BOOK V.

139

the major spaces on the rod, and those which proceed further, mark themiddle of the intervening space which lies between the others. Thestraight lines, which run from the fifth to the sixth semi-circular line, shownothing further. Nor does the line which measures the half, show anythingwhen it has already passed from the sixth straight line to the base of thehemicycle. When the hemicycle is applied to the cord, if its tongue indicatesthe sixth straight line which lies between the second and third semi-circularlines, the surveyor counts on the rod six lines which separate the minorspaces, and if the length of this portion of the rod be taken from the secondcord, as many times as the cord itself is half-fathoms long, the remaininglength of cord shows the distance the tunnel must be driven to reach underthe shaft. But if he sees that the tongue has gone so far that it marks thesixth line between the fourth and fifth semi-circular lines, he counts six lineswhich separate the major spaces on the rod ; and this entire space is deductedfrom the length of the second cord, as many times as the number of wholefathoms which the cord contains ; and then, in like manner, the remaininglength of cord shows us the distance the tunnel must be driven to reachunder the shaft . 19

Stretched

cords : A —First cord. B —Second cord. C —Third cord.D —Triangle.

19It •

°f the staff^i^nr 16 to note t ^ e ra ^° °f an Y length so obtained, to the whole lengthgradation on theh lc . Y equal to the cosine of the angle represented by the correspondingcrvqin ac emicycie ; the gradations on the rod forming a fairly accurate table of