292 Frederick Guthrie on Stationary Liquid Waves. 



At a depth of 30 millims. no fundamental undulations could 

 be preserved. In order to see whether the effect of shallowness 

 took most effect on waves of larger or smaller amplitude, the 

 depth 70 millims. was restored and an initial central ampli- 

 tude of 30 millims. was given. In the first minute 113 were 

 counted ; after a lapse of 10" the same number 113 were counted 

 in the second minute. A second experiment, in which the in- 

 terval between the two minutes was 15", gave for both minutes 

 exactly the same number 113. The general conclusions to be 

 drawn from these results appear to be that the normal rate of 

 pulsation is not reached unless there be at least a depth of about 

 130 to 170 millims. (say 6 inches), and that the effect of shal- 

 lowness is as great on small as on larger amplitudes. No doubt 

 the diminution in rate is due to the increased drag upon the 

 bottom of the vessel. It is at about this depth that the to-and- 

 fro motion of the particles at the bottom of the vessel ceases to 

 be sensible. 



But the examination of the effect of depth is not complete 

 unless we know whether that effect is a function of the diameter 

 or wave-length. Accordingly a circular vessel D was taken of 

 the diameter 314 millims., with the following result : — 





Number of 





Depth of water. 



pulsations in 

 1 minute. 



Mean n. 



millim. 







150 



149, 149, 149 



149 



130 



149, 149, 148 



1487 



120 



by interpolation 



1479 



110 



147, 147, 147 



147 



100 



by interpolation 



146 9 



90 



145, 145, 145 



145-7 



80 



143, 143, 143 



143 



70 



142, 142, 142 



142 



60 



139, 139, 139 



139 



50 



134, 134, 134 



134 



40 



126, 125, 126 



1257 



It appears, then, that in the vessel D, whose diameter is 314 

 millims., the effect of the shallowness begins to be felt at rather 

 lesser depths than is the case in the wider troughs. At depths 

 of 30 millims. and under, the fundamental system cannot maintain 

 itself. 



§ 6. Effect of variation in chemical nature. — A cylindrical ves- 

 sel, which I shall call D, had the diameter of 321 millims. It 

 was filled to a depth of 80 millims. with methylated spirit. This 

 gave in each of three experiments 143 pulsations per minute. 

 Water of the same depth gave also exactly 143. We may con- 

 clude that, as in other oscillatory motions, the density of the 



