November q, 1905] 



NATURE 



31 



been so efficiently carried out by Prof. Rosenmund 

 of Zurich. 



Before the work of boring' and perforation can be 

 begun, there are three elements which have to be 

 determined with an accuracy which must be greater 

 in proportion to the difficulties of construction. These 

 are the direction, the length, and the altitude above 

 sea-level. Assuming that the places of entrance and 

 exit of the tunnel have been marked bv suitable pillars, 

 the determination of these three elements begins; and 

 that of the level is the least difficult, because the 

 surveying engineer trusts to direct measurements. 

 By the aid of accurate levelling instruments, it is 

 possible to derive the difference in altitude of two 

 stations 50 kilometres apart with no greater error 

 than 3 cm. This is effected by the use of the 

 levelling staff, which is read by means of an accurate 

 level, the staff being placed vertically at two stations 

 a convenient distance apart, and the sum of the 

 differences of each pair of readings being taken. The 

 surveyor apparently trusts entirely to the accuracy 

 with which his theodolite can be levelled. Several 

 determinations of the difference of level of the two 

 ends of the tunnel were made, but between the two 

 last there was a discrepancy of only 2 cm., a more 

 than sufficient degree of accuracy. The actual differ- 

 ence of level between the two ends was 52.439 metres. 



The second element, that of the length of the 

 tunnel, is to be derived indirectly from triangula- 

 tion, the length being reckoned from the same points 

 that have served for the determination of difference 

 of level, and, as a matter of fact, these points are 

 at some distance from the actual openings. A base 

 line being given, the construction and the solution 

 of the triangles present little difficulty, for here great 

 accuracy is not required, and the probable error that 

 Prof. Rosenmund was content to leave in his work 

 amounted to ±0-7 metre. The distances measured 

 are as follows : — 



The length between the columns 

 ing the axis of tunnel... 



Distance of northern column 

 tunnel opening ... 



Distance of southern column 

 tunnel opening ... 



Actual length of tunnel ... 



3I/-73 



44-84 

 72871 



The third element, that of direction, at all times 

 presents some difficulty, and, in the case of moun- 

 tains, where local attraction enters as a disturbing 

 factor, the problem requires very delicate treatment. 

 In a tunnel 20 kilometres long, an error in direction 

 of one minute, which is usually the limit of accuracy 

 sought in technical work, would produce an error of 

 6 metres, and the tenth part of such an error would 

 be too great. Recourse is necessarily had to triangu- 

 lation, and the angular measurements must be made 

 with the greatest care. Well-defined signal posts 

 must be erected to mark the angles of the selected 

 triangles, and the points of reference in these pillars 

 defined with the utmost accuracy. The form which 

 Prof. Rosenmund preferred consisted of cylindrical 

 towers of brick about eight feet high, of which the 

 axis was an iron tube the upper edge of which reached 

 the top surface of the tower. A wooden pole carried 

 this iron tube vertically upwards, and the whole was 

 surmounted by a conical tin covering, the highest 

 point of which was vertically over the centre of the 

 iron axis. Eleven of these piers were erected, and 

 when signals were made from any pillar the conical 

 top was removed, and the theodolite was placed cen- 

 trally over the middle of the iron tube in the cylin- 

 drical tower, which afforded a solid support for the 



NO. 1880, VOL. 73] 



instrument and permitted accurate observation of the 

 other stations. With the care exercised, it might have 

 been anticipated that the sum of the angles of any 

 triangle would differ from 180 by the known amount 

 of the spherical excess, within the errors of observ- 

 ation. But the discrepancies were much larger, vary- 

 ing from 4 to 8-5 seconds, and these deviations could 

 be explained only by attributing to the mountain an 

 attractive force, which sensibly displaced the direc- 

 tion of the plumb-line. In other words, the theo- 

 dolite was not placed horizontally. The amount of 

 the deviations from the vertical, with the azimuths in 

 which thev occur, is shown in the following table : — 



Station from vertical 



North point of axis... ... i_vo 



Oberried ... ... ■■■ iim 



Birgischwald 16-4 



Rosswald ... ... ■•■ -\v" 



Spitzhorn ... ... ... 175 



Monte Leone... ... ... 0-0 



Hullehorn ... ... ... 8-2 



Seehorn ... ... ■■■ 5-6 



Alpe Wolf 114 



(ienuina ... ... ... 91 



South point of axis... ... 58 



Assuming these deviations from the vertical to arise 

 from the attraction of the mountain mass, an hypo- 

 thesis which was confirmed by rigorous astronomical 

 observation, it was found possible to reduce the 

 closing errors of the triangles very materially. The 

 solution of the whole network of triangulation showed 

 that the tunnel's axis was fixed with a probable error 

 of ±o"-7, and that the direction of the tunnel could 

 be fixed with sufficient accuracy by pointing the 

 telescope, placed on one of the piers at the entrance 

 of the tunnel, to any other signal tower, and revolving 

 the telescope through a known angle. 



It would be interesting to enter into the details 

 by which the path of the tunnel was checked as the 

 work progressed, more especially as curious refractive 

 effects, akin to those seen in " mirage," occurred to 

 render the observations somewhat difficult and un- 

 certain. These disturbing effects were more noticeable 

 when observing towards the north end of the tunnel, 

 where the difference of temperature between the 

 internal and external atmosphere was greatest. On 

 the southern side, the external air being warmer than 

 on the north side, the " mirage " was not so con- 

 spicuous. But we have only space to refer to the 

 degree of success which resulted from the care 

 bestowed on this difficult undertaking ,i success 

 which could not be adequately tested until the junc- 

 tion of the engineering parties in the middle of the 

 tunnel was effected. To take the three elements in 

 order, it was found that the level agreed within 

 o-i metre of the calculations. The length as measured 

 differed 2 metres from the calculated value, but, as 

 mentioned, this was a factor in which great accuracy 

 was not needed, because, if the direction were given 

 correctly, it was only necessary to continue the 

 borings until the engineers from the south and north 

 sides met in the middle. The direction was most 

 satisfactorv. The wall of one tunnel was absolutely 

 continuous with the wall of the other; an attempt 

 was made to compare the opposite walls of the tunnel 

 for confirmation, but this attempt was frustrated by 

 a projecting piece of rock. No better result could 

 have been anticipated, and the utmost credit attaches 

 to Prof. Rosenmund and his assistants. 



W. E. P. 



