io8 A TEXTBOOK OF OCEANOGRAPHY 



enables the whole internai structure of such a wave to be 

 illustrated. 



At the surface the radius of the circle described by a 

 revolving particle is equal to half the wave-height. Under- 

 surface particles describe similar circles, but with ever- 

 diminishing- radii. It is beyond the scope of this work to 

 give detailed proof of the laws regulating their movements. 



Broadly speaking the heights of the subsurface trochoids 

 diminish in a geometrical progression, while the depth in- 

 creases in arithmetical progression, and the following rule is 

 approximately correct. 



The orbits and velocities of the particles of water are 

 diminished by one-half for each additional depth below the 

 mid-height of the surface wave equal to one-ninth of a wave- 

 length — i.e.: 



Depth in fractions of a wave-length below ^ i "> s. â & 



the mid-height of the surface wave ... j ° " '5" '» » ^ 9. etc. 

 Proportionate velocities and diameters ... i 2 4 h iV bV 2 56' ^tc. 



Waves of 90 mètres length and 3 mètres height are not 

 uncommon with strong winds in the open océan. 



At 10 mètres depth the height of the subsurface trochoid 

 would be i'5 mètres; at 20 mètres depth 0*75 mètres; at 50 

 mètres only 9 centimètres ; in 100 mètres not quite 3 millimètres 

 — that is, hardly perceptible. 



An océan storm-wave 600 feet long and 40 feet high from 

 hollow to crest would hâve at a depth of 200 feet a subsurface 

 trochoid with a height of 5 feet ; at 400 feet (f of the length) a 

 trochoid of 7 or 8 inches only, 



This rule and thèse examples are sufficient for practical 

 purposes. 



" Very often the motions of thèse originally vertical 

 columns of particles hâve been compared to those occurring 

 in a corn-field, where the stalks sway to and fro and a wave- 

 form travels across the top of the growing corn. But while 

 there are points of resemblance between the two cases, there 

 is also this important différence — the corn-stalks are of constant 



