384 



HYDROGRAPHICAL SURVEYING [chap, xvii 



A sheet may be graduated either before or after the chart 

 is drawn on it. The methods are substantially the same, and 

 will diflfer only in some preparatory work necessary in the 

 latter case. 



We A\'ill first consider the case of graduation after the chart 

 is complete, and to do tliis we must suppose our observations 

 to be obtained, and that we know the latitudes and longitudes 

 of two stations on our chart as far apart as possible in opposite 

 corners of the chart. 



We require, first of all, the reciprocal bearings of each from 

 the other, and the distance between them. 



Fig- 75- 



In Fig. 75 let A and B be two stations whose latitudes and 

 longitudes we have obtained ; P is the pole. Add to the diff. 

 long, the spheroidal correction, and use this corrected diff. long. 

 in the calculations. Calculate by spherical trigonometry the 

 bearing of each station from the other. 



We have P B and P A the co-latitudes, and B P A the diflf. 

 longitude. P B A and BAP are the angles required. The 

 latter subtracted from 180° will give us B A Q, and the differ- 

 ence between P A B and B A Q is the convergency. Find also 

 the distance A B, to get the scale. 



Now in Fig. 76 let A B be these same stations plotted on 

 our chart. Required to graduate it. 



Join A B, and from A and B lay off (by chords) the reciprocal 

 bearings of one another, ascertained as above, as A N, B M, 

 which will be meridians passing through those points. 



IjYom A and B measure, on the meridians, A H, B E, the 



