206 Transactions. — Miscellaneous. 



First Pair of Triangles. 

 Side. Bearing. Distance. Bear £f "Stance. 



Links. Links. 



P P 4 53° 03' 07" 27833-3 



P 4 P x 20° 13' 44-6" 290701 + 1-7" - 0-2 



P, P 130° 51' 390" 16120-8 - 03" - 03 



P a P 67° 42' 41-7" 34845-1 + 1-0" - 1-7 



P 2 P 220° 09' 221" 31090-6 - 2-4" - 1-6 



Second Pair of Triangles. ^.„ 

 Side. Bearing. Distance. -p Pyrenees 



Bearing. Distance. 



Links. Links. 



27833-3 



40206-6 - 3-5" + 1-0 

 17873-0 + 0-4" + 1-2 



22497-3 + 0-3" + 2-1 

 31090-6 + 2-6" + 2-7 



The columns headed "Differences" give the differences 

 between the least-square values and the values obained in I. 



A comparison of the values of P 2 P as calculated from 

 each pair of triangles shows that the bearing and distance 

 agree exactly. 



The process of adjustment here described completely 

 satisfies the geometrical conditions of the figure, and it does 

 so by making the sums of the corrections the least possible. 



For the theory of the adjustment reference must be made 

 to any of the treatises on least squares. See in particular 

 "Geodesy," by Colonel A. E. Clarke, C.B., Oxford, 1880, 

 pp. 217-225. The method here outlined differs from that 

 given in Clarke, inasmuch as the triangular error is applied 

 before the condition equations are derived, thus lightening 

 the subsequent work very considerably, and thereby lessening 

 the risk of numerical slips. 



This method also permits of comparison between the 

 ordinary triangular adjustment and the least-square adjust- 

 ment, as will be seen by comparing columns 3 and 11, where 

 column 11 shows the additional corrections necessary to 

 satisfy the geometrical conditions of the figure. 



In this example the calculation has been carried to two 

 decimal places of a second, not because the observations 

 justify so much refinement, but to avoid an unequal distribu- 

 tion of the errors, as, for instance, would occur in distributing 

 an error of 2" among three angles. If this is done to the 

 nearest second, then two angles would receive a correction of 

 one second each and the third angle would remain unaltered. 

 This would not have been consistent with the theory of 

 the adjustment, which provides that exactly one-third of the 

 triangular error must be applied to each angle. 



The whole of the calculations have been done on the Bruns- 

 viga calculating-machine with ease, rapidity, and certainty. 



