102 HYDROGRAPHICAL SURVEYING [chap. iv. 



position, in consequence of the existence of convergency. 

 Mercator's charts are generally on such a small scale that, 

 for navigating purposes, the error of taking the bearing 

 swallows up the error introduced by not allowing for con- 

 vergency. 



The formula for Convergency is — 



Conver- Tangent Convergency = Tan. departure xTan. Mid. lat. (1) 



gency 



Formulae. Qj, Jj^ anything but high latitude, or when the departure is 

 great, it is correct enough to say — 



Convergency (in mins.) = dep. (in mins.) xTan. Mid. lat. (2), 

 which can be converted into — 



Convergency = d. long. X Sin Mid. lat (3) 



Convergency = dist. x Sin Merc. Bearing x Tan. Mid. lat. (4) 



any of which can be used as convenient. 



The proof of the formula is given in the Appendix A. 



Conver- The convergency can also be found when the latitudes of 



Iphericai ^^^ difference of longitude between the two stations is known, 



Triangle by working out the spherical triangle, with the pole, and the 



two stations, as the three points. Here we have the two 



colatitudes as the sides, containing the difference of longitude 



as the polar angle, to find the other two angles, which will be 



the bearings of each station from the other. The difference 



of these will be, as before, the convergency.* 



CALCULATING THE TRIANGULATION. 



We now resume our remarks on working out a calculated 

 main triangulation. All sides being calculated by the ordinary 

 method of plane triangles, we now want the bearing, the mer- 

 catorial bearing, of each side, or, at any rate, a considerable 

 number of them, in order that we can take any triangles or 

 sides to work up details on, on a separate sheet, and that such 

 sheet may be complete in itself as to bearing, distance, and 

 position, with regard to other portions of the main triangula- 

 tion. 



* See following article for application of Couvergency. 



