282 REPORT UNITED STATES GEOLOGICAL SURVEY. 



These two measurements of tbis line, 5^ miles long, dififer only abont 

 2 inches, which is a much more accurate result than that obtained at 

 the Denver base, where the tape was laid on the railroad track and the 

 temperature of a thermometer exposed to the sun was assumed to be 

 the same as that of the tape. San Luis base is, of course, entitled to 

 much more weight than the Denver base in the final adjustment of the 

 triangulation. 



AZIMUTH OF SAN LUIS BASE. 



For determining the azimuth of the base, six observations were made 

 on Polaris at the north end of the base, September 5, and four observa- 

 tions, September 6, at the south end of the base; six observations had 

 been taken August 30, and ten in the evening of August 31. The mean 

 of the observations at the south end of the base, being reduced to the 

 north end, gave at the north end — 



The azimuth of base by south-end observations 340° 49' 29". 32 



The azimuth of base by north-end observations 340<^ 49' 24". 62 



In connecting the triangulation brought down from the Denver base 

 with the expansion from the San Luis base, it was found that there was 

 a difference of 9^ inches to the mile in length between the two systems, 

 that from Denver being the greater. This difference is due, no doubt, 

 partly to the errors in measurements of the two bases, and partly to the 

 accumulatingerrorsof the work as brought from Denver. In this scheme 

 Pike's Peak enters as one of the priucipal points, and owing to its very 

 flat top, it was difficult to locate with a great degree of accuracy. 



The accuracy of the triangulation may be judged by the closure of 

 triangles ; the observed angles of each triangle should sum up to 180° 

 plus the spherical excess. 



The fi.rst sixteen complete triangles used in expanding from the Den- 

 ver base to the high mountain-peaks, summed up with a mean error of 

 closure of six and four-tenths seconds (6".4), and the forty-seven triangles 

 used in carrying the work as far south as the San Luis base and west 

 to the Holy Cross, had a mean error of closure of ten and three-tenths 

 seconds (l6".3). 



In the whole scheme of triangulation of Colorado, there has been used 

 in the determination of the occupied stations one hundred and forty- 

 three complete triangles, with a mean error of closure of thirteen and 

 three-tenths seconds (13".3). 



These errors may be considered small when we consider that natural 

 points were used as stations, and that the angles were taken with an 

 8-inch theodolite, whose vernier was graduated only to ten seconds of 

 arc and reading to five seconds. 



METHOD OF ADJUSTING THE TRIANGULATION. 



I present below a general description of the methods used in the ad- 

 justment of the work, omitting the minor details. In expanding the 

 work from the measured bases, signals were established, forming as 

 nearly equilateral triangles as possible, and the observations on these 

 were repeated several times on different parts of the circle. The errors 

 of closure in this way were reduced to a minimum, and this small error 

 in the first triangles was distributed equally among the three angles. 

 After locating some two or three points in this manner, they were then 

 connected with the mountain staiions, on which monuments had been 

 previously built, in order that they might be more accurately sighted, in 

 the following manner ; 



