294 Frederick Guthrie on Stationary Liquid Waves. 



circumference and back is the diameter ; and the rate of pulsa- 

 tion (that is, the rate of recurrence of the same phase) must for 

 uniform motion vary inversely with the path or diameter. 

 Accordingly if n be the number of undulations in a time-unit, 

 v diameter 



n = C 



diameter 



or n\/d=C. 



We should get a constant on multiplying the square root of the 

 diameter (or radius) of a circular trough with the number of pul- 

 sations per 1'. In the following Table this is done. In column 1 

 are shown the values of n\/d. For more palpable comparison, 

 in column 2 are the numbers got by dividing each of column 1 

 by the least (which is the first). 





nN d. 



(2) 



A . . 



, . 2608-035 



1-0000 



B . 



. . 2613-747 



10022 



C . , 



. . 2615-799 



1-0029 



E . . 



, . 2615-397 



1-0029 



The close coincidence of these numbers establishes the law 

 that the rate of wave-progression varies directly with the square 

 root of the wave-length. The absolute velocities of progression 

 of waves of the lengths established in the troughs are — 



A . 



. . 63-6412 metres per 1', 



B . 



. . 55-8144 



C . 



. . 50-0437 



E . 



. . 45-3000 



and of course these numbers, divided by the square roots of their 

 respective wave-lengths, are constant. 



According to A, a wave 1 metre long travels at the rate of 



83*3060 metres in a minute. 

 According to B, at 82*6053 



C, „ 82-7224 

 E, „ 83-6691 



,->> 



>> 



7} 



Or taking the mean, we may conclude that a wave a metre long 

 would travel at the rate of 83*07 metres in 1' (a little over 3 

 miles an hour) if it expanded circularly, and moved freely and 

 automatically without change of wave-length. 



§ 9. Form of fundamental binodal wave in cylindrical trough. — 

 The beautiful smoothness and persistence of the stationary bino- 

 dal waves in cylindrical vessels enables us to examine their form 



