Frederick Guthrie on Stationary Liquid Waves. 297 



§ 12. Level of node. — When the wave-system is perfect, the 

 vertical height of the node is the same as that of the surface of 

 the liquid when at rest. The movement of particles of powder 

 on the water shows that though the node itself is at rest, the 

 water composing it is in violent motion. It is a stationary 

 market in a shifting population. It shows that, as in solid and 

 gaseous waves, a node is a region where most work is done, and 

 accordingly where least motion ensues — a hinge. 



Rectangular Troughs. 



§ 13. Four troughs of zincked iron were ordered of the common 

 depth of 1 foot, the common width of 1 foot, and the respective 

 lengths of 1 foot, ] foot 6 inches, 2 feet, 2 feet 6 inches. They 

 were found to have the following 'dimensions in millimetres : — 





Width. 



Depth. 



Length. 



w . 



. . 320 



315 



308 



X . 



. . 320 



315 



463 



Y . 



. . 315 



315 



619 



Z . 



. . 322 



315 



767 



About the depth, my only care was to have such a depth of 

 water that there should be no sensible drag by friction. This 

 appears from § 5 to be the case with about 150 millims. of water. 

 It will be shown in § 23 that, at this width, variation in width 

 is without sensible effect. The mean widths are given. The 

 lengths are also the means of twelve measurements 1 inch apart. 

 In no case was there a difference of more than 1 millim. between 

 lengths which should have been identical. 



In rectangular troughs two chief wave - systems can be 

 established which maintain themselves automatically. They 

 may be called binodal and mononodal respectively. The first 

 is the counterpart of the circular waves which we have been 

 considering. The binodal system is got by placing a wooden 

 lath, 2 or 3 inches wide and nearly as long as the trough is wide, 

 and provided with a handle at right angles to its plane, on the 

 surface of the water exactly halfway from either end, and de- 

 pressing and raising it intact. The waves soon grow and main- 

 tain themselves for several minutes. The second or mononodal 

 system is very easily produced by slightly tilting the trough 

 repeatedly around one of its lower end edges. We shall consider 

 the binodal motion first. The troughs were all filled to a depth 

 of 260 millims. As it appears from the whole of the subjoined 

 experiments that the number of undulations in the first minute 

 was the same as those in the second, and so on, it followed 

 that, as in circular troughs, the amplitude was without effect 

 upon the frequency of pulsation. 



