Frederick Guthrie on Stationary Liquid Waves. 299 



the water takes effect in increasing the period on the longer 

 trough before it affects the shorter one. In other words, to ex- 

 hibit its normal (i. e. maximum) rate, a short trough need not 

 be so deep as a longer one. 



It also appears that the depth 260 millims. employed in the 

 experiments in § 14 is sufficient. 



We may therefore compare the results of § 14. 



Length. Number of pulsations. 

 Z ... 767 84-5 



Y 



X 



w 



619 94-5 

 433 110-4 

 308 135-8 



The wave-length is here, of course, the length of the trough. 

 If the rate of progression varies directly as the square root of the 

 wave-length, then, since the rate of repetition of phase varies 

 inversely as the path, which is also the trough-length, we should 

 get (as in § 8) a constant on multiplying the number of pulsa- 

 tions in a minute with the square root of the trough-length. 

 This is done in the following Table, where also the quotients got 

 by dividing all by the smallest are given : — 



n»/T, 

 Z . . . 2340-21 1-0000 



Y . . . 2341-14 1-0004 . 



X . . . 2375-52 1-0108 



W . . . 2383-29 1-0183 



These numbers are even more nearly in accord than those of 

 circular troughs of § 8. They show that the rate of progression 

 of a restrained wave in a trough varies also directly as the square 

 root of its length. But the question asks itself, How is it that 

 wV^/of straight troughs is uniformly less than n^d of circular 

 ones ? The mean value of the constant in the circular system is 

 2618-652; in the rectangular it is 2360-04. These are in the 

 ratio of 1*109 to 1. To this point I shall return in § 23. 

 The absolute velocities of progression of the waves are : — 



z . . . 

 Y . . . 

 X . . . 



w . . . 



64-8115 metres in 1'. 



58-4955 



51-1152 



41-8264 



If we assume the formula 





VI 



to be true for the wave-length of a metre (and we see it is ap- 

 proximately true for 767 millims.), it is found that a wave a 

 metre long in a rectangular trough travels, 



