132 HYDROGRAPHICAL SURVEYING [chap. v. 



visible from each other, and C is visible from all. Z is a peak 

 visible from E, F, B. The peaks X and Y are visible from 



A, D, E, F. The latitudes of A and B and meridian distance 

 between them being determined, and the true bearing of C 

 being observed from both observation spots, angles are observed 

 at all the stations. 



(1) Calculating the spheroidal correction (from the formula 



,,«. , Cos- mid. lat.^ , , n. . 



correction = dm. long. ) and addmg it to the 



150 



true (or chronometric) difference of longitude between A and B, 



obtain the spherical diff. long. ; with this spherical diff. long. 



and the diff. lat. the mercatorial bearing and distance A B is 



found bymiddle latitude sailing. A B is the long side of the plot. 



(2) Assuming A C= 10,000 units, calculate C D, C E, C F, 

 C B in successive triangles. 



(3) Calculate the convergences between A and C, and C and 



B, and apply them to the observed true bearings of C from 

 A and B, to obtain the reversed true bearings. Compare the 

 difference of these reversed true bearings with the sum of the 

 calculated angles ACD, DCE, ECF, FCB; they should 

 agree. 



(4) In A A C B, given Z A C B, and A C and B C in units, 

 find Z « C A B, C B A. 



We have now sufficient data to plot on the line A B. 



The direct shots to X, Y, Z from the intermediate stations 

 will afford the desired check upon the accuracy of the 

 work. 



If some of the stations between A and B are placed somewhat 

 closely to one another, it may be desirable to rely on true 

 bearings of C taken at the different A* instead of carrying on 

 the original true bearing by means of the calculated angles. 



It is very unhkely that the true bearing of B from A, as 

 calculated through the triangulation, will agree with that 

 calculated from their observed astronomical positions ; but 

 this is a discrepancy which must always be expected and must 

 be accepted. 



The final astronomical positions being adjusted on the 

 principle already stated for harmonizing such discordances, 

 the sheet is graduated on the finally accepted astronomical 

 positions of A and B. 



