20 On C. S. Lyman's new form of Wave -apparatus. 



proximately one-iialf for each increase of depth equal to one-ninth 

 of a wave-length ; or more exactly, putting r and r for the radii 

 respectively of a surface-orbit and of one whose middle depth is 

 k, it is h 



B 



11 being, as before, the radius of the rolling circle, and e the base 

 of the Napierian logarithms. 



16. The peculiar swaying motion of continuous lines of particles 

 of equal pressure which at rest are vertical. — These lines are alter- 

 nately lengthened and shortened, and bent to right and left, as 

 represented by the upright elastic wires. 



17. The varying distortions undergone by blocks or sections of 

 water originally rectangular, or rectangular when at rest. — Such 

 sections are represented by the spaces between the wires, and 

 their distortions by the distortions of these spaces. 



18. The fact of sensibly still water at half a wave's length 

 below the surface. — This is exhibited in the absence of lateral 

 motion at the lower extremities of the upright wires, and is a 

 necessary result of the law of diminution of orbits with depth, 

 as given above (15). 



19. The varying strain in wave action on floating bodies. — 

 This is seen in the varying angle made by the upright wires 

 with the upper transverse wire : the latter shows the position of 

 a raft, for example, lying on the wave-surface ; the former, that 

 of a long thin body, as a board floating end down ; hence the 

 varying relative direction of the wires shows the strain to which 

 a body is subjected, having both breadth and depth, as the hull 

 of a vessel. 



Many other points besides the above may be studied to advan- 

 tage in connexion with this apparatus, but it is not important to 

 specify them here. Enough has been stated to illustrate its 

 utility, and indicate in what respects it differs from every other 

 form of wave-apparatus. 



For convenience of reference and for the sake of completeness, 

 a few formulae are added, expressing other relations among wave- 

 phenomena not so directly exhibited by the instrument, but im- 

 portant to be presented in connexion with it. Putting V for the 

 velocity of propagation of a wave, and the other symbols as before, 

 the length of the wave is 



its period 





