a,b = distances along y -axis to adjacent contours 



c .c, = wave velocities at adjacent contours 

 a' b 



X* = curvature of contour 

 *^ c 



Aj2f = angle included by tangents to contour 



m = length of chord connecting points of tangency 



Q = angle between integral curve and s-axis 



)x- = curvature of integral cvirve 

 P 



h = depth of water 



L = wave length in deep water 



)^ = curvature of wave crest 



c = wave velocity in deep water 

 o 



X= parameter depending on p and q 

 Introduction 



The refraction factor, K, which is a linear measure of the effect of 

 refraction on the height of water waves, has been calculated by measuring 

 the separation distance between two 

 neighboring rays (orthogonals) on 

 a refraction diagram. For later con- 

 venience define a ray separation 

 factor 



where Yq designates the distance 

 between the given ray and an ad- 

 jacent ray at some initial depth, 

 and Y the distance between the rays 

 at an arbitrary depth (Fig. 1). 

 The refraction factor is then, 



K = |Pl 



-1/2 



\'\H 



-1/3 



shore 



depending on whether the arbitrary 



depth is outside or at the 



depth of breaking, (Munk and 

 Traylor, 19li7). 



Fig. 



-2- 



