January 4, 1907] 



SCIENCE 



15 



The diiSeulties of surveying the mine are 

 not markedly increased by depth, except in 

 the case of vertical shafts. When these 

 are deep, and it becomes necessary to carry 

 dovsrn an azimuth from the surface by 

 means of two plumb lines hung in the shaft, 

 there is presented a problem of considerable 

 difSculty. It is almost impossible to free 

 the lines entirely from disturbing influences 

 which displace them from their normal 

 positions. If either lines or plumb bobs 

 are of magnetic material the presence of 

 iron pipes in the shaft may result in seri- 

 ously disturbing them. Falling water may 

 be in such quantity and so directed as also 

 to affect the position of the lines. 



However, the air currents, which can not 

 be wholly eliminated, whatever the precau- 

 tions taken, are the most serious cause of 

 disturbance. The temperature at the bot- 

 tom of the shaft is higher than that at the 

 top, and in consequence convection currents 

 are formed. The heat supplied from the 

 surrounding rock keeps them up. Indeed, 

 with moderately steady temperature at the 

 surface, and with the shaft idle, a remark- 

 ably stable condition of these air currents 

 may come about. Elsewhere observations 

 have been published by the writer,^ show- 

 ing that their effect on a plumb line may 

 remain sensibly constant for hours at a 

 time while deflecting the line from its ver- 

 tical position. The stability of the currents 

 is made possible by the large cross section 

 of the vertical shafts, 10 feet by 22 feet to 

 10 feet by 30 feet outside of timbers, thus 

 giving a large air body, and the constancy 

 of the rock temperatures, and the supply 

 of heat through the shaft walls. When we 

 take account of the fact that a force equiva- 

 lent to a horizontal pressure of 10 grains 

 on a 60-pound plumb-bob suspended by a 

 line 4,000 feet long will displace the bob 

 one tenth of a foot from its normal posi- 

 ' See Engineering and Mining Journal, April 26, 

 1902, also Electrical World, April 26, 1902. 



tion, it is easy to see how apparently slight 

 causes may produce appreciable error in 

 azimuth. 



General attention was first attracted to 

 this problem by the very noticeable di- 

 vergence of two long plumb lines hung in 

 shaft number five of the Tamarack mine. 

 Of course, divergence alone would not af- 

 fect azimuth, but the question confronting 

 the surveyor is whether the divergence may 

 not be due to some cause which may also 

 displace one or both of the lines in a direc- 

 tion perpendicular to their plane. In the 

 case mentioned it required a great deal of 

 investigation and experiment to fasten the 

 responsibility on the currents of air. 



It is remarkable how many persons are 

 ready to accept as an explanation of such 

 divergence the statement that there is an 

 excess of gravitation on each bob horizon- 

 tally toward the end wall nearest to which 

 it hangs. All are familiar with the picture 

 in the text-books of the plumb line hang- 

 ing near the face of a precipice being de- 

 flected from the vertical by the attraction 

 of the mountain mass. The idea so stri- 

 kingly conveyed by this picture while quali- 

 tatively correct seems in most minds to be 

 quantitatively wrong. There is an excess 

 of attraction on the bobs as stated, but its 

 amount is far too insignificant to account 

 for any observed divergence. At Tamarack 

 number five it could account for no more 

 than one one-thousandth of a foot. The 

 convergence of vertical lines in that in- 

 stance is over three times this amount. 



The fact remains that the surveyor who 

 must thus transfer an azimuth from the 

 surface down a very deep shaft has a prob- 

 lem the proper handling of which must in- 

 volve a careful study of the local condi- 

 tions, particularly in regard to air circula- 

 tion. 



Increased depth tends to lessen the out- 

 put of a given shaft, and in the effort to 

 prevent this, and also to reduce hoisting 



