20 REPORT — 1842. 



wished to draw the attention of the Section, as amongst the phaanomena 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 indicated 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, extending 

 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 asym- 

 ptotes being determined by the velocity of the motion. Although the exciting 

 point was of no more than T ' F th of an inch in diameter, these waves extend over 

 several feet, and the diagrams exhibited the phasnomena as having great regularity 

 and beauty. Numerical results, showing the number of these waves in an inch of 

 distance from the exciting point, were given, and are nearly as follows : — 



Velocity of moving point. Number of waves in an inch. 



55 feet per minute. 2 



60 „ „ 3 



65 „ „ 4 



72 : , „ 5 



80 „ „ 6 



90 „ ., 7 



103 „ „ 8 



120 „ „ 9 



These waves were examples of capillary waves not in free but constrained motion. 

 He had generated them in a different manner, so as to examine them in free motion 

 uninfluenced by the generating point, and found that the capillary waves when moving 

 freely have a constant velocity of 8^ inches per second; that their duration is short, 

 becoming insensible in about twelve seconds after describing a path not longer than 

 eight or nine feet : in the free state this breadth is very small at first, gradually in- 

 creases, and just before vanishing attains an amplitude of nearly an inch. 



The capillary waves are among the phaenomena we most frequently observe. It is 

 in generating them that a gentle breeze forming over the surface of a smooth lake 

 destroys the translucent and reflective power of the surface ; they are also to be ob- 

 served in all cases of primary and secondary wave motion when the superficial film is 

 by any cause compressed so as to produce corrugation ; and they always disappear in 

 about twelve seconds after the exciting cause is removed. 



The second order of waves had also been made the subject of careful observation. A 

 mode had been discovered of generating those waves in large groups, so that instead of 

 observing single waves the length of one could be deduced from the measured length of a 

 number, thus getting the advantage of repetition of the quantity observed. It had thus 

 been finally determined that these oscillating waves follow Newton's law, in so far that 

 the velocities of transmission are as the square roots of the amplitudes; but the abso- 

 lute velocity differs from that of Newton, so that instead of having the wave whose 

 period is a second of an amplitude = 3-26, it is found to be = 3-57. The velocities 

 determined are as follows : — 



Velocity of transmission of wave. Amplitude. 



3*01 feet per second 2-65 feet 



3-16 „ „ 2-94 „ 



3-29 „ „ 3-125 „ 



3-37 „ „ 3-26 „ 



*3-57 „ „ *3-57 „ 



3-72 „ „ 3-913 „ 



3-84 „ „ 4-20 „ 



4-16 „ „ 5-00 „ 



4'62 „ „ 6-25 „ 



