346 Dr. Eaiikine 07i Waves in Liquids. [May 7j 



In articles 7, 8, and 9 the law whicli connects the speed of advance of a 

 wave with the virtual depth is compared with the already known laws of 

 the transmission of rolling waves in water of limited or unlimited depth . 

 The principal results may be summed up as follows. Let T be the periodic 



time of a wave, in seconds; h^^—-^ the equivalent j^endulum^ that is, the 



47r 



height of the pendulum whose period is the same ; c— ^j^g rolling 



radius, being the radius of a circle whose circumference is equal to a wave- 

 length ; v.^ the greatest horizontal velocity, and ii\ the greatest vertical velo- 

 city of a surface-particle ; a the velocity of advance ; then 



fT 



J. » 



and 



^= _i . c= — i- . h.) 



(10) Oblique Advance of Forced Waves. — Let 5 he the velocity with 

 which a floating solid body is driven horizontally ; the wave which that 

 solid body pushes or drags along with it is forced to advance at the 

 velocity s also ; while the virtual depth of disturbance, bears some rela- 

 tion to the depth of immersion and figure of the sohd body. If the speed 

 of advance corresponding to that depth, a = \/ gk, is less than s, a pair of 

 wave-ridges diverge obliquely from the path of the floating body towards 

 opposite sides ; and the sine of the angle which each of those ridges makes 



with that path is -. Such is the mode of formation of the obliquely spread- 



s 



ing waves which travel along with ships*. 



When the velocity of the floating body is less than the speed of advance 

 corresponding to the depth to which it disturbs the liquid in its immediate 

 neighbourhood, it is probable that the virtual depth of disturbance of parts 

 of the liquid beyond the immediate action of the floating body adjusts itself 



to the velocity, and assumes the value -. 



9 



] 1. Possibilitij of Obliquely Advancing Tidal Waves. — It is possible that 

 instead of a depth less than the virtual depth corresponding to the speed of 

 advance of a tidal wave, the ridge of that wave may place itself in a position 

 oblique to the parallels of latitude, according to the principle stated in 

 article 10. It still remains to be ascertained, by the study of tidal obser- 

 vations, whether such phenomena take place in the tides of the ocean. 



12. Terminal Velocity of Waves. — It is known that in deep water all 

 waves left free from the action of disturbing forces tend ultimately to assum.e 

 the condition of free rolling waves whose velocity of advance depends on 



^ See Watts, Rankine, Napier, and Barnes, *0n Ship-building,' Division I. Article 156, 

 p. 79. 



