Frederick Guthrie on Stationary Liquid Waves. 295 



with some accuracy. It is at once seen that while the only part 

 of the water free from radial motion is that in contact with the 

 walls and the very axis of the cylinder, there is a nodal ring of 

 constant height — which, however, is only a geometrical expres- 

 sion j for the water sweeps to and fro through the node radially. 

 Putting aside for the present the internal motion of the water, let 

 us examine the position of the nodal ring. This can be done by 

 shifting the gauge of § 2 until there is no rise and fall on its 

 stem, and then measuring its distance from the edge. A per- 

 manent record of the nature of the wave-system can be got by 

 immersing a sheet of cardboard in a vertical plane passing 

 through the axis of the cylinder and reaching to the circumfe- 

 rence. The cardboard loses its smoothness where the water has 

 touched it. By both of these methods it appeared that in ves- 

 sel A the node was 99 millims. from the edge, in B it was 75 

 millims., and in C it was 64 millims. The diameters of these 

 being respectively 595, 456, and 366 millims., the fraction of 

 the diameters at which the nodes were formed were respectively 

 601, 6*08, and 5*72. The central amplitude was in each case 

 26 millims. In the vessel C this amplitude causes incipient 

 breakers, so that the nodal point sways. It appears that in a 

 perfect system of such waves the nodal line is \ of the diameter 

 from the circumference. 



§ 10. Relative amplitude at different parts. — When the ampli- 

 tude is great, the elevation at the centre exceeds the depression 

 at the same place. The elevation may be so great as to project 

 water repeatedly, while the corresponding cavity is smooth and 

 round. In such a condition the node sways. With smaller am- 

 plitudes, the alternate depression and elevation at the centre are 

 equal to one another, and the node becomes stationary. 



With great amplitudes, that at the centre is indefinitely greater 

 than that at the edge (when the node sw r ays). With very small 

 amplitudes the amplitude at the edge is nearly exactly one half 

 of that in the centre; this is the more nearly true the less the 

 amplitude, and would, I conceive, be strictly true if the waves 

 were conical instead of being dome-shaped. 



§ 11. Comparison with stationary waves of solids. — A uniform 



elastic rod or lath, a b c, fig. 1, can be set in vibration in the 



manner shown by the dotted Fig. 1. 



lines. It divides itself in 



such a way that a = c — \b #t\ ^;:'"-"-T-~ r -->.. A* 



1 V> ■:'' - — £ ^<n// w 



"//^^^ b ^P%? 



and d=e=f. The nodes 



are at \l from the ends, and 



the amplitude at the ends is 



nearly the same as in the middle. A lath consisting of two 



isosceles triangles (fig. 2) can be thrown into similar waves whose 



