CHAP. IV.] RESULTS OBTAINED ASTRONOMICALLY 111 



CO-ORDINATING RESULTS OBTAINED ASTRONOiVH- 

 CALLY AND BY TRIANGULATION. 



Suppose A and B to be the two terminal points of the 

 survey ; that we have carefully triangulated between the two, 

 have observed the latitude at both, and have measured the 

 meridian distance between them. 



We can now calculate the bearing and distance between 

 A and B both astronomically and by triangulation. As has 

 been said before, we may expect to obtain different results. 

 How to harmonize the two ? 



I. Consider first the Astronomical Result. 



The observed latitudes wall not probably be much in error, 

 yet, as before stated, an error of I" or even 2" may easily occur 

 in either latitude. 



The actual amount of probable error of either latitude can 

 be very fairly estimated after the sights have been worked 

 out ; the sum of the probable errors of the two latitudes will 

 be the '' maximum probable error " of the resulting diff. lat. 



The probable error of the meridian distance can also be 

 estimated, and this Avill be the same thing as the " maximum 

 probable error " of the resulting diff. long. 



II. Consider next the Triangidation Residts. 

 Errors mil occur both in distance and bearing. 



{a) Error in distance will be due to errors in the measured 

 base, and to errors in the angles of the triangles used in cal- 

 culating the triangulation. 



If a base has been measured near A at one end of the survey, 

 and a check base near B at the other end, and the distance 

 A B calculated separately from both bases, it will be as well 

 to adopt the mean of the two values as the accepted length 

 A B (by triangulation), and consider half the difference of the 

 two as the probable error in distance A B. 



Knowing the bearing of the line A B, find the diff. lat. and 

 diff. long, corresponding to this probable error, in seconds, by 

 means of Traverse and Carrington's Tables. 



This is the " maximum probable error " in distance A B 

 (by triangulation) expressed in terms of diff. lat. and diff. 

 long. 



