Messrs. Weber, nor with MM. Professors Mollweide and Mobius, in the precise opinion at 

 which they arrive, although I confess I could wish that he had assumed as an hypothesis the 

 doctrine which in (14.) he deduces as a conclusion from hypotheses less firmly established than 

 this conclusion, unless indeed we should esteem it an argument in favour of his hypothesis, 

 that it conducts him directly to a conclusion of well-known truth. Neither do I find that his 

 hypotheses are so much at variance with the actual conditions of the waves I have observed, 

 as they appear to be in MM. Weber's view of their own experiments. The calculations of 

 M. Gerstner are applied primarily to a kind of standing oscillation. But it does not appear to 

 me that his calculations ought to be applied in any way to the standing oscillations which M. 

 Weber reckons to be their closest representation. In M. Gerstner's first part of the work the 

 wave form is standing, wave oscillation is circular, the fluid is in motion, and the particle paths 

 are identical with the lines which indicate the form of the wave. I conceive, therefore, that 

 the wave which he has examined, and the conditions of its genesis, find a perfect representative 

 in my standing waves of the second order, in running water, which I have represented in Plates 

 LV. and LVI. From this hypothesis it is not difficult to arrive at the moving wave of standing 

 water, for if we conceive the whole channel moved horizontally along in an opposite direction 

 with a velocity equal to the horizontal velocity of transference, the particles will then be re- 

 latively at rest, the cycloidal waves become moving forms, the particle paths stationary circles, 

 and the motion of transmission of the wave equal and opposite to the former mean horizontal 



* Theorie der Wellen. Prague, 1804. 



