are determined from equations (11) through (14), respectively. Hav- 

 ing the first approximation for these quantities, the transform- 

 generated arc length for each curve and weight factors may be deter- 

 mined thus permitting a second approximation. This procedure is 

 repeated for given N until g , B Q and the transform coefficients 

 have converged as indicated by successive values of the error func- 

 tion. The error function approaches a constant value governed by N 

 and the inherent errors in estimating the various integrals by 

 numerical methods. The trapezoidal rule employing M values of £ 

 at equal increments over the interval <_ E, <_ A is used to estimate 

 all integrals. Given the value of E, , the appropriate values of 

 X s , Y s , X c and Y c are computed by an interpolational subroutine 

 called CURV, which was obtained from Dr. Alan Cline, National Center 

 for Atmospheric Research. This routine is based on a numerical 

 analogy to a spline under tension (for example, see Schweikert, 

 1966). In all applications of the conformal mapping procedure, 

 the total number of terms of the series, N , is taken as M or 

 smaller. The limitation on N is imposed since, for a determinate 

 system, the total number of Fourier-type coefficients cannot exceed 

 the number of data points. The selection of N is governed by the 

 desired degree of fit of the functions X s , Y s , X c and Y c . 

 The procedure outlined above follows the rudiments of a conformal 

 mapping technique developed by Reid and Vastano (1966) . 



2. Applications . 



Three regions of the Continental Shelf of the Gulf of Mexico and 

 two regions of the eastern seaboard of the United States have been 

 mapped. These regions are: 



(a) western gulf coast: Laguna Madre, Mexico, to Marsh 



Island, Louisiana; 



(b) central gulf coast: Matagorda Bay, Texas, to Timbalier 



Bay, Louisiana; 



(c) eastern gulf coast: Atchafalaya Bay, Louisiana, to 



Apalachee Bay, Florida; 



(d) lower east coast: Cape Kennedy, Florida, to Pamlico 



Sound, North Carolina; 



(e) upper east coast: Pamlico Sound, North Carolina, to 



Penobscot Bay, Maine; 



and are shown in Figures 2 through 6. The top and bottom curve in 

 each figure represents the coastline and the 180-meter isobath, 

 respectively. The latter is taken to correspond approximately to 

 the shelf break, seaward of which the depths increase abruptly; the 

 180-meter contour may not always be the most appropriate one for the 

 outer limit of the Continental Shelf. The chart scale, orientation 

 of the region, and location of cities and bays along the coast are 

 indicated on each figure. The x's represent the location where 



