Frederick Guthrie on Stationary Liquid Waves. 293 



substance is without effect. This was shown experimentally, in 

 the case of waves progressing in rectangular troughs, fifty years 

 ago by the brothers Weber. 



§ 7. Effect of variation in the diameter. — I used chiefly four 

 cylindrical vessels. Their dimensions were as follows : — 



Vessel A, mean diameter at surface of water 595 millims. 

 )} B, a }> a 4ob „ 



» C, „ „ „ 366 „ 



33 E, „ „ „ 300 „ 



Experiments with A (depth = 290 millims.). 

 In 3' there were 321 pulsations, 



33 ° 33 535 „ 



„ 4' „ 427 



„10' „ 1071 „ 

 or mean A n = 106-96. 



Experiments with B were given in § 3, whence it appeared 

 that (depth =290 millims.) 



mean B w =122 , 4. 



Experiments with C (depth = 285 millims.). 



In 3' there were 411 pulsations, 



„ 3' „ 410 „ 



33 3' » 410 



or mean C n =136. 

 Experiments with E (depth = 870 millims.). 



Id 1' there were 151 pulsations. 



„ r „ isi „ 



„ V „ 151 



or mean E B =151. 



Putting the results together, 





Diameter. 



Number of pulsations 

 per 1'. 



A . 

 B . 

 C . 

 E • 



. . 595 

 . . 456 

 . . 366 

 . . 300 



106-96 

 122-4 

 136-73 

 151 



§ 8. In the binodal system of undulations here set up it is 

 clear that the wave-length is equal to the diameter of the cylinder. 

 If, then, the rate of progression is directly pro portiona l to the 

 square root of its length, we must have v = C Vdiameter, where 

 C is a constant. But the length of path from the centre to the 



