SURVEYING

$\bar{x}=\ \frac{\sum x}{n}$

$\ v=x-\bar{x}$

$\left(x\sigma n-1\right)\ =S_x=\ \pm\ \sqrt{\frac{{\sum\left(x-\bar{x}\right)}^2}{n-1}}$

$S_{\bar{x}}=\ \pm\ \frac{S_x\ }{\sqrt n}$

${PE}_m=\pm0.6745\ S_{\bar{x}}$

${PE}_s=\pm0.6745\ S_x$

$RP\ or\ RE=\ \frac{PE}{mpv}$

$RP\ or\ RE=\ \frac{PE}{PV}$

$W=\ \frac{1}{{PE}^2}$

$W=\ \frac{1}{Distances}$

$W_E=\ \frac{1}{ \# \ of\ trials}$

$E_z=\ \pm\ \sqrt{\left(\frac{\delta(f)}{\delta a}\ E_a\right)^2+\left(\frac{\delta(f)}{\delta b}\ E_b\right)^2+\ldots}$

$E_{sum}=\ \pm\sqrt{{E_a}^2+{E_b}^2+{E_c}^2}$

$E_{series}=\ \pm\sqrt{{E_a}^2+{E_a}^2+{E_a}^2}$

$E_{product}=\ \pm\sqrt{\left({b\ E}_a\right)^2+\left({a\ E}_b\right)^2}$

$H.\ D.\ =\ kS\ +\ C$

$H.\ D.\ =\ \left(kS\ cos\theta\ +\ C\right)\ cos\theta$

$H.D.\ =\ \frac{1\ m}{tan\ \left(\frac{\theta}{2}\right)}$

Toe to Toe Distance of Different Foot
Heel to Heel Distance of Different Foot

Toe to Toe Distance of SAME Foot
Heel to Heel Distance of SAME Foot

$Pace\ Factor\ =\ \frac{distance\ \ travelled}{ave.\ no.\ \ of\ \ paces}$

$True\ Dist.\ =\ Meas.\ Dist.\ \pm\ Corr.\ $

$\frac{{c\ }_L^{single\ err.}\ }{Tape\ Length}\ =\ \frac{{C\ }_L^{total\ err.}}{Meas.\ Dist.}$

$C_t=\ \alpha\ L_{\dfrac{tape}{recd}}\ \left(T_{obs}-T_{stnd}\right)$

$C_p\ =\ \frac{\left(P_{obs}-\ P_{stnd}\right)\ L}{A\ E}$

$C_s\ =\ \frac{w^2\ L^3}{24\ \left(P_{obs}\right)^2}$

$C_h=\ \frac{h^2}{2L_{incl}}$

$C_h=\ \frac{h^2}{2\ L_{\ incl}}\ +\frac{h^2}{8\ \left(L_{incl}\right)^3}$

$C_h=\ L_{incl}\ \left(1-\ cos\ \theta\right)$

$\frac{{L\ '}_{equi.\ \ sea}}{{R\ \ \ }_{earth}^{6400\ km}}\ =\ \frac{L_{\ recd}}{R_{\ earth}+h}$

$elev\ {\rm BM}_B=\ elev\ {\rm BM}_A\ +\ \sum BS-\ \sum FS$

$elev\ {\rm BM}_B=\ \frac{elev\ {\rm BM}_{B1}\ +\ elev\ {\rm BM}_{B2}\ }{2}$
$elev\ {\rm BM}_{B1}=\ elev\ {\rm BM}_A\ +\ \sum{\rm BS}_1-\ \sum{\rm FS}_1$
$elev\ {\rm BM}_{B2}=\ elev\ {\rm BM}_A\ +\ \sum{\rm BS}_2-\ \sum{\rm FS}_2

$elev\ {\rm BM}_{B}=\ elev\ {\rm BM}_A\ +\ \sum{\rm BS}-\ \sum{\rm FS}$

$h=\ \frac{h_1\ +\ h_2\ }{2}$

$elev\ {\rm STA_B}=\ elev\ {\rm STA_A} +{ BS}-{IFS}$

There was a deviation of horizontal sight due to poor calibration

$e_{b1}\ =\ e_{a2}$

$e_{a1}\ =\ e_{b1}\ \ \ \nparallel \nparallel \ \ \ \frac{e_{a2}}{L_1}\ =\ \frac{e_{b2}}{L+\ L_1}$