148 U. S. COAST AND GEODETIC SURVEY. 



In these approximations X must of course be expressed in 

 arc. 



An approximation for km was determined by A. Linden- 

 kohl, of the United States Coast and Geodetic Survey, that 

 is remiarkably close to the one given above. This was given 

 in the form 



£•=4-0.01 



/ X^ cos v? Y 

 V 8.1 )^ 



in which X° is the distance from the central meridian in 



degrees of longitude. In this form E corresponds to the 



X^ . 



term -^ cos ^(p in the first approximation. 



The projection is generally plotted from computed coordi- 

 nates of the intersections of the meridians and parallels. 

 If we take as origin the interesection of the central meridian 

 and the Equator, we shall have 



x — p sin d 



y=s — p cos d. 



It is the more general practice to compute each parallel 

 with its own origm; that is to say, by using as origin the 

 intersection of the parallel in question with the central 

 meridian. 



In this case 



a;=p sin ^ 



6 B 



y=p — p cos B = 2p sin^ o"^ ^^^ 2* 



The B angles have to be computed for each parallel that it 

 is desired to map hy computation. If these are to be at 

 frequent intervals, it is customary to compute certain 

 coordinates and then to interpolate the intervening values. 

 The meridional-arc values are tabulated in meters from 

 minute to minute in the Polyconic Projection Tables, 

 Special Publication No. 5, United States Coast and Geo- 

 detic Survey. If it is desired to refer the coordinates of 

 the various parallels to a common origin, it is merely 

 necessary to add the meridional-arc values reckoned from 

 the chosen origin to the y values as determined above; this 

 is true because the valye of s is given as equal to the 

 meridional arc from the Equator to the paraUelof latitude 

 ^, with the addition of the value of p in terms of ^. It is 



