be accurately laid otf when necessary. The normal position is 

 indicated, and may be found in the dark, when the ribs in the 

 position indicated by the arrows are in conjunction and when the 

 index tooth of the knurled head is at the top. 



Shaft Plumbing with loaded piano wire is generally preferred 

 to telescopic sighting or optical plumbing in vertical shafts; not be- 

 cause it is more accurate, but the usual great depths and dense 

 atmospheres are inimicable to the latter methods. The accuracy of 

 orientation depends somewhat upon the distance between the wires 

 and the facility with which the theodolite is ranged into their 

 alignment. 



When the conditions are such that triangulation is necessary, it 

 has generally been assumed, without reference to the purpose in 

 hand, that the equilateral or isosceles triangle is the best shape. 

 Prior to 1850, however, utilizing the theory of errors as developed 

 byGauss and Bessel, Prof. Weisbach of Freiberg* showed that when 

 the side BC, Fig. 102, was not much greater than AB, in fact, when 



BC -T- AB was as small as 

 possible, and when the 

 angle BCA < 25', that the 

 crudities of linear measure- 

 ment would produce the 

 least effect upon the solu- 

 tion of the triangle. In 

 fixing the limit of errors 

 for angles and distances, 

 the comparison should, no 

 doubt, be consistent. There 

 is no use in measuring 

 angles with extreme accuracy and adjacent distances by close ap- 

 proximation. This theory is elaborately developed in a recent 

 workby Briggs ** which doubtless contains the most profound mathe- 

 matical treatmem of mine surveying problems now available. 



Professor W. H. Rayner of the Univ. of 111. has also con- 

 tributed the resuits of a scholarly investigation into the "Allowable- 

 Use of Small Angles in Surveying." We reproduce his argument 

 as published in th. Eng. Rec. Oct. 18, 1913. He says: 



"Every engineer and surveyor knows that for accurate results 

 he cannot rely on computations which involve the sines and tangents 

 of small angles, but his idea of just what relation exists between 

 these functions and the degree of accuracy he desires is usually 

 rather vague. 



* Die 



-J>,., 1859. 



** Tht T.ftect 



Markx-heidfkunsl, Julius Weisbach, 1st F.dn. % 11W); 2nd. 

 n, in Snrv<')in, ffmry JfrwgS, il,-ti,>t Watt L'ol- 



178 



