mentioned, of the aerial method of determining the 

 refraction pattern, measurement of the co- 

 efficient from aerial photographs suffers because 

 of the fact that waves vary in height along their 

 crests and there is not a single value of Hg appli- 

 cable to all breakers shown in the photographs. 

 At a scale of 1:12,000 a 7-inch print, and a speed 

 of 15,000 feet per minute, for example, each point 



on the shore remains in the field of the camera for 

 about 30 seconds, or long enough for 2 or 3 waves 

 to break. By measuring all the waves visible at 

 many points, random variations may, in part, be 

 eliminated. The accuracy is increased by making 

 several photographic sorties in quick succession 

 while the same wave train prevails. 



GRAPHICAL CONSTRUCTION OF REFRACTION 

 DIAGRAMS DIRECTLY BY ORTHOGONALS 



I. INTRODUCTION 



A system has been devised whereby the orthog- 

 onals to refracted wave fronts may be constructed 

 directly without first drawing the wave fronts. 

 This method has the advantage of eliminating an 

 entire graphical step and its attendant inac- 

 curacies. In trained hands a refraction diagram 

 can be constructed by this method in about a 

 quarter of the time required for its construction by 

 the wave front method. The method requires a 

 higher degree of training, however, and the opera- 

 tion does not become so nearly automatic as does 

 the wave front method. The method is thus 

 suitable for use by specialist draftsmen or engi- 

 neers. 



Physically the method is carried out by a special 

 protractor which incorporates the requisite scales. 

 The protractor is manipulated in steps from con- 

 tour to contour and at each step indicates the 

 direction of the orthogonal. One orthogonal is 

 thus drawn from deep water to shore in each series 

 of operations. The device has been made in the 

 form of a protractor so that it would be entirely 

 adequate for the construction of refraction dia- 

 grams. A drafting machine can be employed to 

 an advantage, however, and the protractor used 

 merely as a graph and tables for obtaining the 

 required values for the manipulation of the 

 drafting machine. 



A detailed description of the development of the 

 method and its application follows: 



II. DEVELOPMENT OF THE METHOD 

 A. Assumptions 



1 . That contours can be drawn at every abrupt 

 change in slope of the chart. 



(a) The depth at a point between contours is a 

 linear function of its distance from the contours. 



2. That, between contours, wave length and 

 velocity may be considered to vary linearly (the 

 usual assumption). 



(a) The wave length and velocity may be 

 considered a linear function of its distance from 

 the contours. 



{b) The radius of curvature of the orthogonal 

 between contours may be considered constant (a 

 circular arc). 



(c) The angle of the arc is equal to the change of 

 angle of the orthogonal. 



3. That the undulations of small magnitude 

 extant in niost contours are more likely to be a 

 measure of observational inaccuracies magnified 

 by rigorous drafting than an indication of the 

 direction of level bottom. Also, that bottom 

 features whose dimensions are small compared 

 with the wave length do not influence the motion 

 of the wave to any appreciable extent. 



(a) If the contours are smoothed out and only 

 those features preserved that are obviously 

 characteristics of the hydrography, the result is 

 more nearly accurate. 



4. That the angle of convergence or divergence 



18 



