GEODESY, Ixi 



log log log log 



s 4.81308 s 4.81308 X sin ajo 4.647 s sin a,, 4.647 



cos a, 2 9.86392 sin a,._, 9.83402 s sin a^-, 4.647 s cos a,o 4.677 



(7i 7.99495 sec ^1 o. 10S90 a.2 0.279 '^- 0-688 



^ 7-9931^ ''^ °-733 



-<4i 2.67195 Bi 2.74916 -(42 9.573 Bo 0.012 



sin <^i 9.79795 Q 0.057 



Ci 2.547 1 1 



log 



A, - 469."84 A + 56i."25 C, - 352-"46 Aa 2.54570 



^, - o."37 B.2— i."o3 C, + i."i4 AA. 2.74S36 



A(/) - 47o."2i AX + 56o."22 Aa — 35i."32 sin ^(c^o + ^i) 9-79734 



15. Trigonometric Leveling. 



a. Computation of heights from observed zenith distances. 



Let s = sea lev-el distance between two points /^i and J'.,} 



Hi, H.y =■ heights above sea level of I\ and Bo, 

 Zi = observed zenith distance of I^o from Bi, 

 z., = observed zenith distance of Bi from B2, 



p = radius of curvature of vertical section at B^ through Bo, or at B2 

 through Bi, the curvature being sensibly the same for both for this 

 purpose, 

 C= angle at centre of curvature subtended by s, 

 iHx, W2 = coefficients of refraction at Bx and B2, 

 Asi, AsTj = angles of refraction at B^ and Bo. 



Then, the fundamental relations are 



C = - , Ac:i = WjC, A02 = WgC, , N 



Zi + 2o + A^i 4- A^. = 180° + C, 



H2-H, = s tan ^(^2 + ^z^ - z, - A^,) (i + ^'tf' + ^+ • • •)• (2) 



When the zenith distances z^ and z^ are simultaneous, or when A^i and ^Zo are 

 assumed to be equal, (2) becomes 



H-Hx^sl^v. \iz2 - .,) (x + ^±^^ + ^ + . . .). (3) 



For the case of a single observed zenith distance z^, say, and a known or 

 assumed value of ;;; = Wj = m.,, the following formula may be applied : 



H2- Hx = s cot z, + — ^ s" + s" COt^ 2i. (4) 



The coefficient of refraction m varies very greatly under different atmospheric 

 conditions. Its average value for land lines is about 0,07. The following table 

 gives the values of log ^(i — 2 w) and log (i — in) for values of ni ranging from 

 0.05 to o.io. It is taken from Appendix 18, Report of U. S. Coast and Geodetic 



