732 BULLETIN UNITED STATES GEOLOGICAL SURVEY. 



in which dh is the difference of level of the two points, K the hori- 

 zontal distance in yards, and A the number of seconds in the vertical 

 angle used. In this formula are contained corrections for both curva- 

 ture and retraction, the latter element being assumed equal to 0.078 of 

 the curvature. On examining the notes carefully it was found that 

 there were sights to many hundreds of different peaks, and it became a 

 difficult problem to utilize all this material and at the same time do it 

 according to a system. After a number of experiments on different 

 methods it was found that to bring order out of this chaos it was neces- 

 sary to take up each link in the chain separately, and use all the data 

 that could be found pertaining to it, and determine the difference of 

 level of these two stations finally. Next the same process had to be 

 gone through with the line from the second point to the next station 

 beyond, and so on. In doing this, it was found that some of these lines 

 were much better determined than the others. In finally reducing these 

 differences of level to a common datum point, this fact might multiply 

 the errors in the work^ For instance, a number of well- determined dif- 

 ferences of level might be transferred through a poorly-determined line, 

 thus vitiating all ^vith the error of the one. In order to obviate this the 

 following scheme was adopted : A central chain of well-determined lines 

 was carried through the heart of the mountain mass, from Mount Wilson, 

 the most westerly of the high peaks, to station 8, five miles east of Un- 

 compahgre Peak, in the northeast corner of the mass. From this main 

 line several secondary branches were carried wherever the short lines 

 could be well determined. This system covered the whole mass of 

 mountains. Other stations, which could not be well enough determined 

 independently, were connected with different points in the main lines. 

 In the central line we have the following parts: From Mount Wilson 

 to station 30, a peak east of it and distant 9.3 miles, is a fall of 383 feet, 

 which is the mean of five determinations having a range of 32 feet; 

 thence east to Sultan Mountain, a distance of 6.88 miles, with a fall of 

 536 feet, the mean of six determinations, range 23 feet; thence northeast 

 to station 16, distant 6.60 miles, a rise of 175 feet, the mean of nine de- 

 terminations, range 35 feet;- thence northeast to Hardie's Peak, 7.51 

 miles, a rise of 456 feet, the mean of eight determinations, range 54 feet; 

 thence north to Uncompahgre Peak, distant 11.14 miles, a rise of 238 

 feet, the mean of nine determinations, range 49 feet ; thence east to sta- 

 tion 8, distant 4.92 miles, a fall of 1,380 feet, the mean of ten determina- 

 tions, range 67 feet. This completes the central or trunk line, whose 

 length is 46.35 miles. From Sultan Mountain a branch was extended 

 eastward from this peak to station 25, distant 10.28 miles, a rise of 209 

 feet, the mean of twelve determinations, range 67 ; thence to Rio Grande 

 Pyramid, distant 8.63 miles, a rise of 197 feet, the mean of nineteen de- 

 terminations, range 95. From station 25, a branch extends to Mount 

 Oso, distant 7.29 miles, a rise of 64 feet, the mean of seven deter- 

 minations, range 37. From station 30, a secondary branch was ex- 



