300 EEPORT UNITED STATES GEOLOGICAL SURVEY. 



in a straight line from the central part of the San Juan country, while 

 the second is 125 miles distant. These distances are too great to give 

 accurate results with the barometer. At several points in the region we 

 succeeded in getting two readings at the same point at intervals of sev- 

 eral days, but finding that the resulting heights as calculated by ref- 

 erence to those distant bases did not agree well enough, it was resolved 

 to collect together all the data possible from the field-notes and see if 

 a fair trigonometric connection between the mountain-peaks could not 

 be established. The result was, under the circumstances, highly satis- 

 factory. It must be remembered, however, that the instrument used 

 read only to minutes of arc. Supj)osing an error of a minute in a read- 

 ing, which is not at all uncommon, the resulting error in the difference of 

 level of two peaks from a single observation will be 15.3 feet for a dis- 

 tance of 10 miles and 23 feet for a distance of 15 miles. If, as is some- 

 times the case, the error be more than one minute, the error in the ele- 

 vation will be still greater. Another large and uncertain element in 

 the problem is refraction, which in the high mountains is so changea- 

 ble as to add much to the uncertainty of the results. In many cases 

 the observations were taken during storms, and often the peaks were 

 sighted through breaks in the clouds, making the refraction still more 

 uncertain. From each station angles of elevation or depression were 

 taken to like surrounding peaks, and especially to previous stations. 

 Had the foresight and backsights between the several stations been sim- 

 ultaneous, the error of the refraction correction would have been very 

 nearly neutralized ; but these two sets of observations were never taken 

 at the same time, and in only one case on the same day. From each of 

 two stations I always succeeded in finding some peaks which had been 

 sighted from both. With this material on hand, the distances were ob- 

 tained from Mr. Wilson's plot of his secondary triangulation, which will 

 not probably involve, in any case used, a greater error than five-huu- 

 dredtbs of a mile, which includes the error due to shrinkage of paper, 

 as these distances were all hastily taken off from the map with a scale. 

 Having, then, the horizontal distance between the two stations, and the 

 angle of elevation or depression from one to the other, of course the dif- 

 ference of level can be determined. But on account of the errors which 

 have crept into these angles from the cause above mentioned, one de- 

 termination of the difference of level is not sufficient. For a still finer 

 approximation, wherever vertical angles had been taken from two sta- 

 tions to the same point, the height 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 an- 

 other unvisited point was calculated, and so on for all the near points 

 sighted from both stations. 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 sights 

 to the different points which have received by mistake the same number 

 in the notes have been used. 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 15 miles in length could not be depended on at all. In 

 the following calculation no sights of that length were used, and in fact 

 very few over 10 miles have been used. In making the calculation, the 

 following formula was used, taken from Lee's tables : 



dh = 0.00000485 K A ± 0.000000667 K^; 

 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 



