106 A TEXTBOOK OF OCEANOGRAPHY 



P on the radius OR' of the rolling circle; then this 

 tracing-point as the circle rolls will trace a curve, known 

 as a " trochoid " (Pc2h2 in the diagram), which is the 

 theoretical wave profile from hollow to crest. To determine 

 a point on the trochoid, as the rolling circle advances a point 

 on its circumference (say 3) comes into contact with the corre- 

 sponding number on the line QR. The centres of the circles 

 must at that instant (S) be vertically below the point of contact 

 (3), and the angle through which the circular disc and the 

 tracing arm OP have both turned is given by QOj. But the 

 angle POc on the original position of the circles =QO^; 

 consequently through S draw 802 parallel to Oc, and make 

 Sc2 = Oc ; then 02 is a point on the trochoid. 



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FIG. 17. A TROCHOID WAVE. 



The tracing-arm OP may, for wave-motion, have any value 

 not greater than the radius of the rolling circle OQ. 



If OP = OQ the tracing-point lies on the circumference of 

 the rolling circle, and the curve traced is a cycloid and corre- 

 sponds to a wave on the point of breaking. 



The curve R f TR shows a cycloid. The crest is a sharp 

 line or ridge (at R), while the hollow is a very flat curve. 



All deep-sea waves have this trochoid profile. 



The length of the wave is its measurement from crest to 

 crest (QR in the figure is half the wave-length) ; the height of 

 the wave is reckoned from hollow to crest; and the period is 

 the time its crest or hollow takes in traversing a distance equal 

 to its own length. 



