BOOK V. 



137 



shaft will roach the bottom of thr tunnel whm it has hern sunk a further 

 light fathoms. 



A TRIANGLE HAVING ALL ITS ANGLES ACUTE AND ITS THREE SIDES UNEQUAL. 



This is the method of the surveyor in measuring the mountain, if the 

 principal vein descends inclined into the depths of the earth or the transverse 

 vein is vertical. But if they are both inclined, the surveyor uses the same 

 method, or he measures the slope of the mountain separately from the slope 

 of the shaft. Next, if a transverse vein in which a tunnel is driven does not 

 cut the principal vein in that spot where the shaft is sunk, then it is necessary 

 for the starting point of the survey to be in the other shaft in which the 

 transverse vein cuts the principal vein. But if there be no shaft on that spot 

 where the outcrop of the transverse vein cuts the outcrop of the principal 

 vein, then the surface of the ground which lies between the shafts must 

 be measured, or that between the shaft and the place where the outcrop of 

 the one vein intersects the outcrop of the other. 



Some surveyors, although they use three cords, nevertheless ascertain 

 only the length of a tunnel by that method of measuring, and determine 

 the depth of a shaft by another method ; that is, by the method by 

 which cords are re-stretched on a level part of the mountain or in 

 a valley, or in flat fields, and are measured again. Some, however, do 

 not employ this method in surveying the depth of a shaft and the 

 length of a tunnel, but use only two cords, a graduated hemicycle^^ and a 

 rod half a fathom long. They suspend in the shaft one cord, fastened 

 from the upper pole and weighted, just as the others do. Fastened to the 

 upper end of this cord, they stretch another right down the slope of the mountain 

 to the bottom of the mouth of the tunnel and fix it to the ground. Then to 

 the upper part of this second cord they apply on its lower side the broad part 

 of a hemicycle. This consists of half a circle, the outer margin of which is 

 covered with wax, and within this are six semi-circular lines. From the 



^^The names of the instruments here described in the original text, their German 

 equivalents in the Glossary, and the terms adopted in translation are given below : — 



