Frederick Guthrie on Stationary Liquid Waves, 383 

 of half the wave-length ; in the rectangular trough this pendulum 

 must be - x wave-length. If reflection does not alter velocity, 



IT 



the circular wave I metre long will travel 83*1 metres in one 

 minute if it preserves its wave-length ; while a wave 1 metre 

 long between walls will only travel 74*7 metres in one minute. 

 In answering the question as to whence this latter difference 

 arises, a few preliminary experiments are useful. That waves 

 in circular troughs endure longer than waves of the same am- 

 plitude in rectangular ones may be attributed in great measure 

 to friction. That element of friction which is due to adhesion 

 and cohesion can be directly compared as follows. In a square 

 trough in one complete undulation the surface rubbed by the 

 two end lines of particles is 4a! if a is the amplitude and / the 

 trough or wave-length. The surface rubbed by the two side- 

 lines of particles is 2al. The whole surface rubbed by the four 

 edges of the top layer of particles is 6aL In the circular trough 

 whose diameter is equal to /, the amplitude at the centre being 

 a, the surface rubbed by the edge ring of particles in a com- 

 plete undulation is 2«7r J/ or airl ; or the cohesive friction on the 

 square trough is for the upper layer 1*9 times that of the cir- 

 cular trough for the same wave-length and edge-wave ampli- 

 tude. If such friction were the cause of the slower rate of wave- 

 progress in rectangular troughs, we should expect the effect to 

 be less in wider troughs than in narrower ones, because, while 

 the surface scraped would be the same, the mass of the water 

 would be greater. 



Accordingly the rectangular troughs W, X, Z, which have the 

 dimensions 



Width. Length. 



W ... 320 308 



X ... 320 463 



Z ... 322 767, 



were filled to a depth of 280 millims., and by means of long 

 laths set in binodal undulation in the direction of their widths. 

 The wave-lengths of W and X were accordingly identical ; 

 and the wave-length of Z was only 4 millims. longer. The 

 mean of four concordant determinations in each case showed 

 in 1', 



for W . . , 134 

 „ X ... 134 

 „ Z ... 133-5 



In brief, the length of the trough across which the system 



