$($a$)$ Using the $"3$ zeros $3"$ and $"5$ zeros $5"$ rules, calculate the practical effect of an angular error of $6^{\text{'}\text{'}}$ of arc over a distance of $1\mathrm{.}6km$ and of an angular error of $1^{\text{'}}{30}^{\text{'}\text{'}}$ of arc at $750m.$

$($b$)$ Explain the difference between precision and accuracy. Draw a "bell curve" graph of precise but inaccurate results. What factors would contribute to precision and accuracy when making distance and direction observations with a Total Station and reducing these to the ellipsoid?

$($c$)$ You are planning to observe $3$ sets $($arcs$)$ of horizontal and vertical angle observations to distant trigonometrical points.

$($i$)$ What horizontal circle settings would you use in order to minimise circle graduation errors for the three arcs?

$($ii$)$ What observing procedure would you use, what would you avoid, and what bookers checks should be made?

$($iii$)$ What times of the day would you choose to observe horizontals to very distant trigs to the East and West respectively, and what time would you use for vertical observations?

$($d$)$ How would a surveyor normally obtain values for:

$($i$)$ Prism Constant $($PC$)$

$($ii$)$ Instrument Constant $($IC$)$

$($iii$)$ Instrument Scale Factor?

$($a$)$ Using a sketch, explain the difference between solar time as read on our clocks and sidereal time as used by GPS satellites.

$($b$)$ What five items are included in the navigation code$/$message modulated onto L$1$ and L$2?$

$($c$)$

$($i$)$ Draw and label two sketches that illustrate the difference between double differencing and triple differencing in GPS$.$

$($ii$)$ What three errors are removed by double differencing?

$($iii$)$ What is the main reason why GPS receivers use triple differencing before returning to double differencing?

$($d$)$ With the aid of a clear sketch or sketches, explain why a failure to use "break lines" may result in erroneous contours in a topographical survey, and how "triangle swapping" techniques may achieve the same effect as using break lines.