Proceedings of the British Association. 555 



case of that species of wave which he had called the wave of trans- 

 lation. In this memoir of observations made in 1834-1835, he had 

 indicated the existence and described some of the phenomena of two 

 other classes of waves, as also in the former printed Reports of the As- 

 sociation. But he had lately embraced an opportunity of extending his 

 observations, and maturing a classification, which he now submitted to 

 the Section. Of waves there seem to be three great orders, obeying 

 very different laws : — 1. Wave of the first order, — the wave of trans- 

 lation, — is solitary, progressive, depending chiefly on the depth of 

 the fluid : has two species, positive and negative. 2. The waves of the 

 second order, — the oscillatory waves, — are gregarious ; the time of 

 oscillation depending on the amplitude of the wave : of two species, 

 progressive and stationary. 3. The waves of the third order, — capillary 

 waves ; gregarious. The oscillation of the superficial film of a fluid, un- 

 der the influence of the capillary forces, extending to a very minute 

 depth : short in duration : of two species : free, constrained. The last 

 of these classes he had not before minutely examined, and to them he 

 wished to draw the attention of the Section, as amongst the phenomena 

 which we most frequently see, and have yet failed to examine. Although 

 these waves were noticed by the author in 1834, and figured in a 

 memoir of his own, which drawing had since been published by 

 M. Poncelet, in his ( Mecanique,' along with an announcement that he 

 had observed the same waves in running water ; yet they had not 

 hitherto attracted notice or been thoroughly examined by Mr. Russell or 

 any one else. He believed them to be the minute waves or dents indi- 

 cated by the theory of Poisson ; he had therefore thought it his duty to 

 examine them. The waves of the third order were observed by Mr. Scott 

 Russell in the following manner : — a slender brass wire was inserted 

 vertically into a still fluid, and drawn in that position slowly along 

 its surface. When the velocity is one foot per second the surface of the 

 water exhibits a group of waves of great beauty and regularity, extend- 

 ing forwards before the exciting point, and spreading on both sides of it 

 in the form of a con-focal group of hyperbolas ; the focal distance of 

 each hyperbola, and its assymptotes being determined by the velocity 

 of the motion. Although the exciting point was of no more than 

 one-sixteenth of an inch in diameter, these waves extend over several 

 feet, and the diagrams exhibited the phenomena as having great regula- 

 rity and beauty. Numerical results shewing the number of these waves 

 in an inch of distance from the exciting point was given, and is nearly 

 as follows : — 



