WILSON.] 



METHOD OF ADJUSTING THE TKIANGULATION. 



283 



Having established these outside points, we then had as many differ- 

 ent bases from which to compute the next point; so we proceeded by 

 simply computing all the triangles we have on Mount Ouray, throwing 

 all the errors of closure at the point sought ; that is, simply using the 

 foresights uncorrected, except for spherical excess ; after calculating 

 all the triangles in this manner, we made a plot of the intersections of 

 these lines as calculated, say on a scale of two feet to one inch (that being 

 the scale used in plotting those at Ouray); see Figure 1, Plate XVII. 



Now, it will be seen that these lines do not meet at a given point, as 

 they should if the work was perfect. All other things being equal, the 

 most probable location of the point would be in the centre of gravity of 

 the small triangles which are formed at the point by the intersections. 

 But there are some other things which are important in determining the 

 most probable position, such as the closure of the different triangles, 

 the value of different sights, &c. 



Taking such things into consideration as may be regarded worthy of 

 note, we choose a point, as at Ouray, Fig. 1, where the two sights cross 

 from Station 23 and Station 24, as the most probable position of the 

 station on Mount Ouray, and calculate the necessary swings from 

 Hunt's Peak and north end base to make those lines meet the other at 

 the chosen jioint. 



Applying these corrections to the angles at Hunt's and north base, 

 recalculating the triangles, and we have the point Ouray located. 



It will bo seen that, although the triangles on Mount Ouray are fixed, 

 we have not yet distributed the errors at the point Ouray. For instance, 

 we have yet an error of closure in the triangle Hunt's, Station 23, 

 Mount Ouray, of + 2"; in the triangles Hunt's, Station 24, Ouray, of 

 + 3"; and in triangle Hunt's, north base, Ouray, an error of 6". 

 Now, how much of this error is due to sighting Hunt's, north base. 

 Station 23, or Station 24, is not settled. The following arbitrary method 

 was used in distributing these errors : 



First. It will be seen that if any one of these backsights become 

 fixed, the others of necessity are fixed also, as the angles between them 

 are already fixed by the location of the point. If we assume a series of 

 swings, say of the sight from Ouray to Hunt's, and tabulate the result 

 as below, we get a series of columns of swings, each one of which will 

 satisfy the conditions of the angles at Ouray, and give a possible ar- 

 rangement of the swings : 



Table of swings from Mount Ouray. 





-5 



-1 



■V 



II 

 -i 

 -2 



+6 



+7 



-3 

 -3 



+5 

 +6 



-2 

 -4 



+4 

 +5 



-1 



-5 



+3 



+4 



II 

 -0 

 -6 



+2 

 +3 





II 



+2 

 -4 



+0 



+1 



II 



+3 

 -3 

 -1 



+0 



II 



+4 

 -2 

 -2 

 -1 



/' 





Station 2'.i 



—3 



Station 24 



-9. 









21 



19 



.17 



15 



13 



11 



9 



7 



7/1 



9 



11 



Adding up these columns, we get the aggregate swings each would 

 require. Other things being equal, it is best to select the column which 

 gives the least aggregate of swings, which in this case is marked a; but 

 there may sometimes be reasons why one point is more liable to error 

 than the others, and in that case another column may be selected if its sum 

 differs but little from the smaller sum ; but, as a rule, it is best always 

 to choose the column that gives the least aggregate swing. These cor- 

 rections, both fore and back, should be recorded immediately in some 



