BOOK V. 



139 



the major spaces on the rod, and those which proceed further, mark the 

 middle of the intervening space which lies between the others. The 

 straight lines, which run from the fifth to the sixth semi-circular line, show 

 nothing further. Nor does the line which measures the half, show anything 

 when it has already passed from the sixth straight line to the base of the 

 hemicycle. When the hemicycle is applied to the cord, if its tongue indicates 

 the sixth straight line which lies between the second and third semi-circular 

 lines, the surveyor counts on the rod six lines which separate the minor 

 spaces, and if the length of this portion of the rod be taken from the second 

 cord, as many times as the cord itself is half-fathoms long, the remaining 

 length of cord shows the distance the tunnel must be driven to reach under 

 the shaft. But if he sees that the tongue has gone so far that it marks the 

 sixth line between the fourth and fifth semi-circular lines, he counts six lines 

 which separate the major spaces on the rod ; and this entire space is deducted 

 from the length of the second cord, as many times as the number of whole 

 fathoms which the cord contains ; and then, in like manner, the remaining 

 length of cord shows us the distance the tunnel must be driven to reach 

 under the shaft. 19 



STRETCHED CORDS : A FIRST CORD. B SECOND CORD. 



D TRIANGLE. 



C THIRD CORD. 



19 It is interesting to note that the ratio of any length so obtained, to the whole length 

 of the staff, is practically equal to the cosine of the angle represented by the corresponding 

 gradation on the hemicycle ; the gradations on the rod forming a fairly accurate table of 

 cosines. 



