CHAP. IV. J CALCULATING THE TRIANGULATION 97 



No rule can be laid down with regard to the amount of Error ad 

 deviation from the 180° that can be admitted, it so much Triangles, 

 depends on the degree of accuracy required ; but in an ordinary- 

 theodolite survey the error should not be more than two 

 minutes, and ought to be under one, working with 5-inch 

 theodolites, and repeating the angles three times if satisfactory, 

 or more if they vary much. 



In the first few triangles, the error should not be more than 

 one minute. 



Having corrected the triangles, we come to the calculation. Calcuia- 



The working out of the triangulation is the very simple g^pig 

 affair of plane triangles which every naval officer understands. 

 The rule of sines, and the rule to fuid the third side,* when 

 two sides and the included angle are given, are all that are 

 required. 



Logarithms of all angles must be taken out to seconds, so Loga- 

 that the possession of tables giving these for every second of ^^^^^ 

 arc will save much time and chance of mistake. 



Into the jfinal calculation of an extended calculated triangu- 

 lation some other considerations enter. 



The actual working of the triangles will be the same ; but Conyer- 

 here we want the bearing of every side, as well as the distance, S^^^^y- 

 and the " convergency of the meridians " must be considered. 

 This convergency will be explained before proceeding further. 



CONVERGENCY OF THE MERIDIANS. 



The true bearing of any two points on the earth, taken one 

 from the other, in both directions, will be found to differ by 

 a quantity which is called the convergency, and varies with 

 the latitude, distance apart, and position of the points in 

 bearing, or, in other words, with latitude and departure. 



Thus, if R and L are two stations lying roughly N.E. and iiiustra- 

 S.W. of one another, R being nearest the pole, in this case the Q^^^er- 

 North Pole, the true bearing of L from R mil be found to be gency. 

 a greater number of degrees and minutes as measured from 

 the meridian than the reverse bearing of R from L. 



This results from the form of the earth. The true bearing Explana- 

 of one position from another is the angle which the arc of a *^*'°- 



* The rule where sines only are involved must be used. 



7 



