ON WAVE MOTION. 



405 



A table in W. H. White's Naval Architecture, p. 197, gives a series 



of other values, based on taking e''" =2, 62^=2^=512, very nearly 

 reallv 536. 



A \va\ e motion is set up by the variable impulse, in which the wave- 

 length L in feet, the period T in seconds, and c the velocity of moving 

 waves or rollers in feet per second (f/s), or K in knots, are connected on 

 the subsequent theory by 



(1) 



^V 



27rL 



9 





gh 

 27r' 



For measurement in wave motion, the easiest quantity to observe is 

 the period T, or its reciprocal when T is short, the number of waves 

 in the second, or else the length I of the simple pendulum which beats 

 \ T seconds, or revolves conically in T seconds ; and then L and c can 

 be determined from 



(2) 





L = 27rl. 



Wave Length and Velocity. 



2. For these rollers, surface waves advancing over water of practically 

 unlimited depth, the landsman employs simple rules in his foot-second 

 units, such as 



(1) 



c=5i, 0^=5/, 



l=5t'\ 



connecting the velocity c in f/s of surface waves of length I feet and 

 period t seconds, over deep water. 



Taking the formula c'-=^, this implies that J~ is replaced by 5 



Ztt 2it ^ 



in 



round numbers instead of the more exact value 5-12, but within 

 2 per cent. 



The sailor employs the cosmopolitan unit of the geographical or 

 nautical mile, which he divides into 1,000 fathom, so that his fathom is 

 6 feet and a little over, say, 608 feet. 



Then if E denotes the radius of the earth in nautical (N) miles the 

 circumference ' 



27rE=:860x 60=21600, making E=8438=cosec V, 



the number of minutes is the radian. 



1919. 



H H 



