378 Frederick Guthrie on Stationary Liquid Waves, 



Collecting and multiplying each number of waves by the 

 square root of its trough-length (trough-length = -|- wave-length, 

 the ratio is the same) , and dividing all such products by the least 

 of them, we get the following numbers : — 







Mean number 









Length of trough, 



of waves 









I. 



in l'=n. 



n^/l. 





z . 



. . 767 



55 



1523-21 



1-00 



Y. 



. . 619 



63 



1568-42 



1-03 



X 



. . 463 



76 



1635-32 



1-07 



w 



. . 308 



94 



1649-70 



108 



In spite, therefore, of the apparent attainment of maximum 

 rate at 280 millims., we must reject the two longest waves in 

 adopting a constant, which, taking the mean of the two shorter 

 systems, is 1642*5. 



In all the four cases, namely mono- and binodal waves in 

 circular and rectangular troughs, the value of n^lov n^d in- 

 creases as the length of / or d decreases. The increase of rate 

 of wave progress due to increased wave-length is somewhat more 

 than counterbalanced by the increased path, so that the u con- 

 stant " is larger with smaller troughs. 



§ 21. Comparison between mononodal and binodal waves in 

 rectangular troughs. — In the same trough the wave-length of the 

 mononodal system is always that of the binodal system, the 

 former being 21 (/= trough-length). If the ratio of progression 

 be as the square root of the wave-length, then the number n of 

 waves in a given time, varying directly as the rate of progression 

 and inversely as the distance, in the same trough 



number of binodal ,_ 



number of mononodal 



How far this is borne out in the experiments is seen in the 

 following comparison of the shorter troughs, where the mono- 

 nodal system is normal. 



Length of trough. V2X mononodal. No. of binodal. 

 X. . . 463 107-47 110-4 



W . . 308 132-94 135-8 



§ 22. If we take a binodal system and insert a rigid plane 

 diaphragm vertically down the middle and at right angles to the 

 plane of the wave, we divide it under little disturbance obviously 

 into two mononodal systems of half the trough-length, but of 

 the same wave-length as before. These should oscillate (inde- 



