WILSON ON GEOGRAPHICAL WORK OF THE SURVEY. 73 L 



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. Supposiug an error of a minute in a reading, 

 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 distance of 

 10 miles and 23 feet for a distance of 15 miles. If, as is sometimes the 

 case, the error be more than one minute, the error in the elevation will 

 be still greater. Another large and uncertain element in the problem 

 is refraction, which in the high mountains is so changeable as to add 

 much to the uncertainty of the results. In many cases tbe 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 sur- 

 rounding peaks, and especially to previous stations. Had the foresight 

 and backsights between the several stations been simultaneous, the 

 error of the refraction correction would have been very nearly neutral- 

 ized ; 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 iil finding some peaks which had been sighted from 

 both. With this material on hand, the distances were obtained from 

 Mr. Wilson's plot of his secondary triangulation, which will not i)rob- 

 ably 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 dis- 

 tances 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 difference 

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

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

 tion of the difference of level is not sufficient. For a still fluer approx- 

 imation, wherever vertical angles had been taken from two stations 

 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 

 another 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 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 

 followiug 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: — 

 f7/< =0.00000485 K A i 0.0000006G7 K^: 



