630 GEOLOGICAL SURVEY OF THE TERRITORIES. 



be determined independently of the barometer. The elevations should, 

 be known to within five feet to satisfy the present needs of meteor- 

 ology. 



The use of this large and admirably-arranged collection was kindly 

 offered me, and to its assistance I am largely indebted for the complete- 

 ness of this investigation. 



The principal difficulties encountered in the present work were : the ' 

 discrepancies between the different official reports of the profiles of the 

 same railroad or canal ; the difficulty of finding the points referred, to 

 at the ends of the profiles; the difficulty of connecting them with the 

 mean surface of the ocean ; and. the clerical errors or mistakes in figures 

 evidently due to.coi)ying. 



The differences between the reports of the profile of a railroad or canal 

 seem to arise from want of care in computing from the level-notes, and 

 from the fact that they are actually reports of different levelings which 

 do not agree. Generally, a preliminary line of levels is first run over 

 the whole line of the railroad, and bench-marks established ; then, when 

 .construction is commenced, the different divisions of the line each take 

 one of these bench-marks as the datum for their levels, and build their 

 part of the work from this point. Thus, the line as a wbole is really 

 built from many separate datum-planes. Where the different divisions 

 join, they connect their levels so that the relative height of the different 

 datum-iilanes may be calculated, and all may be reduced to one base. 

 The notes of these connections are generally correct ; but, in the first 

 calculations of them, many errors almost always occur, incident upon the 

 hurry and confusion of closing the work and dismissing the engineers 

 for the sake of economy. After the railroad is running, and the chief 

 engineer has leisure to examine the records of his office, errors are found 

 in the calculations of his profiles, and the whole is reviewed and a new 

 profile constructed. It often happens that, after a number of years, 

 either a part or the whole of line is releveled, and a new profile is the 

 result. 



Among the profiles which I have examined are representatives of all 

 these classes : 



First. Profiles of preliminary lines of survey. 



Second. Profiles from first calculation of constructed lines. 



Third. Profiles of final calculation of constructed lines. 



Fourth. Profiles of final releveling of constructed lines. 



Fifth. Profiles made up in the offices by mixing the results of two or 

 more of the above classes. 



It is evident that these classes must differ very much in accuracy ; and 

 necessarily the first step in this examination was to determine uj)on 

 methods of testing the profiles so as to fix their j)roper relative weights. 

 This was a very complicated and difficult process on account of the num- 

 ber of factors to be considered. Some of the principles may, however, 

 be stated. 



If two points were connected by several independent lines of railroad 

 or canal, the agreement of these lines as to the difference of altitude of 

 the termini was considered one of the best tests of accuracy. 



If one of these lines was a canal which had been releveled many times, 

 and the termini carefully connected with the other lines, and of which we 

 had a final official report, this was taken as true and used as a standard 

 of comparison for the accuracy of the other lines. 



If the lines were all canal-levels, their relative weight was determined 

 by the number of times they had been releveled, the recentness of the 

 work, the recentness of the official report, and its detailed character. 



