384 "Frederick Guthrie on Stationary Liquid Waves, 



was established produced no sensible variation in Fig. 6. 

 rate of phase-recurrence, and therefore presumably 

 none in wave-progression. 



But a wave in a rectangular trough undergoes 

 a constraint quite other than that of friction . 

 Its motion is repressed by the sides. It presses 

 equally and radially in all directions. The wall 

 offers resistance perpendicular to itself. The re- 

 sultant of the quadrant of the forces in fig. 6 makes an angle of 



45° with the wall. The lateral pressure on the wall is -y= 



of the total radial pressure ; the onward pressure is also equal to 



-y=., the total pressure. The constant obstruction thus offered 



by the walls is the cause of the preservation of amplitude. The 

 constant obstruction thus offered by the rigid parallel walls, while 

 preserving amplitude, is, I imagine, the main cause of the lesser 

 rate of wave-progress in rectangular troughs ; and could exact 

 measurement be effected, I should expect that the ratio between 

 the times of subsidence from one amplitude to a lower one 

 in a circular and rectangular trough would be found to be 

 nearly the ratio of 83*1 to 74i'7. The measurements of rate 

 of subsidence cannot be made of sufficient exactness to test 

 this experimentally ; but it is clear enough that binodal waves 

 in circular troughs are far more enduring than those of rect- 

 angular ones. 



§ 27. It may be shown that in rectangular troughs, when 

 mononodal undulation takes place, the path of the centre of 

 gravity is a parabolic arc, supposing the surface to remain 

 flat. But as this condition never obtains in reality, and as no 

 one particle remains in its motion the centre of gravity of the 

 moving mass, this parabolic motion of the centre of gravity is of 

 no direct account. 



§ 28. Cross binodal undulations in circular troughs. — On press- 

 ing simultaneously two opposite points of the rims of A and B, 

 they yield sufficiently to start undulations which are analogous 

 to the ring of a bell or the fundamental quadrant vibration 

 of a Chladni plate. By repeating the push at proper intervals, 

 a well-shaped system of undulation is established, consisting 

 of quadrant waves separated by diametral nodes at right angles 

 to one another. The rate of recurrence of these in troughs A 

 and B was examined. The troughs were filled with 300 millims. 

 of water. 



