A two$-$peg test is applied to determine the collimation error of an automatic level. First,

set up the instrument at X$,$ a point halfway between Station P and Station Q$.$ The staff

readings $p_l$ and $q_1$ are $1\mathrm{.}483m$ and $1\mathrm{.}942m$ respectively. Then, move the instrument to $Y,$

a point very close to Station $P.$ The staff readings $p_2$ and $q_2$ are $2\mathrm{.}131m$ and $2\mathrm{.}412m$

respectively. The distance between the two stations is $50m.$ Calculate the collimation

error, and the true difference in level between $P$ and $Q.$