300 Frederick Guthrie on Stationary Liquid Waves. 



According to Z, at the rate of 74'006 metres in 1'. 

 Y, „ 74-348 



X, „ 75-088 „ 



W „ 75 371 



The mean of these is 74 # 7, and this is the distance which a 

 wave a metre long would pass over in V when moving in deep 

 water between parallel walls. This is under the assumption that 

 no velocity is lost by reflection ; and the same assumption must 

 be made in § 8 with circular troughs, where the velocity of the 

 metre wave in circular troughs was found to be 83*1 metres in 1'. 



§ 16. As the circular undulation was referred to an oscillating 

 triangle or vibrating pair of triangular laths, so may the motion 

 of the water above described in the rectangular trough be likened 

 to the balancing of two rectangular laths supported at their lines 

 of gravity, or, more closely, to the binodal vibration of a rectan- 

 gular lath (see §11). The lines of gravity are now from each 

 end \ of the joint length. The nodes are at \l from each end. 

 Accordingly in rectangular troughs the nodes are at exactly ±1 

 from the ends when the undulation is binodal. Also, on taking 

 a paper section of the system (see § 9), it is found that the am- 

 plitude at the centre only exceeds that at the ends by a very 

 small amount. As before, the node is not a line of material 

 rest. The water sweeps through it towards the mountain which 

 is forming at one side or the other. 



§ 17. Mononodal undulation in circular troughs. — In circular 

 troughs the mononodal waves can be produced by tilting or by a 

 segmental stirrer. The former, of course, lifts the node and pro- 

 duces at first a longer wave than is due to the proper limits of 

 the trough. This very fact causes the wave to accommodate itself 

 to the trough, and to establish a nodal line which is a diameter 

 of the cylinder at right angles to the plane of the wave. The 

 same system is produced at once by the careful use of the seg- 

 mental stirrer. Two kinds of irregularities may show them- 

 selves. The one depends upon the partial degeneration of the 

 mononodal system into circular bi- or quadrinodal systems ; the 

 second consists of an almost unavoidable rotation of the node. 

 Such rotation, which need not exceed a quadrant in three or four 

 hundred waves, must of course bean experimental fault, since no 

 reason can be assigned why it should take place in one rather 

 than in the other direction. Neither irregularity appears to 

 affect the rate of the mononodal system ; the first gradually 

 effaces itself probably by disaccord between the older and newer 

 effects. 



§ 18. Effect of depth on the mononodal system in circular 

 troughs. 



