﻿438 Lord Kayleigh on ^.Tlolian Tones. 



The only procession which can possess a practical permanence 

 is thus defined. 



The corresponding motion is expressed by the complex 

 potential ((/> potential, ty stream-function) 



... if' sin{7r(£ — z)/l\ , . 



in which f denotes the strength o£ a vortex, z = x + iy, 

 z =±l + ih. The #-axis is drawn midway between the two 

 lines o£ vortices and the ?/-axis halves the distance between 

 neighbouring vortices with opposite rotation. Karman gives 

 a drawing of the stream-lines thus defined. 



The constant velocity of the processions is given by 



«=|tanh^ = ] ^ (8) 



This velocity is relative to the fluid at a distance. 



The observers who have experimented upon water seem 

 all to have used obstacles not susceptible of vibration. For 

 many years I have had it in mind to repeat the seolian harp 

 effect with water*, but only recently have brought the 

 matter to a test. The water was contained in a basin, about 

 36 cm. in diameter, which stood upon a sort of turn-table. 

 The upper part, however, was not properly a table, but was 

 formed of two horizontal beams crossing one another at 

 right angles, so that the whole apparatus resembled rather a 

 turn-stile, with four spokes. It had been intended to drive 

 from a small water-engine, but ultimately it was found that 

 all that was needed could more conveniently be done by 

 hand after a little practice. A metronome beat approximate 

 half seconds, and the spokes (which projected beyond the 

 basin) were pushed gently by one or both hands until the 

 rotation was uniform with passage of one or two spokes in 

 correspondence with an assigned number of beats. It was 

 necessary to allow several minutes in order to make sure 

 that the water had attained its ultimate velocity. The axis 

 of rotation was indicated by a pointer affixed to a small 



* From an old note-book. "Bath, Jan. 1884. 1 find in the baths 

 here that if the spread lingers be drawn pretty quickly through the 

 •water (palm foremost was best), they are thrown iuto transverse vibra- 

 tion and strike one another. This seems like seolian string The 



blade of a flesh-brush about 1£ inch broad seemed to vibrate transversely 

 in its own plane when moved through water broadways forward. It is 

 pretty certain that with proper apparatus these vibrations might be 

 developed and observed." 



