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11 <br />DIRECTIONS FOR USE OF TABLES <br />41, <br />Distance o <br />stake for any <br />TABLE No. 1. <br />f slope stake from side or shoulder <br />1 I2 to 1. <br />If ground is nearlylevel, the cut, or fill at side <br />stake is located by the double entry method in <br />left column and top row. The. number in body <br />of table in same row and column gives di <br />from side stake to slope stake. If <br />level estimate the difference in elegy <br />the side stake and sl <br />_ amount if cut, <br />width roadway, slope <br />aground <br />stance <br />is not <br />lion between <br />oPe wake, Lower target by this <br />elevate il fill. Add this amount <br />fn cut or fill and find distance in table. Set up <br />rod at this point, <br />and line of sight <br />target. If it does not make, the slight <br />necessary". <br />TABLE No. 9. <br />should cut <br />adjustnient <br />o find Tangent and External for curve of <br />any other degree, divide by degree of curve and <br />add correction found i*n column of corrections. <br />Degree of curve with a given I may be found <br />iby dividing tangent,, (or external), opposite I 1)y <br />given tangent, (or external). <br />IMe distance from a point on the tangent to <br />the curve is very nearly the square of the tangent <br />length divided by twice the radius. <br />a <br />i <br />r.� <br />F <br />TABLE II <br />r <br />TRIGQNUMETRIC FORMULIIZEo <br />MOPL A --� ,� Z B - = L POiN = Z LPL <br />R = OB c <br />a a <br />yin A a _.._ cos B LP <br />C 1 <br />b b <br />cos A_.' C --- b sin B OL <br />a <br />fan A -- � � MQ ..r. MQ <br />b _ OM1 M� cad E MQ <br />cat A ._.------- NT � NT � <br />ON i NIT tan B -- NIT <br />sec A = OQ � OQ _.... p ._ esc B0 N-1 <br />-- Q <br />OT OT <br />Curvature o£ Earth's surface about 0.7 feetin I mike <br />Curvature in feet = 0,667 (Dist... in miles)' <br />Difference between are and chord length, 0.00' feet in I I 2 miles <br />Probable error of a single observation = 0.6754 � V-% x <br />n ---- 1 <br />Error in chaining o� O.Q� feet in 100 feet: <br />Due t o--- <br />l.. Leiigth of tape error of 0.0 1 feet <br />2. Alignment, One end 1.4 feet out of dine <br />3. Sag of tape at centre of 0.61 feet. <br />4. Temperature di*fference of 150 <br />5.. Dinerence of pull of 15 lbs. <br />STADIA REDUCTION FORMULAE,, <br />Horizontal Distance = R -- R, sin a -'- C'. cis a <br />Vertical Distance = R f sin 2 a + C sin a <br />distance from 0b-*r,-,1,.et glass to crass hairs <br />R = Reading X distance between cross hairs <br />4 <br />C distance from abject glass to cross hairs + -Aistance fronpt Abject <br />Mass to center of instrument. <br />a ankle of elevation for mid Reading <br />r <br />6 <br />4. <br />