STAKING OUT SIDE STAKES.

301

such that An' would be the point where, if the ground werelevel, the side stake would come), and the reading n'n" (?•')taken there, 4 feet; n'rn‘ would = 10—4, or r- — r = 6 feet; mea-sure 6 feet further away from A to p, and without moving thelevel, read off p'p" (r") = 2 feet.

Now po or pr—n'n—p'p"—k —2=2 feet, measure 2 feetstill further from A. Let the next reading be 1 foot, then2—1 will be the distance still further to be taken, thus makingthe whole distance Ay=44 feet. This will be in the directionup the slope; Ax in the direction downwards will be less thanAn. AC (r) will of course read as before, 10 feet, [shouldthe ground, however, fall so much as to be more than 12 feetunder the level line of the telescope LS', then it will be ne-cessary to take, if possible, all the readings on the right of thecentre line first, and move the instrument for those on theleft,] and let the reading at n, n" be 16 feet (r) nm—nri"—Ac—r —r=l 6—10 ~%—no~np. Now, because the second read-ing is greater than the first, measure np— 6 feet toioards A,and read pp'"(r") 14 feet; nri"— pp"—po~r — r"~ 16—14=2 :because the third reading is less than the second, measure thistwo feet away from A; the next reading will be found greaterthan r"\ let r"—15 feet; measure this therefore or

15—14=1 back towards A to x. The distance Ax thus takenwill be found to be

= 35—(16—10) + (16—14) —(15—14)=30fect,

and generally where r, r‘, r", r'“. &e., are the respective read-ings, and Ay represents the rising ground, and Ax the falling:then in a cutting, and vice versa, in an embankment,

Ay=-|- -j-«(/t)+ ?«(?•—r')-|-?H(r'— r")-\-m(r“—r ll/ ), &e.and A— m(r '—;•) — r"), &c.

Now ~ will probably vary with every chain; they