203 



case on the same day. From each of two stations I always succeeded 

 in finding some pealis which had been sighted from both. With this 

 material on hand the distances were obtained from Mr. Wilson's plot of 

 his secondary triangnlation which will not probably involve, in any case 

 used, a greater error than five hundredths of a mile, which includes 

 the error due to shrinkage of paper, as these distances were all 

 hastily taken oii from the map with a scale. Having then the horizontal 

 distance between the two stations and the angle of elevation or depres- 

 sion from one to the other, of course the difference of level is deter- 

 mined. But on account of the errors which have crept into these angles 

 from the causes above mentioned one determination of the differ- 

 ence of level is not sufficient. The back sight is then calculated, and 

 brings a different result. For a still finer approximation, wherever ver- 

 tical angles had been taken from the two stations to the same ])oint, 

 the heigTit of that above and below each station was calculated. From 

 this, another determination of the difference in the height of the two 

 stations was determined. Then the height of another unvisited point 

 was calculated, and so on for all the near i)oints sighted from both sta- 

 tions. Each point gives one determination of the difference of the two 

 stations. In some cases it will be found that one result is far out from 

 the rest. This may be due to the fact that you have used sights to dif- 

 ferent points, which have received, by mistake, the same number in the 

 notes. Such cases are thrown out, and a mean of the rest assumed 

 as the true difference of level. It was found that, on account of errors 

 of refraction and imperfections of the instrument, sights over fifteen 

 miles could not be depended on at all. In the following calculations no 

 sights of that length were used, and in fact very few over ten miles 

 have been used at all. 



For convenience in making the calculation, the following formula was 

 used, taken from Lee's tables: 



dh = 0.00000485 K A ± 0.000000667 K^ 

 In which ^/t is the difference of level of the two points, K the horizontal dis- 

 tance in yards, and A the number of seconds in the vertical angle used. In 

 this formula are contained corrections for both curvature and refraction, 

 the latter element being assumed equal to 0.078 of the curvature. On ex- 

 amining the notes carefully it was found that there were sights to many 

 hundred different peaks, audit became a difficult problem to utilize all this 

 material, and at the same time do it according to a system. After a num- 

 ber of experiments on different methods it was found that to bring order 

 out of this chaos, it was necessary to take up each link in the chain sep- 

 arately, 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 was 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 differences of level might be transferred through a poorly- 

 determined line, thus vitiating all with 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 Uncompahgre 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 cov- 

 ered the vrhole mass of mountains. Uther stations, which could not be 



