CHAP. IV.] CALCULATING THE TRIANGULATION 109 



of every side will have to be corrected by the difference of 

 the bearings of the extreme points. 



Thus, referring again to our example (which, for the sake of 

 brevity, we have confined to only a few sides), let us suppose 

 we find by observations that A F is N. 12° 36' W. 26-248 

 miles. 



Dividing this distance by the former one, we get a propor- 

 tion whose logarithm is 0-012097. Adding this to the log of 

 each side required to be corrected will give us the true value. 



The difference of bearing is 3' 15" more to the westward. 

 The bearing of each side will then have to be corrected by 

 this amount. Thus, the bearing of A B Avill stand N. 69° 

 13' 52" W. 



This difference is somewhat exaggerated. It should seldom, 

 when true bearings have been well observed, amount to so 

 much, but in some chmates it may be unavoidable. 



In a case of this land the result of both triangulation and 

 astronomical observations would be transmitted home, as their 

 concurrence or otherwise will form a good test of the value of 

 the work generally. 



In stating as we have that the ultimate scale of the chart 

 of an extended piece of coast will depend upon the astro- 

 nomical positions at either end, it is not intended to lay down 

 a too hard-and-fast rule. The conditions of each element, 

 triangulation and positions by astronomical observations, must 

 be considered. Both, under the ordinary circumstances of a 

 marine survey, are liable to error. In a rigorous trigono- 

 metrical survey, the triangulation is more likely to be correct 

 owing to the unknown error in the astronomical positions 

 due to local attraction of the pendulum, or in other words 

 of the mercury in the artificial horizon ; but, in an ordinary 

 marine survey, the triangulation is carried on under condi- 

 tions which prevent the possibility of ensuring freedom from 

 errors in it. Nevertheless, should the discrepancy in bearings 

 be large, when we know our true bearings have been well 

 observed and our triangulation to have carried it on within 

 the limits of the discrepancy, it is desirable to adjust the 

 astronomical positions so as to reduce the discrepancy in 

 bearings. 



In such circumstances we must examine critically the various 



